INVESTIGATING THE SPECIATION AND EXTRACTION OF COMMERCIALLY
IMPORTANT METALS FROM SPENT NUCLEAR FUEL RAFFINATES: AN
INTEGRATED COMPUTATIONAL AND EXPERIMENTAL APPROACH
By
ALEX CHRISTOPHER SAMUELS
A dissertation submitted in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
WASHINGTON STATE UNIVERSITY
Program in Materials Science and Engineering
August 2014
© Copyright by ALEX CHRISTOPHER SAMUELS, 2014 All Rights Reserved
© Copyright by ALEX CHRISTOPHER SAMUELS, 2014 All Rights Reserved
To the Faculty of Washington State University:
The members of the Committee appointed to examine the dissertation of ALEX CHRISTOPHER SAMUELS find it satisfactory and recommend that it be accepted.
______
Aurora E. Clark, Ph.D., Co-Chair
______
Nathalie A. Wall, Ph.D., Co-Chair
______
Kirk A. Peterson, Ph.D.
______
Kenneth L. Nash, Ph.D.
iii
Acknowledgments
This work could not have been completed without the support of my family, advisors, committee members, and colleagues. Without their help I would not have found my true passion and enjoyed my time at Washington State University.
I would like to thank my wife for being there for me during these past few years.
Without her I am not sure if I would have remembered to take a break from research and
writing to eat a meal. Most importantly you always believed in me and pushed me to be
my best.
My advisors were key in helping me to find my true passion in chemistry. I struggled my first few years trying to find exactly what kind of project I wanted to work on. Aurora Clark and Nathalie Wall, along with my committee, saw my strengths and helped me to my passion of using a combined theoretical and experimental approach to solving chemical problems. This change in research direction reinvigorated my passion
for science. Aurora and Nathalie always pushed my to do by best and would not accept
anything less. I know the knowledge and skills they have passed on to me will help to me
grow in my career. Most importantly, Aurora and Nathalie made me at home at WSU and
like an important member or their respective groups.
My committee was always there to challenge me and make me better. I will never
forget what Dr. Nash told me during my defense, “If you want to make it as a chemist,
you need to be a badass. You need to have passion for what you do and be confident
about it.” That quote has followed me throughout the last few years. When I found my
passion I was able to gain a new confidence that allowed me to grow as a professional.
iv
Additionally, Dr. Peterson helped me to find my footing in an area of chemistry where I was the weakest: quantum mechanics. Dr. Peterson always welcomed my questions and did not turn me away even when I visited his office several times a day during my first few years.
My colleagues became more than my co-workers and more like family over my time at WSU. From Yasi Bross helping me with my research, to Aaron Johnson teaching me practical aspects of solvent extraction, I was well supported by those I worked with
v
INVESTIGATING THE SPECIATION AND EXTRACTION OF COMMERCIALLY
IMPORTANT METALS FROM SPENT NUCLEAR FUEL RAFFINATES: AN
INTEGRATED COMPUTATIONAL AND EXPERIMENTAL APPROACH
Abstract
by Alex Christopher Samuels, Ph.D. Washington State University August 2014
Co-Chairs: Aurora E. Clark and Nathalie A. Wall
Understanding the solution chemistry of fission products in solution is central to the operation of the nuclear fuel cycle and to the environmental remediation of any byproducts that
migrate away from waste disposal facilities. Actinides can be separated from fission products and can be reprocessed into mixed oxide fuel (MOX). The actinides also pose an hazard if
released into the environment. Additionally other fission products, such as the platinum group
metals, could potentially be extracted from spent fuel raffiniates and spent nuclear fuel (SNF)
provide a new domestic feedstock for these commercially important metals.
Actinides that leach from waste tanks can exist in various oxidation states in solution,
thereby complicating the chemistry. Computational studies can supplement experimental work in
this area and can help to create a holistic understanding of actinides in solution. A starting point
for computational studies is to gain fundamental insight into their static geometries and
electronic structure. In the past, several computational studies have examined different actinides in solution, but a systematic study of the actinide series, including various oxidation states, does
vi
not exist. In this study uranium, neptunium, and plutonium are examined in various oxidation
states.
The separation of rhodium (III) from other platinum group metals (PGM) continues to be relevant to modern separations chemistry, as natural deposits become depleted and SNF is being considered a potential feedstock. Rhodium, as well as other PGMs are produced by 235U fission,
and in a commercial light water reactor around 4 kg of PGMs can be produced per ton of waste.
This potential source could provide this much needed element used primarily in automotive
catalytic converters for years to come.
A combination of computational and experimental techniques have been applied to
understand the aqueous behavior of selected fission products. Using computational calculations
at the quantum mechanical level the hydration numbers of U, Pu, and Np in various oxidation states been determined. A combined approach was utilized to understand the speciation of
Rh(III) in acidic media along with solvent exaction of Rh(III) from nitric acid was developed.
vii
TABLE OF CONTENTS
ACKNOWLEDGEMENTS ...... iv ABSTRACT ...... vi-vii LIST OF TABLES ...... xi LIST OF FIGURES ...... xiv CHAPTER 1: INTRODUCTION ...... 1 CHAPTER 2: COMPUTATIONAL METHODS ...... 7 INTRODUCTION ...... 7 INTRODUCTION TO DENSITY FUNCTIONAL THEORY ...... 7 BASIS SET SELECTION ...... 9 GEOMETRY OPTIMIZATION AND FREQUENCY CALCULATIONS ...... 10 SOLUTION PHASE FREE ENERGY AND CONTINUUM MODELS ...... 14 SIMULATION OF UV-VIS SPECTRA ...... 17 REFERENCES ...... 18
CHAPTER 3: EXPERIMENTAL METHODS...... 20 INTRODUCTION ...... 20 EXTRACTION EQUILIBRIA AND FREE ENERGY ...... 20 SLOPE ANALYSES ...... 21 EXTRACTANT SELECTION ...... 21 LABORATORY MATERIALS AND METHODS ...... 23 CONTROLLING PH OF EXTRACTIONS ...... 24 ION COUPLED PLASMA – OPTICAL EMISSION SPECTROSCOPY (ICP-OES) DETECTION OF RH(III) ...... 24 REFERENCES ...... 25
CHAPTER 4: THERMODYNAMIC AND SPECTROSCOPIC ASSIGNMENT OF THE AQUEOUS SOLVATION ENVIRONMENTS OF TRI- TO HEXAVALENT U, NP, AND PU USING LARGE HYDRATED CLUSTERS CALCULATED BY DENSITY FUNCTIONAL THEORY ...... 26 INTRODUCTION ...... 26
viii
COMPUTATIONAL METHODS ...... 28 RESULTS AND DISCUSSION ...... 31 CONCLUSIONS ...... 55 ACKNOWLEDGEMENTS ...... 57 REFERENCES ...... 57 CHAPTER 5: An Integrated Computational and Experimental Protocol for Understanding Rh(III) Speciation in Hydrochloric and Nitric Acid Solutions: ...... 60 INTRODUCTION ...... 60 EXPERIMENTAL AND COMPUTATIONAL METHODS ...... 62 RESULTS AND DISCUSSION ...... 67 CONCLUSIONS ...... 85 SUPPLEMENTARY INFORMATION ...... 86 ACKNOWLEDGEMENTS ...... 89 REFERENCES ...... 90 CHAPTER 6: Rh(III) Extraction by Phosphinic Acids: A Combined Experimental and Computational Protocol: ...... 92 INTRODUCTION ...... 92 EXPERIMENTAL AND COMPUTATIONAL METHODS ...... 93 RESULTS AND DISCUSSION ...... 97 CONCLUSIONS ...... 106 CONTINUING WORK AND FUTURE DIRECTIONS ...... 107 SUPPLEMENTARY INFORMATION ...... 110 REFERENCES ...... 111 CHAPTER 7: Conclusions ...... 113
APPENDIX A: Applications of Polarizable Continuum Models to Determine Predictive Solution Phase Thermochemical Properties Across A Broad Range of Cation Charge – The Case of U(III-VI) : ...... 115 INTRODUCTION ...... 115 COMPUTATIONAL METHODOLOGY ...... 118 RESULTS AND DISCUSSION ...... 121 CONCLUSIONS ...... 136
ix
SUPPLEMENTARY INFORMATION ...... 137 ACKNOWLEDGEMENTS ...... 140 REFERENCES ...... 141
APPENDIX B: Modulation of Hydride Formation Energies in Transition Metal Doped Mg by Alteration of Spin State: ...... 144 INTRODUCTION ...... 144 COMPUTATIONAL METHODS ...... 147 RESULTS AND DISCUSSION ...... 148 SUPPLEMENTARY INFORMATION ...... 156 ACKNOWLEDGEMENTS ...... 163 REFERENCES ...... 163
x
List of Tables
Table 4.1. UB3LYP calculated ΔGhyd values (in kcal/mol) for tetravalent actinides using reaction r2 calculated in aqueous solutions using different dielectric continuum models. The free energy
for water addition, ΔGadd, using reaction r6 is also presented...... 39
4+ Table 4.2. Average UB3LYP
Table 4.3. UB3LYP calculated ΔGhyd values (in kcal/mol) for trivalent actinides using reactions r2 calculated in aqueous solutions using different cavity models. The free energy for water addition to the first solvation shell ΔGadd using reaction r6 is also presented...... 47
Table 4.4. UB3LYP calculated ΔGhyd values (in kcal/mol) for hexavalent actinides using reaction r4 calculated in aqueous solutions using different cavity models. The free energy for water
addition to the first solvation shell ΔGadd using reaction r8 is also presented...... 50
Table 4.5. Average UB3LYP equatorial, rAn-OH2, and axial metal-oxygen bond lengths, rAn=O, in 2+ + (Å) for AnO2(H2O)4,5(H2O)26,25 and AnO2(H2O)4,5(H2O)26,25 in comparison with experimental values (in parentheses). Average charges (q) are reported, determined by NPA for the metal center, actinyl oxo-atom, O-atoms associated with the inner-sphere (IS) and outer-sphere (OS) water molecules...... 53
Table 4.6. UB3LYP calculated ΔGhyd values (in kcal/mol) for pentavalent actinides using reaction r4 calculated in aqueous solutions using different cavity models. The free energy for
water addition to the first solvation shell ΔGadd using reaction r8 is also presented...... 55
Table 5.1. Concentrations of Rh (in M) used for each portion of the UV-Vis spectrum as a
function of concentration of added HCl or HNO3...... 63
Table 5.2. Calculated solution phase free energies of the successive nitrate addition reactions to 3+ the initial Rh(H2O)6 species (in kcal/mol), along with the TDDFT calculated λmax (in nm) of the 3-x Rh(NO3)x(H2O)y (x = 0 – 3; y = 6 – 2x) products between 180 and 800 nm...... 68
Table 5.3. Calculated excited state transitions and their corresponding oscillator strength...... 73
xi
Table 5.4. Literature UV-Vis λmax for individual Rh species and UV-Vis absorption maxima as a function of the HCl concentration of the Rh chloride salt solutions. The observed λmax values from Figure 5.3 are also presented ...... 75
Table 5.5. Solution phase B3LYP/cc-pVDZ predicted ΔGrxn (kcal/mol) of chloride complexation reactions in aqueous solution...... 81
Table 5.6. Calculated speciation of Rh(III) complexes in various concentrations of HCl with ranges that provide a NRMSD ≤ 5%. For HCl concentrations above 2 M a a fit with a NRMSD ≤ 5% was not found. Fits with minimized NRMSD are presented in Table S5.3 in Supplementary Information...... 82
Table S5.1. Average bond lengths (Å) of Rh(III) nitrate species ...... 86
Table S5.2. Molar absorptivity of λmax (202 nm) for Rh(NO3)3 in various concentrations of HNO3...... 86
Table S5.3. Calculated speciation of Rh(III) complexes in various concentrations of HCl with error expressed as NRMSD of the UV-Vis spectra fit to experiment...... 87
Table S5.4 Predicted speciation of Rh(III) species in various concentrations of HCl from CZE...... 87
Table 6.1. Calculated free energy of extraction using proposed equations in kJ/mol compared to experimentally determined free energy...... 104
Table E6.1. Calculated ΔGD (kcal/mol) for acac distribution between water and hexane. DZ and TZ refer to the aug-cc-pVDZ and aug-cc-pVTZ basis sets, respectively...... 108
Table A.1. Gas-phase ΔGhyd values (in kcal/mol) for actinide hydration (reactions r1 and r3), where RSC(1994)-C and RSC(1994)-U refer to the contracted and uncontracted forms of the RSC(1994) basis set, and so forth...... 123
Table A.2. Gas-phase ΔGadd values (in kcal/mol) for reactions r5 and r7, where RSC(1994)-C and RSC(1994)-U refer to the contracted and uncontracted forms of the RSC(1994) basis set, and so forth...... 125
Table A.3. UB3LYP calculated ΔGsolv values (in kcal/mol) for U(III-VI) ...... 136
Table SA1. Gas-phase UB3LYP calculated ΔErxn values (in kcal/mol) for actinide hydration for the second solvation shell, where RSC(1994)-C and RSC(1994)-U refer to the contracted and uncontracted forms of the RSC(1994) basis set, and so forth...... 138
xii
Table SA2. UB3LYP calculated ΔGsol values (in kcal/mol) for actinide hydration using IEF- PCM...... 140
Table SA3. UB3LYP calculated ΔGsol values (in kcal/mol) for water addition reactions for actinide ions using IEF-PCM...... 140
Table SB1: NPA charges for Mg-TM (TM = Ti, V, Fe) clusters calculated at the CCSD(T) optimized geometries, at the DFT/B3LYP level of theory. LS = low-spin, IS = intermediate-spin, HS = high-spin. Mg is always positive, while the TM is always negatively charged...... 156
Table SB2: Mg-TM (TM = Ti, V, Fe) bond lengths (in Å) calculated at the DFT (B3LYP), MP2, and CCSD(T) levels...... 157
Table SB3: Reaction energy ∆ for Mg2 + TM Mg-TM + Mg (TM = T, V, Fe), given in kcal/mol...... 158
Table SB4. ∆ (kcal/mol) for the substitution reaction Mg7 + TM Mg6TM + Mg at the ring and apical positions of cluster (shown in Figure B.3) as a function of TM spin state S using B3LYP/aug-cc-pVTZ...... 159
Table SB5. Average rMg-Mg and rMg-TM distances (in Å) within the Mg6TM clusters optimized using B3LYP/aug-cc-pVTZ for different values of total S...... 160
Table SB6: Hydride formation energy, ∆ , defined by the reaction: Mg-TM + H2 Mg- TM(H)2 where TM = Ti, V, and Fe. Given in kcal/mol...... 161
Table SB7: H-H distance in Mg-TM-H2 (TM = Ti, V, Fe) clusters. Given in Å...... 162
Table SB8: Hydride formation energy, ∆ ∆ , defined by the reaction: Mg6TM + H2 Mg6TM(H)2 where TM = Ti, V, and Fe. Calculated using B3LYP/aug-cc-pVTZ Given in kcal/mol. Only structures with zero imaginary vibrations have been used...... 162
Table SB9: H-H distance in Mg6TM(H)2 (TM = Ti, V, Fe) clusters. Calculated using B3LYP/aug-cc-pVTZ. Given in Å. Only structures with zero imaginary vibrations have been used...... 163
xiii
List of Figures
Figure 1.1. Mass distribution of fission fragments formed by neutron-induced fission of isotopes of U and Pu...... 2 Figure 2.1. Sample thermodynamic cycle for the calculation of extraction free energy...... 16 3+/4+ Figure 4.1. Representative geometries for: (a) An(H2O)8 , a square antiprism (SAP); (b) 3+/4+ An(H2O)9 , a tricapped trigonal bipyrimid (TTBP); (c) the solvation shell structure of 3+/4+ 1+/2+ 1+/2+ st nd An(H2O)9(H2O)21 ; (d) AnO2(H2O)4 ; (e) AnO2(H2O)5 ; (f) the 1 and 2 solvation 1+/2+ shell structure AnO2(H2O)4(H2O)26 ...... 32 Figure 4.2. Calculated reaction energies (in kcal/mol) for reactions r1, r2 and r9 in the gas-phase and in aqueous solution, determined using different dielectric continuum models...... 36
Figure 4.3. Electrostatic contribution (Eelec) to the free energy of solvation correction for (H2O)n 4+ reactant clusters and U(H2O)n product clusters in the solvation reactions r1, r8, and r9...... 37
Figure 4.4. Comparison of the error in the calculated free energy of hydration (ΔΔGhyd = theory expt 4+/3+ ΔGhyd – ΔGhyd ) for the An(H2O)8,9 ions...... 40 4+ Figure 4.5. Simulated and experimental XANES spectra of An(H2O)8,9(H2O)22,21 . The theoretical spectra have only been aligned to the maximum of the white line, no other shifting was performed...... 43 50,51 3+ Figure 4.6. Simulated and experimental XANES spectra of An(H2O)8,9(H2O)22,21 . The theoretical spectra have only been aligned to the maximum of the white line (for Np(III) and Pu(III)), no other shifting was performed...... 48
Figure 5.1. Experimental spectrum of Rh(NO3)3 dissolved in pure water (blue) overlayed with the LC-wPBE/aug-cc-pVTZ (red) predicted UV-Vis spectrum with the primary orbitals involved in the dominant transition shown...... 70 Figure 5.2. LC-wPBE/aug-cc-pVDZ Predicted TD-DFT UV-Vis absorption spectra of 3-x RhClx(H2O)x-6 (x = 0-6) species...... 72 Figure 5.3. UV-Vis Absorptivity spectra of Rh solutions in different HCl concentration, (A) between 210 and 300 nm ([Rh] = 10-5 M) and (B) between 325 and 625 nm ([Rh] = 10-3 M). Results are averages of data obtained from triplicate samples...... 74
Figure 5.4. LMCT and d-d band positions (λmax) of aqueous Rh(III) solutions as a function of HCl concentration. Errors are reported as 2, from triplicate samples...... 76
xiv
3-x Figure 5.5. Experimental spectrum of RhClx(H2O)y (x = 0 – 6; y = 6 – x) dissolved in pure water (blue) overlayed with the LC-wPBE/aug-cc-pVTZ (red) predicted UV-Vis spectrum. The optimized structures of the major species along with their key bond lengths are presented...... 79
Figure 5.6. Experimental spectrum of RhCl3∙nH2O dissolved in (A) 0.1 M HCl, (B) 0.5 M HCl, and (C) 1.0 M HCl (blue) overlayed with the fitted LC-wPBE/aug-cc-pVTZ (red). The approximated concentration of each contributing chloridated species is shown...... 84 n-3 Figure S5.1. Experimental spectrum of RhCln(H2O)n-6 dissolved in pure water (blue) overlayed with LC-wPBE/aug-cc-pVTZ (red) predicted UV-Vis spectrum fit using only RhCl3(H2O)3 isomers...... 88
Figure S5.2. Experimental spectrum of RhCl3∙nH2O dissolved in (A) 2 M HCl, (B) 6 M HCl, (C) 8 M HCl, and (D) 9 M HCl (blue) overlayed with the fitted LC-wPBE/aug-cc-pVTZ (red)...... 89 Figure 6.1. Thermodynamic cycle for the extraction of Rh(III) by an acidic extractant...... 97 Figure 6.2. Influence of extractant concentration on the extraction of Rh(III). Aqueous phase: -4 -3 + 5.3x10 M Rh, 1.5·10 M NO3 , pH = 3.32; Organic phase: (A) DPPA in 1-pentanol. (B) DPDTPA in toluene...... 99 - -4 Figure 6.3. Influence of NO3 concentration on the extraction of Rh(III). Aqueous phase: 5.3·10 - -2 -2 M Rh in NO3 , pH = 3.32; Organic phase: (A) 1.9·10 M DPPA in 1-pentanol (B) 1.9·10 M DPDTPA in toluene...... 100 Figure 6.4. Influence of HCl concentration on the extraction of Rh(III). Aqueous phase: 5.3·10-4 -3 -2 -2 M Rh in HCl, NO3 = 1.5·10 M; Organic phase: (A) 1.9·10 M DPPA in 1-pentanol (B) 1.9·10 M DPDTPA in toluene...... 101 Figure 6.5. B3LYP/cc-pVDZ/aug-cc-pVDZ Optimized gas phase structures of the (A)
Rh(NO3)2DPPA and (B) Rh(NO3)2DPDTPA extracted complexes with extractant-metal bond distance shown...... 105
Figure S6.1. Absorption at 400 nm for Rh(NO3)3 stock solution adjusted to various pH using NaOH...... 110
Figure S6.2. Absorption at 400 nm for Rh(NO3)3 stock solution adjusted to 1 M HCl over 24 hour time period...... 111 3+/4+ Figure A.1. Representative geometries for: (a) U(H2O)8 , a square antiprism (SAP); (b) 3+/4+ U(H2O)9 , a tricapped trigonal bipyrimid (TTBP); (c) the solvation shell structure of 3+/4+ 1+/2+ 1+/2+ st nd U(H2O)9(H2O)21 ; (d) UO2(H2O)4 ; (e) UO2(H2O)5 ; (f) the 1 and 2 solvation shell 1+/2+ structure UO2(H2O)4(H2O)26 ...... 123 Figure A.2. Calculated reaction energies (in kcal/mol) for reactions r1, r2 and r9 for U4+ in the gas-phase and in aqueous solution, determined using different dielectric continuum models. ..128
xv
Figure A.3. Electrostatic contribution, Gelec, (in kcal/mol) to the free energy of solvation 4+ correction for (H2O)n reactant and U(H2O)n product clusters in the solvation reactions r1, r8, and r9 for (A) the SMD continuum model, (B) the UFF cavity within IEF, and (C) the UAKS cavity within the IEF model...... 308 prod Figure A.4. The electrostatic contribution, ΔGelec, in kcal/mol to ΔGsolv, defined as: Gelec - react Gelec ...... 131
Figure A.5. Convergences of the solution phase correction to the free energy, ΔGcorr, for trivalent, hexavalent, and pentavalent uranium as a function of the size of the molecular hydrated cluster employed...... 132
Figure A.6. Comparison of the error in the calculated free energy of solvation (ΔΔGsolv = theory expt 4+/3+ ΔGsolv – ΔGsolv ) in kcal/mol for the U(H2O)8,9 ions as a function of (A) cavity volume, and (B) cavity surface area...... 134
Figure SA1. Change in ΔGhyd upon adding g-functions in the basis as a function of the f-orbital occupation of the ion using Lowdin population analysis ...... 137 Figure SA2. Spin-orbit coupling contributions (in kcal/mol) vs the Lowdin charges of the bare ions and the metal ion on hydrated complexes ...... 139 Figure B.1. Representative B3LYP/aug-cc-pVTZ geometries of the Mg-TM dimer and heptamers, where the TM is placed in either a ring or apical position, and their associated hydrides...... 148 Figure B.2. Energetic and structural parameters for (A) reaction (r1) and (B) reaction (r2) calculated using CCSD(T)/AVTZ as a function of spin state (LS = low spin, IS = intermediate spin, HS = high spin. LS is S = 0, 1/2, and 0, while IS has S = 1, 3/2, and 1, and HS is S = 2, 5/2, and 2 for Ti, V, and Fe, respectively)...... 149 Figure B.3. MO diagram of the valence orbitals for Mg—TM dimer. Changes in the TM spin state modulate population of the 4s transition metal AO, which in turn alters the occupation of the σ* MO...... 154
xvi
This work is dedicated to my wife and my son Luke
xvii
Chapter 1
Introduction
The United States is currently the world’s largest producer of nuclear energy with 100 online
nuclear reactors. Annual nuclear waste generation is approximately 2,000 metric tons with
67,000 metric tons in interim storage on reactor sites.1 In the U.S. spent nuclear fuel is handled
in a once through process where the waste is disposed of after use. The other option, not
practiced by the U.S., is reprocessing which extracts the useful components present in the waste.
This is practiced in countries such as France, where the reprocessing techniques focus heavily on
the extraction of important actinides such as uranium and plutonium.
Several benefits are obtained from reprocessing nuclear fuel. Reprocessing fuel allows
for waste volume to be minimized, and offers a potential option to the treatment of fuel currently
in interim storage. Additionally, the recovered U and/or Pu can be reused in a reactor for
additional power generation, leading to an overall efficiency boost to the nuclear fuel cycle.
Another benefit to recycling is that other materials could be extracted from the waste.
As shown with Figure 1.1, several other fission products are present in nuclear waste in significant quantities, include precious metals, such as Ru, Rh and Pd. These precious metals are reported to be present in High Level Liquid Waste (HLLW) at a ratio of 4 kg of Ru, Rh, and Pd after PUREX reprocessing of 1 ton of initial heavy metal (IHM) with burn-up of 33,000 MWd/t
IHM and after cooling for 50 years.2 Extraction of these metals from nuclear waste is becoming
increasingly profitable as demand increases. While extraction of these precious metals is possible
in theory, a commercial method of retrieval has not been achieved thus far.
1
Figure 1.1. Mass distribution of fission fragments formed by neutron-induced fission of isotopes of U and Pu.3
Unfortunately, a fundamental understanding of solvent extraction mechanisms for precious metals retrieving from spent nuclear fuel has not been achieved. Methods such as
PUREX and TRUEX for the extraction of important actinides are experimentally successful; however the exact mechanisms of the reactions relevant to extraction are not fully understood.
Computational chemistry can be used to complement the experimental data and improve the
2
understanding of extraction processes. One way computational studies can complement
experimental studies is through molecular level system simulations. These methods provide key
electronic structure, geometric and thermodynamic information, which are helpful when systems
are difficult to study spectroscopically. Additionally, information can be obtained
computationally when experiments are difficult to perform (e.g. for species that are unstable or
transient in solution). In the case of the chemistry of principal actinides present in the nuclear
fuel cycle, uranium (V) readily disproportionates to uranium (IV) and uranium (VI). Since
uranium (V) is highly unstable in solution, experimental data are sparse.
The dissertation explores the chemistry of important metals present in spent nuclear fuel
(SNF). The chemistry of f-elements in solution has been investigated in Chapter 4 where the hydration numbers of U, Np, and Pu are determined in their various oxidation states. This
Chapter also explores the utility of density functional theory for determining the coordination environment and speciation of f-elements in solution. The first solvation shell of uranium, neptunium, and plutonium in the (III-VI) oxidation states were examined and the coordination number was determined by comparing computational free energies of solvation with experimentally determined values from calorimetric studies. Additionally, simulated X-ray absorption fine structure (XAFS) and X-ray absorption near-edge structure (XANES) spectroscopic data was compared to experimental values to confirm hydration numbers.
Furthermore, water addition thermodynamics were analyzed to determine if water addition is favorable to the first solvation shell. Determining the species within solution is important because ligand binding occurs upon disruption of the coordinating waters, a phenomenon that ought to be thermodynamically favorable.
3
The second part of the work is to develop a method to extract the rhodium (III) from
spent fuel raffinates. Rhodium (Rh), a platinum group metal (PGM), is used primarily in
automotive catalytic converters for the reduction of toxic nitrogen oxides to nitrogen and
oxygen.4 To a lesser degree, Rh is used as a catalyst for the production of acetic acid and in the
technology sector as a component of liquid crystal display (LCD) glass making equipment.5,6
Global consumption of Rh continues to rise, reaching 30,000 kg in 2012.7 The United States is
dependent on foreign imports to obtain Rh, with 99% of the country’s annual consumption of
12,800 kg coming from imports.6,7 Rh is primarily found present in platinum ore mined
predominantly in South Africa, and Russia.7 Mining production in these countries is unstable due
to frequent strikes and mine closures.7,8 Mining operations in the United States come from a
limited number of mines, with future mining projects limited by environmental concerns and
financial constraints.6 Due to these circumstances, another source becoming more feasible is Rh
present in SNF raffinates.910,11
Chapter 5 presents data regarding Rh(III) speciation in hydrochloric and nitric acid
solutions. This study is a first step into understanding the behavior of rhodium in nuclear fuel
raffinates. Studies of Rh speciation in acidic solutions received significant interest in the 1960’s
and 1970’s, in part motivated by precious metal refining and in part due to complex and
interesting solution phase chemistry. The separation of Rh from other platinum group metals
(PGM) continues to be relevant to modern separations chemistry, as spent nuclear fuel (SNF) is
being considered a potential feedstock.10,11 Rhodium, as well other PGMs are produced by 235U fission, yielding around 4 kg of PGMs per ton of waste for a commercial light water reactor
-1 235 14 - (PWR fuel, 32.3 GW·d· t ; 880 d irradiation; 3.2% U as UO2; fluence, F = 3.24 x 10 n·cm
2·s-1) .12 It is estimated that by the year 2030, the amount of fission-generated Rh could exceed
4 known natural reserves.12 The only stable Rh isotope, 103Rh, is obtained directly as a fission
- 103 13 product; it is also produced by decay of the fission product, Ru (t1/2=40 d). Thus, upon proper separations and after cooling time for at least 50 years, Rh extracted from spent nuclear fuel could be used for industrial purposes.14 Rh(III) will be subject to high chloride and nitrate environments in SNF raffinates. Chapter 5 describes Rh(III) speciation in chloride and nitrate media, so that an appropriate extractant can then be determined.
Chapter 6 explores the extraction of Rh(III) by phosphinic acids. Phosphinic acid extractants where chosen given the success of these complexes for the extraction of trivalent f- elements.15-19 This work explores a computational and experimental protocol for calculating the free energy of an extraction process. The benchmarking of computational methods for extraction could potentially lead to the ability to determine the performance for a novel extractant without a wet chemistry approach.
References
(1) Werner, J. D. U.S. Spent Nuclear Fuel Storage Congressional Research Service, 2012. (2) Bush, R. Platinum Metals Rev 1991, 35, 202-208. (3) James, M. F.; Mills, R. W.; Weaver, D. R. Progress in Nuclear Energy 1991, 26, 1-29. (4) Shelef, M.; Graham, G. W. Catalysis Reviews 1994, 36, 433-457. (5) Roth, J. F. Platinum metals review 1975, 19, 12-14. (6) Wilburn, D. R.; Bleiwas, D. I. Platinum-Group Metals—World Supply and Demand U.S. Geological Survey, 2004. (7) Loferski, P. J. PLATINUM-GROUP METALS, U.S. Geological Survey, 2012. (8) Loferski, P. J. PLATINUM-GROUP METALS IN JANUARY 2014, U.S. Geological Survey, 2014. (9) Feasibility of separation and utilization of ruthenium, rhodium and palladium from high level wastes, IAEA, 1989. (10) Kolarik, Z.; Renard, E. V. Platinum metals review 2003, 47, 74-87. (11) Kolarik, Z.; Renard, E. V. Platinum metals review 2005, 49, 79-90. (12) International Atomic Energy, A. Technical reports series; The Agency, 1989. (13) Smith, F. J.; Mc Duffie, H. F. Separation Science and Technology 1981, 16, 1071-1079. (14) Naito, K.; Matsui, T.; Tanaka, Y. Journal of Nuclear Science and Technology 1986, 23, 540-549. (15) Freiderich, M. E.; Peterman, D. R.; Klaehn, J. R.; Marc, P. L. J.; Delmau, L. H. Industrial & Engineering Chemistry Research 2014.
5
(16) Alimarin, I. P.; Rodionova, T. y. V.; Ivanov, V. M. Russian Chemical Reviews 1989, 58, 863-878. (17) Modolo, G.; Wilden, A.; Geist, A.; Magnusson, D.; Malmbeck, R. Radiochimica Acta 2012, 100, 715. (18) Xu, Q.; Wu, J.; Chang, Y.; Zhang, L.; Yang, Y. Radiochimica Acta International journal for chemical aspects of nuclear science and technology 2008, 96, 771-779. (19) Li, K.-a.; Freiser, H. Solvent extraction and ion exchange 1986, 4, 739-755.
6
Chapter 2
Computational Methods
2.1 Introduction
Ab-initio computational methods are a useful complement to experimental methods for elucidating structural and spectroscopic properties of relevant molecules and energetic properties of pertinent reactions. This chapter outlines the underlying principles that allow calculation of the electronic energy of a molecule, the optimization of structural parameters, thermodynamic values, and spectroscopic properties. In the remaining chapters these computational approaches have been utilized to understand the hydration numbers of key actinides, Rh(III) speciation in acidic media, and the solvent extraction free energies of Rh(III).
2.2 Introduction to Density Functional Theory
Calculating the electronic energy of a system at a fixed guess geometry is the first step in determining its optimized structure (invoking the Born–Oppenheimer approximation). There are several ways to approach the calculation of the electronic energy, and in this work Density
Functional Theory (DFT) will be used. In DFT the electronic energy is calculated using the physical observable of electron density rather than using a many body wave function. In DFT, the Hamiltonian depends on the electron density, ρ, instead of the positions of each individual electron. The kinetic energy term is easily found for the Hamiltonian. The external potential term and the electron-electron interaction term have to be addressed in a new way to deal with densities. Hohenberg and Kohn discovered a new relationship between the electron density and an external potential; such that, no two external potentials can give the same ground state
7
density. This allows for the external potential to be determined for a known density. DFT is
fundamentally based upon the Hohenberg-Kohn Theorem, which asserts that the electron density
follows the variational principle.
To address the electron-electron interaction, Kohn and Sham proposed a method of treating
the system as a non-interacting system of electrons. Using the Kohn Sham theorem, the electron-
electron term in the Hamiltonian is replaced with a sum of one electron orbitals. The Kohn Sham
potential is then constructed by combining an external potential (Coulomb interactions) and the
electron-electron interactions (contained in the exchange-correlation potential). The Slater
determinant is constructed as a collection of single electron orbitals
∑〈 | | 〉 (2.1)
where
∑ | | (2.2)
Using the wave function and the Hamiltonian the energy can be calculated as
(2.3)
where the energy as a function of electron density is the sum of kinetic energy, the nuclear-
electron interaction potential
(2.4)
and the exchange-correlation energy. The exchange-correlation energy includes the terms for
electron-electron interaction. The energy associated with the exchange-correlation can be calculated using
dr (2.5)
8
where the exchange-correlation potential and electron density are integrated over all space. The
Exc term varies by the chosen exchange-correlation functional combination and is the term the
differentiates functionals.
The Becke, three-parameter, Lee-Yang-Parr (B3LYP) exchange-correlation functional has
shown good agreement with predicting gas phase energies of acidic and organic molecules.1,2
The B3LYP functional is defined by
1 ∆ 1 (2.6)
where a, b, and c have been optimized to 0.20, 0.72, and 0.81, respectively.3,4 The co-efficients
in the B3LYP functional were determined by a linear least-squares fit to 56 ionization energies,
42 ionization potentials, 8 proton affinities, and the 10 first-row total atomic energies.5
2.3 Basis Set Selection
Calculations performed will utilize correlation consistent basis sets on main group elements.
The correlation consistent basis sets have several advantages over Pople basis sets (e.g. 6-31G*).
For example, they are designed to converge systematically to the complete basis set limit for a
given method. In this work, all main group elements used the cc-pVDZ, aug-cc-pVDZ, or aug-
cc-pVTZ basis sets. For the actinide ions, the Stuttgart RSC60 RECP was employed for all An
which replaces the 60 inner-shell ([Kr]4d104f14) electrons with a pseudopotential.6 The corresponding Stuttgart basis describes the valence electrons of the actinide ions and consists of segmented contracted 8s7p6d4f functions. This relativistically corrected effective core potential
(RECP) was developed so that a valence-only calculation using this pseudopotential should reproduce atomic valence spectra from all-electron reference calculations as accurately as possible. A RECP replaces the low lying core electrons with pseudopotential that incorporates
9
both scalar and spin-orbit relativistic effects. It is assumed that these inner-most orbitals do not participate in bonding, therefore approximating them with a pseudopotential is appropriate. The basis set for Rh(III) used a relativistically corrected pseudopotential to replace the inner most electrons that are assumed to not participate in bonding.7 The RECP was adjusted at the multiconfiguration Dirac-Hartree-Fock level using a Dirac-Coulomb Hamiltonian. The Rh(III) basis set consists of contracted 4s4p3d1f functions, along with a matching pseudopotential that replaces the 28 inner-shell ([Ar]4s23d8) electrons.
2.4 Geometry Optimization and Frequency Calculations
Following the calculation of the energy at a fixed geometry, it is a natural extension to modify the geometry to determine the atomic coordinates at the global minimum on the potential energy surface, which is called the optimized geometry. In order to find the optimized geometry, the first and second derivatives of the energy with respect to all atomic coordinates must be determined. The first derivative gives the gradient, while taking the second order partial derivative yields the hessian, which is used to determine if the energy is at minimum with respect to atomic coordinates. Different software programs implement alternative algorithms for this purpose. NWChem uses a quasi-Newton optimization method, which searches for the stationary point of the potential energy surface.8 This stationary point is defined as having a zero gradient.
To find this point, the quasi-Newton method assumes that the function can be modeled quadratically in the region near the stationary point. The first and secondary derivatives are then taken to find the minimum.
Following a geometry optimization calculation, a frequency calculation is performed. This calculation provides several important pieces of information; it gives insight into whether the
10
energy is at a true minimum in all directions, yields IR and Raman data, and it allows for thermodynamic properties to be determined. To determine the frequencies, the mass weighted hessian is calculated as
(2.7) where V is the second derivative of the potential and qi,j refers to the mass weighted Cartesian coordinates. The hessian is then transformed into internal coordinates and diagonalized. At this point the frequencies are calculated using
(2.8) where λi are the eigenvalues of the diagonalized Hessian and c is the speed of light. The eigenvectors are then used to obtain the normal modes.
Once the optimized geometry and frequencies have been determined, the partition function is found so that the thermodynamic properties can be calculated. The total partition function
, , , (2.9) ! where
, (2.10) can be broken down into the individual contributions from translational, electronic, rotational and vibrational energy. The vibrational partition is constructed from the harmonic frequencies determined in the frequency calculation. After the partition function is constructed, entropy and enthalpy be calculated such that the free energy can be determined. To determine the entropy, the molecular partition function is used, such that
, (2.11)
This equation can be written in terms of molar values
11
, (2.12)
such that n=N/NA , and NAkB=R. The partition function can be broken up into the individual
contributions and the first two terms can be combined yielding the entropy equation.
(2.13)
The internal thermal energy of the system, obtained from the partition function, can be expressed as
(2.14)
Starting with the contribution from translational motion, it is found that
5 2 (2.15)
(2.16)
With regards to the electronic motion contribution to the entropy, it is found that
(2.17)
For the rotational contribution, three cases exist; single atom, linear polyatomic, and non-linear
polyatomic. For a non-linear polyatomic case
3 2 (2.18)
(2.19)
For vibrational motion, the contributions of each vibrational mode, K, will need to be
determined. Since only real modes can be considered, it is necessary that there are no imaginary
frequencies. The existence of a single imaginary frequency suggests the formation of a transition
state; however, transition states will not be explored in this work. If imaginary frequencies are
12
present, the energy is not truly at a minimum in all degrees of freedom for the system. The
contributions from vibrational motion are
, , ∑ 1 (2.20) ,
∑ , (2.21) ,
where the sums are over the vibrational modes.
To calculate the thermal corrections to the electronic energy, first the zero point energy is
calculated using the non-imaginary frequencies. The zero point energy is the difference between
the bottom of the potential energy well and the first vibrational quantum state. All of the
thermodynamic parameters will include this correction. The thermal corrected energy, Etot, is calculated using Eq. (2.14), once all of the contributions to the partition function are determined.
For this study, this correction includes the temperature of 298.15 K. Furthermore the thermal corrections for Enthalpy and Gibbs Free Energy are given, where
(2.22)
(2.23)
and Stot is the sum of the entropy contributions from translational, electronic, rotational, and
vibrational movement. The free energy of a reaction can now be calculated using
° ° ° ∆ 298.15 ∑ 298.15 ∑ 298.15 (2.24)
Within NWChem the zero-point energy, the thermal corrections to energy and enthalpy, and the
total entropy are listed in the output file. In addition, the individual components are given. Using
Eq. (2.23) – (2.25) the Gibbs free energy can be calculated for both products and reactants.
13
2.5 Solution Phase Free Energy and Continuum Models
If the free energy of extraction is going to be compared with experimental data, solvation
effects must be considered. Ideally, an explicit solvation model should be used. An explicit
solvation model includes individual solvent molecules and thus models all solvent interactions.
298 As the number of explicit solvent molecules approaches infinity, the ΔGgas would be
equivalent to ΔGtot. To keep the computational cost down, while still trying to model the
electrostatic and non-electrostatic effects of a system surrounded by a solvent, implicit
continuum solvation models can be used. The solvation effects are traditionally included through
the use of a dielectric continuum model. Continuum models approximate interactions of a
molecule by embedded the molecule in dielectric medium. Therefore, the free energy in solution
becomes:
ΔGtot=ΔGgas + ΔGsol (2.25) where the total free energy in solution is a combination of the gas phase free energy with the solvent corrections added. The free energy of solvation is determined by
(2.26)
where the non-electrostatic, cavitation, and electrostatic energies are added. The non-electrostatic free energy is based on the dispersion interactions of the solvent with the solute. The cavitation energy is the amount of energy needed to embed the solute in a cavity within the dielectric. The final term accounts for the electrostatic interactions between the solvent and solute. The cavity is usually created by the overlapping spheres defined by the van der Waals radii of each atomic component. The reaction field is applied as point charges on the surface of the cavity for standard polarizable continuum models (PCM). Another type of continuum model, conductor-
14
like polarizable continuum models (CPCM) treat the solvent as an ideal conductor. This
approximation allows for the charge on the surface of the cavity to be removed.
Past studies have shown mixed results when a continuum model is used to determine
solution phase thermodynamic free energies. The recent work of Goddard et. al. demonstrated
that experimental free energies of Cu(II) hydration can be reproduced (within 2 kcal/mol) with
the use of a single coordination shell and a continuum model.9 The ability to reproduce hydration
free energies without considering an extended solvation environment has also been accurately
reproduced for several monovalent organic and inorganic species.10,11 Gutowski and Dixon
considered ion hydration by using various size water clusters. Their results were mixed, and
concluded that a second solvation shell improve convergence with experimental values.12 The
approach applied by Gutowski and Dixon was limited to the use of a single solvation model for
the larger cluster calculations. A systematic approach to understanding the performance of
different solvation models (IEF-PCM, SMD), and various cavities (UAKS, UFF, UA0, Pauling)
with increasing water cluster size is presented in Appendix A. Water Cluster sizes up to 80 were
used. As expected, ΔGgas approached the experimental determined values as the water cluster
size was increased. With the addition of the first and second solvation shell ΔGsolv decreased.
This is expected as an infinite sized cluster should have a ΔGsolv = 0, yet adding clusters to form
beyond a second solvation shell does not show a smooth convergence to zero for ΔGsolv.
Additionally, there are significant differences in ΔGsolv for single solvation shell calculations
when the cavity and/or model are varied. Upon the addition of the second solvation shell, ΔGsolv converged to a narrow range for all cavities and models employed. This suggests that the model/cavity combinations converge at different rates given the wider range of ΔGsolv for the
single solvation calculation. It was found that ΔGgas converged to experiment bulk solvation
15
value as additional solvent molecules beyond the first solvation shell of each metal; however,
ΔGsolv did not converge as quickly to 0. This indicates that the use of a PCM should be restricted to two solvation shells as slow convergence in ΔGsolv leads an overestimation in error cancelation. When using a continuum model to include solvation effects the molecular cluster size, cavity and model need to be chosen carefully. Changing any of these parameters will alter the rate of convergence.
To apply solvation corrections to a reaction that mimics extraction, the solvent effects in both the aqueous and organic phase must be considered. As an example, consider the following extraction reaction
⇄M (2.27) in which the where with a bar are present in the organic phase and the others species are present in the aqueous phase, and where an extractant binds to the metal for transport into the organic can be modeled by the thermodynamic cycle presented in Figure 2.1.
Figure 2.1. Sample thermodynamic cycle for the calculation of extraction free energy.
The free energy of extraction can be calculated in a similar manner
16
ΔGext=ΔGgas +ΔΔGsolv (2.28) where a solvation correction is applied to the gas phase energies for reactants and products. For these calculations the solvent with corresponding dielectric need to be specified in the calculation. It is important to note that continuum model are not only specified by the dielectric, and adjusting the dielectric for a given solvent does not guarantee accurate results. Once the free energy of extraction has been determined, the values can be compared to experimentally determined logK values where
∆ (2.29)
2.6 Simulation of UV-Vis Spectra
Time Dependent Density Functional Theory (TD-DFT) is a computational tool that can be used to predict UV-Vis spectra by determining the electronic transitions allowed upon absorption of light. Using linear response DFT, the excited states can be determined, as long as the applied potential does not disrupt the ground state configuration. The linear response of the electron density to a perturbation yields a function that has poles at the excitation energies.
The output of a TD-DFT calculation gives the excitation energy (nm) and corresponding oscillator strength of the transition. Additionally, the orbitals whose change in electron occupation gives the change in density required to have a pole in the linear response function.
Oscillator strength is directly related to molar absorptivity using
√ ṽ‐ṽ ε ṽ exp ‐ (2.30)
-10 23 where εi is the electronic excitation of interest, e = 4.803204x10 esu, N = 6.02214199x10 ,
10 -31 c = 2.997924x10 cm/s, me = 9.10938x10 g, fi is the oscillator strength, σ = 0.5 eV which is
the standard deviation in wavenumbers and is related to the width of the band, and at the
17
13 maximum of the band where the energy of the incident radiation, ṽ, is equal to ṽi. The band width of 0.5 eV is the standard width employed in Guassian09.14 When there are multiple electronic excitations in the spectral region of interest, the spectrum becomes a sum of all of the individual bands
ṽ ∑ ṽ (2.31)
When the bands are combined, a UV-Vis spectrum can be constructed.
For use in this work, the theoretical spectra were used to approximate the speciation of
Rh(III) in solution by fitting the theoretical spectra to experimentally obtained spectra. This was quantitatively measured by minimizing the normalized root mean squared deviation (NRMSD) between the combined theoretical spectrum and the experimental one through modification of the percent contribution of each Rh(III) chloride species. The root mean square provides a measure in the deviation between a predicted data set and the real data set.
2.7 References
(1) Burk, P.; Koppel, I. A.; Koppel, I.; Leito, I.; Travnikova, O. Chemical physics letters 2000, 323, 482‐489. (2) Tirado‐Rives, J.; Jorgensen, W. L. Journal of Chemical Theory and Computation 2008, 4, 297‐306. (3) Becke, A. D. Physical Review A 1988, 38, 3098‐3100. (4) Lee, C.; Yang, W.; Parr, R. G. Physical Review B 1988, 37, 785‐789. (5) Becke, A. D. The Journal of chemical physics 1993, 98, 5648‐5652. (6) Andrae, D.; Häußermann, U.; Dolg, M.; Stoll, H.; Preuß, H. Theoretica Chimica Acta 1990, 77, 123‐141. (7) Peterson, K. A.; Figgen, D.; Dolg, M.; Stoll, H. Journal of Chemical Physics 2007, 126, 124101. (8) Valiev, M.; Bylaska, E. J.; Govind, N.; Kowalski, K.; Straatsma, T. P.; Van Dam, H. J. J.; Wang, D.; Nieplocha, J.; Apra, E.; Windus, T. L. Computer Physics Communications 2010, 181, 1477‐1489. (9) Bryantsev, V. S.; Diallo, M. S.; Goddard Iii, W. A. The Journal of Physical Chemistry B 2008, 112, 9709‐9719. (10) Asthagiri, D.; Pratt, L. R.; Ashbaugh, H. S. The Journal of chemical physics 2003, 119, 2702‐2708. (11) Pliego, J. R.; Riveros, J. M. The Journal of Physical Chemistry A 2001, 105, 7241‐7247. (12) Gutowski, K. E.; Dixon, D. A. The Journal of Physical Chemistry A 2006, 110, 8840‐8856. (13) Stephens, P. J.; Harada, N. Chirality 2010, 22, 229‐233.
18
(14) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. Inc.: Wallingford, CT 2009, 115.
19
Chapter 3
Solvent Extraction Methods
3.1 Introduction
Solvent extraction is a widely used tool in the nuclear industry. The International Union
of Pure and Applied Chemistry (IUPAC) defines solvent extraction as the process of transferring
a substance from any matrix to an appropriate liquid phase.1 Currently, nuclear industry
reprocessing methods use only solvent extraction to remove metal ions from acidic solution into
an immiscible organic phase using a ligand and/or extractant. So far, only the actinides and
lanthanides are separated from spent nuclear fuel raffinates. This work uses solvent extraction to
remove Rh(III) from nitrate solutions.
3.2 Extraction Equilibria and Free Energy
Solvent extraction relies on the condition that two phases are immiscible. This ensures
the ability to easily remove a desired phase after extraction. When a solute, M, distributes
amongst an immiscible aqueous and organic phase the distribution ratio becomes
(3.1)
where the total concentration of the solute M in the organic phase is divided by the total
concentration of M in the aqueous phase. The solvent extraction reaction equation for a solute
M3+, a tri-valent metal binding to an acidic extractant, could be written as:
⇄M (3.2)
The equilibrium expression where and are species present in the organic phase, Kex, is
20
(3.3)
or by substituting in the distribution ratio
(3.4)
The free energy of extraction can then be calculated as a function of Kex
∆ (3.5)
where R is the gas constant and T is temperature. Knowledge of the identity of species originally
in solution and the formula of the extracted product(s) is vital to calculate the Kex .
3.3 Slope Analysis
A slope analysis method can be used to predict the products of a solvent extraction
process. The logarithm of Eq. (3.4) yields
(3.6)
where the distribution is dependent on the concentrations of the extractant and pH. The value of
x is equal to the slope of the logD v.s. pH plot at fixed extractant concentration; x is also equal to
the slope of the logD v.s. log plot at fixed pH. It is important to note that speciation
determined by slope analysis is only applicable to the concentration ranges used in the analysis.
Additionally, the choice of the extractant used will directly affect which species form in solution.
3.4 Extractant Selection
A extractable complex can exist in aqueous solution as an ion, cation or anion, or as a
neutral complex. The complex Rh(NO3)3 is present in an Rh(III) in nitric acid solution (See
Chapter 5). The neutrally charged Rh(NO3)3 species can potentially extracted by a neutral, or
- acidic extractants. It would be expected that a neutral extractant would cause NO3 binding
21
bidentate to become monodentate, thereby interacting with one of Rh(III) octahedral binding
sites. The extraction of Rh(NO3)3 using TBP was attempted, but no measurable extraction was
- measured. Acidic extractants, like phosphinic acids, are hypothesized to replace NO3 ions bound
to Rh(III) and therefore bind Rh(III). The acidic extractants are expected to bind bidentate;
monodentate binding could occur but mostly needs to be considered in theoretical work to
- calculate thermodynamic data. If an anion, for instance TcO4 , was the target of a separation an
extractant such as iodonitrotetrazolium chloride (INT) accepts electron density and binds to the
anion.
In past studies the extraction of Rh(III) has focused primarily on chloride media.2-6
Complete extraction has not been reported with the use of only neutral extractant.2,3 Levitin and
Schmuckler explored the use of the neutral Alamine 336 for the extraction of Rh(III) from HCl.2
The addition of HCl suppressed extraction and the largest distribution ratio observed was 1.5.
Lee and co-workers recently used the neutral Alamine 308 to separate Pt(IV) and Rh(III) from
HCl. It was found that extraction increased as the HCl concentration was adjusted to 8.0 M. It
was found by Zou and co-workers that the addition of Sn(II) improved the extraction of Rh(III)
by neutral extractants. The Sn(II) acts as an aqueous ligand that binds to Rh(III) leading to
complete extraction by tributyl phosphate (TBP). The use of acidic extracts has shown similar
results to neutral extractants.4,6 The 1995 work of Yan and Alstad found that the acidic extractant
bis(2-ethylhexyl) hydrogen phosphate (HDEHP) weakly extracted Rh(III) with distribution ratio
never exceeding 1. With the addition of Sn(II), Alam and Inoue showed that 7-(4-Ethyl-1-
methylocty)-8-hydroxyquinoline (Kelex 100) completely extracted Rh(III) from HCl. The results
of these previously reported extractions suggest that Rh(III) is extracted equally well by acidic and neutral extractants. With the conditions employed in previous studies, the appropriateness of
22
the use of an acidic or neutral extractant is not easily assessed for those analogous to spent fuel
raffinates. Therefore, both neutral and acidic extractants were tested in the extraction studies
reported in this document.
Only a single extraction study is easily obtained in the literature for Rh(III) in nitric acid.
The extraction of Rh(III) in nitric acid by dinonylnapthalene sulphonic acid was reported by
Patel and Thornback in 1987. A maximum of 20% extraction was measured; however, it was
unclear which Rh(III) species was in solution as the oxide form was used to prepare stock
solutions. In the work described in Chapter 6, acidic phosphinic acids are considered for Rh(III).
It is important to note that preliminary extractions performed using TBP in dodecane showed no
measurable extraction of Rh(III) and lead to the consideration of acidic extractants.
3.5 Laboratory Materials and Methods
Equipment used in solvent extraction may change, depending on the conditions of the
extraction. Glass poly-seal vials were chosen for this study. These vials where chosen for the
ability to store organic solvent for several days without measurable evaporation and vial
degradation. The extractions were performed using a Glas-Col rotator where samples where spun
in a circular motion perpendicular to the lab bench. The motion of the rotator allowed for
adequate mixing of the aqueous and organic phases, and allowed for uninterrupted contact times
of weeks to months. The phases need separation using a centrifuge prior to preparing the aqueous
phase for analysis, even if they appear to have partitioned upon resting on the bench; samples in
this work were centrifudged (Thermo Scientific Centra CL2) for 20 minutes at 4,100 rpm to
ensure adequate phase separation. The aqueous phases of the samples were sampled and HNO3 was added to obtain 1 – 2% HNO3 for Rh quantification by ion coupled plasma optical emission
23
spectroscopy (ICP-OES) (Perkin Elmer Optima 3200 RL), previously calculated using dilution
of a standard concentrated Rh solution.
3.6 Controlling pH of Extractions
The ability to fix the pH of a given extraction is a key requirement for our study. An
appropriate base is required to offset the protons being donated to solution from the extractant to
fix the pH of the aqueous phase during an extraction. One area of concern is that the base may
interact with the target species (e.g. Rh) in solution and form an new complex. In this work
NaOH was used to maintain a constant pH. The use of UV-Vis spectroscopy (Agilent Cary 5000
UV-visible spectrophotometer) allowed the speciation to be monitored as Rh(III) hydroxide
complexes can be monitored in the 300 – 800 nm region of the spectrum. No changes was
observed in the UV-Vis spectrum at pH < 5.0 and speciation was then considered to remain
stable. A standard pH electrode is used to monitor the pH and small amounts of NaOH (~ 10 μL
of 0.1 M NaOH) were added hourly to maintain the initial pH of the stock solutions (3.32). This
same approach was used for monitoring speciation upon the addition of HCl and is discussed
further in Chapter 6.
3.7 Ion Coupled Plasma – Optical Emission Spectroscopy (ICP-OES) Detection of Rh(III)
ICP-OES was used to quantify Rh(III) concentrations. Rh, like other metals, has a unique
set of atomic spectral lines. As Rh is excited by the plasma it emits electromagnetic radiation at
wavelengths characteristic to only Rh. Samples to be analyzed by ICP-OES must contain 1 – 2%
HNO3 to provide a fixed solution matrix for all samples. Optimum IPC-OES are obtained for sample Rh(III) concentrations of ca. 10-4 M (quantification limit of detection of Rh(III) = 10-6 M)
24
as errors are reduced and samples are not concentrated enough to disrupt flow though the
instrument.
3.8 References
(1) Rice, N. M.; Irving, H.; Leonard, M. A. Pure and applied chemistry 1993, 65, 2373-2396. (2) Levitin, G.; Schmuckler, G. Reactive and functional polymers 2003, 54, 149-154. (3) Lee, J.-Y.; Rajesh Kumar, J.; Kim, J.-S.; Park, H.-K.; Yoon, H.-S. Journal of hazardous materials 2009, 168, 424-429. (4) Yan, G. L.; Alstad, J. Journal of Radioanalytical and Nuclear Chemistry 1995, 201, 191-198. (5) Zou, L.; Chen, J.; Pan, X. Hydrometallurgy 1998, 50, 193-203. (6) Shafiqul Alam, M.; Inoue, K. Hydrometallurgy 1997, 46, 373-382.
25
Chapter 4
Thermodynamic and Spectroscopic Assignment of the Aqueous Solvation Environments of Tri- to Hexavalent U, Np, and Pu Using Large Hydrated Clusters Calculated by Density Functional Theory
Aurora E. Clark,1 Alex Samuels,1 Katy Wisuri,1 Sarah Landstrom,2 Tessa Saul3
1Department of Chemistry, Washington State University, Pullman, WA 99164 2Kutztown University, Kutztown, PA 3Moscow High School, Moscow, ID 83843
Submitted to the Journal of Inorganic Chemistry
4.1 Introduction The solvation environment about a metal cation has a practical impact upon reaction
dynamics and understanding potentially complex speciation. Nowhere is this more apparent than
in the early actinides (An), including U, Np, and Pu. Four common oxidations states exist for
these species (III-VI) and in-situ redox reactions (disproportionation and reproprotionation) as
well as radiolysis can cause remarkably complex chemistry, even in pure water.1 Significant
experimental work has gone toward elucidating the aqueous coordination numbers (CN), polyhedral geometry adopted within the first solvation shell and the associated An-OH2 bond distances of An(III-VI) under varying pH conditions. Extended X-ray absorption fine structure
(EXAFS), X-ray absorption near-edge spectroscopy (XANES), neutron diffraction and electronic absorption have been primarily been employed (see ref. 2 and references therein), however,
interpretation of this data is often model dependent which can lead to inconsistent or
contradictory reports. For example, the precision in an EXAFS measurement of the coordination
number may vary within a few percent, yet the absolute accuracy may depend more on the
modeling technique or the assumption of the CN. Thermodynamic properties, like the free
energy of solvation (ΔGhyd) have been studied using calorimetry, however the solutions phase
26
conditions that stabilize a particular metal charge may also lead to unanticipated affects upon the
data.
Given these experimental challenges, computational chemistry has been used to complement experiment and help assign the solvation environments of actinides based upon matching either structural, spectroscopic and/or thermodynamic data. Typically a hydrated cluster consisting of a 1st solvation shell approximates the structure in solution. Density
functional theory (DFT) is most commonly used, as it is practical from a resource perspective
and relativistic affects are taken into account as part of the method itself (e.g. the zero order
regular approximation – ZORA DFT) or in the basis sets used to describe the metal atomic
orbitals (using a relativistically corrected effective core potential – RECP). However, in spite of
a growing body of work, there are still unassigned aqueous actinide species in the (III-VI)
oxidation states and there are few systems for which there is strong agreement in the community.
This is in part because computed properties are also highly sensitive to the chemical model
employed (for example, the number of explicit solvation shells used to describe the hydrated ion
or the density functional used). Thus, there exists in the literature many isolated computational
studies that use different methods, basis sets, and chemical models to investigate actinide
solvation. It is then difficult to compare computed properties across oxidation states or the
period. The goal of the current work is two-fold. First, to provide a consistent series of predicted
thermodynamic, structural, and spectroscopic properties of solvated U, Np, and Pu in the III-VI
oxidations states using a benchmarked computational protocol. Benchmarking in this context
refers to understanding the convergence of the theoretical data with respect to system size (the
number of explicit waters in the hydrated cluster), which is incredibly important and has been
discussed minimally in the literature. The combined predicted properties have then been used
27
assign the primary solvation environment of An(III-VI), helping to resolve prior inconsistencies
in the literature and providing missing pieces of information, both of which can serve a baseline
interpretation for future work. Each oxidation state is discussed at length, with detailed
discussions of prior work, the current interpretation based upon the computed properties and
potential errors that may arise due to the cluster model employed.
4.2 Computational Methods
It has been previously noted that the computed geometrical parameters of hydrated f- element ions are most sensitive to the basis set employed to describe the atomic orbitals of the ion (small-core vs. large-core RECPs) and the number of shells of explicit waters of solvation.3,4
3+/4+ +/2+ As such the geometries of the first solvation shell clusters An(H2O)8,9 and AnO2(H2O)4,5
nd 3+/4+ as well as the 2 solvation shell clusters An(H2O)8,9(H2O)21,22 and
+/2+ 5 AnO2(H2O)4,5(H2O)25,26 (An=U, Np, Pu) have been optimized using the NWChem software
package. The B3LYP6,7 combination of density functionals was employed (unrestricted (U) for open shell systems), as benchmarking studies have shown that this DFT method yields reasonable structural and thermodynamic parameters.8-13 Optimizations employed an SCF energy
convergence criterion of 10-6, an integral internal screening threshold of 10-16, a numerical integration grid of 10-8, and a tolerance in Schwarz screening for the Coulomb integrals of 10-12.
The Stuttgart “small-core” RSC60 RECP was employed for all An which replaces the 60 inner- shell ([Kr]4d104f14) electrons with a pseudopotential.14 The corresponding Stuttgart basis
describes the valence electrons of An and consists of segmented contracted 8s7p6d4f functions.
The aug-cc-pVDZ basis set was employed for the H- and O-atoms in the clusters with a single
15 solvation shell, while those clusters containing 30 H2O utilized the 6-311G** basis. Thus
28
calculations on the single solvation shell clusters are denoted by the method and basis set as
UB3LYP/RSC60/aug-cc-PVDZ while those calculations on the larger clusters are denoted by
UB3LYP/RSC60/6-311G**. Frequency calculations were performed to obtain thermochemical
corrections and ensure that structures correspond to local minima. All calculations neglected
spin-orbit (SO) effects within the 5f subshell, however prior spin-orbit configuration interaction
studies have indicated that SO coupling is negligible for determining structural features.16,17
Further, the SO contributions to the thermodynamic properties should be fairly similar for the reactants and products considered, leading to significant cancellation of errors in the calculated
ΔG values. The computation of the L3-edge XANES spectra for the optimized hydrated clusters
were carried out using the multiple-scattering code FEFF9,18,19 following the methodology of
Ankudinov et. al. for Pu hydrates.20 Details of the input parameters used in these calculations are
described in the Supplementary Information.
Single point polarized continuum model (PCM) calculations were performed to account
for the effects of the bulk solvent upon the computed thermodynamic parameters. Prior work has
noted the significant variability of PCM performance according to the way in which the solute
cavity is constructed and embedded in the dielectric continuum and the means by which the electrostatic interaction at the solute cavity boundary is determined. The ability of several PCMs to calculate reasonable thermodynamics for reactions r4.1 – r4.8 has been investigated. The
UA0, UAKS and Pauling (α = 1.1) cavity models were studied as implemented in Gaussian03,21 while integral-equation-formalism-protocol (IEF-PCM) calculations were performed using the development version of Gaussian0922 using a series of overlapping spheres, initially devised by
Tomasi and coworkers and Pascual-Ahuir and coworkers.23 The IEF-PCM implementation using
the radii and non-electrostatic terms of Truhlar and coworker’s SMD solvation model (denoted
29
24 as IEF-PCM(SMD), was also examined. The free energies of hydration (ΔGhyd) were calculated
according to reactions:
3+/4+ 3+/4+ An + (H2O)8,9 An(H2O)8,9 (r4.1)
3+/4+ 3+/4+ An + (H2O)30 An(H2O)8,9(H2O)22,21 (r4.2)
+/2+ +/2+ AnO2 (H2O)4,5 AnO2(H2O)4,5 (r4.3)
+/2+ +/2+ AnO2 + (H2O)30 AnO2(H2O)4,5(H2O)26,25 (r4.4) while the free energies of water addition (ΔGadd) were investigated using:
3+/4+ 3+/4+ An(H2O)8 + H2O An(H2O)9 (r4.5)
3+/4+ 3+/4+ An(H2O)8(H2O)22 An(H2O)9(H2O)21 (r4.6)
+/2+ +/2+ AnO2(H2O)4 + H2O AnO2(H2O)5 (r4.7)
+/2+ +/2+ AnO2(H2O)4(H2O)26 AnO2(H2O)5(H2O)25 (r4.8)
The solvent corrected free energies of these reactions are defined by:
Δ Δ ΔΔ , (4.1)
298 tot which has Ggas as the free energy of the reaction in the gas-phase, Gsolv , as the solvation
contribution to the free energy of the reaction, and SScorr as the standard-state thermodynamic
25 correction (-4.3 kcal/mol for each (H2O)n water cluster). Counter-poise corrections were not
included to correct for basis set superposition error, as prior studies have shown that the
magnitude of the correction is minimal compared to water binding energies to trivalent
lanthanides.26 Where relevant to the discussion of structural trends, the electronic structure and
bonding of each species was analyzed via natural population analysis and natural bond order
analysis27,28 in Gaussian09, using the partitioning of the core/valence/Rydberg space for the An of: 5s5p5d6s6p/5f6d7s7p/6f7d7f8s8p8d8f9s9p9d10s10p10d11s11p.29
30
The convergence of the hydration energetics in the gas-phase and in solution was
examined via single point calculations for the reactions:
3+/4+ 3+/4+ U + (H2O)n U(H2O)8(H2O)n-8 (r4.9)
+/2+ +/2+ UO2 + (H2O)n UO2(H2O)5(H2O)n-5 (r4.10)
where n = 41 and 77. The configurations for these very large clusters were obtained by first
3+/4+ +/2+ immersing a rigid U(H2O)8 and UO2(H2O)5 molecular species inside a box of 2039
classical TIP3P30 water molecules, then allowing for 1ns of equilibration in NPT and NVT
ensembles, followed by a 1ns production run in NVE using the DL_POLY431,32 software program. The equilibrated density was 0.998 g/cm3. A 1 fs timestep was used with an ewald
cutoff of 9 Å and a threshold of 10-8. The larger water clusters were carved out of a
representative snapshot of the simulation box by removing a sphere of water within 6.5 and 8.0
3+/4+ +/2+ Å from the U metal center and 6.7 and 8.25 Å from the UO2 solute. Spherical (H2O)41,77
clusters were removed from a similarly equilibrated pure TIP3P water simulation. Each cluster
was then subjected to a single point calculation in the gas-phase and with each of the
aforementioned dielectric continuum methods using UB3LYP/RSC60/6-311G**.
4.3 Results and Discussion
The results herein are first presented for those systems for which the most is known
experimentally. This enables benchmarking of the predicted structural, spectroscopic, and thermodynamic properties to experiment, in addition to understanding the convergence properties of the dielectric continuum models utilized so as to better guide future study. The goal is to resolve which hydration environments are thermodynamically preferred and most likely to be observed in aqueous solution near the infinite dilution limit. Representative optimized
31
geometries of the first and extended solvation shell structures are presented in Figure 4.1. Note
that in the extended solvation clusters there may be waters in both 2nd and 3rd solvation shells.
For the sake of computational expedience the same number of total waters was maintained for all
nd species. On average there are 18-19 H2O in the 2 solvation shell and two or three waters in the
3rd.
3+/4+ Figure 4.1. Representative geometries for: (a) An(H2O)8 , a square antiprism (SAP); (b) 3+/4+ An(H2O)9 , a tricapped trigonal bipyrimid (TTBP); (c) the solvation shell structure of 3+/4+ 1+/2+ 1+/2+ st nd An(H2O)9(H2O)21 ; (d) AnO2(H2O)4 ; (e) AnO2(H2O)5 ; (f) the 1 and 2 solvation 1+/2+ shell structure AnO2(H2O)4(H2O)26 .
Tetravalent Actinide Ions and the General Performance of Polarized Continuum Models.
Due to a high electric charge, tetravalent An have a strong tendency toward hydrolysis in
aqueous solution and can undergo polynucleation or colloidal formation.33 The 4+ ions of U, Np, and Pu are also easily oxidized to the linear dioxo “yl” species. While experimental free energies of hydration have been determined for all of the tetravalent ions under study and EXAFS has
32
obtained average An-OH2 bond lengths, there is a large discrepancy in the number of solvating waters that directly coordinate the metal (the coordination or hydration number). In the case of hydration about U(IV), reported CN from electronic absorption, XANES, and EXAFS methods range from 8 to 11.34-40 Prior DFT results for hydrated U(IV) have supported CN=9 using a
single solvation shell cluster model.41 A similar dispersion of results exists in the literature
concerning the coordination of Np(IV), which has reported coordination numbers of 8,2,36,42 92 and 1143,44 according to electronic absorption and EXAFS, and similarly for Pu(IV) which has
reported CN of 8 and 9.20,36,45 Previous computational studies using B3LYP DFT have not
determined a preference for 8 or 9 water molecules in the first hydration sphere for Np(IV),41 and, to our knowledge no computational studies have explored Pu(IV) hydration. Herein, the sensitivity of thermodynamic solvation properties to the method and cluster size is first studied, then the agreement of key bond lengths within the hydrated clusters to experiment is investigated, and finally we compare reported and simulated XANES spectra for the hydrated clusters with two solvation shells as these represent a compelling comparison to the experimental data obtained from bulk solution.
From a thermodynamic perspective, two quantities can be utilized for predicting the favored hydration environment: the free energy of solvation (ΔGhyd), and the energetics of water
addition reactions in the first solvation shell (ΔGadd). Since the experimental ΔGhyd are known for all of the tetravalent ions in this work, it is possible to thoroughly examine the performance of the various dielectric continuum models as a function of the charge of the cluster and the convergence properties with increasing number of solvating waters. The latter in particular is quite important as our and other groups have reported vastly different calculated ΔGhyd values for metal ions depending upon the number of explicit waters in the cluster.46,47 The typical
33
computational protocol for determining ΔGhyd utilizes an explicit first solvation shell and sometimes an incomplete 2nd solvation shell. In such systems, Gutowski and coworkers noted that the cavity volume was the primary factor in governing the solvation contribution to the free
2+ 46 energy of UO2 reactions in solution, while our own work on trivalent lanthanides has indicated that the surface area, which is a better indicator of the shape of the cavity, correlated with PCM performance.4
These observations represent only part of the computational dilemma when considering the ability to calculate accurate free energies of reaction in solution. In the case of hydration, the error in ΔGhyd is a composite of errors deriving from the gas-phase energetics as well as the
298 solvation correction. It is possible that the gas-phase ΔGgas and the solvation correction,
tot Gsolv , converge to the bulk limit at different rates with increasing explicit waters in the
298 cluster (Eqn. 4.1). For clusters of infinite size (the bulk limit), the ΔGgas would be equivalent
tot to ΔGhyd and the Gsolv should go to zero. However, different convergence properties of the gas-phase energetics and solvation corrections may lead to the aforementioned deviations in the calculated ΔGhyd as a function of system size and continuum model. This is illustrated in Table
4.1, wherein the UAKS and UA0 PCMs are in good agreement with the experimental free energy of hydration when there is a single solvation shell in the cluster, while the IEF-PCM implementation performs better when a 2nd solvation shell is present.
To further investigate this issue the convergence in the gas-phase hydration energy
(ΔEhyd) has been examined for U(IV), as described by reactions r4.1, r4.2 and r4.9, which consists of addition of U4+ to clusters containing 8, 30, 41, and 77 water molecules. The
4+ configurations of (H2O)41,77 and U(H2O)41,77 were taken from snapshots of an equilibrated classical water box, described by the TIP3P30 water model (see Computational Methods). It is
34
computationally impractical to perform complete geometry optimizations of the 41 and 77-H2O clusters, thus single point calculations were performed and the convergence of ΔEhyd was
tot monitored. Similarly, the convergence in the Gsolv was examined for each PCM employed,
tot and then the sum of ΔEhyd and the Gsolv was plotted to approximate how the relative
cancellation of errors in the two numbers would impact a calculated ΔGhyd value (where ΔGhyd ≈
tot ΔEhyd + Gsolv ).
As seen in Figure 4.2, the gas-phase ΔEhyd for the reaction converges nicely to the
experimental value for ΔGhyd for U(IV) since the explicit aqueous environment about the ion is
approaching the bulk. At a cluster size consisting of 77 water molecules ΔEhyd is within the
experimental error for ΔGhyd. As the size of the explicit water cluster is increased, the solvation
corrections to the reaction energy should approach zero, however it is apparent that in general the
PCM convergence is significantly slower than that of ΔEhyd. Note that the non-electrostatic
tot contribution to the Gsolv is essentially zero for the 41- and 77-water clusters, and thus it is
tot the electrostatic contribution to Gsolv that does not approach zero fast enough for accurate
ΔGhyd to be calculated even at a cluster size (77-waters) that includes what one could construe as a 4th solvation shell.
35
Figure 4.2. Calculated reaction energies (in kcal/mol) for reactions r4.1, r4.2 and r4.9 in the gas- phase and in aqueous solution, determined using different dielectric continuum models.
The convergence behavior of the different PCMs also varies significantly. IEF-PCM and
tot IEF-PCM(SMD) exhibit early linear behavior until Gsolv begins to plateau after the 41- water cluster. In contrast, UAKS and UAKS converge much more slowly than the IEF methods because they are already plateauing between 30 and 41 explicit waters of solvation. At the 77-
tot water cluster, Gsolv values calculated by IEF-PCM and IEF-PCM(SMD) are 138 and
86 kcal/mol below the bulk-limit, respectively, while and UA0 are still ~300 kcal/mol below.
The difference in these convergence patterns can be further dissected by examination of the electrostatic contribution, Eelec, to the solvation correction for the (H2O)n reactants and the
4+ U(H2O)n products in the solvation process. As seen in Figure 4.3, the Eelec of the metal ion using the united atom methods becomes less negative at a steady and nearly linear rate, while at the same time the Eelec of the water cluster slowly becomes more negative. There is thus an imbalance in the rates of change in the product and reactant electrostatic contributions to the
tot Gsolv which leads to a slow convergence of that quantity toward zero. In contrast, the ability
36
tot of Gsolv to approach zero in the bulk limit for the IEF methods derives from the cancellation of two very large negative quantities. This has implications in the less highly charged ions, where the Eelec of the metal becomes much smaller than Eelec of the water clusters (vide infra).
Figure 4.3. Electrostatic contribution (Eelec) to the free energy of solvation correction for (H2O)n 4+ reactant clusters and U(H2O)n product clusters in the solvation reactions r4.1, r4.8, and r4.9.
Given the emphasis within the literature upon aqueous clusters that contain 1-2 solvation
shells, it is worthwhile to discuss the means by which cancellation of errors can lead to a free
energy of hydration in good agreement with experiment (ΔGhyd determined by Eqn. 4.1). In these cases, the significantly underestimated gas-phase energy for the reaction must be compensated for by a large solvation correction. The latter is dominated by a negative electrostatic contribution that is highly sensitive to the cavity volume and surface area. The error in the
4+/3+ calculated ΔGhyd for An(H2O)8 relative to experiment is plotted as a function of these parameters in Figure 4.4. First considering cavity volume, it is apparent that too small of a cavity volume leads to overestimated (too negative) ΔGhyd values, but that the error in the hydration free energy trends approximately linearly as a function of volume size. Interestingly, the errors when compared to cavity surface area do not trend linearly and too large a surface area can lead to
37
either significant over- or underestimations of ΔGhyd. Importantly, those methods that produce the smallest cavity surface area do generally have the smallest errors with respect to experiment, including the traditional Pauling, UAKS and UA0 methods. The more recently developed IEF-
PCM method predicts large cavity volumes with large surface areas, leading to underestimation of ΔGhyd for both the tri- and tetravalent actinides, while the IEF-PCM(SMD) implementation
results in small cavity volumes but larger surface areas, causing an overestimated ΔGhyd. When a second solvation shell is added, the gas-phase reaction energy drops significantly toward the infinite bulk limit. At the same time the presence of a 2nd shell of solvating waters decreases the
electrostatic interactions on the cavity surface and thus the sensitivity of the calculated ΔGhyd
upon the specific PCM employed. As such, the standard deviation in the theoretical ΔGhyd for all
nd tot methods drops in half when a 2 solvation shell is added (Table 4.1). The slopes for Gsolv
4+ 4+ between the U(H2O)8 and U(H2O)8(H2O)22 data points in Figure 4.2 are between 3.0 – 4.0 for
all PCMs employed. This is nearly half that of ΔEhyd (slope of 7.6), and thus those methods
4+ tot nd which started off in U(H2O)8 with a smaller calculated Gsolv are benefitted in the 2 solvation shell cluster by not over-cancelling the error in ΔEhyd. Thus IEF-PCM yields ΔGhyd values that are in very good agreement with experimental data for all ions under study when a 2nd solvation shell is present. As such, for the remaining discussions of the thermodynamics of solvation, the data using IEF-PCM with the (H2O)30 cluster will be emphasized.
38
Table 4.1. UB3LYP calculated ΔGhyd values (in kcal/mol) for tetravalent actinides using reaction r2 calculated in aqueous solutions using different dielectric continuum models. The free energy for water addition, ΔGadd, using reaction r6 is also presented.
4+ 4+ An + (H2O)n+m An(H2O)n(H2O)m U Np Pu n,m = 8,0 n,m = 9,0 n,m = 8,0 n,m = 9,0 n,m = 8,0 n,m = 9,0 UAKS -1450.01 -1426.42 -1465.34 -1437.37 -1486.92 -1460.28 UA0 -1427.65 -1441.25 -1441.07 -1453.40 -1464.47 -1476.21 Pauling -1411.35 -1418.99 -1424.28 -1425.92 -1447.79 -1450.24 IEF- -1474.58 -1470.52 -1498.71 -1487.75 -1529.07 -1519.25 PCM(SMD) IEF-PCM -1379.42 -1381.62 -1390.23 -1392.55 -1415.01 -1413.99 a <ΔGhyd> -1429±73 -1428±65 -1444±82 -1439±70 -1469±86 -1464±77 Expt.48, 1 -1432.6 ±10 -1446.0 ±10 -1459.1 ±10 n,m = 8, 22 n,m = 9, n,m = 8, 22 n,m = 9,21 n,m = 8,22 n,m = 9,21 21 UAKS -1459.60 -1468.73 -1473.86 -1482.69 -1500.12 -1500.47 UA0 -1468.76 -1477.17 -1491.70 -1490.45 -1509.60 -1506.96 Pauling -1459.23 -1464.01 -1480.38 -1477.70 -1499.17 -1495.80 IEF- -1477.62 -1479.55 -1507.08 -1506.34 -1528.27 -1517.00 PCM(SMD) IEF-PCMb -1437.92 -1436.65 -1450.53 -1447.84 -1475.34 -1462.86 a <ΔGhyd> -1461±30 -1465±34 -1481±42 -1481±43 -1503±38 -1497±41 Expt.48, 1 -1432.6 ±10 -1446.0 ±10 -1459.1 ±10 4+ 4+ An(H2O)8(H2O)22 An(H2O)9(H2O)21 U Np Pu IEF-PCM 1.27 2.69 12.47 aaverage and standard deviation using all PCM data brecommended for clusters with two solvation shells.
39
Figure 4.4. Comparison of the error in the calculated free energy of hydration (ΔΔGhyd = theory expt 4+/3+ ΔGhyd – ΔGhyd ) for the An(H2O)8,9 ions.
The experimental error in ΔGhyd prevents any distinction regarding the favorability of the
8- or 9-coordinate solvation environment in aqueous solution. Investigation of the water addition
4+ 4+ nd st reaction An(H2O)8(H2O)22 An(H2O)9(H2O)21 , wherein a 2 shell water migrates into the 1 shell, provides clearer evidence regarding which species is thermodynamically favored. For these
2nd solvation shell clusters IEF-PCM predicts a slight preference for the 8-coordinate species in
tetravalent U (ΔGadd = 1.27 kcal/mol) and Np (ΔGadd = 2.69 kcal/mol), while there is definite
4+ 4+ thermodynamic favorability of Pu(H2O)8 over Pu(H2O)9 (ΔGadd = 12.47 kcal/mol). The small
40
magnitude of ΔGadd for U(IV) is within the error of these calculations, and thus it is mostly likely
that the equilibrium between the 8- and 9-coordinate species leads to significant populations of
4+ both species in solution. In Np(IV) the equilibrium likely favors the Np(H2O)8 , however there
is strong likelihood that Pu(IV) exists solely as the octa-aqua species. The results for U(IV)
contrast the conclusions drawn by Tsushima and coworkers,41 who found a thermodynamic
preference for the 9-coordinate species, though we do agree with the potential equilibrium
between 8- and 9- coordinate species for Np(IV). However, it is important to note that while
those calculations used a comparable method and basis set, symmetry was imposed during
geometry optimization and the cluster model employed only consisted of a single solvation shell
and used IEF-PCM (the default in Gaussian03), which we have demonstrated above as having
very poor agreement with experiment in the calculation of ΔGhyd using that cluster size.
Comparison of calculated and experimental structural data as well as XANES spectra
also reinforce the thermodynamic predictions from the large hydrated clusters. As seen in Table
4.2, the calculated rAn-OH2 distances in the first solvation shell are within the 0.01 Å error of the
reported bond lengths from EXAFS and neutron diffraction methods.2,45,49 The polyhedral arrangement and extended solvation structure is better compared to results from XANES. Within this method, a Fourier transform of the X-ray absorption spectrum results in a radial distribution function that can be interpreted as shells of nearest neighbor atoms surrounding the central ion.
The position and intensity of the peaks in the Fourier transform are related to the atomic identity, distance, and number of atoms in each shell. Thus, XANES is sensitive to the bond angles the
st solvating H2O adopt about the ion and the unique polyhedral geometry of the 1 solvation
shell.44 It can thus (in principle) distinguish between first solvation shells that are 8-coordinate
41
and adopt a square antiprism geometry (SAP) versus the 9-coordinate tri-capped trigonal
bipyramidal (TTBP) structure (Figure 4.1).
4+ Table 4.2. Average UB3LYP
4+ An(H2O)n(H2O)m
42
50,51 4+ Figure 4.5. Simulated and experimental XANES spectra of An(H2O)8,9(H2O)22,21 . The theoretical spectra have only been aligned to the maximum of the white line, no other shifting was performed.
43
4+ Figure 4.5 presents the simulated XANES spectra of An(H2O)8(H2O)22 and
4+ 50,51 An(H2O)9(H2O)21 overlayed with experiment and containing inset tables with the root mean square error (RMSE) within different spectral regions. In the case of U(IV) the nona-aqua
species has the best agreement with the edge of the white line, however the octa-aqua species has
the least error in the peak position and height, and in the high energy feature. This further
supports the conclusions that U(IV) likely exists in equilibrium with significant contributions of
both species in solution. Similarly, for Np(IV) the octa-aqua ion has significantly better
agreement with the white line edge, while the peak positions and height and the high energy
4+ 4+ feature are essentially equally well-described by both Np(H2O)8 and Np(H2O)9 . These data contrast somewhat with conclusions drawn by Chaboy and coworkers,35 who, using 1st solvation shell clusters obtained from the work of Tsushima et. al.,41 found better agreement with the
experimental XANES spectra using a 9-coordinate TTBP structure. We were unable to reproduce the unique structural features observed within the simulated XANES spectra of the square antiprismatic structure utilized by Chaboy et. al. using any of our hydrated clusters and thus it is unclear where this discrepancy may arise. Nevertheless, the thermodynamic, geometric, and spectroscopic data presented in this work is consistent and provides strong evidence for equilibrium between the 8- and 9-coordinates solvation environments for U(IV) and Np(IV). In
4+ the discussion of aqueous Pu(IV) it is very apparent that Pu(H2O)8 has the closest agreement
with the entire experimental spectrum, clearly indicating in combination with the thermodynamic data that it is the predominant species in aqueous solution.
44
Trivalent Actinide Ions. Trivalent U, Np, and Pu ions are obtained under acidic conditions at ~pH 0 within non-complexing media.2,51 The specific CN have been a subject of some debate
experimentally, with 9-10 reported for U and Np,2,49 and 8 - 10 waters of hydration for
Pu(III).20,43,45,49 Prior to 2007 there were few computational studies,2,11,52 however at that time a comprehensive thermodynamic investigation using DFT and Moller-Plesset perturbation theory
3+ provided strong evidence that trivalent U, Np, and Pu likely exist as An(H2O)8 in aqueous
solution.53 In that work, clusters based upon a primary solvation environment were utilized in
conjunction with a single continuum method to approximate the effects of the bulk, and no comparisons to spectroscopic data were made. The aforementioned convergence properties of the
PCMs with the trivalent ions in conjunction with simulated XANES spectra provided herein help to solidify our understanding of the solvation behavior of these species.
Table 4.3 presents the calculated and experimental free energies of hydration of
3+ An(H2O)8,9(H2O)22,21 clusters along with the average values and standard deviations. The PCM
convergence properties have also been studied in a similar manner as the tetravalent ions; only
the most salient features are discussed for brevity. Focusing first on U(III), we note that even
with a single solvation shell the calculated ΔGhyd values are in better accord with experiment
than previously observed in the An(IV) ions (See Appendix A). Further, the predicted ΔGhyd for the second solvation shell species exist within a standard deviation of ± 20 kcal/mol, meaning
tot that the various PCMs have more similar Gsolv values than observed in An(IV). At the same
tot time, examination of the slope of Gsolv between the two data-points consisting of the 8- and
tot 30-water species, reveals a 2x increase in rate of convergence toward the bulk limit of Gsolv
= 0 than in the tetravalent species. The combination of the smaller standard deviation in
tot Gsolv and the faster convergence for the 8- and 30-water species thus leads to more PCMs
45
capable of predicting Ghyd within experimental error. In fact, for the 30-water clusters nearly
every PCM for every ion predicts a reasonable Ghyd. The thermodynamics of water addition
reveals preference for the 8-coordinate solvation environment for all ions studied (Table 4.3), in
agreement with the previous thermodynamics assessments using DFT.53 The PCM performance beyond the 30-water cluster begins to degrade for the calculation of Ghyd. Specifically, the
electrostatic contribution to the metal ion solvation correction decreases significantly, which
leads to an imbalance in the cancellation of the electrostatic contribution to the solution phase
correction of the products and reactants in the solvation process (as described for Figure 4.3).
tot Thus, the Gsolv term in Eqn. 4.1 begins to behave strangely as the water cluster size is increased toward a bulk limit (See Appendix A). This behavior becomes more pronounced in the di- and monocations of the actinyl species.
The structural and spectroscopic data of the 30-water cluster has been examined, and
3+ further supports the presence of An(H2O)8 in solution. Reduction of An(IV) to An(III) leads to
an increase in the average bond lengths that is in excellent agreement with experimental data
(Table 4.2). Prior EXAFS study has shown that for the oxidation of Np(III) to Np(IV) aquo ions,
elongation of 0.11Å in the average Np-O bond lengths from 2.37(1) to 2.48(2), is observed.2 The
predicted contraction in the analogous reduction process is nearly identical at 0.12 Å. Subtle
changes in the electronic structure are also observed upon reduction of the tetravalent to trivalent
species. Electron donation from the coordinating waters decreases from ~0.25 e- to ~0.15 e-
(Table 4.2). In the case of U(III), the nona-aqua species has bond distances within experimental
error, though the octa-aqua species has the more correct bond lengths for Np(III) and Pu(III)
clusters.
46
Table 4.3. UB3LYP calculated ΔGhyd values (in kcal/mol) for trivalent actinides using reactions r2 calculated in aqueous solutions using different cavity models. The free energy for water addition to the first solvation shell ΔGadd using reaction r6 is also presented.
3+ 3+ An + (H2O)n+m An(H2O)n(H2O)m U Np Pu n,m = 8, 22 n,m = 9, n,m = 8, 22 n,m = 9,21 n,m = 8,22 n,m = 9,21 21 UAKS -782.94 -787.81 -790.05 -795.98 -807.71 -811.28 UA0 -790.71 -794.54 -797.92 -803.09 -815.72 -815.49 Pauling -780.17 -783.84 -786.13 -791.05 -803.63 -805.80 IEF- -794.57 -789.66 -813.99 -820.95 -827.89 -824.35 PCM(SMD) IEF-PCMa -766.94 -761.56 -773.11 -770.40 -786.33 -781.06 b <ΔGhyd> -783±21 -783±26 -792±30 -796±37 -808±30 -808±33 Expt48, 1 -773.9 ±10 -783.5 ±10 -791.8 ±10 3+ 3+ An(H2O)8(H2O)22 An(H2O)9(H2O)21 U Np Pu IEF-PCM 5.37 2.71 5.27 a recommended for clusters with two solvation shells. b average and standard deviations including all PCM data
To our knowledge no XANES data has been reported for aqueous U(III), however as seen in Figure 4.6, distinct spectral signatures are observed for the square antiprism first
3+ solvation shell within U(H2O)8(H2O)22 versus the tricapped trigonal bipyramid
3+ U(H2O)9(H2O)21 . The latter is observed to have significantly more intensity in the white line peak, with a spacing between that and the high energy feature of 37 eV. In contrast the SAP structure has an interpeak separation of 31 eV. In both the Np(III) and Pu(III) systems the simulated XANES spectrum of the cluster with eight primary solvating waters is in best agreement with experiment.50,51
47
50,51 3+ Figure 4.6. Simulated and experimental XANES spectra of An(H2O)8,9(H2O)22,21 . The theoretical spectra have only been aligned to the maximum of the white line (for Np(III) and Pu(III)), no other shifting was performed.
48
3+ Though the white line peak is equally well-described by Np(H2O)8(H2O)22 as
3+ Np(H2O)9(H2O)21 , the former clearly does a better job of tracking the high energy feature. The simulated spectra of the Pu(III) clusters are even more straightforward, with the
3+ Pu(H2O)8(H2O)22 having the smallest root mean square error across all regions of the
experimental spectrum. Based upon these data we cannot unequivocally conclude that U(III)
exists as the octa-aqua species, however it is likely. It is proposed that Np(III) and Pu(III) exist
3+ primarily as An(H2O)8 in aqueous solution.
2+ Aqueous AnO2 Ions. The An(VI) oxidation states are experimentally observed in near
neutral pH and under slightly basic conditions54 as linear di-oxo cations that have unique
hydration properties associated with the directed ligation of water into the equatorial plane
2+ (Figure 4.1). The UO2 cation, due to its oxidation state stability, has been extensively studied by
experiment and computation. Its hydration number was a point of contention for several years as
both 4 and 5 waters in the equatorial plane had been reported. 54-57 However, the most recent
2+ experimental data of UO2 has supported the 5 H2O case, which has been further bolstered by
extensive computational studies utilized DFT and other methods such as MP2, CASSCF,
CASPT2, CCSD, and CCSD(T).10,46,58-60 Hexavalent Np and Pu are much less studied in the
literature, however experimental data has pointed to a CN of five in the equatorial plane for
2+ 2+ 44,61 NpO2 and five or six for PuO2 . The latter value is somewhat problematic because an
increase in CN would not be anticipated due the actinide contraction wherein the ionic radius
decreases from 0.73 Å in U(VI) to 0.72 Å in Np(VI) to 0.71 Å in Pu(VI).62 Most computational
studies have assumed a 5-coordinate first solvation shell structure for Np(VI) and Pu(VI) and
found good agreement between the structural and electronic properties (bond lengths, redox
potentials, etc) of these species and experiment.60,63
49
Table 4.4. UB3LYP calculated ΔGhyd values (in kcal/mol) for hexavalent actinides using reaction r4 calculated in aqueous solutions using different cavity models. The free energy for water addition to the first solvation shell ΔGadd using reaction r8 is also presented.
2+ 2+ AnO2 + (H2O)n+m AnO2(H2O)n(H2O)m U Np Pu n,m = 4, 26 n,m = 5, n,m = 4, 26 n,m = 5,25 n,m = 4,26 n,m = 5,25 25 UAKS -390.24 -397.85 -547.07 -555.07 -538.34 -548.19 UA0 -392.02 -402.70 -550.60 -559.29 -540.92 -554.22 Pauling -397.56 -401.27 -553.31 -555.53 -543.45 -549.66 IEF- -417.51 -412.11 -580.56 -581.00 -569.72 -559.15 PCM(SMD) IEF-PCMa -387.38 -389.66 -542.21 -548.38 -532.38 -531.56 b <ΔGhyd> -39724 -40116 -55530 -56025 -54529 -54921 Expt64 -39715 2+ 2+ AnO2(H2O)4(H2O)26 + H2O AnO2(H2O)5(H2O)25 U Np Pu IEF-PCM -2.28 -6.17 0.82 a recommended for clusters consisting of two solvation shells b average and standard deviation using all PCM data
2+ As observed in Table 4.4 for UO2 , all of the PCMs (except for IEF-PCM(SMD)) predict values for ΔGhyd that are within the experimental error using the hydrated clusters consisting of
30 water molecules. The error in IEF-PCM(SMD) derives from the small electrostatic contribution to the free energy correction of the hydrated metal ion, and the large negative contribution to the pure water cluster, as described above. In fact, for both uranyl di- and mono- cations the IEF formalisms over-compensate the electrostatic contributions in the larger 41- and
tot 77-water clusters such that positive ΔΔGsolv values on the order of 10-100 kcal/mol are observed as the bulk limit is approached (See Appendix A). At the 30-water cluster, each PCM
(except for the SMD variant) behaves reasonably, each agreeing that addition of water to
2+ UO2(H2O)4(H2O)26 to form the 5-coordinate species is thermodynamically favorable. The IEF-
50
PCM value of ΔGadd is -2.28 kcal/mol, in excellent agreement with prior studies by Gutowski
46 2+ and Dixon. Water addition to form the NpO2(H2O)5H2O)25 species is also predicted to be
favorable, however the process for plutonyl appears to be an approximately energetically neutral
process. Thus, the thermodynamic data would indicate that predominant species in solution for
2+ uranyl and neptunyl is AnO2(H2O)5 species, while there may be an equilibrium between the 4-
2+ and 5-coordinate species for aqueous PuO2 . Unfortunately, the simulated XANES spectra of
the linear di-oxocations do not readily distinguish between the two coordination environments
because the angular differences in the first solvation shell are modest – consisting of only an 18°
change in the OH2-An-OH2. This is in contrast to the differences between the SAP and TTBP
geometries found in the aqueous An4+/3+ species, which consisted of large variations in both
OH2-An-OH2 and also dihedral angles.
2+ 2+ The thermodynamic preference of the UO2(H2O)5 and NpO2(H2O)5 is further
supported by the close agreement of the calculated bond lengths to those reported from EXAFS
43,44,61 2+ studies (Table 4.5). Structurally, the most consistent data with experiment for PuO2
2+ appears in the PuO2(H2O)5(H2O)25 species. The average An=O distances,
Interestingly, the reported ionic radii for these ions fits a linear function, while in the calculated changes in bond distance from U – Pu, it appears that the contraction in the diyl Pu=O bond is more than would be expected from the actinide contraction alone. Investigation of the average actinide-water bond distance reveals the best agreement with the experimental values when there are 5 waters in the equatorial plane about U, Np, and Pu, having an average deviation of only
0.015 Å. In both the literature and current work, when five waters are present in the 1st solvation shell a significant increase in rAn-OH2 is observed when moving from Np to Pu. These data are
51
reflective of the slight increase in 6d atomic orbital energies and decrease in the 5f orbital
energies that occurs moving from U to Pu, which modulates the electronic structure, dramatically increasing the charge donation across the diyl bond, and thus decreasing the electrostatic interaction between the metal and equatorial waters. As seen in Table 4.5, the average charge of
2+ the diyl oxo-atoms in AnO2(H2O)5(H2O)25 is -0.41, meaning that 1.59 electrons are donated per oxo-atom (which are formally 2-) to the 6+ metal center. Moving from U to Pu results in a 35% increase in charge donation from the diyl-oxo to the actinide. These added electrons are donated
2+ primarily into the 5f orbitals, where the 5f electron configuration is 5f in UO2(H2O)5(H2O)25
2+ and 5f in PuO2(H2O)5(H2O)25 (See Appendix A). This is ~0.3 electrons more than anticipated
based upon the fact that Pu(VI) formally has two more f-electrons than U(VI). Commensurate
with the enhanced electron donation by the diyl oxo-atoms is a slight decrease in the electron
donation to the metal from the equatorial water O-atom lone-pair orbitals. Thus, the electrostatic interaction between the An and the H2O decreases slightly across the U, Np, Pu series and the
An-OH2 bond lengths increase.
52
Table 4.5. Average UB3LYP equatorial, rAn-OH2, and axial metal-oxygen bond lengths, rAn=O, in 2+ + (Å) for AnO2(H2O)4,5(H2O)26,25 and AnO2(H2O)4,5(H2O)26,25 in comparison with experimental values (in parentheses). Average charges (q) are reported, determined by NPA for the metal center, actinyl oxo-atom, O-atoms associated with the inner-sphere (IS) and outer-sphere (OS) water molecules.
AnO2(H2O)n(H2O)m
+ Aqueous AnO2 Ions. Though U(V) cations are highly reactive and readily
66,67 + + disproportionate to a formal IV and VI oxidation states, NpO2 and PuO2 have been
observed in acidic conditions.68 Experimental studies have found the dioxo mono-cations to have
42 + 4-6 waters in the first solvation shell. In the gas-phase, AnO2 hydrates have been recently
produced by electrospray ionization, wherein only four H2O were found in the first solvation
shell.69 To our knowledge, no experimental free energies of hydration exist for any of the 1+ diyl
cations and water addition reactions have only recently been studied using a single solvation
shell in the gas-phase (for comparison to the reported electrospray data).
53
As seen in Table 4.6, the standard deviation in the predicted ΔGhyd are comparable to that
2+ of the trivalent ions and AnO2 species. At the cluster size consisting of 30 waters, each PCM
tot + predicts a ΔΔGsolv less than 100 kcal/mol from the bulk limit. In the case of uranyl, UO2 , each
PCM (except for IEF-PCM(SMD)) predicts a small favorability of the 5-coordinate species over the primary solvation shell consisting of four equatorial waters. The IEF-PCM implementation
predicts ΔGadd to be -1.05 kcal/mol and thus equilibrium between the two configurations cannot
+ + be eliminated. In stark contrast, the NpO2(H2O)5 and PuO2(H2O)5 species are uniformly
+ predicted to be much less stable than the AnO2(H2O)4 . In fact, the 5-coordinate plutonyl
monocation could not be optimized without migration of the fifth water into the second solvation
shell. These data support the gas-phase electrospray observations and complementary DFT
calculations recently reported by Rios and coworkers69 for gas-phase neptunyl and plutonyl,
+ however it is possible that the proposed equilibrium between aqueous UO2(H2O)4 and
+ UO2(H2O)5 may get shifted to favor the 4-coordinate species during the electrospray process.
Thus, it is highly likely that the same 4-coordinate species is observed in solution as in the gas-
phase.
As previously mentioned, the electrostatic contribution to the solvent correction of the
metal ions becomes significantly imbalanced relative to the Eelec of the pure water cluster
reactant in reaction r9. For the IEF formalisms, the Eelec of the pure cluster is much more
tot negative and thus when the ΔΔGsolv is calculated (products – reactants) the net result is a high
positive number (See Appendix A). In contrast, the united atom methods over-compensate the
tot Eelec to the metal ion, thus leading to a downward slope of ΔΔGsolv toward more negative values as the number of explicit waters is increased. For these monocations it does not appear that
54
PCMs should be utilized to approximate the aqueous properties of clusters with more than a
single solvation shell.
Table 4.6. UB3LYP calculated ΔGhyd values (in kcal/mol) for pentavalent actinides using reaction r4 calculated in aqueous solutions using different cavity models. The free energy for water addition to the first solvation shell ΔGadd using reaction r8 is also presented.
+ + AnO2 + (H2O)n+m AnO2(H2O)n(H2O)m U Np Pu n,m = 4, 26 n,m = 5, n,m = 4, n,m = n,m = n,m = 25 26 5,25 4,26 5,25 UAKS -258.93 -263.98 -306.57 -265.48 -485.42 NAa UA0 -260.77 -268.74 -308.32 -270.57 -487.04 NA Pauling NAb -288.71 -313.22 -267.11 NAb NA IEF-PCM(SMD) -283.23 -278.04 -336.10 -282.87 -517.01 IEF-PCMc -259.73 -260.78 -300.18 -256.23 -486.14 NA d <ΔGhyd> -266±20 -272±23 -313±28 -268±19 -494±27 + + AnO2(H2O)4(H2O)26 + H2O AnO2(H2O)5(H2O)25 U Np Pu IEF-PCMe -1.05 43.95 NA a + unable to optimize PuO2(H2O)5(H2O)25 b unable to converge Pauling SCF energy c recommended for clusters consisting of two solvation shells d average and standard deviation using all PCM data
4.4 Conclusions.
DFT calculations employing large hydrated clusters of U, Np, and Pu in the III-VI oxidation states have been performed so as to elucidate the most likely solvation environment in aqueous solution. Assignment of the first solvation shell of these ions is an essential starting point toward understanding their reaction dynamics and complex speciation in aqueous conditions relevant to the nuclear fuel cycle, separations, and environmental remediation. Three
criterion have been used to assign structure of these ions in aqueous solution: 1) the free energies
of hydration and water addition to the first solvation shell, 2) geometrical parameters (metal-
oxygen bond lengths), and 3) simulated XANES spectra. The combination of these data indicate
55
that tetravalent U and Np exist in equilibrium between the 8- and 9-coordinate species
4+ 4+ 4+ (An(H2O)8 An(H2O)9 ), while Pu(IV) should exist solely as the Pu(H2O)8 species.
Trivalent ions have a distinct thermodynamic favorability for the octa-aqua species, whose features also lead to excellent reproduction of the XANES spectra. The actinyl di-cations,
2+ AnO2 , have a preferred environment in the equatorial plane consisting of 5 solvating waters,
however an equilibrium between the 4- and 5-coordinate species cannot be eliminated for
2+ + PuO2 . Similarly, the uranyl monocation is likely in equilibrium between UO2(H2O)4 ⇄
+ UO2(H2O)5 , while the neptunyl and plutonyl species are proposed to exist solely as
+ AnO2(H2O)4 .
An essential aspect of this work has been the study of the convergence properties of the
thermodynamics of the free energy of hydration as a function of the size of the cluster of
explicitly solvating waters about the ion. Specifically, the error in ΔGhyd has been decomposed
into the errors deriving from the gas-phase energetics as well as the solvation correction. The
rates of convergence of both quantities toward the bulk limit have been found to be quite
different, and to vary significantly between dielectric continuum models. The dominant
tot contribution to the ΔΔGsolv component of ΔGhyd is the electrostatic interaction at the surface of
the cavities of the products and reactants in the solvation process. In highly charged species the
tot ΔΔGsolv converges nicely toward the bulk limit of zero using all PCM methods, though the
united atom methodologies converge much more slowly. As the charge of the metal decreases,
tot ΔΔGsolv may not converge toward the correct bulk limit because the electrostatic contributions
to the products and reactants no longer cancel one another. This implies that PCMs should not be
utilized with very large hydrated metal clusters ( > 2 solvation shells) when the cation is di- or
monovalent.
56
4.5 Acknowledgements
This work was supported by a grant from the Department of Energy, Basic Energy
Sciences, Heavy Element program (DE-SC0001815). S.L. acknowledges the PHY-0649023
Research for Undergraduates program, sponsored by the National Science Foundation. This work was performed in part at the William R. Wiley Environmental Science Laboratory and using the Molecular Science Computing Facility (MSCF) therein, a national scientific user facility sponsored by the U.S. Department of Energy’ s Office of Biological and Environmental
Research and located at the Pacific Northwest National Laboratory, operated for the Department of Energy by Battelle. The authors thank Dr. Marco Caricato (Gaussian Inc) for thoughtful discussion regarding the performance of polarizable continuum models.
4.6 References
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(44) Reich, T.; Bernhard, G.; Geipel, G.; Funke, H.; Hennig, C.; Rossberg, A.; Matz, W.; Schell, N.; Nitsche, H. Radiochim. Acta 2000, 88, 633. (45) Conradson, S. D. App. Spec. 1998, 52, 252A. (46) Gutowski, K. E.; Dixon, D. A. J. Phys. Chem. A 2006, 110, 8840. (47) Kuta, J.; Clark, A. E. J. Phys. Chem. C 2011, 115, 21120. (48) Bratsch, S. G.; Lagowski, J. J. J. Phys. Chem. B 1986, 90, 307. (49) David, F. H.; Fourest, B.; Hubert, S.; Revel, R.; Auwer, C. D.; Madic, C.; Morss, L. R.; Ionova, G.; Mikhalko, V.; Vokhmin, V.; Nikonov, M.; Berthet, J. C.; Ephritikhine, M. In Speciation, Techniques and Facilities for Radioactive Materials at Synchrotron Light Sources; Nuclear Energy Agency: Organisation for Economic Cooperation and Development: Grenoble, France, 1998, p 95-100. (50) Hennig, C. Phys. Rev. B 2007, 75, 035120. (51) Conradson, S. D.; Al Mahamid, I.; Clark, D. L.; Hess, N. J.; Hudson, A. E.; Neu, M. P.; Palmer, P. D.; Runde, W. H.; Tait, C. D. Polyhedron 1998, 17, 599. (52) Blaudeau, J.-P.; Zygmunt, S. A.; Curtiss, L. A.; Reed, D. T.; Bursten, B. E. Chem. Phys. Lett. 1999, 310, 347. (53) Wiebke, J.; Moritz, A.; Cao, X.; Dolg, M. Phys. Chem. Chem. Phys. 2007, 9, 459. (54) Neuefiend, J.; Soderholm, L.; Skanthakumar, S. J. Phys. Chem. A 2004, 108, 2733. (55) Evans, H. T. J. Science 1963, 141, 154. (56) Semon, L.; Boehme, C.; Billard, I.; Hennig, C.; Lutzenkirchen, K.; Reich, T.; Rossberg, A.; Rossini, I.; Wipff, G. Chem. Phys. Chem. 2001, 2, 591. (57) Bardin, N.; Rubini, P.; Madic, C. Radiochim. Acta 1998, 83, 189. (58) Wahlren, U.; Moll, H.; Grenthe, I.; Schimmelpfennig, B.; Maron, L.; Vallet, V.; Gropen, O. J. Phys. Chem. A 1992, 103, 8257. (59) Spencer, S.; Gagliardi, L.; Handy, N. C.; Ioannou, A. G.; Skylaris, C.-K.; Willetts, A.; Simper, A. M. J. Phys. Chem. A 1999, 103, 1831. (60) Hay, P. J.; Martin, R. L.; Schreckenbach, G. J. Phys. Chem. A 2000, 104, 6259. (61) Cotton, S. Lanthanide and Actinide Chemistry; John Wiley and Sons, 2006. (62) Shannon, R. D. Acta Cryst. 1976, A 32. (63) Shamov, G. A.; Schreckenbach, G. J. Phys. Chem. A 2005, 109, 10961. (64) Gibson, J. K.; Haire, R. G.; Santos, M.; Marcalo, J.; Matos, A. P. d. J. Phys. Chem. A 2005, 109, 2768. (65) Conradson, S. D. Applied Spectroscopy 1998, 52, 252A. (66) Harris, W. E.; Kolthoff, I. M. J. Am. Chem. Soc. 1946, 67, 1484. (67) Steele, H.; Taylor, R. J. Inorg. Chem. 2007, 46, 6311. (68) Hindman, J. C.; Magnusson, L. B.; LaChapelle, T. J. J. Am. Chem. Soc. 1949, 71, 687. (69) Rios, D.; Michelini, M. C.; Lucena, A. F.; Marçalo, J.; Bray, T. H.; Gibson, J. K. Inorg. Chem. 2012, 51, 6603.
59
Chapter 5
An Integrated Computational and Experimental Protocol for Understanding Rh(III) Speciation in Hydrochloric and Nitric Acid Solutions
Alex C. Samuels†,‡, Cherilynn A. Boele†, Kevin T. Bennett†, Sue B. Clark†, Nathalie A. Wall†,‡, Aurora E. Clark†,‡
†Department of Chemistry, Washington State University, Pullman, WA 99164, USA, ‡Materials Science and Engineering Program, Washington State University, Pullman, WA 99164, USA
Submitted to the Journal of Inorganic Chemistry, June 2014
5.1. Introduction
Raffinates from extraction processes that have the heavier lanthanide and actinides
removed typically leave the PGMs at near room temperature in aqueous acidic solutions
containing chloride or nitrate.1 The pH is generally smaller than 1, with moderate to concentrated chloride concentrations (up to 6 M), and nitrate concentrations between 2 M and 4 M are employed.1,2 Rh is quite stable in the trivalent oxidation state; however, the speciation kinetics in
chloride media is particularly complicated. The completely aquated hexaaquo-rhodate,
3+ 3- Rh(H2O)6 , the hexachloro-rhodate, RhCl6 , and all mixed aquo/chloro complexes, including
3-x isomers, (RhClx(H2O)6-x with x=1-5) can exist simultaneously in solution. At high chloride
3- concentrations and millimolar Rh(III) concentrations, a dimer, Rh2Cl9 , has been reported to
form.3 Further adding to the variety of complexes possibly present are chloride and oxygen
bridged polymeric Rh species, of which very little is known.4 The formation of polymeric
species is not unique to Rh(III) and is observed with Cr(III) and Fe(III), where the pH < 7 and
metal concentrations of ≥ 10-3 M.5,6 The concentration of each complex depends primarily on the
chloride concentration, but also, to a lesser degree, on the temperature, age, and pH of the
60
solution. For example at pH > 2.9, the aquo/chloro complexes are believed to undergo hydrolysis
2-7 to RhCl4(OH)(H2O). As a result of the complicated species distribution in solution, study of
the chloro-aqua species has relied upon purification of a specific species of interest via ion
exchange chromatography, followed by characterization using polarography and/or ultraviolet-
visible (UV-Vis) spectroscopy (focusing upon the low-energy portion of the spectrum, λ ≥
300 nm ). Significant efforts have been devoted to understanding the mechanistic aspects of
aquation reactions of various chloro-aqua species.8-12 In principle, speciation under varying
chloride concentrations should be straightforward to determine provided the binding constants of
all potential molecular species; however, the available speciation diagrams are suspect as
different interpretations of the polarographic data yield a range of binding constants. Even less is
understood about the speciation of Rh(III) in nitric acid media, as nucleophilic substitution of
chloride by nitrate has been observed.13
Examination of Rh speciation under conditions relevant to extraction from raffinates is necessary to design extraction protocols for this metal from spent fuel. To aid in the assignment of species within solution and to understand the potentially intricate distribution and dynamic nature of species, modern studies can take advantage of computational chemistry to understand the thermodynamic favorability for the formation as well as the prediction of the UV-Vis spectra of individual entities. The goal of this work is twofold: first, to investigate Rh(III) speciation in acidic media under conditions that are relevant to separations applied to spent fuel raffinates, and second, to demonstrate that the speciation can be understood through a combined experimental and theoretical approach that relies upon identification of the number of species present using electrophoretic methods, experimental measurement of ligand-metal charge transfer (LMCT) bands in the UV-Vis region, simulation of the UV-Vis spectra, and calculated thermodynamic
61
quantities. The speciation of Rh(III) nitrate is shown to be straightforward; however, Rh(III)
chloride speciation in acidic aqueous solutions is significantly more complex than prior work
indicates.
5.2. Experimental and Computational Methods
Materials and Methods. Solid RhCl3∙nH2O (99.99% Rh purity, Fisher) was dissolved in deionized distilled 18 MΩ water (D-DIW), under constant stirring at room temperature, except for daily low heating (1 h/day), until equilibrium was reached. Solutions were protected from light at all times. The Rh chloride speciation was perturbed by adding aliquots of RhCl3 stock solutions, described above, to D-DIW and enough 12 M HCl (Fisher) to obtain various chloride concentrations (Table 5.1). The resulting solutions were stirred for 1 minute before being placed in a 50 °C oven, where they remained until solutions reached equilibrium. During this time, the solutions were stirred for 1 min daily and momentarily removed from the oven at recorded times for UV-Vis analysis (the solutions were allowed to cool down before measurements). Sodium
(Na) concentrations in the RhCl3 solutions in water were determined using an Atomic
Absorption Flame Emission Spectrophotometer (Flame AA) (Shimadzu AA-6200) (Buck
Scientific Na/K Hollow Cathode Lamp, lamp current 14V, slit width 0.2 nm, wavelength
589.0 nm). The instrument was calibrated with dilutions of a 1003 ppm Na standard solution in
5% HNO3 (VHG Labs). Rhodium nitrate solutions were prepared in a similar fashion. Solid
Rh(NO3)3∙nH2O (36% Rh metal basis by weight, Sigma-Aldrich) was dissolved in D-DIW. Once
dissolved, the Rh nitrate solution turned yellow. An attempt was made to prepare Rh(NO3)x (with x > 3), by adding aliquots of Rh(NO3)3 to D-DIW and concentrated HNO3 (Fisher). Rh chloride
and nitrate samples reached equilibrium when UV-Vis spectra remained unchanged between two
consecutive daily measurements.
62
UV-Vis spectra of the Rh chloride and Rh nitrate solutions were obtained at regular time
intervals (at least weekly) using a Cary 5000 UV-visible spectrophotometer (Varian/Agilent).
Solution absorbances were measured between 300 nm and 800 nm for the low-energy absorption
feature, and between 190 nm and 600 nm for the high-energy band. Rh samples were
equilibrated with Rh concentrations of ca. 10-3 M, but subsequent UV-Vis measurements
required dilutions. Low-energy UV-Vis measurements were performed with Rh concentrations at
ca. 10-3, while high-energy absorbance required Rh concentrations of ca. 10-5 M (Table 5.1). Rh
concentrations were determined by Inductively Coupled Plasma Optical Emission Spectrometry
(ICP-OES, Perkin Elmer Optima 3200 RL). The instrument was calibrated using dilutions of a
1000 ppm Rh standard solution in 10% HCl (Acros Organic).
Table 5.1. Concentrations of Rh (in M) used for each portion of the UV-Vis spectrum as a function of concentration of added HCl or HNO3.
Acid λ (190 – 600 nm) λ (300 – 800 nm) Concentration UV-Vis UV-Vis 0.0 M 9.2 (± 0.1)∙10-6 M (HCl) 9.2 (± 0.1)∙10-4 M (HCl) -5 2.69 (± 0.06)∙10 M (HNO3) 0.1 M 1.09 (± 0.03)∙10-5 M (HCl) 1.09 (± 0.03)∙10-3 M (HCl) 0.5 M 1.05 (± 0.02)∙10-5 M (HCl) 1.05 (± 0.02)∙10-3 M (HCl) 1.0 M 1.03 (± 0.06)∙10-5 M (HCl) 1.03 (± 0.06)∙10-3 M (HCl) 2.0 M 9.9 (± 0.3)∙10-6 M (HCl) 9.9 (± 0.3)∙10-4 M (HCl) -5 5.36 (± 0.05)∙10 M (HNO3) -5 4.0 M 2.73 (± 0.06)∙10 M (HNO3) 6.0 M 9 (± 1)∙10-6 M (HCl) 9 (± 1)∙10-4 M (HCl) -5 2.73 (± 0.05)∙10 M (HNO3) 8.0 M 9.4 (± 0.6)∙10-6 M (HCl) 9.4 (± 0.6)∙10-4 M (HCl) -5 5.36 (± 0.07)∙10 M (HNO3) 9.0 M 1.1 (± 0.1)∙10-5 M (HCl) 1.1 (± 0.1)∙10-3 M (HCl) -5 10.0 M 5.22 (± 0.05)∙10 M (HNO3) -5 12.0 M 2.99 (± 0.05)∙10 M (HNO3)
63
Capillary zone electrophoresis (CZE) (Agilent 7100 Capillary Electrophoresis System) was performed using the Rh solutions described in Table 5.1 to determine the minimum number of chloridated species and to estimate species charge. The observed number of species from CZE is considered the minimum number because the molar absorptivity for each of the Rh chlorides is quite small and may not be detectable at the concentrations employed. The capillary (PolyMicro
Technologies) was 60 cm long (53 cm to the detection window), with an inner diameter of 75
µm. The applied voltage was ranged from -30 and 30 kV to enable identification of both negative and positive species. The temperature of the capillary was held constant at 25 °C. Solutions were injected hydrodynamically at 5 mbar for 10 sec. UV-Vis (200 - 600 nm) was used for detection, in 2.0 nm increments. New capillaries were conditioned by flushing with 1.0 M KOH (5 min), D-
DIW (5 min), 1.0 M HCl (5 min), D-DIW (5 min), and background electrolyte (BGE) (5 min).
The preconditioning of the capillary consisted of flushing with 0.1 M KOH (5 min), D-DIW
(5 min), 1.0 M HCl (5 min), D-DIW (5 min), and BGE (5 min). After the final run, post conditioning of the capillary consisted of flushing with D-DIW for 20 min. The background electrolytes that were used contained 10 mM NaClO4, and various concentrations of HCl to
match the concentration of the HCl of the different samples (Table 5.1). The pH of the BGE was
adjusted to 3.7 with HClO4. Acetone (1 M) was also added in some cases to identify the
electroosmotic flow (EOF) band. Once the EOF was identified, the samples were run again in the
absence of acetone to identify the absorption associated with Rh-containing species. Acetone that
was added to some of the samples was detected at a wavelength of 280 nm and also with a
contactless conductivity detector (TraceDec Contactless Conductivity Detector). OpenLAB CDS
ChemStation (Agilent Technologies) was used for data analysis.
64
Computational Methods. The B3LYP combination of density functionals was employed
3+ for the optimization of hydrated Rh(III) as Rh(H2O)6 and the chloride and nitrate substituted
3-x 3-x species RhClx(H2O)y (x = 0 – 6; y = 6 – x), Rh(NO3)x(H2O)y (x = 0 – 3; y = 6 – 2x) and
14-17 Rh2Cl9 using the NWChem software package. Geometry optimizations employed an SCF
energy convergence criterion of 10-6, an integral internal screening threshold of 10-16, a numerical integration grid of 10-8, and a tolerance in Schwarz screening for the Coulomb
integrals of 10-12. The cc-pVDZ basis set was used to describe all atoms. In the case of Rh(III),
this consists of segmented contracted 4s4p3d1f functions, along with a matching pseudopotential that replaces the 28 inner-shell ([Ar]4s23d8) electrons.18,19,20 Frequency calculations were
performed on all optimized structures to obtain thermochemical corrections and ensure they
correspond to a local minima.
Single point conductor polarized continuum model (CPCM) calculations were performed
as implemented in the development version of Gaussian09.21 The solvent corrected free energies
(in water) of the replacement reactions that produce the chloride and nitrate species from the
hydrated ion are defined by:
∆ ∆ ∆ (5.1)
298 which has Ggas as the free energy of the reaction in the gas phase, Gsolv, as the solvation
contribution to the free energy of the reaction, and SScorr as the standard-state thermodynamic
22 correction (-4.3 kcal/mol for each (H2O)n water cluster).
As multiple species may exist experimentally, the goal of this work is to utilize the
computed oscillator strengths for the electronic transitions to simulate the experimental UV-Vis
spectrum in aqueous solution. A computational protocol that is easily adopted by a broader
community is desired so as to maximize the general applicability of a combined experimental
65
and computational approach to dissect the complex speciation of metal ions in solution. As such,
Time-Dependent DFT (TD-DFT) was used to compute the excited state energies and transition
oscillator strengths in solution for each optimized Rh(III) species. It is, however, quite difficult
for a single density functional to optimally describe all of the different types of excited states in a
transition metal complex simultaneously (charge transfer vs. d-d transitions, for example). Thus,
we have focused upon accurate reproduction of the charge-transfer based electronic transitions
for Rh complexes using the long range corrected PBE0 (LC-wPBE) functional, which has
exhibited much success in predicting these types of excitations.23,24 The basis sets for the TD-
DFT calculations utilized the aug-cc-pVTZ with the corresponding pseudopotential for Rh (III)
and aug-cc-pVTZ basis sets for all other atoms.18-20 Larger basis sets were used in the TD-DFT
calculations as opposed to geometry optimizations, as a more complete basis set yields better
orbital descriptions.
To compare theoretical data with experiment, oscillator strengths for the electronic
transitions calculated in Gaussian09 were converted to molar absorptivity using:
√ ṽ‐ṽ ε ṽ exp ‐ (5.2)
-10 23 where εi is the electronic excitation of interest, e = 4.803204x10 esu, N = 6.02214199x10 ,
10 -31 c = 2.997924x10 cm/s, me = 9.10938x10 g, fi is the oscillator strength, σ = 0.5 eV which is
the standard deviation in wavenumbers and is related to the width of the band, and at the
25 maximum of the band where the energy of the incident radiation, ṽ, is equal to ṽi. When there
are multiple electronic excitations in the spectral region of interest, the spectrum becomes a sum
of all of the individual bands:
ṽ ∑ ṽ (5.3)
66
The resulting theoretical spectra were then used to fit the experimental spectrum based upon the
relative concentrations of different Rh(III) species by minimizing the normalized root mean
squared deviation (NRMSD) between the combined theoretical spectrum and the experimental
one through modification of the percent contribution of each Rh(III) chloride species. A NRMSD
of 5% was chosen as a threshold for a fit to be considered reasonable, and the combinations that
yielded a NRMSD below the threshold were examined. This is directly analogous to deconvoluting the experimental spectrum into sub-species experimental spectra.9
5.3 Results and Discussion
Thermochemical and UV-Vis Identification of Rh(III) Species in Nitric Acid Media.
Prior to this work, the speciation of Rh in nitric acid had not been extensively studied, but is believed to be heavily influenced on the initial Rh complex dissolved in solution.7,13,26 X-ray diffraction studies performed by Belyaev et. al. and Caminiti et. al. suggest the presence of a Rh
- -1 13,26 (III) dimer in acidic solutions where the [NO3 ] > 1 M and Rh concentrations of 10 M. At
lower Rh(III) concentrations, like those present in SNF, a monomeric Rh (III) nitrate species was
suggested, which has been supported by UV-Vis and capillary electrophoresis data obtained in
acidic media by Aleksenko et. al.13
Here, the speciation of Rh(III) in nitric acid was first examined by calculating the
3+ thermodynamic favorability of successive nitrate additions to an initial Rh(H2O)6 cluster in
aqueous solution (Table 5.2). Initial geometries presumed a bidentate coordination geometry for
the nitrate, as observed previously with other transition metal nitrate complexes.27,28 Stable
monovalent bound nitrates were pursued but no low-energy optimized structures were found, nor
were any species that contained four or more nitrates in the primary coordination sphere. The
optimized structures exhibited an increase in the bond length rRh-O2NO and rRh-OH2 (Table S5.1 in
67
Supplementary Information), with each subsequent nitrate replacement. Beginning with the
octahedral hydrated ion, each nitrate addition is very thermodynamically favorable (ΔGrxn ≤ -
44 kcal/mol), indicating that the trinitrate complex is likely to be present in aqueous solution
(Table 5.2) and that bound nitrates are unlikely to dissociate until a stronger complexant is added to solution. The theoretical spectra of the aqueous mono-, di-, and tri-nitrate species of Rh(III) are predicted to have distinct peak positions between 184 to 202 nm in the UV-Vis spectrum.
These absorption bands are found to derive from LMCT transitions. Based upon these calculations, different nitrate species should be clearly evident within the experimental UV-Vis spectrum.
Table 5.2. Calculated solution phase free energies of the successive nitrate addition reactions to 3+ the initial Rh(H2O)6 species (in kcal/mol), along with the TDDFT calculated λmax (in nm) of the 3-x Rh(NO3)x(H2O)y (x = 0 – 3; y = 6 – 2x) products between 180 and 800 nm.
Rxn ΔGrxn λmax(product) 3+ - 2+ Rh(H2O)6 (aq)+NO3 (aq)Rh(H2O)4(NO3) (aq)+ 2H2O(aq) -44.55 184 2+ - + Rh(H2O)4(NO3) (aq)+NO3 (aq)Rh(H2O)2(NO3)2 (aq)+ 2H2O(aq) -15.73 196 + - Rh(H2O)2(NO3)2 (aq)+ NO3 (aq) Rh(NO3)3 (aq)+2H2O(aq) -13.05 202
The experimental data reinforces the thermodynamic predictions of a single species of
-3 Rh(III), Rh(NO3)3, in nitrate media. The stock solution of 10 Rh(III) nitrate reached equilibrium
after three weeks of continuous stirring, during which the solution color changed from clear to
yellow. A UV-vis spectrum was obtained in the 800 – 300 nm range to examine the low-energy
transitions, where d-d transitions are typically manifested. No distinct peaks were observed; however, evidence of a peak below 300 nm with a molar absorptivity much larger than 1000 was observed, having a peak position of 202 nm. The samples of the stock solutions with nitrate concentration between 0 and 12 M, presented in Table 5.1, were continuously stirred and reached
68
equilibrium in a week. UV-Vis spectra exhibit one absorbance band in all solutions with a
- λmax = 202 nm (molar absorptivies were within error of each other and had a value of 22,310 M
1∙cm-1, see Table S5.2 Supplementary Data). Examination of the theoretical spectrum of
Rh(NO3)3 using a 0.5 eV Gaussian bandwidth and Eq. (5.1) – (5.2) reveal a single peak deriving
from LMCT transitions also centered at 202 nm. As shown in Figure 5.1, the Rh(NO3)3
theoretical spectrum has only a 3% NRMSD with the experimental spectrum of Rh(NO3)3 dissolved in water, with the position of the band at 202 nm, the band shape, and its absorptivity, being accurately reproduced. In combination, the theoretical and experimental data indicate that the presumed Rh(NO3)3 salt that was initially dissolved in solution is maintained in the molecular
form in the aqueous phase and at varying concentration of nitric acid. Based upon calculated
thermodynamic data, it is further anticipated that in other solution phase environments where 10-
3 M Rh(III) is dissolved in nitric acid, once the Rh(NO3)3 is formed it will be the stable kinetic
and thermodynamic end product in the absence of another strong complexant. The significantly
2+ + different λmax values predicted for each of the Rh(H2O)4(NO3) , Rh(H2O)2(NO3)2 , and
Rh(NO3)3 species should help in species identification in future studies.
69
Figure 5.1. Experimental spectrum of Rh(NO3)3 dissolved in pure water (blue) overlayed with the LC-wPBE/aug-cc-pVTZ (red) predicted UV-Vis spectrum with the primary orbitals involved in the dominant transition shown.
Thermochemical and UV-Vis Identification of Rh(III) Species in Hydrochloric Acid
Media. Past studies have demonstrated that speciation of Rh(III) in hydrochloric acid is complex. Species identification has relied heavily on UV-Vis spectroscopy, focusing on the absorptions between 300 and 800 nm (presumably the d-d absorption bands).8-12,29 After separation using chromatography, a study of Wolsey et. al. determined the identifying UV-Vis peak positions and molar absorptivities in this range for all of the chloridated Rh(III) aqua species in solution conditions that spanned 0.1 M to 2 M HCl.8-12 Subsequent studies focused on the chloride exchange reactions in the first coordination sphere. These works have suggested that
3+ 2- successive chloride substitution reactions of Rh(H2O)6 to form RhCl5(H2O) are favorable in
3- solution where the concentration of HCl is greater than 0.07 M. The formation of RhCl6 is unfavorable and is only possible at temperatures above 70 °C.9 Most of these studies have been
performed at temperatures greater than or equal to 50 °C and in the presence of perchloric acid.
70
Thus the reported thermodynamic favorability of chloride substitution may be diminished under
the room temperature conditions anticipated for SNF raffinates. Importantly, the complex species
distribution of Rh(III) in HCl solution has not been pursued extensively, i.e. the relative
concentrations of different species has not been identified as a function of the concentration of
HCl. Aleksenko et. al., studied Rh(III) speciation under the two extremes of 0.1 M and 11 M HCl
using capillary electrophoresis to separate the species in solution and reported the UV-Vis
spectra of LMCT bands for identification of the individual species.7 In general, as the
concentration of HCl was increased, the number of chlorides coordinated to Rh(III) increased,
and a mixture of Rh chloride species was suggested at both chloride concentrations. Aleksenko’s
reported UV-Vis λmax = 250 nm differs from other reports that established a stepwise shift to
- shorter wavelengths of all the absorbance bands upon substitution of H2O for Cl ligands,
suggesting the presence of a complex mixture in solution. Thus, disparity exists regarding the
higher energy absorbance bands in the UV-Vis spectra of individual Rh(III) chloridated species.
In general, the speciation of Rh(III) as the concentration of hydrochloric acid is increased is not
readily understood. The results and discussion herein first describe the overall features of the
TD-DFT predicted spectra of Rh(III) chloride species as the number of chloride ligands is
increased, and experimental UV-Vis spectra as the concentration of HCl is increased. Then the
speciation of dissolved Rh(III) chloride salt is established using data from the predicted
thermodynamic properties of chloride substitution, the TD-DFT spectra along with capillary
zone electrophoresis data.
3-x The TD-DFT UV-Vis absorption spectra of RhClx(H2O)6-x (x = 0 - 6) species contain
one to two distinct absorption peaks below 300 nm for each species (Figure 5.2, Table 5.3). The
general trend is a red shift upon the substitution of each chloride. It is important to note that there
71
are distinct differences in the spectra of Rh(III) chloride species where isomers can be present.
+ - In the case of the cis- and trans- isomers of the RhCl2(H2O)4 and RhCl4(H2O)2 , individual species have λmax differing by ≥ 10 nm. This is relevant as prior separations and identification of the high energy region of the UV-Vis spectra have not distinguished contributions from different isomeric species that may be present.30 When considering the spectra obtained from Rh(III) in a wide range of chloride concentrations (Figure 5.3), unique absorption bands are observed;
however, the peak positions and shapes do not agree with the single species spectra presented in
Figure 5.2 nor the prior reported peak positions reported by Blasius or Aleksenko for isolated
Rh(III) chloride species.7,30
Figure 5.2. LC-wPBE/aug-cc-pVDZ Predicted TD-DFT UV-Vis absorption spectra of 3-x RhClx(H2O)x-6 (x = 0-6) species.
72
Table 5.3. Calculated excited state transitions and their corresponding oscillator strength.
Excited State λmax Species (i) 1 2 3 4 5 6 7 (nm) 3- RhCl6 fi 0.0394 0.1697 0.1927 0.0236 0.4564 0.4564 0.4561 218 λ (in nm) 288.54 272.62 272.24 272.21 218.05 218.05 217.98 2- RhCl5(H2O) fi 0.1160 0.1156 0.0996 0.1531 0.2652 0.1635 0.3168 212 λ (in nm) 267.55 267.38 227.23 215.93 214.65 211.77 199.76 - cis-RhCl4(H2O)2 fi 0.0283 0.0398 0.0451 0.3472 0.1291 0.0780 0.5178 202 λ (in nm) 291.53 246.95 231.69 228.50 211.35 209.15 195.57 trans- 212 - RhCl4(H2O)2 fi 0.0193 0.1225 0.1086 0.0232 0.0867 0.466 0.5835
li (in nm) 285.95 263.65 263.44 234.9 228.87 215.4 214.29
fac-RhCl3(H2O)3 fi 0.002291 0.0891 0.0891 0.0051 0.0177 0.0093 0.4591 194 λ (in nm) 263.52 230.16 230.15 219.19 214.45 204.56 192.92 mer-RhCl3(H2O)3 fi 0.0159 0.0118 0.0131 0.0197 0.5218 0.0669 0.3123 215 λ (in nm) 298.03 281.68 244.58 231.54 221.62 207.83 192.01 + cis-RhCl2(H2O)4 fi 0.0071 0.0011 0.0105 0.0198 0.0450 0.0196 0.5618 192 λ (in nm) 285.87 272.35 250.15 233.07 223.40 209.62 193.64 trans- 217 - RhCl2(H2O)4 fi 0.0019 0.0066 0.7320 λ (in nm) 268.11 251.47 223.15 2+ RhCl(H2O)5 fi 0.0045 0.0039 0.0087 0.0060 0.0004 0.4044 0.0384 190 λ (in nm) 268.48 261.53 247.66 240.04 220.12 194.90 184.50 3- Rh2Cl9 fi 0.0696 0.5966 0.1290 0.0338 0.0579 0.3050 0.7858 214 λ (in nm) 273.81 261.49 253.14 240.61 236.60 221.72 209.82
73
Figure 5.3. UV-Vis Absorptivity spectra of Rh solutions in different HCl concentration, (A) between 210 and 300 nm ([Rh] = 10-5 M) and (B) between 325 and 625 nm ([Rh] = 10-3 M). Results are averages of data obtained from triplicate samples.
The experimental spectra also exhibit the anticipated red-shift in the 300 - 800 nm absorbance peaks, consistent with an overall increase in chloride coordination with increased
HCl. Interestingly, this red shift is also observed in the higher energy (200 - 300 nm) features of the UV-Vis spectra with increasing chloride concentrations (Figure 5.3, Figure 5.4, Table 5.4), agreeing well with the overall trends predicted by TD-DFT and seen by Blasius et. al. for these high energy transitions.
74
Table 5.4. Literature UV-Vis λmax for individual Rh species and UV-Vis absorption maxima as a function of the HCl concentration of the Rh chloride salt solutions. The observed λmax values from Figure 5.3 are also presented
Species λ1 λ2 Reference λ3 λ4 Reference 29 2+ 335 426 RhCl(H2O)5 9 + 355 450 cis-RhCl2(H2O)4 201 220 30 trans- 9 + 350 450 RhCl2(H2O)4 29 cis-RhCl3(H2O)3 376 474 201 223 30 trans- 370 471 29 RhCl3(H2O)3 - 30 29 RhCl4(H2O)2 201 223 385 488 2- 30 29 RhCl5(H2O)1 201 242 402 507 3- 30 29 RhCl6 207 253 411 518 3- 3 Rh2Cl9 414 524
HCl (M) λ1 λ2 λ3 Reference 0 M 221 357 449 Present work 0.1 M 225 368 465 Present work 0.5 M 225 374 471 Present work 1.0 M 226 385 484 Present work 2.0 M 226 396 497 Present work 6.0 M 249 410 511 Present work 9.0 M 250 408 517 Present work
75
Figure 5.4. LMCT and d-d band positions (λmax) of aqueous Rh(III) solutions as a function of HCl concentration. Errors are reported as 2, from triplicate samples.
Speciation of Dissolved Rh Chloride in Pure Water. The dissolution of the Rh chloride salt in D-DIW occurred within minutes, while several months were necessary to reach a meta- stable solution equilibrium defined by unchanging UV-Vis spectra over the course of several days. This is important, as prior work has suggested that the solution composition can change for
Rh(III) in HCl over the course of years. During the dissolution and equilibrium process the solution color changed from red to yellow. The high-energy feature of the UV-Vis spectrum for the 0 M HCl solution has a maximum at 221 nm, while the lower energy portion of the spectrum contains two features with maxima at 369 nm and 463 nm, respectively (Table 5.3). Prior assignment of the low-energy absorptions of the isolated meridional isomer of aqueous
RhCl3(H2O)3 have wavelength maxima of 471 nm and 370 nm, while the facial isomer has maxima at 474 nm and 376 nm.8,29
76
Based upon these literature data, it is apparent from the experimental low-energy
absorbance bands in the current work that a mixture of species must result from dissolution of
the salt, as the peak at 463 nm cannot arise from either the facial or meridional isomers (λmax of
474 nm and 471 nm, respectively), or any mixture of these two species.3,9,29 The reported d-d
+ absorbance bands of isolated cis-RhCl2(H2O)4 are located at 358 nm and 453 nm, while that of
2+ 29 RhCl(H2O)5 occur at 335 nm and 426 nm. Thus, it is likely that some of these mono- and
dichloride species exist in solution and are responsible for the deviations in the d-d band positions. The possibility of the Rh(III) chloride salt having impurities that may result in multiple species in the aqueous solution is in part confirmed by Flame AA analysis, which indicates a Na-
-3 to-Rh mole ratio in the solution of RhCl3∙nH2O salt prepared in D-DIW of 3∙10 . Consequently,
+ it is envisioned that some of the Na in the salt is bound to chloride and the RhCl3∙nH2O salt
3-x maybe a mixture of RhClx(H2O)x-6 species deriving on the methodology for RhCl3(H2O)3 preparation.31 The capillary electrophoresis data indicates the presence of a neutral species in solution; however, this value is used as a lower bound to the potential number of species present because the CZE may omit the presence of some species due to the low molar absorptivities at the concentration employed. A linear combination of the TD-DFT spectra of the facial and
meridional aqueous RhCl3(H2O)3 yields in only a reasonable fit to the LMCT portion of the
experimental UV-Vis spectrum (Figure S5.1 in Supplementary Information), and instead an
excellent reproduction of the experimental spectrum occurs when the composition is 3% (±3) is
+ + trans-RhCl2(H2O)4 , 49% is cis-RhCl2(H2O)4 (±1), and 48% is mer-RhCl3(H2O)3 (±2) (Figure
5.5) is used. Note that the absorption intensity in the UV-Vis spectrum below 210 nm is due to
excess aqueous chloride, which has a λmax of 193 nm and has not been modeled in the TD-DFT
simulations.32 From a thermodynamic perspective, prior work and the free energies for chloride
77
substitution determined here (Table 5.5, vide infra) indicate a strong driving force for chloride
substitution. However, in pure water there is little excess chloride and thus it is believed that the
speciation in the 0 M HCl solution is unchanged relative to the original salt sample.
78
3-x Figure 5.5. Experimental spectrum of RhClx(H2O)y (x = 0 – 6; y = 6 – x) dissolved in pure water (blue) overlayed with the LC-wPBE/aug-cc-pVTZ (red) predicted UV-Vis spectrum. The optimized structures of the major species along with their key bond lengths are presented.
Speciation of Aqueous Rh(III) Under Varying Chloride Concentration. As reported in
Table 5.2, addition of chloride to the mono and trichloride species believed to be present in pure water should be exergonic until formation of the hexachloro species. As chloride is added, the
2- ΔGrxn becomes systematically less favorable, with formation of the RhCl5(H2O) species from
- RhCl4(H2O) having a free energy of only ca. -5 kcal/mol. Therefore, we expect the highly chloridated species should only form only at high chloride concentration. Under these conditions, oligomers of Rh chloride species can also be produced and thus the competitive reactions of the
3- various chloridated species to form the dimer Rh2Cl9 were also investigated. As seen in Table
5.5, the addition of chloride to RhCl3(H2O)3 is thermodynamically favored with a ΔGrxn of -13.5 kcal/mol; however, a secondary pathway that is also favored is the bimolecular reaction of
79
3- RhCl3(H2O)3 with itself to form Rh2Cl9 , having ΔGrxn of -4.5 kcal/mol. Given that we do not
3- know the activation barriers for these processes, it is possible that Rh2Cl9 could accumulate
over time and be present in solution with the various monomeric chloridated Rh species. As the
chloride solutions were equilibrated with millimolar concentrations of Rh(III), the formation of
4-6 3- polymeric species solution would be expected. . The formation of Rh2Cl9 is also predicted
3- from reaction of RhCl6 with RhCl3(H2O)3; however, this pathway is less likely in solution, as it
would require significant concentrations of both the hexa- and trichloro- species, and the DFT
results indicate that formation of the hexachloro complex is thermodynamically unfavorable.
Thus, based upon the thermodynamic analysis of the different chloride addition and bimolecular
reactions outlined in Table 5.2, DFT predicts that as chloride concentration increases, more
3- substituted chloride species, should form with the potential for dimeric RhCl9 being present after the formation of the trichloro complex RhCl3(H2O)3.
80
Table 5.5. Solution phase B3LYP/cc-pVDZ predicted ΔGrxn (kcal/mol) of chloride complexation reactions in aqueous solution.
Chemical Reaction ΔGrxn 3+ - 2+ Rh(H2O)6 + Cl RhCl(H2O)5 + H2O -32.9 2+ - + RhCl(H2O)5 + Cl cis-RhCl2(H2O)4 + H2O -4.2 2+ - + RhCl(H2O)5 + Cl trans-RhCl2(H2O)4 + H2O -2.2 + - cis-RhCl2(H2O)4 + Cl fac-RhCl3(H2O)3 + H2O -13.1 + - trans-RhCl2(H2O)4 + Cl fac-RhCl3(H2O)3 + H2O -14.0 + - cis-RhCl2(H2O)4 + Cl mer-RhCl3(H2O)3 + H2O -12.6 + - trans-RhCl2(H2O)4 + Cl mer-RhCl3(H2O)3 + H2O -13.5 - - fac-RhCl3(H2O)3 + Cl cis-RhCl4(H2O)2 + H2O -7.4 - - fac-RhCl3(H2O)3 + Cl trans-RhCl4(H2O)2 + H2O -6.2 - - mer-RhCl3(H2O)3 + Cl cis-RhCl4(H2O)2 + H2O -7.9 - - mer-RhCl3(H2O)3 + Cl trans-RhCl4(H2O)2 + H2O -6.7 - - 2- cis-RhCl4(H2O)2 + Cl RhCl5(H2O) + H2O -4.8 - - 2- trans-RhCl4(H2O)2 + Cl RhCl5(H2O) + H2O -6.0 2- - 3- RhCl5(H2O) + Cl RhCl6 + H2O 1.9 - 3- RhCl3(H2O)3 + RhCl3(H2O)3 + 3Cl Rh2Cl9 + 6H2O -4.5 - - 3- RhCl3(H2O)3 + RhCl4(H2O)2 + 2Cl Rh2Cl9 + 5H2O 0.8 - - - 3- RhCl4(H2O)2 + RhCl4(H2O)2 + Cl Rh2Cl9 + 4H2O 6.0 - 2- 3- RhCl4(H2O)2 + RhCl5(H2O) Rh2Cl9 + 3H2O 6.5 2- - 3- RhCl5(H2O) + RhCl3(H2O)3+ Cl Rh2Cl9 + 4H2O 1.2 3- 3- RhCl3(H2O)3 + RhCl6 Rh2Cl9 + 3H2O -0.7
Table 5.3 presents the d-d band positions and associated molar absorptivity (assuming
only one species in solution) determined in this work as a function of HCl concentration and as
3-x reported previously for specific aqueous RhClx(H2O)x-6 complexes that had been separated
from HCl solutions using a Dowex 5 resin.29 While there are many similarities in the two sets of
3-x data, important differences exist that indicate complex mixtures of aqueous RhClx(H2O)x-6 complexes within the solutions prepared here. Prior work indicates that the d-d band wavelengths increase with increasing chloride coordination. Similarly, our data shows increasing wavelengths of the d-d bands with an increasing HCl concentration from 0 to 2 M, while this trend stops above 6 M HCl. Increasing absorptivity of the d-d bands was previously observed for isolated Rh
- tri- through hexa-chloride (except for RhCl4(H2O)2 ); in the data presented here an increase of the
81
d-d band absorptivities occurs with increasing HCl concentration, from ca. 60 to 120 M-1cm-1,
for the lowest wavelength d-d band and from ca. 70 to 125 M-1cm-1, for the highest wavelength
d-d band. However, as in 0 M HCl solution, the d-d band wavelengths and associated
absorptivities in this work do not exactly match the values reported for the isolated RhClx complexes, indicating that the Rh solutions prepared herein include mixtures of Rh complexes that change as a function of the concentration of HCl.
Table 5.6. Calculated speciation of Rh(III) complexes in various concentrations of HCl with ranges that provide a NRMSD ≤ 5%. For HCl concentrations above 2 M a fit with a NRMSD ≤ 5% was not found. Fits with minimized NRMSD are presented in Table S5.3 in Supplementary Information.
Rh(III) Species 0 M 0.1 M 0.5 M 1.0 M 2.0 M + cis-RhCl2(H2O)4 48 - 50% 0% 0% 0% 0% trans- 0 - 6% 46 - 50% 40 - 48% 0% 0% + RhCl2(H2O)4 fac-RhCl3(H2O)3 0% 0% 32 - 34% 56 - 60% 0% mer-RhCl3(H2O)3 46 - 50% 50 - 54% 20 - 26% 34 - 36% 0% - cis-RhCl4(H2O)2 0% 0% 0% 1 - 3% 78 - 86% - RhCl5(H2O)2 0% 0% 0% 0% 0% 3- RhCl6 0% 0% 0% 0% 0% 3- Rh2Cl9 0% 0% 0% 4 - 6% 14 - 22%
3-x Using the calculated UV-Vis absorption spectra of the individual RhClx(H2O)6-x species, the experimental spectra were fitted to determine the relative concentrations of complex under different HCl concentrations. As seen in Figure 5.6, the width of the LMCT peak broadens even at an HCl concentration of 0.1 M (NRMSD’s reported in Table 5.6), indicating a change in the speciation that is described by the linear combination of TD-DFT excitations of both
+ RhCl2(H2O)4 (48% of the spectrum) and RhCl3(H2O)3 species (52%). This is also supported by
CZE data, as a neutral species is observed (Table S5.4 in Supplementary Information). Increasing
82
the concentration to 0.5 M reveals further broadening of the absorption band and a shift in the
peak position by 1 nm. The best fit to the experimental curve results from a mixture of the
+ absorption spectrum of RhCl2(H2O)4 (44%) and RhCl3(H2O)3 (56%). Data from CZE data
indicates the presence of a minimum of a single neutral species in solution in 0.5 M HCl. This is
+ in agreement with the theoretically predicted speciation as only the species RhCl2(H2O)4 and
RhCl3(H2O)3 are predicted to be present in solution. The dominant species in 1.0 M HCl solution
is predicted to be the RhCl3(H2O)3 species (contributing 98% to the observed spectrum), with a
- small amount of RhCl4(H2O)2 . Two species are observed in 1.0 M HCl solution based on the
CZE data. The CZE data also suggests that one species is neutral and the other negatively charged (Table S5.4 in Supplementary Information).
83
Figure 5.6. Experimental spectrum of RhCl3∙nH2O dissolved in (A) 0.1 M HCl, (B) 0.5 M HCl, and (C) 1.0 M HCl (blue) overlayed with the fitted LC-wPBE/aug-cc-pVTZ (red). The approximated concentration of each contributing chloridated species is shown.
84
Determination the speciation in solution using TD-DFT becomes difficult as the
concentration of chloride reaches 2 M. The NRMSD for each fit becomes unacceptably large for
each sample above 2 M HCl which suggests either a more complex solution is formed and some
unknown species may be present or that the change in the bulk solution properties (ionic strength
and dielectric constant) begin to alter the experimental spectrum. When the chloride
concentration reaches 6 M the contributions from Rh2Cl9 begin to dominate the spectrum and the
entire LMCT band shifts to a value between 250 and 260 nm. Data from CZE for the solutions
for 2 M HCl and above all indicate the presence of two species in solution. This agrees well with
predicted speciation determined through TD-DFT fitting in that only two species are seen to
dominate in solution where the concentration of HCl is ≥ 2 M. It is important to note that the
hexa-chloro complex is not seen in the range of 0 to 12 M HCl. This is also consistent with the
calculated thermodynamic data from both literature and the data presented in this work.9
5.4 Conclusions
The speciation of Rh(III) in hydrochloric and nitric acid solutions has been investigated
using experimental (UV-Vis, CZE) and theoretical (thermodynamic, simulated UV-Vis)
techniques. The evidence presented indicate that in HCl solutions, Rh(III) exists as a mixture of
3-x 3- 3- species specifically RhClx(H2O)6-x (x = 2 - 5) and Rh2Cl9 . The RhCl6 species was not
observed in this study, agreeing well with data reported in the literature showing the substitution
of the sixth chloride as non-spontaneous at room temperature.9 As the concentration of HCl
increases, increased chloride coordination is observed with Rh(III) and an apparent red shift
occurs for both the LMCT and d-d bands of the UV-Vis spectra. This trend is supported by
theoretical free energies of chloride addition and CZE data. In contrast the speciation of Rh(III)
85
in HNO3 is invariant to the concentration of HNO3. The UV-Vis spectra for Rh(III) in 0-12 M
HNO3 show a single peak with a λmax of 202 nm; in agreement with the simulated TD-DFT
spectrum of Rh(NO3)3. In combination, these data help to clarify and assess the speciation of
Rh(III) in acidic media relevant to separations and purification of this precious metal from spent
fuel raffinates. The utilization of modern computational methods in combination with
experimental techniques also points to a general protocol that can be successfully pursued to
determine speciation of precious metals in acidic media.
5.5 Supplementary Information
Table S5.1. Average bond lengths (Å) of Rh(III) nitrate species
rRh- rRh- O2NO OH2
Rh(NO3)(H2O)4 2.09 2.00
Rh(NO3)2(H2O)2 2.11 2.03
Rh(NO3)3 2.05
Table S5.2. Molar absorptivity of λmax (202 nm) for Rh(NO3)3 in various concentrations of HNO3.
[HNO3] ε 0 22310 (±108) 2 22322 (±112) 4 22315 (±104) 6 22260 (±120) 8 22290 (±86) 10 22332 (±115) 12 22340 (±121)
86
Table S5.3. Calculated speciation of Rh(III) complexes in various concentrations of HCl with error expressed as NRMSD of the UV-Vis spectra fit to experiment.
Rh(III) Species 0 M 0.1 M 0.5 M 1 M 2 M 6 M 8 M 9 M + cis-RhCl2(H2O)4 49% 0% 0% 0% 0% 0% 0% 0% trans- 3% 48% 44% 0% 0% 0% 0% 0% + RhCl2(H2O)4 fac-RhCl3(H2O)3 0% 0% 33% 58% 0% 0% 0% 0% mer-RhCl3(H2O)3 48% 52% 23% 35% 0% 0% 0% 0% - cis-RhCl4(H2O)2 0% 0% 0% 2% 82% 0% 0% 0% - RhCl5(H2O)2 0% 0% 0% 0% 0% 18% 2% 12% 3- RhCl6 0% 0% 0% 0% 0% 0% 0% 0% 3- Rh2Cl9 0% 0% 0% 5% 18% 82% 98% 88% Error 4% 3% 3% 4% 3% 11% 11% 14%
Table S5.4. Predicted speciation of Rh(III) species in various concentrations of HCl from CZE.
HCl (M) Species 1 Species 2 0.1 0 Estimation of Charge 226 Wavelength (nm) 0.5 0 Estimation of Charge 227 Wavelength (nm) 1 0 -1 Estimation of Charge 225 250 Wavelength (nm) 2 -2 -3 Estimation of Charge 248 254 Wavelength (nm) 6 -2 -3 Estimation of Charge 248 254 Wavelength (nm) 8 -3 Estimation of Charge 254 Wavelength (nm) 9 -2 -3 Estimation of Charge 248 254 Wavelength (nm)
87
n-3 Figure S5.1. Experimental spectrum of RhCln(H2O)n-6 dissolved in pure water (blue) overlayed with LC-wPBE/aug-cc-pVTZ (red) predicted UV-Vis spectrum fit using only RhCl3(H2O)3 isomers.
88
Figure S5.2. Experimental spectrum of RhCl3∙nH2O dissolved in (A) 2 M HCl, (B) 6 M HCl, (C) 8 M HCl, and (D) 9 M HCl (blue) overlayed with the fitted LC-wPBE/aug-cc-pVTZ (red).
5.6 Acknowledgements
This work was supported by a grant from the U.S. Department of Energy Nuclear Energy
University Program (NEUP) (MS-FC-11-3095). A portion of the computational studies were performed using EMSL, a national scientific user facility sponsored by the Department of
Energy’s Office of Biological and Environmental Research and located at Pacific Northwest
National Laboratory.
89
5.7 References
(1) Paiva, A. P.; Malik, P. Journal of Radioanalytical and Nuclear Chemistry 2004, 261, 485-496. (2) Philip Horwitz, E.; Diamond, H.; Martin, K. A. Solvent extraction and ion exchange 1987, 5, 447-470. (3) Levitin, G.; Schmuckler, G. Reactive and functional polymers 2003, 54, 149-154. (4) Cotton, F. A.; Seong-Joo, K.; Mandal, S. K. Inorganica chimica acta 1993, 206, 29-39. (5) Rai, D.; Sass, B. M.; Moore, D. A. Inorganic Chemistry 1987, 26, 345-349. (6) Spiro, T. G.; Allerton, S. E.; Renner, J.; Terzis, A.; Bils, R.; Saltman, P. Journal of the American Chemical Society 1966, 88, 2721-2726. (7) Aleksenko, S. S.; Gumenyuk, A. P.; Mushtakova, S. P.; Timerbaev, A. R. Fresenius' journal of analytical chemistry 2001, 370, 865-871. (8) Palmer, D. A.; Harris, G. M. Inorganic Chemistry 1975, 14, 1316-1321. (9) Pavelich, M. J.; Harris, G. M. Inorganic Chemistry 1973, 12, 423-431. (10) Robb, W.; Harris, G. M. Journal of the American Chemical Society 1965, 87, 4472-4476. (11) Swaminathan, K.; Harris, G. M. Journal of the American Chemical Society 1966, 88, 4411-4414. (12) Robb, W.; Steyn, M. M. d. V. Inorganic Chemistry 1967, 6, 616-619. (13) Caminiti, R.; Atzei, D.; Cucca, P.; Anedda, A.; Bongiovanni, G. The Journal of Physical Chemistry 1986, 90, 238-243. (14) Cramer, C. J.; Truhlar, D. G. Physical Chemistry Chemical Physics 2009, 11, 10757-10816. (15) Niu, S.; Hall, M. B. Chemical Reviews-Columbus 2000, 100, 353-406. (16) Valiev, M.; Bylaska, E. J.; Govind, N.; Kowalski, K.; Straatsma, T. P.; Van Dam, H. J. J.; Wang, D.; Nieplocha, J.; Apra, E.; Windus, T. L. Computer Physics Communications 2010, 181, 1477-1489. (17) Braun-Sand, S. B.; Wiest, O. The Journal of Physical Chemistry A 2003, 107, 285-291. (18) Peterson, K. A.; Figgen, D.; Dolg, M.; Stoll, H. Journal of Chemical Physics 2007, 126, 124101. (19) Dunning Jr, T. H. The Journal of chemical physics 1989, 90, 1007. (20) Woon, D. E.; Dunning Jr, T. H. The Journal of chemical physics 1993, 99, 3730. (21) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. Inc.: Wallingford, CT 2009, 115. (22) Asthagiri, D.; Pratt, L. R.; Kress, J. D. Physical Review E 2003, 68, 041505. (23) Vicek, A.; Zalis, S. Coordination chemistry reviews 2007, 251, 258-287. (24) Tawada, Y.; Tsuneda, T.; Yanagisawa, S.; Yanai, T.; Hirao, K. The Journal of chemical physics 2004, 120, 8425. (25) Stephens, P. J.; Harada, N. Chirality 2010, 22, 229-233. (26) Belyaev, A. V.; Fedotov, M. A.; Khranenko, S. P.; Emel'yanov, V. A. Russian Journal of Coordination Chemistry 2001, 27, 855-864. (27) Critchlow, P. B.; Robinson, S. D. Inorganic Chemistry 1978, 17, 1896-1901.
90
(28) Lever, A. B. P.; Mantovani, E.; Ramaswamy, B. S. Canadian Journal of Chemistry 1971, 49, 1957-1964. (29) Wolsey, W. C.; Reynolds, C. A.; Kleinberg, J. Inorganic Chemistry 1963, 2, 463- 468. (30) Blasius, E.; Preetz, W. Chromatographic reviews 1964, 6, 191-213. (31) Brauer, G. Handbook of preparative inorganic chemistry; Academic Press, 1963. (32) Higashi, N.; Ozaki, Y. Applied Spectroscopy 2004, 58, 910-916.
91
Chapter 6
Rh(III) Extraction by Phosphinic Acids: A Combined Experimental and Computational Protocol
Alex C. Samuels†,‡, Emily M. Victor†, Aurora E. Clark†,‡, Nathalie A. Wall†,‡,
† Department of Chemistry, Washington State University, Pullman, WA 99164, USA, ‡ Materials Science and Engineering Program, Washington State University, Pullman, WA 99164, USA
Manuscript in preparation for the Journal of Solvent Extraction and Ion Exchange
6.1 Introduction
Current spent nuclear fuel (SNF) reprocessing schemes focus on the removal of actinides and lanthanides (using solvent extraction), and the isolation of high activity waste isotopes (e.g. technetium) for disposal.1-5 In the waste streams of these techniques, platinum group metals
(PGM) are grouped with non-transuranic elements and aimed to be immobilized in waste forms
(e.g. cementitious materials).6 After removal of lanthanides and actinides, fission platinoids
could be retrieved using solvent extraction.7 In this scenario, rhodium (Rh) would exist in the trivalent oxidation in nitrate solutions; therefore, a method of extracting Rh(III) from other fission products needs to be designed.
The solvent extraction of Rh(III) in chloride media has been established in the literature – although not necessarily in conditions relevant to SNF raffinates, with an emphasis upon separating Rh(III) from other PGMs.8-14 Independent studies by Mhaske et. al. and Zou et. al. have demonstrated that Rh(III) can be separated from other PGMs in HCl using commercially available extractants and tin.12,14 Indeed Rh(III) is nearly completely extracted in these
conditions. Alam et. al. went on to explore the use of the extractant kelex 100 (7-(4-Ethyl-1-
methylocty)-8-hydroxyquinoline) with which tin was not used, however Rh(III) was only weakly
92
extracted, Rh(III) extraction never exceeding 20%.8 A recent study by Lee et. al. has shown that
Rh(III) can be extracted and separated from other fission platinoids using the neutral extractant
tri-iso-octylamine, with a maximum extraction of 36.3% in presence of 8 M chloride.11 Despite advances in the solvent extraction of Rh(III) in chloride media, few studies on the extraction of
Rh(III) from nitrate media similar to SNF raffinates are present in the literature.15 Patel and
Thornback showed Rh(III) separation from nitric acid using dinonylnapthalene sulphonic acid
and showed that Rh(III) was found to extract well with the addition of nitrite to the aqueous phase and at temperatures above 50 °C.15 Importantly, that work demonstrated that an acidic
extractant can be used to target Rh(III).
The aim of the current work is to test other commercial extractants for the ability to
extract Rh(III) in nitrate media, coinciding with conditions applicable to SNF raffinates. In
particular, diphenylphosphinic acid (DPPA) and diphenyldithiophosphinic (DPDTPA) acid were
tested. These extractants were chosen for their stability in contact with nitric acid and radiolytic
stability.15-19 Using experimental and computational techniques this work sets out to determine
extraction equilibrium constants with these organic acids.
6.2 Experimental and Computational Methods
Materials and Methods. Solid Rh(NO3)3∙nH2O (36% Rh metal basis by weight, Sigma-
Aldrich) was dissolved in deionized distilled 18 MΩ water (D-DIW) and prepared similarly to
previous work.20 Working Rh(III) solution concentrations were ca. 10-4 M. Speciation
20 determined by earlier work indicates that the primary Rh(III) species in solution is Rh(NO3)3.
Rh(III) concentrations were determined by Inductively Coupled Plasma Optical Emission
93
Spectrometry (ICP-OES) (Perkin Elmer Optima 3200 RL). The instrument was calibrated with
dilutions of a 1000 ppm Rh(III) standard solution in 10% HCl (Acros Organic).
Extractant Solutions. DPPA (99%) was purchased from Acros Organics. The DPDTPA
was obtained from Alfa Aesar. A 1.9·10-2 M stock solution of DPPA was prepared in 1-pentanol
(99%, Extra Pure, Acros Organics). The DPDTPA stock solution was prepared in toluene
(99+%, extra pure, Acros Organics) to be 1.89·10-2 M. The stock solutions were continuously
stirred for at least 24 hours before use. Extractant solutions were kept in the dark when not in
use.
Extraction Methods. Equal volumes of aqueous solutions of Rh(III) nitrate and
extractant solutions (Vaq = Vorg = 4 mL) were equilibrated in triplicate using a sample rotator
(Glas-Col). Rh(III) concentrations in the original and final aqueous solutions were measured
using Inductively Coupled Plasma Optical Emission Spectrometry (ICP-OES, Perkin Elmer
Optima 3200 RL), and was calibrated with dilutions of a 1000 ppm Rh(III) standard solution in
10% HCl (Acros Organic). Rh(III) concentration of sample organic phases were calculated by
subtraction of original and final aqueous solution concentrations. To study the extractant
concentration dependency, the sample pH was adjusted to 3.32 with diluted sodium hydroxide
solutions (certified ACS, Fisher) using a double junction Ag/AgCl reference accuTupH Rugged
Bulb pH electrode (Fisher) and an Accumet Basic AB15 pH meter (Fisher). UV-Vis
spectroscopy (Agilent Cary 5000 UV-visible spectrophotometer) measurements were performed
so as to monitor Rh(III) speciation changes that may occur with the addition at NaOH for pH < 5
(Figure S6.1 in supplementary information). Sample pH values were checked and adjusted
94
hourly until equilibration was reached. The samples were equilibrated until the pH remained
unchanged between two hourly time intervals; it was assumed that the extraction had then
reached equilibrium. The extraction samples were given an additional 16 hours on the rotator and the pH was checked again to ensure that the pH remained unchanged and that equilibrium was indeed reached. The nitrate concentration dependency was tested in a similar fashion as the extractant dependency work; the extractant concentration was fixed at 1.9·10-2 and pH was fixed
at 3.32; the nitrate concentration was varied from 1.0·10-3 M to 1 M. To study the pH dependency, HCl (Certified ACS Plus, Fisher) was used to vary the pH. It is important to ensure that Rh(III) speciation was not affected by the presence of chloride, as prior work has indicated the ability of chloride to undergo substitution with nitrates coordinated to Rh(III). UV-Vis spectroscopy was used to monitor change of Rh(III) speciation (Figure S6.2 Supplementary
Information) and a noticeable change in the UV-Vis Rh(III) solution spectrum was found
12 hours after addition of HCl indicating a change in Rh(III) speciation. Furthermore, it was determined that a contact time of 8 hours was sufficient to reach extraction equilibrium with both
extractants when the pH was not fixed. The hydrogen ion concentrations were varied from
3.0x10-4 M to 1.0 M in the pH dependent extractions while extractant and nitrate concentration
were held constant at 1.9·10-2 and 1.0·10-3, respectively.
Back extractions were performed to test the reversibility of each extraction system. 1 M
- HNO3 or 1 M NO3 were added to samples that had already undergone extraction; the samples
were then allowed to rotate for an additional 24 hours before the extraction was tested in these
new conditions.
95
Computational Methods. The B3LYP combination of density functionals was employed
for the geometry optimization of the Rh(III) complex, Rh(NO3)3, and the extractant species
Rh(NO3)x(DPPA)3-x and Rh(NO3)x(DPDTPA)3-x (x = 0 - 3) using the NWChem software
package.21-24 The cc-pVDZ basis set was used to describe Rh(III) and the aug-cc-pVDZ basis set
was used to describe all other atoms. In the case of Rh(III), this consists of segmented contracted
4s4p3d1f functions, along with a matching pseudopotential that replaces the 28 inner-shell
([Ar]4s23d8) electrons.25,26,27 Frequency calculations were performed on all optimized structures
to obtain thermochemical corrections and ensure they correspond to a local minima.
Single point integral equation formalism polarized continuum model (IEF-PCM)
calculations were performed as implemented in the development version of Gaussian09.28 The
solvent corrected free energies of the of extraction is defined by:
∆ ∆ ∆∆ (6.1)
which has Ggas as the free energy of the optimized structures of the species present in Eq. (6.1)
in the gas phase, Gsolv, as the solvation correction. Using the generalized equation
⇄ (6.2)
where a phosphinic acid extractant binds to the metal and is transported into the organic phase,
the Gext was calculated using the thermodynamic cycle presented in Figure 6.1. For these
calculations the solvent with corresponding dielectric need to be specified in the calculation. For
DPPA, 1-pentanol with a dielectric of 15.13 was used for the organic phase and toluene with a
dielectric of 2.37 was used for DPDTPA. In both cases water with a dielectric of 78.36 was
utilized. Additional extraction schemes were considered, such that
⇄ (6.3)
96
where a number up to two waters bind to Rh(III), either causing the nitrates or extractant to bind
mondentate. An optimized geometry could not be found for the hydrated extracted product. For
this study only reactions that fit Eq. (6.2) were reported.
Figure 6.1. Thermodynamic cycle for the extraction of Rh(III) by an acidic extractant.
6.3 Results and Discussion
Slope Analysis. It is hypothesized that Rh(III) extraction occurs through exchange of the acidic extractant proton and the nitrate originally bound to Rh(III), as shown Eq. (6.2) where HL is the protonated phosphinic acid and L is the deprotonated phosphinic acid. Assuming each
- phosphinic acid displaces a NO3 to bind to Rh(III), Eq. (6.2) can then be rewritten as the equilibrium equation:
(6.3) where D is the distribution coefficient, calculated as the Rh(III) concentration in the organic phase divided by the Rh(III) concentration in the aqueous phase. Taking the logarithm of Eq.
(6.3) yields
log (6.4)
97
- Plots of logD as a function of log[HL], log[NO3 ], or pH should provide a straight line with slope
of x.
Solvent Extraction. The pH of the extraction samples with varied DPPA remained stable after 7 hours of equilibration and remained unchanged after an additional 16 hours. The distribution ratio increased linearly with increasing extractant concentration, supporting the hypothesized reaction shown with Eq. (6.2). The plot of logD as a function of log[DPPA], shown in Figure 6.2 (A), is a straight line with a slope of 0.96 (± 0.07), which suggests that one DPPA binds to the reactant Rh(NO3)3 for extraction.
Samples prepared to study the DPDTPA concentration dependency showed that the pH
stabilized after 7 hours of equilibration and did not change after 16 hours of additional contact
time. A larger Rh distribution was observed for extractions performed with DPDTPA than with
DPPA; for example, 1.9∙10-2 M DPDTPA yields an Rh(III) distribution ratio of 5.19 (± 0.07)
while the same concentration of DPPA only yields a distribution ratio of 4.25 (±0.05). The plot
of logD as a function of log[DPDTA] (Figure 6.2 (B)) is linear with a slope of 0.98 (±0.05)
suggesting that Rh(III) extraction by DPDTPA involves the complexation of one DPDTPA to
one Rh(III), as was the case for DPPA.
98
Figure 6.2. Influence of extractant concentration on the extraction of Rh(III). Aqueous phase: -4 -3 + 5.3x10 M Rh, 1.5·10 M NO3 , pH = 3.32; Organic phase: (A) DPPA in 1-pentanol. (B) DPDTPA in toluene.
- The Rh(III) extraction as a function of NO3 concentration was tested to determine the number of nitrates coordinated to each extracted Rh(III) complex. Rh(III) extraction decreases
- with an increasing [NO3 ], as shown with Figure 6.3 (A). A Rh(III) distribution ratio of 1.70 is
- -3 observed in presence of a NO3 concentration of 1.0·10 M, but negligible Rh(III) extraction is
- - measured in presence of 1 M NO3 . The plot of logD as a function of log[NO3 ] results in a straight line with a slope of -1.04 (± 0.06), suggesting the loss of a single nitrate during the complexation and subsequent extraction of Rh(III) by DPPA.
- Figure 6.3 (B) shows a decreased Rh(III) extraction by DPDTPA with increasing NO3
- concentration. The Rh(III) distribution ratio drops to from 2.143 to 0 as NO3 concentration
-3 - increases from 2.5·10 M to 1.0 M The plot of logD as a function of log[NO3 ] also yields a straight line with a slope of -1.03 (± 0.07), which suggests the loss of a single nitrate during
Rh(III) extraction by DPDTPA.
99
- - Figure 6.3. Influence of NO3 concentration on the extraction of Rh(III). Aqueous phase: 5.3·10 4 - -2 -2 M Rh in NO3 , pH = 3.32; Organic phase: (A) 1.9·10 M DPPA in 1-pentanol (B) 1.9·10 M DPDTPA in toluene.
It is expected and observed (Figure 6.3 (A)) that Rh(III) extraction by DPPA decreases with an increasing HCl concentration, as the pH drops below the pKa of DPPA (2.32) causing a predominance of the protonated form of DPPA, which is less susceptible to undergo complexation with Rh(III).29 The distribution ratio drops from 1.24 (± 0.05) to less than 0.01 (±
0.02) if the HCl concentration increases from 1∙10-4 M to 1∙10-2 M HCl. A reliable pH could not be determined for extraction solutions as the pH < 2, as it is not measureable with a standard pH electrode. The plot of logD as a function of log[HCl] is a straight line with a slope of -0.95
(± 0.06), which indicates that a single proton is exchanged during Rh(III) extraction by DPPA.
The pKa of DPDTPA, 2.70, is similar to that of DPPA.30 Therefore, DPDTPA should behave in a similar fashion as DPPA in the acid dependency study. Rh(III) extraction with
DPDTPA should diminish with decreasing pH due to the formation of protonated extraction species that cannot extract Rh(III).30 Figure 6.4 (B) shows that an increasing H+ concentration leads to a decreased extraction. The plot of logD as a function of log[HCl] is a straight line with
100
a slope of -1.03 (± 0.06), suggesting a single proton exchange during Rh(III) extraction by
DPDTPA.
Figure 6.4. Influence of HCl concentration on the extraction of Rh(III). Aqueous phase: 5.3·10-4 -3 -2 -2 M Rh in HCl, NO3 = 1.5·10 M; Organic phase: (A) 1.9·10 M DPPA in 1-pentanol (B) 1.9·10 M DPDTPA in toluene.
- + These data show that 1 M of either NO3 or H concentration lead to negligible Rh(III) extraction. Rh(III) extraction samples containing low concentration of NaNO3 or HNO3 were equilibrated as Rh(III) extraction experiments described above, to test the back-extractions; results showed that 99% (±1%) Rh(III) was stripped from the organic phases back into the aqueous phases upon addition of 1 M of either NaNO3 or HNO3. The ability to back-extract
- + Rh(III) with NO3 or H helps to validate the applicability and reversibility of the Eq. (6.2).
The slope analysis results suggest that for both extraction systems, Eq. (6.2) can be rewritten as:
⇄ (6.5) and the extraction equilibrium expression then becomes:
101
(6.6)
-5 Using Eq. (6.6), Kex=4 (± 1)∙10 for both DPPA and DPDTPA, and the free energy of extraction,
ΔGex, at 298 K is calculated to be 25 (± 7) and 25 (±3) kj/mol for DPPA and DPDTPA,
respectively. This is unexpected as the Hard and Soft Lewis Acids and Bases (HSAB) principal
would predict that DPDTPA would bind preferentially to Rh(III) because of the favorable
interactions between the “soft” Rh(III) and sulfur coordinating atoms of DPDTPA than between
Rh(III) and oxygen coordinating atoms of DPPA.31 Thus, the binding energies would be
expected to be quite different due to the different donor groups present within the extractant,
however, this is not observed experimentally, when considering the overall free energy of the
extraction. The ΔGext is a combination of several components, including the extractant binding, the transport between phases, and the stability of the product in a given phase. Differences in the binding energies may exist, however these differences may be minimal compared to the energy associated in transport across the interface and/or the stability of the extracted products in the organic phase. Additionally, positive values of ΔGext indicate a non-spontaneous reaction at room temperature and suggest a Le Châtelier type equilibrium is occurring wherein extraction is driven by the presence of excess ligand. Extractant concentrations must be two order greater than
the concentration of Rh(III) to reach an 80% recovery from solution when Rh(III) is at
millimolar concentrations.
Computational Thermodynamics. A protocol for the calculation of ΔGex using
quantum mechanical calculations was performed similar to previous studies.32,33 Theoretical
calculations performed by Dolg and coworkers using DFT and continuum models have
previously reproduced the experimental free energy trends of the separation Am(III)/Cm(III)
from Eu(III) with Cyanex 301.33 There, the gas phase extraction free energies of Cyanex 301
102
with Am(III), Cm(III), and Eu(III) were positive (ca. 100 kJ/mol). Interestingly solvation
corrections employed both theoretical and semi-empirical data. The theoretical hydration
energies of the metal ions came from large cluster calculations, while semi-empirical metal ion
free energy values derived from fitting theoretical data to X-ray spectroscopy information
(XAFS, XANES). When the theoretical hydration energies were used the free energies extraction
were negative, suggesting the reaction is spontaneous at room temperature. When the semi-
emperical values for the hydration of the metal ions was used, the free energy of extraction of
Eu(III) and Am(III) were determined to be 12.3 kJ/mol and -1.5 kJ/mol, respectively. This differs
significantly from the experimental values of 63.3 kJ/mol for Eu(III) and 44.1 kJ/mol for
Am(III). The work of Dolg and coworkers was unable to reproduce experimentally measured
extraction thermodynamic values; however, the trends in the energies were reproduced
accurately with the use of both theoretical and empirically derived metal ion hydration free
energies. That work clearly demonstrates that the way the metal ion hydration is calculated can
make a significant difference in the free energies of extraction. Batista and Keith expanded upon
the work of Dolg et. al. by applying the same thermodynamic cycle to a extraction new system.32
Their calculations found the extraction of Am(III) and Eu(III) by dithiophosphinic acids to be favorable (-5 to -10 kcal/mol). Batista and Keith reported similar behavior depending on the metal ion hydration energy used, and the use semi-empirical values was required to reproduce experimental values. The work herein explores the development of a reliable and robust protocol for theoretically determining the free energy of extraction.
To model extraction of Rh(III) by DPPA and DPDTPA, the three following reactions were considered:
⇄ (6.7)
103
O ⇄ (6.8)
⇄ (6.9)
- within Eq. (6.7) the deprotonated phosphinic binds to Rh(III), displacing a NO3 and the resulting
metal – extractant complex resides in the organic phase. Another approach is to consider the
protonated extractant losing a proton to a water in solution, as seen in Eq. (6.8). A third reaction
may encompass the thermodynamic cycle that Batista and Keith used, shown in Figure 6.1 and
Eq. (6.9), where the semi-empirical value of 1104 kj/mol is used for the solvated proton.32,34
When the free energy of extraction is calculated using Eq. (6.7) – (6.9) (Table 6.1) from the optimized extracted complexes shown in Figure 6.5, a range from 91.67 - 244.40 kJ/mol and
49.75 - 14 3.45 kJ/mol using DPPA and DPDTPA extractants respectively. The predicted bond lengths do not indicate a difference in bond strength as the ionic radii of sulfur is ca. 0.3 Å larger than oxygen.35 Interestingly, an energetic difference is observed between DPPA and DPDTPA in
all cases. The energetic difference is in agreement of with the differences predicted using the
HSAB principal. However, what observed experimentally is not accurately reproduced
computationally indicating the methods applied in this study may not be adequate, and explicit
solvation may be required to reproduce experimental values. In Batista and Keith’s investigation,
the binding energy may have dominated, allowing for the approximation of solvent interactions
with a continuum model. Additionally, the IEF-PCM model may not be able to accurately
produce solvation free energies in the organic phase.36 Using only a continuum model for
calculating solvent interactions may not be appropriate in this situation, as significant solvent
interactions occurring in experimental solutions are dominating the observed free energy of
extraction.
104
Table 6.1. Calculated free energy of extraction using proposed equations in compared to experimentally determined free energy.
Eq. DPPA (ΔG kJ/mol) DPDTPA (ΔG kJ/mol) 7 92.0 50.0 8 244 143 9 161 61 Experiment 25 (±10) 25 (±4)
Figure 6.5. B3LYP/cc-pVDZ/aug-cc-pVDZ Optimized gas phase structures of the (A) Rh(NO3)2DPPA and (B) Rh(NO3)2DPDTPA extracted complexes with extractant-metal bond distance shown.
105
6.4 Conclusions
The extraction of Rh(III) from nitric acid solutions has been investigated using
experimental and theoretical techniques. Experimental data indicates that extraction of Rh(III)
using DPPA and DPDTPA is non-spontaneous at room temperature. The experimentally
determined Kex were equal for both extractants within error. Theoretical thermodynamic data
presented suggests a marked difference in the ΔGex for each phosphinic acid. The computational finding would agree with the principal of HSAB, however, HSAB only describes the binding of
Rh(III) and each extract and does not consider intermolecular interactions solution. The
discrepancy in experimental and theoretical findings questions the appropriateness of using only
a single solvation shell combined with a PCM to model for calculating extraction
thermodynamic information. A better approach may include the use of explicitly modeling
beyond the first coordination sphere of the metal by including additional solvent molecules.
106
6.5 Continuing Work and Future Directions
This initial work of examining the thermodynamics associated with the extraction of
Rh(III) by phosphinic acids demonstrates the need to develop a reliable and robust computational protocol. The experimentally determined free energy of extraction contains all of the processes occurring in solution, such as the energies associated with extractant binding, transport across the aqueous/organic interface, and intermolecular interactions occurring in each phase. The energy associated with the extractant binding is difficult to model computationally as the mechanism must be known. Therefore, an attempt to explore develop a protocol that can reproduce experimental distribution equilibrium of a ligand will be made, such that the ability of the method to correctly intermolecular interactions can be determined. The intermolecular interactions will be studied first as intermolecular interactions will be a component of understanding transport. This will allow for the theoretical error associated with the modeling of these interactions to be assessed.
Work currently being performed examines the distribution of acetyl acetone (acac) between water and several organic solvents. To establish an appropriate protocol the various
DFT functionals, continuum models, and basis sets were compared. The B3LYP, PBE1W, and
X3LYP functionals were used. The PBE1W and X3LYP functionals were chosen, as they were parameterized for hydrogen bonding.37,38 This is important, as acac contains an internal hydrogen bond. The continuum models considered include the integral equation formalism polarizable continuum model (IEF-PCM), solvent model based on electron density (SMD), and conductor- like screening model (COSMO). Additionally double zeta and triple zeta basis sets were compared.
107
The distribution of acac between water and hexane has been determined experimentally
39 with a distribution equilibrium constant (KD) of -0.02. This suggest that acac should be equally distributed between hexane and water. The distribution of acac can be calculated computationally using the reaction
→ (10) where
∆ ∆ ∆
Table E6.1 presents the results of the computational calculations for acac distribution between water and hexane. The results of these calculations do not agree well with the experimentally determined value.
Table E6.1. Calculated ΔGD (kcal/mol) for acac distribution between water and hexane. DZ and TZ refer to the aug-cc-pVDZ and aug-cc-pVTZ basis sets, respectively.
B3LYP PBE1w X3LYP
DZ TZ DZ TZ DZ TZ
COSMO 3.52 3.44 3.79 3.72
IEF-PCM 2.58 2.54 2.42 2.38 2.60 2.55
Pauling 5.24 5.08 4.75 4.62 5.27 5.11
SMD -1.15 -1.27 -1.69 -1.78 -1.13 -1.25
UA0 2.28 2.23 2.18 2.13 2.29 2.24
UAKS 5.80 5.69 5.23 5.14 5.83 5.72
108
The disagreement of the calculated and experimental value arise may arise from the absence of explicitly solvent intermolecular interactions that are missed when using only a continuum model. In an attempt to remove the error associated with intermolecular interactions, molecular dynamics (MD) was used to generate the extended solvation environment of acac in water and hexane. The MD equilibrated geometries that are generated are then used in single point quantum mechanical calculations with the previously mentioned functionals and continuum models. This work is ongoing, and should provide a key insight into understanding the potential errors associated with modeling the partitioning of a complex between two immiscible solutions.
109
6.6 Supplementary Information
Figure S6.1. Absorption at 400 nm for Rh(NO3)3 stock solution adjusted to various pH using NaOH. The absorption at 400 nm was chosen as the change is absorption was most prevalent at this wavelength as NaOH concentration was increased.
110
Figure S6.2. Absorption at 400 nm for Rh(NO3)3 stock solution adjusted to 1 M HCl over 24 hour time period. The absorption at 400 nm was chosen as the change is absorption was most prevalent at this wavelength as HCl concentration was increased.
6.7 References
(1) Philip Horwitz, E.; Diamond, H.; Martin, K. A. Solvent extraction and ion exchange 1987, 5, 447-470. (2) Mathur, J. N.; Murali, M. S.; Nash, K. L. Solvent extraction and ion exchange 2001, 19, 357-390. (3) Nash, K. L.; Jensen, M. P. Separation Science and Technology 2001, 36, 1257-1282. (4) Nilsson, M.; Nash, K. L. Solvent extraction and ion exchange 2007, 25, 665-701. (5) Weaver, B.; Kappelmann, F. A. TALSPEAK: A new method of separating americium and curium from the lanthanides by extraction from an aqueous solution of an aminopolyacetic acid complex with a monoacidic organophosphate or phosphonate, Oak Ridge National Lab., Tenn., 1964. (6) Chamberlain, D. B.; Leonard, R. A.; Hoh, J. C.; Gay, E. C.; Kalina, D. G.; Vandegrift, G. F. TRUEX hot demonstration, Argonne National Lab, 1990. (7) Kolarik, Z.; Renard, E. V. Platinum metals review 2003, 47, 74-87. (8) Shafiqul Alam, M.; Inoue, K. Hydrometallurgy 1997, 46, 373-382. (9) Levitin, G.; Schmuckler, G. Reactive and functional polymers 2003, 54, 149-154. (10) Charlesworth, P. Platinum Met Rev 1981, 25, 106.
111
(11) Lee, J.-Y.; Rajesh Kumar, J.; Kim, J.-S.; Park, H.-K.; Yoon, H.-S. Journal of hazardous materials 2009, 168, 424-429. (12) Zou, L.; Chen, J.; Pan, X. Hydrometallurgy 1998, 50, 193-203. (13) Tertipis, G. G.; Beamish, F. E. Analytical Chemistry 1962, 34, 623-625. (14) Mhaske, A. A.; Dhadke, P. M. Hydrometallurgy 2001, 61, 143-150. (15) Freiderich, M. E.; Peterman, D. R.; Klaehn, J. R.; Marc, P. L. J.; Delmau, L. H. Industrial & Engineering Chemistry Research 2014. (16) Alimarin, I. P.; Rodionova, T. y. V.; Ivanov, V. M. Russian Chemical Reviews 1989, 58, 863-878. (17) Modolo, G.; Wilden, A.; Geist, A.; Magnusson, D.; Malmbeck, R. Radiochimica Acta 2012, 100, 715. (18) Xu, Q.; Wu, J.; Chang, Y.; Zhang, L.; Yang, Y. Radiochimica Acta International journal for chemical aspects of nuclear science and technology 2008, 96, 771-779. (19) Li, K.-a.; Freiser, H. Solvent extraction and ion exchange 1986, 4, 739-755. (20) Samuels, A. C.; Boele, C.; Benette, K.; Wall, N. A.; Clark, A. E. Inorganic Chemistry 2014, Submitted 06/18/2014. (21) Cramer, C. J.; Truhlar, D. G. Physical Chemistry Chemical Physics 2009, 11, 10757- 10816. (22) Niu, S.; Hall, M. B. Chemical Reviews-Columbus 2000, 100, 353-406. (23) Valiev, M.; Bylaska, E. J.; Govind, N.; Kowalski, K.; Straatsma, T. P.; Van Dam, H. J. J.; Wang, D.; Nieplocha, J.; Apra, E.; Windus, T. L. Computer Physics Communications 2010, 181, 1477- 1489. (24) Braun-Sand, S. B.; Wiest, O. The Journal of Physical Chemistry A 2003, 107, 285-291. (25) Peterson, K. A.; Figgen, D.; Dolg, M.; Stoll, H. Journal of Chemical Physics 2007, 126, 124101. (26) Dunning Jr, T. H. The Journal of chemical physics 1989, 90, 1007. (27) Woon, D. E.; Dunning Jr, T. H. The Journal of chemical physics 1993, 99, 3730. (28) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. Inc.: Wallingford, CT 2009, 115. (29) Buckingham, J. Dictionary of Organic Compounds; 5th ed.; Chapman Hall, 1982. (30) Modolo, G.; Odoj, R. Journal of Alloys and Compounds 1998, 271-273, 248-251. (31) Pearson, R. G. Journal of the American Chemical Society 1963, 85, 3533-3539. (32) Keith, J. M.; Batista, E. R. Inorganic Chemistry 2011, 51, 13-15. (33) Cao, X.; Heidelberg, D.; Ciupka, J.; Dolg, M. Inorganic Chemistry 2010, 49, 10307- 10315. (34) Tissandier, M. D.; Cowen, K. A.; Feng, W. Y.; Gundlach, E.; Cohen, M. H.; Earhart, A. D.; Coe, J. V.; Tuttle, T. R. The Journal of Physical Chemistry A 1998, 102, 7787-7794. (35) Shannon, R. D. t. Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography 1976, 32, 751-767. (36) Klamt, A.; Mennucci, B.; Tomasi, J.; Barone, V.; Curutchet, C.; Orozco, M.; Luque, F. J. Accounts of Chemical Research 2009, 42, 489-492. (37) Xu, X.; Goddard, W. A. Proceedings of the National Academy of Sciences of the United States of America 2004, 101, 2673-2677. (38) Dahlke, E. E.; Truhlar, D. G. The Journal of Physical Chemistry B 2005, 109, 15677- 15683. (39) Stary, J.; Liljenzin, J. O. Pure and applied chemistry 1982, 54, 2557-2592.
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Chapter 7
Conclusions
Using quantum mechanical calculations, the hydration free energies and inner sphere coordination numbers of U, Np, and U in the trivalent to hexavalent oxidation states have been determined. For the trivalent actinides 8-coordinate species are observed, while the tetravalent actinides, U and Np exhibit an equilibrium between 8- and 9-coordinate species, and with Pu the
9-coordinates species predominates. This study found that using a second explicit solvation shell allowed for close reproduction of experimental hydration free energies. The use of water addition thermodynamics combined with X-ray spectroscopic data was essential to determining coordination number of the studied actinides.
To design a successful solvent extraction method for the separation of Rh(III) from spent nuclear fuel (SNF) raffinates, the speciation of the metal ion in acidic media. The speciation of this metal in solution can be determined by fitting theoretical UV-Vis spectra obtained using time dependent density functional theory to experimentally measured solution spectra. It was found that Rh(III) exists as a mixture of species in HCl solutions, while in HNO3 solutions only the Rh(NO3)3 species is observed.
In SNF raffinates, Rh(III) would be expected to be found as a nitrate species. Using phosphinic acids, Rh(III) is extracted from nitrate solutions. The chosen phosphinic acids poorly extracted Rh(III). A computational protocol to model the extraction is currently in development, so that new extractants can be investigated theoretically before experimental use.
This dissertation demonstrates the utility of applying theoretical and experimental techniques for understanding key components of SNF raffiniates. Using computational methods,
113 accurate aqueous phase geometric and thermodynamic information can be obtained.
Additionally, experimental XANES, EXAFS, and UV-Vis spectra can be reproduced at the quantum mechanical level. Experimentally, a method for extracting Rh(III) using phosphinic acids has been explored while a method to reproduce experimentally determined solvent extraction thermodynamics needs to be further pursues.
114
Appendix A
Applications of Polarizable Continuum Models to Determine Predictive Solution Phase Thermochemical Properties Across A Broad Range of Cation Charge – The Case of U(III-VI)
Payal Parmar*, Alex Samuels, Aurora E. Clark*
Department of Chemistry and the Materials Science and Engineering Program, Washington State University, Pullman, WA 99164
Submitted to the Journal of Computational and Theoretical Chemistry
This work provides a more detailed approach to understanding the solution phase thermochemistry of actinides in solution; focusing on U (III-VI)
A.1 Introduction
Polarizable continuum models (PCMs) have become an increasingly useful tool for predicting the electronic structures of ground and excited states, as well as the geometries of molecules in solution.1-4 Their application for predicting accurate solution phase
thermochemistry has been thoroughly examined for organic and small molecules, wherein a
general utility has been demonstrated.5 Several studies have utilized PCMs to closely reproduce
the experimental solvation free energies of neutral and ionic organic species.6-10 In the case of
cations, the comparably stronger solute-solvent interactions often leads to use of a molecular
cluster model wherein explicit solvent molecules are added to mimic the ions immediate
solvation environment. The hydrated cluster is then embedded within the continuous dielectric.
This approach represents the intersection of the continuum approach and discrete solvation
models, yet it is bolstered by the general acceptance11 that such hydrated cations exist in solution
as meta-stable and dynamically evolving species (meaning that a specific solvation configuration
has a measurable lifetime in solution and can be considered a distinct molecular species). Within
embedded molecular cluster models, gas-phase optimizations are often performed, followed by
115
further refinement of the geometry of the molecular cluster using the PCM.12,13 It has been
observed that the PCM optimized geometries are quite sensitive to the continuum solvation
model. Further the solvation contribution to the free energies of many ions, particularly metal
cations, has been demonstrated to be highly sensitive to the size of the molecular cluster and the
continuum model and or cavity.14,15
For many ions, the solution phase thermochemistry is particularly important, as they may
exhibit complex speciation that in turn influences reactivity. Nowhere is this more evident than
in the actinide (An) cations, which not only exhibit solvation coordination environments that are
highly sensitive to solution phase conditions, but also complex equilibria between oxidation
states, with the possibility that several oxidation states co-exist in solution. In this scenario, large
changes in the electrostatic interaction between the ion and water necessitate a molecular cluster
model with an appropriate number of explicit waters to be paired with a PCM that can
adequately describe multiple oxidation states. While prior work has demonstrated that solution
phase cation thermochemistry can depend upon the number of explicit water molecules and the
continuum model,14,16 no systematic investigation has examined the physical premise of this
behavior or its sensitivity to ion charge. This is particularly relevant as most PCM’s have been
parameterized for the solvent effects in the absence of explicit solvent molecules and using ions
of low charge.1,17-26
Toward this end a series of hydrated uranium ion clusters has been examined, where the
metal oxidation state is varied from III to VI, leading to molecular cluster charges that span +4 to
+1. The free energy of solvation, ΔGsolv, has been determined using a representative computational approach that encompasses the reactions
3+/4+ 3+/4+ U + (H2O)n U(H2O)n (A.1)
116
1+/2+ +/2+ UO2 + (H2O)n UO2(H2O)n (A.2)
that represent the hydration reactions of the bare ions. Gas phase calculations determine the free
energy for this process, ΔGhyd, followed by single point PCM calculations that determine the
solvation correction (Gcorr) to the (H2O)n and hydrated metal cluster so as to determine ΔGsolv for
ion. Note that the bare ion is left in the gas-phase as this is consistent with the experimental
calorimetry approximations associated with the heat released from dissolving the ion containing
27 salt. A “standard state” correction, SScorr, may also be applied, however it is quite small
relative to the other two terms.28 The total solution-phase free energy of solvation is then:
Δ Δ Δ (A.3)
The errors associated with this approach are a composite deriving from ΔGhyd as well as
ΔGcorr. Errors in the gas-phase energetics may derive from either the method or the basis set, or
other approximations including those associated with relativistic effects. The cluster model
employed to define the explicit solvation environment about the ion also influences both the gas-
and solution-phase calculations. For clusters of infinite size (the bulk limit) ΔGhyd is equivalent
to ΔGsolv and the solvation correction ΔGcorr for the solvation reaction should go to zero.
However different convergence properties may be observed for the gas-phase energetics and
solvation corrections which may contribute to the aforementioned deviations in ΔGsolv as a function of system size and continuum model.
The underlying premise of the current work is to first establish that the typical gas-phase computational protocols for determining thermochemistry of An ions represents a sound basis for subsequent solution-phase corrections determined by the PCM approach, then to investigate the performance of different models and cavities as a function of cation charge and the number of explicit water molecules utilized in the molecular cluster. This is of paramount importance
117
because the solvation correction can be nearly 50% of the total free energy of solvation. Very
different convergence properties are observed for the gas-phase hydration energies and the
solvation corrections, often leading to an imbalance in cancellation that leads to large errors in the resulting free energies of solvation. Favorable cancellation of errors is consistently observed across all systems when using the UFF cavity within the IEF model is used for chemical reactions wherein the chemical model consists of a molecular cluster with two explicit solvation shells.
A.2 Computational Methodology
Significant prior work has established that ΔGhyd of f-element ions is relatively
insensitive to the density functionals within those that form the so-called rungs on the Jacob’s
14,16,29-35 ladder of density functionals. The range of ΔGhyd for Ln(III) with varying density
functional is generally ~ 5 kcal/mol using a double zeta basis set on H2O and a small-core
relativistically corrected effective core potential (SC-RECP) on the metal. However, ΔGhyd can be quite sensitive to the basis set, particularly that of the metal, with large variations observed depending on whether a small- or large-core RECP is used, the latter resulting in significant underestimations of the reaction energy.14 A double-zeta quality basis set for the O- and H-atoms
of water has been observed to result in consistent quality ΔGhyd for actinide and lanthanide (Ln)
ions.14,36 While SC-RECPs are generally considered to be of sufficient quality for determining
ΔGhyd, recent developments in the valence basis sets for uranium contain g-functions, which play important role in the correlation of 5f-electrons. It is unclear what practical impact this may have
upon gas- or solution-phase thermochemistry. Explicit consideration of relativistic affects is
generally not needed for most computational applications involving local minima on the
118
potential energy surface of An bearing species, however the role of spin-orbit coupling upon the energetics of hydrated species may gain importance because explicitly solvating water molecules donate their electron density to the ion center, potentially increasing the f-orbital occupation.
32,35,37 Taking these issues into account, the gas-phase free energies of hydration (ΔGhyd) were first calculated for the reactions:
3+/4+ 3+/4+ U + (H2O)8,9 U(H2O)8,9 (rA.1)
3+/4+ 3+/4 U + (H2O)30 U(H2O)8,9(H2O)22,21 (rA.2)
1+/2+ +/2+ UO2 (H2O)4,5 UO2(H2O)4,5 (rA.3)
1+/2+ 1+/2+ UO2 + (H2O)30 UO2(H2O)4,5(H2O)26,25 (rA.4)
The geometry of each molecular species was optimized using the unrestricted form of
B3LYP38,39 (UB3LYP) using the NWChem40 software program. Two sets of SC-RECPs41,42 were
employed along with their associated basis sets for valence electrons (vide infra). The aug-cc-
pVDZ basis set was employed for the H- and O-atoms of clusters that contained a single
43 solvation shell (4 – 9 H2O), while for those clusters containing 30 H2O, the 6-311G** basis was used. Geometries of the 1st solvation shell clusters (in rA.1 and rA.3) were optimized
employing the contracted as well as uncontracted versions of both basis sets, while the 2nd solvation shell clusters (in rA.2 and rA.4) were optimized using the contracted basis with subsequent single point calculations being performed using the uncontracted basis to save computational time. Thermodynamic corrections were obtained from normal mode analysis, which in addition verified all structures to be actual minima with real frequencies. The contributions of spin-orbit coupling to the reaction energetics were determined from single point spin-orbit DFT (SO-DFT) calculations using the small core RECP42 of Dolg, which includes the spin-orbit potential functions (SO-ECP). Counter-poise corrections were not included to correct
119
for basis set superposition error, as prior studies have shown that the magnitude of the correction
is minimal compared to water binding energies to Ln(III).44 The thermodynamics of the water addition reactions (ΔGadd) to the first solvation shell were then explored using the same methods
and basis sets:
3+/4+ 3+/4+ U(H2O)8 + H2O U(H2O)9 (rA.5)
3+/4+ 3+/4+ U(H2O)8(H2O)22 U(H2O)9(H2O)21 (rA.6)
1+/2+ 1+/2+ UO2(H2O)4 + H2O UO2(H2O)5 (rA.7)
1+/2+ 1+/2+ UO2(H2O)4(H2O)26 UO2(H2O)5(H2O)25 (rA.8)
Single point polarizable continuum model (PCM) calculations were performed on all
species except the bare ions within reactions rA.1 – rA.8. The UFF, UA0, UAKS and Pauling (α
= 1.1) cavities were studied using the integral-equation-formalism-protocol (IEF) implemented
in Gaussian03,45 wherein the cavity is created using a series of overlapping spheres, initially
devised by Tomasi and coworkers and Pascual-Ahuir and coworkers.5,46,47 The IEF model using
the radii and non-electrostatic terms of Truhlar and coworker’s SMD solvation model in
Gaussian09 (denoted as SMD), was also examined.48 There are two primary difference between the Gaussian03 and Gaussian09 cavities: 1) the former uses point charges while the latter uses gaussian charges so that discontinuities in the cavity are avoided (when two point charges on different spheres get to close to each other), and 2) Gaussian03 uses added spheres to fill regions of space that are not accessible to the solvent (for instance, when two spheres on different centers
may get close to each other without yet touching) while in Gaussian09 these added spheres are
not used because they complicate the equations with the gaussian charges. For the sake of
brevity, the different cavities within IEF will simply denoted as: UFF, UA0, UAKS, and Pauling.
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The convergence of the hydration energetics in the gas-phase and in solution was
examined via single point calculations for the reactions:
3+/4+ 3+/4+ U + (H2O)n U(H2O)8(H2O)n-8 (rA.9)
1+/2+ 1+/2+ UO2 + (H2O)n UO2(H2O)5(H2O)n-5 (rA.10)
where n = 41 and 77. The configurations for these very large clusters were obtained by first
3+/4+ +/2+ immersing a rigid U(H2O)8 and UO2(H2O)5 molecular species inside a box of 2039
classical TIP3P49 water molecules, then allowing for 1 ns of equilibration in NPT and NVT
ensembles, followed by a 1 ns production run in NVE using the DL_POLY450,51 software
program. The equilibrated density was 0.998 g/cm3. A 1 fs timestep was used with an ewald
cutoff of 9 Å and a threshold of 10-8. The larger water clusters were carved out of 5
representative snapshots of the simulation box by removing a sphere of water within 6.5 and 8.0
3+/4+ 1+/2+ Å from the U metal center and 6.7 and 8.3 Å from the UO2 solute. Five spherical
(H2O)41,77 clusters were removed from a similarly equilibrated pure TIP3P water simulation.
Each cluster was then subjected to a single point calculation in the gas-phase and with each of
the aforementioned dielectric continuum models and cavities using UB3LYP/RSC60/6-311G**
(average values reported).
A.3 Results and Discussion
Gas Phase Energetics: Basis Sets and Relativistic Effects Using UB3LYP. This
section focuses upon the gas-phase ΔGhyd of U(III-VI) as a function of computational approach
so as to establish the quality of the gas-phase thermochemistry prior to solvation corrections. The
sensitivity of thermodynamic values to the Gaussian basis sets and relativistic effective core
potentials employed and the importance of spin-orbit effects have been examined. Representative
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optimized geometries of the first and nominal 2nd solvation shell structures are presented in
Figure A.1. For the sake of computational expedience the same number of total waters was
st maintained for all clusters that encompass more than the 1 solvation shell. The ΔGhyd, and
ΔGadd, reactions rA.1 – rA.8 were first considered.
The small-core, energy-optimized RECP for uranium published in 1994 by the Stuttgart
group41 considers the core to be comprised of 60 electrons (i.e. the 1s-4s, 2p-4p, 3d-4d and the 4f
shells), and has been shown to yield comparatively accurate results for geometries and
energies.34,52-54 In order to better describe the correlation of the valence electrons in uranium, g-
functions in the basis sets are expected to be important, particularly when the 5f orbitals actively
participate in bonding. In 2009, Dolg and Cao42 reported a new SC-RECP that improved upon
the original 1994 Stuttgart one41 for uranium by accounting for relativistic behavior more
accurately by constructing it using the (two-component) multiconfigurational Dirac-Hartree-
Fock (MCDHF) approach as opposed to the Wood-Boring quasi-relativistic approach in the 1994
Stuttgart RECPs. The associated valence basis functions have additionally two s-, two p- and six
g-functions. Therefore one is required to use the 2009 RECP along with its segmented basis sets
for valence electrons for the calculation of more accurate description of the properties, like spin-
orbit contributions, in the uranium systems. For the sake of clarity, the older Stuttgart SC-RECP
basis set is referred to a RSC(1994), while the latter is referred to as RSC(2009). Table A.1
compares the ΔGhyd as a function of uranium oxidation state using both the contracted and
uncontracted forms of RSC(1994) and RSC(2009).
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3+/4+ Figure A.1. Representative geometries for: (a) U(H2O)8 , a square antiprism (SAP); (b) 3+/4+ U(H2O)9 , a tricapped trigonal bipyrimid (TTBP); (c) the solvation shell structure of 3+/4+ 1+/2+ 1+/2+ st nd U(H2O)9(H2O)21 ; (d) UO2(H2O)4 ; (e) UO2(H2O)5 ; (f) the 1 and 2 solvation shell 1+/2+ structure UO2(H2O)4(H2O)26 .
Table A.1. Gas-phase ΔGhyd values (in kcal/mol) for actinide hydration (reactions rA.1 and rA.3), where RSC(1994)-C and RSC(1994)-U refer to the contracted and uncontracted forms of the RSC(1994) basis set, and so forth.
3+ 3+ U + (H2O)n U(H2O)n RSC(1994)-C RSC(1994)-U RSC(2009)-C RSC(2009)-U n = 8 -397.3 -396.4 -395.5 -394.8 n = 9 -407.1 -406.0 -405.1 -404.7 4+ 4+ U + (H2O)n U(H2O)n RSC(1994)-C RSC(1994)-U RSC(2009)-C RSC(2009)-U n = 8 -737.5 -736.1 -732.1 -730.9 n = 9 -760.1 -758.5 -754.9 -753.7 + + UO2 + (H2O)n UO2(H2O)n RSC(1994)-C RSC(1994)-U RSC(2009)-C RSC(2009)-U n = 4 -80.7 -80.4 -79.5 -76.8 n = 5 -84.4 -84.1 -82.4 -81.8 2+ 2+ UO2 + (H2O)n UO2(H2O)n RSC(1994)-C RSC(1994)-U RSC(2009)-C RSC(2009)-U n = 4 -177.2 -179.0 -178.5 -178.7 n = 5 -192.4 -196.3 -194.1 -193.1
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When using the contracted basis sets the ΔGhyd for reactions (rA.1) and (rA.3) is altered on an average by 2.6 kcal/mol when switching from RSC(1994) to RSC(2009). Addition of g-
functions typically cause an increase in the hydration energy of the tri- and tetravalent, as well as
1+ 2+ the UO2 ions (becoming less negative), while the ΔGhyd of the closed shell UO2 ion slightly
shifted to the more negative. No trend is observed regarding the impact of the g-functions upon
ΔGhyd as a function of the f-orbital occupation of the ion (Figure SA1 is given in the
Supplementary Information). Uncontracting the RSC(1994) basis set generally increases ΔGhyd by about 1.0 kcal/mol on an average, while uncontracting RSC(2009) alters ΔGhyd by
~1.1 kcal/mol. This is similar to what was observed in prior study31 of the hydration reactions of
the Ln(III) which indicated that the difference in the total electronic energies with the SCF-
optimized DFT for La3+ and Lu3+ cations with small core contracted and uncontracted basis is
significantly small provided that there is no major change in the DFT density while
uncontracting the basis. The affect of the additional g-functions was also examined for hydration
reactions that encompass energies for the second solvation shell, reaction (rA.2 and rA.4),
presented in Table SA1 in Supplementary Information, however the same behavior is observed.
Thus the RSC(2009) RECP and basis does not present a significant improvement to the
energetics of these ions relative to the oft-used RSC(1994) basis sets.
The influence of basis set may be more important to ΔGadd (reactions rA.5 and rA.7)
because the magnitude of these energies is much smaller than ΔGhyd and subtle effects can have a
large impact upon the thermodynamically favored coordination environment. As observed in
st Table A.2 for the 1 solvation shell clusters, the ΔGadd values are within 1.0 kcal/mol of each
other using either RSC(1994) or RSC(2009). Uncontraction of either basis set also has negligible
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impact upon the calculated energetics, similar behavior is observed for the reactions of the 2nd shell hydrated clusters (rA.6 and rA.9).
Table A.2. Gas-phase ΔGadd values (in kcal/mol) for reactions rA.5 and rA.7, where RSC(1994)- C and RSC(1994)-U refer to the contracted and uncontracted forms of the RSC(1994) basis set, and so forth.
x+ x+ U(H2O)8 + H2O U(H2O)9 RSC(1994)-C RSC(1994)-U RSC(2009)-C RSC(2009)-U x = 4+ -23.6 -23.5 -23.7 -23.8 x = 3+ -10.8 -10.6 -10.6 -10.9 m+ m+ UO2(H2O)4 + H2O UO2(H2O)5 RSC(1994)-C RSC(1994)-U RSC(2009)-C RSC(2009)-U x = 2+ -14.3 -15.6 -14.7 -13.3 x = 1+ -2.7 -2.5 -2.1 -3.9
The use of the uncontracted basis sets provides the opportunity to investigate the impact of
spin-orbit (SO) coupling using the SO DFT formalism. The magnitude of SO coupling for the
hydration reactions of all ions varies from 0.4 - 2.1 kcal/mol, indicating that the spin-orbit effects
essentially cancel for the reactants and the products The magnitude of the SO contribution to the
hydration energies does not correlate well with the formal f-electron occupation (or oxidation
states) for each ion but it does correlate with the charge transfer and the effective f-electron
4+ 2+ occupation of the gas-phase cation vs. the hydrated complexes for U and UO2 . The SO increases as the Lowdin charges decrease on ions (see Figure SA2 in Supplementary
3+ 1+ Information). However for U and UO2 , the change in the SO is almost neglible (0.4 - 1.0
kcal/mol) between the bare and hydrated ions. In the water addition reactions the difference in f-
electron occupation of the metal is negligible between the reactants and products of the water
addition reactions, and thus the SO contribution is essentially zero.
Solution Phase Energetics: Performance of Polarizable Continuum Models Relative to Cluster Size. In its simplest form, the solution-phase correction to the gas-phase free energy
of a species, Gcorr, derives from three terms: 1) a free energy term associated with creation of a
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cavity around the solute, 2) a free energy contribution that results from dispersion-repulsion interactions between the cavity boundary and the dielectric continuum, and, 3) an electrostatic free energy contribution between the cavity and the continuum:
(A.1)
Both the IEF and SMD models employed in this work account for all three terms, however by
default the dispersion-repulsion term may not be included and thus care must be taken to ensure
consistency when comparing Gcorr between different models and cavities. When considering the
solution phase correction for a chemical reaction, the total correction can be written as:
∆ (A.2)
Prior work has demonstrated that the solution phase corrections obtained from
polarizable continuum models for the hydration properties of lanthanides are not significantly
influenced by the specific density functional used, nor the basis set.14 It is thus not surprising that
neither uncontraction of the basis, nor the addition of g-functions has a significant impact upon
the solution-phase energetics for either the hydration reactions or the water addition reactions
considered above (see Tables SA2 and SA3 in Supplementary Information). As such, within the
remainder of this work the UB3LYP functional will be used in conjunction with the typically
used RSC(1994) basis set, wherein comparisons are made between continuum models and
cavities.
When considering the ability to calculate accurate free energies of solvation for ions, the
error in ΔGsolv will be a composite of errors deriving from the gas-phase energetics as well as the solvation correction. Assuming that the intrinsic error in the gas-phase is minimized (as discussed above), the remaining error in the gas-phase hydration energy lies in the limited number of explicit waters of solvation. For clusters of infinite size (the bulk limit), the ΔGhyd is
equivalent to ΔGsolv and ΔGcorr should go to zero as the Gcav, Gdisp-rep, and Gelec of the reactants
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and products should cancel (Eq. (A.1) – (A.2)). The Gelec term in particular should approach zero
for all species as the bulk limit is approached, however this is not necessarily the case and thus
cancellation is desired. It is possible that the gas-phase ΔGhyd and the solvation correction for the
reaction, Gcorr, converge to the bulk limit at different rates with increasing explicit waters in the
cluster (Eqn. A.1). It is then of interest to thoroughly examine the performance of the various
dielectric continuum models and cavities as a function of the charge of the cluster and the
convergence properties with increasing number of solvating waters. The latter in particularly
important as our and other groups have reported vastly different calculated ΔGsolv values for
metal ions depending upon the number of explicit waters in the cluster and the cavity
employed.16,55
The convergence of the gas-phase hydration energy (ΔEhyd) has been examined for
4+ U(IV), as described by reactions rA.1, rA.2 and rA.9, which consists of addition of U to (H2O)n clusters containing 8, 30, 41, and 77 water molecules. It is computationally impractical to perform complete geometry optimizations of the 41 and 77-H2O clusters, thus single point
calculations were performed and the convergence of ΔEhyd was monitored. Similarly, the
convergence of Gcorr was examined for each PCM employed, and then the sum of ΔEhyd and
Gcorr was plotted to approximate how the relative cancellation of errors in the two terms would
impact a calculated ΔGsolv value (where ΔGsolv ≈ ΔEhyd + Gcorr).
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Figure A.2. Calculated reaction energies (in kcal/mol) for reactions rA.1, rA.2 and rA.9 for U4+ in the gas-phase and in aqueous solution, determined using different dielectric continuum models.
As seen in Figure A.2, the gas-phase ΔEhyd for the reaction converges nicely to the
4+ experimental value for ΔGsolv for U since the explicit number of water molecules (n) about the ion is approaching the bulk. The slight bump in the convergence when transitioning from the n =
30 to n = 41 system is attributed to the fact that the n = 30 is the single configuration optimized with UB3LYP, while the energy of the n = 41 system represents the average of 5 single point energies of configurations obtained from MD. At a cluster size consisting of 77 water molecules
ΔEhyd is within the experimental error for ΔGsolv. As the size of the explicit water cluster is increased, the solvation corrections to the reaction energy should approach zero, however it is apparent that in general the PCM convergence is significantly slower than that of ΔEhyd.
Note that the non-electrostatic contributions (Gcav and Gdisp-rep) to the Gcorr is essentially zero for the 41- and 77-water clusters, and thus it is the electrostatic contribution to Gcorr that does not approach zero fast enough for accurate ΔGsolv to be calculated even at a cluster size (77- waters) that includes what one could construe as a 4th solvation shell. While all cavities and models exhibit a large positive slope when going from the n = 8 to n = 30, the rate of
128 convergence for UAKS and UA0 cavities dramatically drops off such that slopes of ~2 are observed when transitioning from n = 41 to n = 77 molecular clusters. If this convergence rate is assumed to be constant as cluster size in increased then the UAKS and UA0 cavities would not converge to a Gcorr value of zero until a cluster with at least 210 explicit waters was utilized (in reality the rate of convergence will decrease as n increases). In contrast, the UFF cavity within the IEF model and the SMD model maintain a faster rate of convergence until the n = 41 cluster size is reached. As such, the approximate size of hydrated metal ion cluster needed to reach the bulk solvation limit is only ~100-120 explicit waters.
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Figure A.3. Electrostatic contribution, Gelec, (in kcal/mol) to the free energy of solvation 4+ correction for (H2O)n reactant and U(H2O)n product clusters in the solvation reactions rA.1, rA.8, and rA.9 for (A) the SMD continuum model, (B) the UFF cavity within IEF, and (C) the UAKS cavity within the IEF model.
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prod Figure A.4. The electrostatic contribution, ΔGelec, in kcal/mol to ΔGsolv, defined as: Gelec - react Gelec .
The difference in these convergence patterns can be further dissected by examination of
the electrostatic contribution, Gelec, which is the dominant term in the solvation correction for the
4+ (H2O)n reactants and the U(H2O)n products (Eqns. A.2 – A.3). This quantity has been plotted in
Figure A.3 for the SMD model and the UFF and UAKS cavities within the IEF model. It should be first noted that in general the electrostatic contribution to the (H2O)n reactant clusters becomes more negative as cluster size is increased, while the contribution to the products becomes less negative. This behavior is consistent with an increase in the amount of cancellation of Gelec of the products minus reactants and thus a general convergence of Gcorr toward zero. However, both the rate of change of Gelec and the values of Gelec specifically for the reactants and products differ in Figure A.3. The Gelec of the metal ion using UAKS becomes less negative at a steady and nearly linear rate with a slope of +4, while at the same time the Gelec of the water cluster slowly becomes more negative with a slope of -2. There is thus an imbalance in the rates of change in the product and reactant electrostatic contributions to Gcorr which leads to a slow convergence
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of that quantity toward zero. Similar behavior is observed for UA0. The UFF cavity and SMD
model exhibit less linear and more exponential behavior in Gelec. The ability of Gcorr to approach zero in the bulk limit for SMD and UFF derives primarily from a steep increase in Gelec as the product cluster is increased from n = 8 to n = 30, while the reactant cluster Gelec becomes much more negative when n > 30. Thus Gcorr approaches zero via the cancellation of much larger negative quantities than in UAKS.
Figure A.5. Convergences of the solution phase correction to the free energy, ΔGcorr, for trivalent, hexavalent, and pentavalent uranium as a function of the size of the molecular hydrated cluster employed.
The behavior of the Gelec term for the reactant (H2O)n clusters is particularly important when considering less highly charged metal ions. As observed in Figure A.4, the Gelec of the
132 product cluster can become less negative than Gelec of the water reactant cluster, leading to an
prod react unphysical positive ΔGelec contribution to ΔGsolv (where ΔGelec = Gelec - Gelec ). As the total charge of the solute decreases, it becomes more likely for ΔGelec to become positive. In turn,
ΔGcorr may also become positive, and importantly, it begins to diverge for the UAKS and UA0 cavities versus the SMD and UFF when using cluster models with more than two solvation shells
(Figure A.5). Based upon the combined data presented in Figures A.2 – A.5, explicit water cluster models that utilize waters beyond a second solvation shell of the solute are not recommended for determining predictive thermochemistry for metal ions across a range of oxidation states.
Given the constraint of smaller explicit water cluster models, it is worthwhile to discuss the means by which cancellation of errors can fortuitiously and possibly consistently lead to a
ΔGsolv value in good agreement with experiment (Eqn. A.1). When a single solvation shell is present, the significantly underestimated gas-phase energy for the reaction must be compensated for by a large solvation correction. The latter is dominated by a negative ΔGelec that is highly sensitive to the cavity volume and surface area. The error in the calculated ΔGsolv for
4+/3+ expt 56 U(H2O)8 relative to experiment (ΔGsolv = -1432.6 ± 10 kcal/mol ) is plotted as a function of these parameters in Figure A.5. First considering cavity volume, it is apparent that too small of a cavity volume leads to overestimated (too negative) ΔGsolv values, but that the error in the solvation free energy trends approximately linearly with increasing volume. Interestingly, the errors when compared to cavity surface area do not trend linearly and too large a surface area can lead to either significant over- or underestimations of ΔGsolv. Importantly, those methods that produce the smallest cavity surface area do generally have the smallest errors with respect to experiment, including the traditional Pauling, UAKS and UA0 methods. The UFF cavity has a
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large volume with large surface area, leading to underestimation of ΔGsolv for both tri- and tetravalent uranium, while the SMD model results in small cavity volumes but larger surface areas, causing an overestimated ΔGsolv. The net result of the sensitivity to cavity volume and surface area is an ~140 kcal/mol range in the predicted ΔGsolv values for tri- and tetravalent uranium as seen in Table A.3.
Figure A.6. Comparison of the error in the calculated free energy of solvation (ΔΔGsolv = theory expt 4+/3+ ΔGsolv – ΔGsolv ) in kcal/mol for the U(H2O)8,9 ions as a function of (A) cavity volume, and (B) cavity surface area.
When a second solvation shell is added, the gas-phase reaction energy drops significantly toward the infinite bulk limit. At the same time the presence of a 2nd shell of solvating waters decreases the electrostatic interactions on the cavity surface and thus the sensitivity of the
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calculated ΔGsolv upon the cavity and model employed. As such, the standard deviation in the
nd theoretical ΔGsolv for all methods drops in half when a 2 solvation shell is added (Table A.3).
4+ 4+ The slopes of Gcorr between the U(H2O)8 and U(H2O)8(H2O)22 data points in Figure A.2 are
between 3.0 – 4.0, which is nearly half that of ΔEhyd (slope of 7.6). Thus those cavities which
4+ nd started off in U(H2O)8 with a smaller calculated Gcorr are benefitted in the 2 solvation shell cluster by less over-cancellation of the error in ΔEhyd. As such, the UFF cavity yields ΔGsolv values that are in very good agreement with experimental data for uranium across all oxidation states when a 2nd solvation shell is present. Based upon the information obtained from the
convergence properties of the different contributions to Gcorr it is apparent that good performance for this cavity derives from a consistent cancellation of the errors contained in the electrostatic contribution to Gcorr and ΔEhyd. Based upon these data we suggest further
exploration of the UFF cavity as one that can consistently yield accurate solution phase
energetics of metal ions of varying oxidation state.
135
Table A.3. UB3LYP calculated ΔGsolv values (in kcal/mol) for U(III-VI)
4+ 3+ 2+ + U + (H2O)n+m U + (H2O)n+m UO2 + (H2O)n+m UO2 + (H2O)n+m 4+ 3+ 2+ + U(H2O)n(H2O)m U(H2O)n(H2O)m UO2(H2O)n(H2O)m UO2(H2O)n(H2O)m n,m = 8,0 n,m = 9,0 n,m = 8,0 n,m = 9,0 n,m = 4,0 n,m = 5,0 n,m = 4,0 n,m = 5,0 UAKS -1450.0 -1426.4 -765.0 -772.7 -363.4 -373.1 -269.4 -270.6 UA0 -1427.7 -1441.3 -776.8 -783.7 -370.1 -380.5 -273.9 -276.6 Pauling -1411.4 -1419.0 -757.6 -759.5 -369.7 -370.7 -271.0 -267.5 SMD -1474.6 -1470.5 -804.1 -801.4 -400.5 -400.0 -293.9 -289.1 UFF -1379.4 -1381.6 -743.4 -742.4 -357.5 -360.8 -265.1 -262.2 n,m = 8, n,m =9, n,m = 8, n,m = 9, n,m = 4, n,m = 5, 25 n,m = 4, n,m = 5, 22 21 22 21 26 26 25 UAKS -1459.6 -1468.7 -782.9 -787.8 -390.2 -397.9 -258.9 -264.0 UA0 -1468.8 -1477.2 -790.7 -794.5 -392.0 -402.7 -260.8 -268.7 Pauling -1459.2 -1464.0 -780.2 -783.8 -397.6 -401.3 - -288.7 SMD -1477.6 -1479.6 -794.6 -789.7 -417.5 -412.1 -283.2 -278.0 UFF -1437.9 -1436.7 -766.9 -761.6 -387.4 -389.7 -259.7 -260.8 Expt57,27,58 -1432.6 ±10 -773.9 ±10 -39715
A.4 Conclusions
The work herein demonstrates that PCMs can be an effective approach for determining
consistently accurate free energies of solvation for metal cations across multiple oxidation states.
However this conclusion derives from a deeper understanding of the contributions to the
solvation correction for both reactants and products in the hydration reaction of a bare ion. In
particular, the cancellation of errors in the gas-phase and solvation corrections must be
appreciated as the fundamental factor necessary for obtaining an accurate ΔGsolv. Different cavities (UAKS, UFF, UA0, Pauling) and models (IEF and SMD) exhibit very different convergence properties as a function of the number of explicit solvating molecules in the
molecular cluster and this is believed to be the primary source behind previous discrepencies in
ΔGsolv as a function of PCM cavity and model. Thus extreme care must be taken when choosing
a molecular cluster size, cavity and model within the computational protocol for determining the
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solution phase thermochemistry. The UFF cavity is demonstrated to result in consistent and
fortuitous cancellation of errors when determining the ΔGsolv for U(III-VI) using molecular clusters that consist of a second solvation shell.
A.5 Supplementary Information
Figure SA1. Change in ΔGhyd upon adding g-functions in the basis as a function of the f-orbital occupation of the ion using Lowdin population analysis
f‐orb occ (Lowdin) RSC(2009) 4.10
4.00
3.90
3.80
3.70 f‐orb occ (Lowdin) RSC(2009) 3.60
3.50
3.40
3.30 ‐4.00 ‐2.00 0.00 2.00 4.00 6.00
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Table SA1. Gas-phase UB3LYP calculated ΔErxn values (in kcal/mol) for actinide hydration for the second solvation shell, where RSC(1994)-C and RSC(1994)-U refer to the contracted and uncontracted forms of the RSC(1994) basis set, and so forth.
3+ 3+ U + (H2O)n+m U(H2O)n(H2O)m RSC(1994)-C RSC(1994)-U RSC(2009)-C RSC(2009)-U n,m = 8, 22 -557.7 -557.9 -555.9 -556.7 n,m = 9, 21 -559.5 -559.4 -557.5 -558.7 4+ 4+ U + (H2O)n+m U(H2O)n(H2O)m RSC(1994)-C RSC(1994)-U RSC(2009)-C RSC(2009)-U n,m = 8, 22 -1054.6 -1053.9 -1048.5 -1049.2 n,m = 9, 21 -1049.2 -1048.1 -1043.4 -1043.8 + + UO2 + (H2O)n+m UO2(H2O)n(H2O)m RSC(1994)-C RSC(1994)-U RSC(2009)-C RSC(2009)-U n,m = 4, 26 -106.9 -111.4 -108.4 -113.8 n,m = 5, 25 -120.1 -125.5 -122.1 -128.7 2+ 2+ UO2 + (H2O)n+m UO2(H2O)n(H2O)m RSC(1994)-C RSC(1994)-U RSC(2009)-C RSC(2009)-U n,m = 4, 26 -279.7 -283.3 -281.0 -285.6 n,m = 5, 25 -293.2 -297.9 -295.2 -300.8
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Figure SA2. Spin-orbit coupling contributions (in kcal/mol) vs the Lowdin charges of the bare ions and the metal ion on hydrated complexes
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Table SA2. UB3LYP calculated ΔGsol values (in kcal/mol) for actinide hydration using IEF- PCM.
3+ 3+ U + (H2O)n U(H2O)n RSC(2009)- RSC(1994)-C RSC(1994)-U RSC(2009)-C U n = 8 -742.9 -742.4 -738.4 -740.2 n = 9 -74218 -740.8 -739.4 -739.4 4+ 4+ U + (H2O)n U(H2O)n RSC(2009)- RSC(1994)-C RSC(1994)-U RSC(2009)-C U n = 8 -1378.3 -1376.3 -1373.1 -1371.0 n = 9 -1378.7 -1376.3 -1372.9 -1371.6 + + UO2 + (H2O)n UO2(H2O)n RSC(2009)- RSC(1994)-C RSC(1994)-U RSC(2009)-C U n = 4 -134.7 -133.5 -133.5 -132.0 n = 5 -132.3 -132.4 -130.9 -130.4 2+ 2+ UO2 + (H2O)n UO2(H2O)n RSC(2009)- RSC(1994)-C RSC(1994)-U RSC(2009)-C U n = 4 -357.3 -358.9 -358.9 -359.1 n = 5 -359.7 -363.1 -361.5 -360.3
Table SA3. UB3LYP calculated ΔGsol values (in kcal/mol) for water addition reactions for actinide ions using IEF-PCM.
m+ m+ U(H2O)8 + H2O U(H2O)9 RSC(2009)- RSC(1994)-C RSC(1994)-U RSC(2009)-C U m = 3+ 5.4 6.3 3.7 5.6 m = 4+ 4.3 4.8 4.9 4.2 m+ m+ UO2(H2O)4 + H2O UO2(H2O)5 RSC(2009)- RSC(1994)-C RSC(1994)-U RSC(2009)-C U m = 1+ 5.8 4.9 6.1 5.3 m = 2+ 1.0 0.1 0.9 2.4
A.6 Acknowledgment
This research was performed using the Molecular Science Computing Facility (MSCF) at the William R. Wiley Environmental Molecular Sciences Laboratory, a national scientific user
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facility sponsored by the (U.S.) Department of Energy’s (DOE) Office of Biological and
Environmental Research located at the Pacific Northwest National Laboratory, operated for the
Department of Energy by Battelle. Research in the authors’ laboratories is funded by the
Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences
of the U.S. Department of Energy, through Grant (DE-SC0001815).
A.7 References
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(20) Still, W. C.; Tempczyk, A.; Hawley, R. C.; Hendrickson, T. Journal of the American Chemical Society 1990, 112, 6127-6129. (21) Curutchet, C.; Orozco, M.; Luque, F. J. Journal of Computational Chemistry 2001, 22, 1180-1193. (22) Giesen, D. J.; Hawkins, G. D.; Liotard, D. A.; Cramer, C. J.; Truhlar, D. G. Theoretical Chemistry Accounts 1997, 98, 85-109. (23) Li, J. B.; Zhu, T. H.; Hawkins, G. D.; Winget, P.; Liotard, D. A.; Cramer, C. J.; Truhlar, D. G. Theoretical Chemistry Accounts 1999, 103, 9-63. (24) Luque, F. J.; Bachs, M.; Aleman, C.; Orozco, M. Journal of Computational Chemistry 1996, 17, 806-820. (25) Luque, F. J.; Zhang, Y.; Aleman, C.; Bachs, M.; Gao, J.; Orozco, M. Journal of Physical Chemistry 1996, 100, 4269-4276. (26) Sitkoff, D.; BenTal, N.; Honig, B. Journal of Physical Chemistry 1996, 100, 2744-2752. (27) Rizkalla, E. N.; Choppin, G. R.; Schneider, J. K. A., eyring, L., Choppi, G. R., Lander, G. H., Eds.; North-Holland: New York, 1994; Vol. 18, p 529. (28) Asthagiri, D.; Pratt, L. R.; Ashbaugh, H. S. Journal of Chemical Physics 2003, 119, 2702-2708. (29) Mattsson, A. E. Science 2002, 298, 759-760. (30) Perdew, J. P.; Schmidt, K. in: V.E. Van Doren, C. Van Alsenoy, P. Geerlings (Eds.), Density Functional Theory and its Application to Materials, AIP, Melville, New York 2001. (31) Clark, A. E. Journal of Chemical Theory and Computation 2008, 4, 708-718. (32) Schreckenbach, G.; Shamov, G. A. Accounts of Chemical Research 2010, 43, 19- 29. (33) Shamov, G. A.; Schreckenbach, G. The Journal of Physical Chemistry A 2005, 109, 10961-10974. (34) Batista, E. R.; Martin, R. L.; Hay, P. J.; Peralta, J. E.; Scuseria, G. E. Journal of Chemical Physics 2004, 121, 2144-2150. (35) Schreckenbach, G.; Hay, P. J.; Martin, R. L. Journal of computational chemistry 1999, 20, 70-90. (36) Kuta, J.; Clark, A. E. Inorganic Chemistry 2010, 49, 7808-7817. (37) Pyykko, P.; Li, J.; Runeberg, N. Journal of Physical Chemistry 1994, 98, 4809- 4813. (38) Becke, A. D. Journal of Chemical Physics 1993, 98, 5648-5652. (39) Lee, C. T.; Yang, W. T.; Parr, R. G. Physical Review B 1988, 37, 785-789. (40) Bylaska, E. J. e. a.; 5.1 ed. NWChem, A Computational Chemistry Package for Parallel Computers, Pacific Northwest National Laboratory, Richland, Wa 99352, 2007. (41) Kuchle, W.; Dolg, M.; Stoll, H.; Preuss, H. Journal of Chemical Physics 1994, 100, 7535-7542. (42) Dolg, M.; Cao, X. Y. Journal of Physical Chemistry A 2009, 113, 12573-12581. (43) T.H., D. J. Journal of Chemical Physics 1989, 90. (44) Kvamme, B.; Wander, M. C. F.; Clark, A. E. International Journal of Quantum Chemistry 2009, 109, 2474-2481. (45) M. J. Frisch, e. a.; C.02 ed.; Gaussian Inc.: Wallingford, CT, 2004.
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(46) Pascualahuir, J. L.; Silla, E.; Tunon, I. Journal of Computational Chemistry 1994, 15, 1127-1138. (47) Tomasi, J.; Mennucci, B.; Cances, E. Journal of Molecular Structure-Theochem 1999, 464, 211-226. (48) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. J. Phys. Chem. B 2009, 113, 6378. (49) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926. (50) Smith, W.; Todorov, I. T. (51) Todorov, I. T.; Smith, W.; Trachenko, K.; Dove, M. T. J. Mat. Chem. 2006, 16, 1911. (52) Vallet, V.; Schimmelpfennig, B.; Maron, L.; Teichteil, C.; Leininger, T.; Gropen, O.; Grenthe, I.; Wahlgren, U. Chemical Physics 1999, 244, 185-193. (53) Garcia-Hernandez, M.; Lauterbach, C.; Kruger, S.; Matveev, A.; Rosch, N. Journal of Computational Chemistry 2002, 23, 834-846. (54) Straka, M.; Kaupp, M. Chemical Physics 2005, 311, 45-56. (55) Kuta, J.; Wander, M. C. F.; Wang, Z. M.; Jiang, S. D.; Wall, N. A.; Clark, A. E. Journal of Physical Chemistry C 2011, 115, 21120-21127. (56) Bratsch, S. G.; Lagowski, J. J. Journal of Physical Chemistry 1986, 90, 307-312. (57) Bratsch, S. G.; Lagowski, J. J. J. Phys. Chem. B 1986, 90, 307. (58) Gibson, J. K.; Haire, R. G.; Santos, M.; Marcalo, J.; de Matos, A. P. Journal of Physical Chemistry A 2005, 109, 2768-2781.
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Appendix B
Modulation of Hydride Formation Energies in Transition Metal Doped Mg by Alteration of Spin State
Abdullah Ozkanlar, Alex Samuels, Aurora E. Clark
Department of Chemistry, Washington State University, Pullman, Wa 99164
Published in Chemical Physics Letters February 2013
Ozkanlar, A.; Samuels, A.; Clark, A. E. Chemical Physics Letters 2013, 560, 10-14.
This was a preliminary project performed during the summer of 2009.
B.1 Introduction
Metal hydrides that act as matrices for H2 storage have been intensely investigated for
1 many years. Magnesium has low cost and high storage capacity, however it exhibits slow H2 absorption kinetics and a high temperature for hydride desorption.2 Studies indicate that
3 dissociation/recombination of H2 is rate-limiting, potentially due to a highly stable surface
4 hydride film that blocks H2 diffusion into (and out of) the Mg matrix. In response, researchers
have focused upon increasing surface area through the synthesis of smaller Mg particles,5 and
upon the introduction of transition metal (TM) catalysts that bond to the hydrogen with a
strength that correlates with the hybridization energy between the bonding and anti-bonding
adsorbate states and the metal s-, p-, and/or d-bands.6-10 In mixed Mg-TM systems, the TM orbital energies decrease across the period, rationalizing the general observation that early TMs have the strongest tendency for hydride formation.8 Structural issues may also contribute to
catalysis, as recent computational work11 has shown Fe diffusion upon dehydrogenation,
suggesting that Fe, and most probably other TMs stay in the MgH2/Mg surface regions where
144
they can continuously catalyze dehydrogenation. Computational studies (primarily using Density
Functional Theory - DFT) have been instrumental toward understanding and predicting structural and thermodynamic properties of Mg solids and clusters. Topics that span the effects of crystal grain size upon thermodynamic stability,5 to the calculation of formation energies for metal
hydrides,8,9 the metallic evolution of Mg clusters,12-16 detailed bonding descriptions, and specific
mechanistic aspects of (de)hydrogenation,3,7,11,17 have all been investigated.
Our contribution lies in the computational study of TM doped Mg clusters and the
structural and energetic impact of the TM spin state. This is particularly important as TM doped
Mg-clusters have exhibited residual paramagnetism of unknown origin18 and the synthesis of
Mg-TM composites and alloys under an external magnetic field (B) have revealed a previously
unexplored dependence of the phase composition and chemical reactivity.19 Specifically, under
an applied magnetic field smaller crystallite sizes are observed for 2Mg-Fe and the
dehydrogenation kinetic properties are greatly improved, leading to a decrease in the dehydriding
temperature as well as an increase in the H2 desorption capacity. While much experimental work
needs to be performed to assess the origin of these observations, these data present two intriguing
questions. How could B influence the synthesis of TM doped alloys/composites? Second, could
B also influence the fundamental interaction of H2 with the metal? If indeed this experimental
result is solely attributed to the application of the magnetic field, and not to any other physical
phenomena, then the change in phase composition may derive from differences in the localized
Mg-TM and nearby Mg-Mg electronic structure that occurs under B, implying sensitivity of the
bonding upon spin state (S). Transition metals in particular have a number of available S that
derive from different arrangements of the electrons amongst the s and d-orbitals.
145
In the absence of an external magnetic field, temperature dependent spin transitions can be
initiated when the free energy separation between two spin states (Δ for HS and
LS states) is roughly kBT. Thermal equilibrium is reached when Δ 0, and the corresponding
temperature is / Δ /Δ . When B is turned on, the magnetic free energy expression becomes:
Δ Δ (B.1) where is the magnetic susceptibility. In this case, the spin transition temperature is obtained by setting Δ 0 whereupon
/ / Δ / (B.2)
with
Δ / (B.3)
20,21 which is the negative magnetic field induced shift in the equilibrium temperature / . Hence
the effect of the external magnetic field on the spin transition is to lower the temperature that the
transition takes place, equivalently, to reduce the energy separation between spin states, by a
factor roughly the square of the strength of B.
To explore a simple chemical model that may describe the experimental observations, the
geometries, bonding, and thermodynamic properties of gas-phase TM doped Mg clusters as well
as their reaction with H2 have been examined as a function of S using DFT/B3LYP and Coupled-
Cluster with Single and Double and perturbative Triple excitations (CCSD(T)) levels of theory.
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B.2 Computational Methods.
The structures of clusters of the form Mg-X (X = Mg, Ti, V, Fe) and their corresponding
hydrides were optimized using DFT/B3LYP,22,23 MP2,24 as well as CCSD(T)25 methods and the
aug-cc-pVTZ basis set26 using the MOLPRO 2009.1 program package.27 The orbital occupations
for all methods were set to be the same so that the calculated trends can be compared. The
1 structure of Mg2 was optimized for the singlet ( Ag) state. The structures of MgTi were
1 3 5 optimized for the singlet ( A1), triplet ( A1), and quintet ( A1) states; the structures of MgV were
2 4 6 optimized for the doublet ( A2), quartet ( A1), and sextet ( A1) states; and the structures of MgFe
1 3 5 were optimized for the singlet ( A1), triplet ( A2), and quintet ( A1) states. The energy of formation Mg-X bond was determined as the difference in total energies:
E [E(Mg X) E(Mg)][E(Mg ) E(X)] (B.4) rxn 2
The structures dihydrogen/hydride Mg(X)H2 clusters were also optimized to study the
favorability of hydride formation at the X site in these complexes. The structure of Mg2H2
1 hydride was optimized for the singlet ( A) state. The structures of MgTiH2 were calculated for
1 3 5 the singlet ( A), triplet ( A), and quintet ( A) states; structures of MgVH2 were calculated for
2 4 6 the doublet ( A), quartet ( A), and sextet ( A) states; and structures of MgFeH2 were
calculated for the singlet (1A), triplet (3A), and quintet (5A) states. The hydride formation energy for the hydride clusters is given as,
E E(MgX H ) E(MgX) E(H ) (B.5) rxn 2 2
Geometry optimization of Mg6X and MgX6H2 in the absence of symmetry constraints
was performed using the NWChem program package with the B3LYP combination of exchange-
28 correlation functionals and the aug-cc-pVTZ basis. The substitution reaction, Mg7 + TM
Mg6TM + Mg (TM = Ti, V, Fe), was studied for the apical and ring isomers of Mg6-TM (Figure
147
B.1). The relevant spin states considered were: S = 0 1, and 2 for TM = Ti, Fe; S = 1/2, 3/2 and
5/2 for TM = V. The hydride formation energetics was examined for the reaction Mg6TM + H2
Mg6TMH2. The substitution energies were determined as,
E [E(Mg TM ) E(Mg)][E(Mg ) E(TM )] 6 7 (B.6) and, the hydride formation energy is given as,
E E(Mg TMH ) E(Mg TM ) E(H ) 6 2 6 2 (B.7)
Frequency calculations were carried out for all species to take into account the zero-point energy and the thermal correction to the energies (at 298.15 K).
Figure B.1. Representative B3LYP/aug-cc-pVTZ geometries of the Mg-TM dimer and heptamers, where the TM is placed in either a ring or apical position, and their associated hydrides.
B.3 Results and Discussion.
The geometries, bonding, and thermodynamic properties of gas-phase clusters of the form
MgX and Mg6X (X= Mg, Ti, V, Fe), as well as their reaction with H2 have been examined as a function of S using DFT/B3LYP and Coupled-Cluster with Single and Double and perturbative
Triple excitations (CCSD(T)) levels of theory. For each metal the high-spin (HS), intermediate
(IS), and low-spin (LS) cases were examined. A capped pentagonal biprism was used for the
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16,29 starting geometry of Mg7, as in prior studies of Mg and TM doped Mg clusters. Isomers where the TM was substituted at the both the apical and ring positions were examined (Figure
B.1). The DFT and CCSD(T) calculated structural parameters for the Mg2 and Mg7 clusters are in excellent agreement with prior experimental studies (< 0.1 Å error) and show improved performance relative to prior theoretical works,16,29,30 however MP2 appears to underestimate the strength of the Mg-Mg interactions.
Figure B.2. Energetic and structural parameters for (A) reaction (rB.1) and (B) reaction (rB.2) calculated using CCSD(T)/AVTZ as a function of spin state (LS = low spin, IS = intermediate spin, HS = high spin. LS is S = 0, 1/2, and 0, while IS has S = 1, 3/2, and 1, and HS is S = 2, 5/2, and 2 for Ti, V, and Fe, respectively).
Given the respective geometries about each TM the HS and IS states are found to be the ground electronic states within the Mg-TM and Mg6TM species. As expected, the energetic gap between the HS and LS states, ΔEHS-LS, increases going across the period. Within the Mg-TM dimers ΔEHS-LS is 27.16, 42.11 and 68.16 kcal/mol for Mg-V, Mg-Ti, and Mg-Fe, respectively
149
(CCSD(T) results). Comparable data is obtained from B3LYP. As the cluster size is increased
ΔEHS-LS decreases to between 5 – 25 kcal/mol depending on the TM involved and its position in
the Mg6TM cluster (B3LYP results). We do not emphasize the absolute value of the spin state splitting, as these values will decrease with increasing system size and with the appropriate B a
change in spin state population is possible as indicated by Eqn (3). Instead, we propose that the fundamental changes in electronic structure described as a function of S should be extensible to larger systems if the doping of the transition metal within the Mg-TM composite system leads to localized defect states, a phenomena that is well-known within the experimental surface electronic structure community.31
The energetics of the formation of the Mg-TM bond was first investigated using the reactions:
Mg2 + TM → Mg-TM + Mg (rB.1) Mg7 + TM → Mg6TM + Mg (rB.2)
The reaction energies for (rB.1) calculated by CCSD(T) and B3LYP are generally the most
favorable for bond formation with Fe, while Ti and V have comparable smaller values, however
this is significantly dependent upon S. CCSD(T) predicts the most favorable reaction energy for
ZPE Mg-Ti in the HS, S = 2, state (Figure B.2 (A)) (ΔE298 = −6.80 kcal/mol), while the Mg-Ti
interaction is negligible in the low spin (S = 0) and intermediate (S = 1) states (Table SB3).
Comparable results are observed for the Mg-V dimer. These bond-strength trends differ in Mg-
ZPE Fe, as the most negative reaction energy is predicted for the LS (S = 0, ΔE298 =
ZPE −19.1 kcal/mol) and the IS (S = 1, ΔE298 = −16.2 kcal/mol) states (Figure B.2 (A)). Yet the
reaction energy for the HS S = 2 state is a comparable to that observed for the HS states of the
ZPE early TM dimers (ΔE298 = −6.3 kcal/mol). The DFT reaction energetics for reaction (r1)
follow the same trend as CCSD(T) though their magnitudes are generally shifted in a positive
direction, due to the inability of B3LYP to account for the weak VdW and dispersion interactions
150 that “hold together” the dimer in some spin states. This does not imply that DFT is entirely inappropriate for these systems, as the electronic structure is very similar to the CCSD(T) results and DFT reproduces the same general energetic trends. However, DFT should not be used for a quantitative assessment of these small, dispersion dominated systems. The DFT reactions energetics for formation of Mg6TM (rB.2) indicate that the apical isomer is generally the most stable, and substitution is energetically favored in all spin states with the most energy released in
30 ZPE the LS and IS states (Table SB4). Deviations in ΔE298 of up to 30 kcal/mol are observed as a function of S for reaction (rB.2) using a given TM (Table SB4)
Analysis of the electronic structure of these clusters lends much insight into the reaction energetics. Of specific interest is the observation that the Mg-TM interaction can vary from being dominated by van der Waals and electrostatic forces, to full covalent bonding, depending upon the position of the TM within the period, as well as its S. Fundamentally, this derives from not only the ability of the TM 4s and 3d atomic orbitals (AOs) to overlap with the Mg 3s and 3p, but also the resulting electron distribution amongst the σ and σ* orbitals. As illustrated in Figure
B.3, within Mg-TM dimer the TM 4s AO mixes with the Mg 3s AO to form doubly occupied σ and σ* orbitals in the low spin (LS) ground states, with a formal bond order of zero. Uncoupling the first set of electrons to create the intermediate spin (IS) state typically occurs within the non- bonding 3d-orbital manifold, and alters the vdW and electrostatic interaction, as indicated by differences in the atomic charges, calculated by Natural Population Analysis, using DFT (see
Supporting Information, Table SB1). The net result can be either a slight bond length expansion or contraction, depending on the TM involved. However, in all cases the high spin (HS) state derives from uncoupling of the σ* electrons, placing an extra electron into the non-bonding 3d manifold.
151
Thus, the electron occupation of the σ* orbitals decreases in the HS states, which increases
the covalent bonding between the Mg and TM and leads to a formal bond order of 1/2. At the
same time, the extent of charge transfer between the atoms also increases significantly (DFT
result). In the Mg-Ti dimer, these changes in electronic structure lead to a significant reduction
(~1 Å) in the bond distance in the HS state relative to the IS case (Figure B.2 (A), Table SB2).
As a result of changes in the TM 4s and 3d orbital energies and the d-orbital occupancy
CCSD(T) predicts that Mg bonding with Fe is significantly stronger than in the early TM. Here,
mixing between the Fe 4s and Mg 3s AOs forms a doubly occupied σ orbital, while the σ* is
unoccupied, leading to a formal bond order of 1 in the LS state. The intermediate spin state
uncouples the electrons in the non-bonding d-manifold, unaffecting the Mg-Fe bonding, while
the HS state finally places a single electron into the σ* orbital leading to a formal bond order of
1/2. As the size of the cluster is increased to Mg6TM the MO diagram becomes more complex,
however Natural Bond Order analysis indicates similar changes in the occupation of the bonding
and antibonding orbitals as a function of S, manifesting itself by changes in the Mg-TM bond
length of up to 0.5 Å (Table SB5).
These results indicate clear changes in the nature of the Mg-TM bond as a function of S,
which in turn influences the bond lengths and energetic favorability of Mg-TM bond formation.
The data supports a postulate that changes in spin state populations could alter the phase
composition within TM doped Mg alloys/composites synthesized under an applied magnetic
field (provided the TM was doped in high enough concentration to alter bulk structural parameters). Of equal interest, however, is whether or not B has the ability to influence the reaction of H2 with the TM doped Mg cluster. It is assumed within the experimental literature that the change in phase composition alone is responsible for decreasing the dehydriding
152
temperature and increasing H2 desorption capacity in the presence of the applied magnetic field.
Thus H2 addition to the dimer and heptamer at the catalytically active TM site (Figures B.1 and
B.2) has been investigated as a function of S:
Mg-TM + H2 → MgTM(H)2 or MgTM(H2) (rB.3) Mg6TM + H2 → Mg6TM(H)2 or Mg6TM(H2) (rB.4)
The interaction of the H2 with the cluster changes the ground spin state in the early TM systems
to IS or LS, while Fe containing systems remain HS ground states. Broadly, the reactions (rB.3)
– (rB.4) in the HS states form physisorbed products characterized by a H-H bond, while LS
states form stable hydrides where the H-H bond has broken and strong TM-H bonds have
formed. For the purposes of comparing trends in hydride formation as one moves from the early-
to mid-transition metals, the reaction energetics can be examined where the reactants are in the
same spin state, or where the reactants and products are in their electronic ground states (i.e.
letting the spin state change along the reaction coordinate). The former is illustrated for the H2
addition to dimers in Figure B.2 (B). In this case, the hydride formation energy is the most
negative for the LS state and the hydride-TM bond strength follows the order Fe > V > Ti. This
is in reasonable agreement with prior DFT studies of MgTM alloys using a perovskite
geometry.9 Alternatively, if the reaction energetics for (rB.3) and (rB.4) are considered within the electronic ground states, the strength of the TM-H interaction generally decreases across the period, in good agreement with trends predicted by DFT studies of TM hydrides.8
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Figure B.3. MO diagram of the valence orbitals for Mg—TM dimer. Changes in the TM spin state modulate population of the 4s transition metal AO, which in turn alters the occupation of the σ* MO.
The electronic structure of the (rB.3) – (rB.4) products depends somewhat on the geometry
adopted. In the Mg-TM dimer system, each geometry optimization of the H2 sorbed species was initiated with the H2 approaching the TM side on. However the LS products have individual hydride units that can either remain bound solely to the TM, or may bridge the Mg-TM axis,
− which subtly alters the bonding (Figure B.1). Consider that MgTi(H)2 has each H bound to Ti, thus hydride bonding occurs via mixing of the H-atom 1s AO with the Ti 4s and 3d. When the
TM is changed to V or Fe, the LS geometry has a single μ2 bridging hydride and as a result the H
1s AOs mix with both the TM 4s and Mg 3s AOs. Irrespective of the geometry formed, the IS state results from unpairing a set of electrons within the non-bonding TM 3d manifold which leads to a slight decrease in the favorability of hydride formation. Breaking of the H2 σ bond is prevented when the TM is HS, as the now filled 4s of the TM cannot not mix with the H2 σ orbital. Thus the H2 does not dissociate to form hydride and instead only physisorption is
observed in the HS systems.
154
Necessarily, CCSD(T) indicates that formation of MgTiH2 hydride is the most favorable
ZPE (ΔE298 = −21.42 kcal/mol) in the S = 0 state (Figure B.2 (B)). As S increases to 1 and 2, the ability to form hydridse decreases such that it is no longer favorable in the HS state and only a
ZPE physisorbed species is formed (ΔE298 = −3.61 kcal/mol, Table SB6). Similar results are obtained for the reactivity of MgV with H2. CCSD(T) and DFT/B3LYP have similar predictions regarding the reactivity of the MgTi and MgV with H2, however deviations are observed for
MgFe. CCSD(T) predicts that the formation of LS MgFe(H)2 is the most favored while
ZPE DFT/B3LYP predicts that IS (S = 1) state to be the most favored (ΔE298 = −31.44 kcal/mol),
ZPE followed by the LS, S = 0, state (ΔE298 = −14.22 kcal/mol, Table SB6, SB7). H2 addition to the TM site in the Mg6-TM species at both the ring and apical positions (Figure B.1) follows the
same trends (Table SB8). Thus for all TM doped dimers and heptamers the formation of stable
hydrides (in the LS and IS states) or stable physisorbed H2 (in the HS state) can be modulated as:
These data indicate that multiple factors could be responsible for the enhanced dehydrogenation kinetic properties of 2Mg-Fe in the presence of B. First, the magnetic field can decrease the thermal energy needed to populate excited spin states during synthesis. The current work has shown that the local Mg-Fe bond is highly sensitive to the Fe spin state and it is anticipated that the metallic bonding in TM doped Mg alloys/composites will also exhibit sensitivity to S. Prior synthesis conditions of 2Mg-Fe-H composite had T = 770 K,19 which is enough thermal energy to overcome spin state gaps of 1.5 kcal/mol. Addition of a 2 – 5 Tesla magnetic field makes it likely that an entire band of excited spin states is responsible for a decreased in crystalline size. Though the increased surface area that is brought about by these changes in phase composition may contribute to the enhanced dehydrogenation kinetics, it is also
155 indicated that B influences the fundamental interaction of H2 with the Mg-Fe alloys/composites.
Specifically, population of the HS state of the Fe fills the 4s AO and prevents it from hybridizing with the H2 σ bond. Such hybridization is an essential feature for breaking the H-H bond at the catalytically active TM site. These observations also hold true for the early TM doped Mg clusters studied herein.
B.4 Supplementary Information
Table SB1: NPA charges for Mg-TM (TM = Ti, V, Fe) clusters calculated at the CCSD(T) optimized geometries, at the DFT/B3LYP level of theory. LS = low-spin, IS = intermediate-spin, HS = high-spin. Mg is always positive, while the TM is always negatively charged.
LS IS HS Mg-Ti (0.06069) (0.04476) (0.13484) Mg-V (0.06008) (0.05990) (3.86013) Mg-Fe (0.48867) (0.71962) (1.09724)
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Table SB2: Mg-TM (TM = Ti, V, Fe) bond lengths (in Å) calculated at the DFT (B3LYP), MP2, and CCSD(T) levels.
MgTi Method S=0 S=1 S=2 DFT/B3LYP 3.18 3.88 3.00 MP2 3.75 4.10 3.14 CCSD(T) 3.79 3.96 2.91 MgV Method S=1/2 S=3/2 S=5/2 DFT/B3LYP 3.90 3.41 2.90 MP2 4.06 3.84 2.99 CCSD(T) 3.95 3.66 2.88 MgFe Method S=0 S=1 S=2 DFT/B3LYP 2.81 2.69 2.76 MP2 2.33 2.29 2.75 CCSD(T) 2.30 2.36 3.00 Method Mg2 DFT/B3LYP 3.90 MP2 4.13 CCSD(T) 4.06
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Table SB3: Reaction energy ∆ for Mg2 + TM Mg-TM + Mg (TM = T, V, Fe), given in kcal/mol.
MgTi Method S=0 S=1 S=2 DFT/B3LYP 2.13 5.72 -0.56 MP2 0.89 0.89 -2.07 CCSD(T) -0.18 0.84 -6.80 MgV Method S=1/2 S=3/2 S=5/2 DFT/B3LYP 8.03 5.41 -5.22 MP2 1.03 1.33 -2.78 CCSD(T) 1.68 1.19 -6.27 MgFe Method S=0 S=1 S=2 DFT/B3LYP -10.79 -5.75 -7.44 MP2 -47.34 -40.96 -4.62 CCSD(T) -19.07 -16.19 -6.31
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Table SB4. ∆ (kcal/mol) for the substitution reaction Mg7 + TM Mg6TM + Mg at the ring and apical positions of cluster (shown in Figure B.3) as a function of TM spin state S using B3LYP/aug-cc-pVTZ.
Position TM S=0 S=1 S=2
Ring Ti -29.23* -15.94 -19.42
Apical Ti -54.31* -34.52 -29.09
S=1/2 S=3/2 S=5/2
Ring V -40.67 -30.55* -22.29*
Apical V -57.31 -30.12 -27.21
S=0 S=1 S=2
Ring Fe NA** NA** -18.87
Apical Fe -77.16 -25.12 -27.27
*data obtained from structures with ≥ 1 imaginary vibration less than 100 cm-1.
** unable to obtain adequate convergence
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Table SB5. Average rMg-Mg and rMg-TM distances (in Å) within the Mg6TM clusters optimized using B3LYP/aug-cc-pVTZ for different values of total S.
Ti ring position
S=0 S=1 S=2 rMg-Mg 3.30* 3.24 3.33 rMg-Ti 2.85* 3.12 3.03
Ti apical position rMg-Mg 3.22* 3.23 3.37 rMg-Ti 2.82* 2.93 2.92
V ring position
S=1/2 S=3/2 S=5/2 rMg-Mg 3.22 3.31* 3.38* rMg-V 2.89 2.90* 2.86*
V apical position rMg-Mg 3.20 3.20 3.38 rMg-V 2.78 2.96 2.85
Fe ring position
S=0 S=1 S=2 rMg-Mg NA NA** 3.43 rMg-Fe NA NA** 2.79
Fe apical position rMg-Mg 3.40 3.29 3.34 rMg-Fe 2.41 2.61 2.67
*has ≥ 1 imaginary vibration less than 100 cm-1. ** unable to obtain adequate convergence
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Table SB6: Hydride formation energy, ∆ , defined by the reaction: Mg-TM + H2 Mg- TM(H)2 where TM = Ti, V, and Fe. Given in kcal/mol.
MgTiH2 Method S=0 S=1 S=2 DFT/B3LYP -30.77 -14.76 -0.33 MP2 -24.07 -7.07 -2.19 CCSD(T) -21.42 -13.08 -3.61 MgVH2 Method S=1/2 S=3/2 S=5/2 DFT/B3LYP -30.53 -19.58 +2.07 MP2 -17.44 -10.76 +1.76 CCSD(T) -22.76 -17.46 +0.47 MgFeH2 Method S=0 S=1 S=2 DFT/B3LYP -14.22 -31.44 +1.43 MP2 +9.48 NA* +0.12 CCSD(T) -36.04 -30.87 -2.63 * unable to obtain adequate convergence
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Table SB7: H-H distance in Mg-TM-H2 (TM = Ti, V, Fe) clusters. Given in Å.
MgTiH2 Method S=0 S=1 S=2 DFT/B3LYP 3.09 3.26 0.78 MP2 3.43 3.46 0.78 CCSD(T) 3.24 3.48 0.79 MgVH2 Method S=1/2 S=3/2 S=5/2 DFT/B3LYP 2.97 2.98 0.77 MP2 2.99 3.14 0.76 CCSD(T) 3.27 3.13 0.77 MgFeH2 Method S=0 S=1 S=2 DFT/B3LYP 3.22 2.29 0.75 MP2 3.14 NA* 0.80 CCSD(T) 3.26 2.25 0.80 Method Mg2H2 (S=0) DFT/B3LYP 3.40 MP2 3.42 CCSD(T) 3.43 * unable to obtain adequate convergence
Table SB8: Hydride formation energy, ∆ ∆ , defined by the reaction: Mg6TM + H2 Mg6TM(H)2 where TM = Ti, V, and Fe. Calculated using B3LYP/aug-cc-pVTZ Given in kcal/mol. Only structures with zero imaginary vibrations have been used.
Mg6TiH2 Position of TM S=0 S=1 S=2 Apical NA -0.23 3.41 Ring NA -33.72 -3.49 Mg6VH2 S=1/2 S=3/2 S=5/2 Apical -23.41 0.28 1.33 Ring NA NA NA Mg6FeH2 S=0 S=1 S=2 Apical NA -19.10 0.74 Ring NA NA NA
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Table SB9: H-H distance in Mg6TM(H)2 (TM = Ti, V, Fe) clusters. Calculated using B3LYP/aug-cc-pVTZ. Given in Å. Only structures with zero imaginary vibrations have been used.
Mg6TiH2 Position of TM S=0 S=1 S=2 Apical NA 0.77 0.77 Ring NA 3.44 0.78 Mg6VH2 S=1/2 S=3/2 S=5/2 Apical 2.57 0.87 0.78 Ring NA NA NA Mg6FeH2 S=0 S=1 S=2 Apical NA 0.83 0.80 Ring NA NA NA
B.5 Acknowledgements.
The authors wish to thank Prof. Kirk Peterson for thoughtful discussions regarding this work.
B.6 References
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