AMMONIA: A REVIEW OF MECHANISTIC MODELS OF AMMONIA

VOLATILIZATION AND THEORETICAL STUDIES OF

THE CATALYTIC REDUCTION OF DINITROGEN

TO AMMONIA BY A BORON CATION, A

BORON DIHYDRIDE CATION, AND

BERYLLIUM DIHYDRIDE

by

CARY JANEANNE BELL, B.S.

A THESIS

IN

INTERDISCIPLINARY STUDIES

Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of

MASTER OF SCIENCE

Approved

Greg Gellene Chairperson of the Committee

Moira Kenina Ridley

George P. Cobb

Accepted

John Borrelli Dean of the Graduate School

August, 2006 ACKNOWLEDGEMENTS

I would like to thank God for loving me so much that He sent Jesus, His only begotten Son, to die for me. At each point of anxiety and writer’s block, He lifted me up, inspired me, gave me words, and continually reminded me that I was not alone. Thank You, God! I would also like to thank the following people for all of their support: My family for loving, encouraging, and supporting me through the many years of school and for continually asking me how things were going, especially with the ‘mammoth’. My church family, especially Janis, Job, Jessica, Sandra, Stephanie Wehmeyer, Bethany, Angela, and Carrie, for encouraging me in my walk with Christ, lifting me up, and praying for me. My advisor, Dr. Gregory Gellene, for teaching me so much and for guiding and encouraging me to continue in my graduate pursuits. Stephanie Austin for encouraging me, for long talks on the phone, and for fun Friday movie nights. Danny for your patience and kindness in teaching me and for always answering my e-mails about computer problems. Danny, Thom, Jen, and Ben for all the lunches, parties, trips to lands ‘far, far away’, and more importantly for listening and advising. Thank you.

ii TABLE OF CONTENTS

ACKNOWLEDGEMENTS...... ii ABSTRACT...... vi LIST OF TABLES...... vii LIST OF FIGURES ...... xi I. INTRODUCTION ...... 1 1.1 References...... 4 II. A REVIEW OF THE MECHANISTIC MODELS OF AMMONIA VOLATILIZATION FROM FIELD-APPLIED SLURRY...... 5 2.1 Introduction ...... 5 2.2 Core Equation for Ammonia Volatilization...... 6 2.3 Boundary Layer Theory ...... 7 2.4 Estimation of the Convective Mass Transfer Coefficient ...... 8 2.4.1 Resistance Approach ...... 8 2.4.2 Advection Model...... 13 2.5 Slurry and Soil Chemistry ...... 14 2.6 Convection and Diffusion in Soil...... 16 2.7 Summary and Conclusions...... 20 2.8 References ...... 41 III. CATALYTIC REDUCTION OF DINITROGEN TO AMMONIA...... 42 3.1 References ...... 50 IV. METHODS ...... 51 4.1 References ...... 53 V. ORGANIZATION AND LABELING SYSTEM OF THE FIGURES AND TABLES OF THE BORON CATION, BORON DIHYDRIDE CATION, AND BERYLLIUM DIHYDRIDE CATALYTIC SYSTEM...... 54 5.1 References ...... 58 VI. CATALYTIC REDUCTION OF DINITROGEN TO AMMONIA BY B+...... 59

iii 6.1 Introduction ...... 59 6.2 Results ...... 60 6.2.1 Formation of Diimide...... 60 6.2.2 Formation of Hydrazine ...... 63 6.2.3 Formation of Ammonia...... 66 6.3 Discussion ...... 69 6.3.1 Electrostatic Hydrogen Bonding ...... 69 6.3.2 Boron-Nitrogen Bonds ...... 73 6.3.2.1 Boron-Nitrogen Sigma Bonds...... 74 6.3.2.2 Boron-Nitrogen Pi Bonds ...... 81 6.3.3 Steps of B+ Catalyzed Reduction of Dinitrogen to Form Ammonia...... 84 6.3.3.1 Steps of Dinitrogen and Diimide Reduction...... 84 6.3.3.2 Steps of Hydrazine Reduction ...... 95 6.3.4 Overall Trends of the B+ Catalytic System ...... 97 6.4 References...... 168 VII. CATALYTIC REDUCTION OF DINITROGEN TO AMMONIA + BY BH2 ...... 169 7.1 Introduction...... 169 7.2 Results ...... 169 7.2.1 Formation of Diimide and Hydrazine ...... 169 7.2.2 Formation of Ammonia...... 170 7.3 Discussion...... 172 7.3.1 Steps of Dinitrogen and Diimide Reduction ...... 173 7.3.2 Steps of Hydrazine Reduction...... 175 + 7.3.3 Summary of the BH2 Catalytic System...... 186 7.4 References...... 216 VIII. CATALYTIC REDUCTION OF DINITROGEN TO AMMONIA BY BeH2 ...... 217 8.1 Introduction...... 217

iv 8.2 Results ...... 217 8.2.1 Formation of Diimide...... 217 8.2.2 Formation of Hydrazine...... 220 8.2.3 Formation of Ammonia...... 221 8.3 Discussion...... 223 8.3.1 Beryllium-Nitrogen Bonds...... 223 8.3.1.1 Beryllium-Nitrogen Sigma Bonds ...... 226 8.3.1.2 Beryllium-Nitrogen Pi Bonds ...... 231

8.3.2 Steps of BeH2 Catalyzed Reduction of Dinitrogen to Form Ammonia...... 233

8.3.3 Overall Trends of the BeH2 Catalytic System...... 238 8.4 References...... 283 IX. COMPARISON OF AMMONIA SYNTHESIS CATALYSTS ...... 284 9.1 Comparison of the Boron Cation, Boron Dihydride Cation, Beryllium, and Beryllium Dihydride Catalytic Systems...... 284 9.1.1 Activation of Dinitrogen...... 284 9.1.2 Mechanisms of Dinitrogen, Diimide, and Hydrazine Reduction...... 287 9.1.3 Catalytic Efficiencies...... 291 9.2 Comparison of the Boron Cation, Boron Dihydride Cation, Beryllium, and Beryllium Dihydride Catalytic Systems to the Systems of Other Ammonia Synthesis Catalysts ...... 293 9.3 References...... 303 APPENDIX A OPTIMIZED GEOMETRIES ...... 304 B HARMONIC FREQUENCIES...... 323

v ABSTRACT

In order to maintain the food production necessary for sustaining the world's ever increasing population, millions of tons of ammonia fertilizer are produced each year. Studies have been performed to investigate how ammonia fertilizers can be used efficiently and how they can be made more efficiently. A significant amount of nitrogen fertilizer applied to crops is lost through ammonia volatilization. Many investigations have been implemented to study the factors and processes controlling ammonia volatilization including the models that are reviewed. At the core of these models is the calculation of the rate of ammonia volatilization, which is a function of a mass transfer coefficient and the difference between the concentration of gaseous ammonia at the slurry/soil surface and that of the free air, which is input. In general, the mass transfer coefficient equation is a function of friction wind velocity, aerodynamic roughness length, the distance the ammonia is estimated to travel, and in the case of the advection model method, the length of the field. The concentration of gaseous ammonia at the slurry/soil surface is a function of the equilibrium constant, Henry's Law constant, pH, + concentration of total ammoniacal nitrogen (NH3 and NH4 ), time, depth of ammonia infiltration into the soil, soil water content, porosity, and bulk density, and is dependent on physical and chemical processes such as adsorption, convection, and diffusion. In industrial ammonia synthesis, high temperatures and pressures are required to

cleave the bond between the nitrogen atoms of N2 prior to hydrogenation. This study + + theoretically investigates catalytic reductions of N2 to ammonia by B , BH2 , Be, and

BeH2, in which N2 cleavage is avoided through sequential hydrogenation of the N2. The stationary points and transition states of these catalytic systems are located and characterized at the MP2 and CCSD(T) levels of theory with 6-31g* and double and triple zeta basis sets. Each catalyzed reduction of a nitrogen species (N2, substituted diimide and hydrazine) occurs by hydrogenating one nitrogen atom and then the other. + When H2 is restricted, B is the most effective in activating N2. However, BeH2 is calculated to be the most efficient catalyst.

vi LIST OF TABLES

2.1 Symbols...... 22 2.2 Mass Transfer Coefficients in Ammonia Volatilization Models...... 29

2.3 Equilibrium or Dissociation Constants, Ka ...... 33 2.4 Henry’s Law Equations...... 34 2.5 Convective and Diffusive Flux Equations ...... 35 2.6 Mass Balance Equations of Ammonical Nitrogen in Soil ...... 39 3.1 Viability of Various Elements as Ammonia Synthesis Catalysts ...... 47 + + 5.1 Calculated Geometries, Energy, and Stretching Frequencies of the B , BH2 , BeH2 ...... 56

5.2 Calculated Geometries, Energy, and Stretching Frequencies of the N2 and H2 Reactants and the NH3 Product...... 57 6.1 Calculated Geometry and Relative Energy of the stationary points on the + + minimum energy pathway for B + N2 + H2 → BHNNH (3) ...... 99 6.2 Calculated Geometry and Relative Energy of the stationary points on the + + minimum energy pathway for BHNNH (3) + H2 → BH2NHNH ...... 101 6.3 Calculated Geometry and Relative Energy of the stationary points on the + + minimum energy pathway for BH2NHNH + H2→ (H2)BHNHNH2 (2)...... 103 6.4 Calculated Geometry and Relative Energy of the stationary points on the + + minimum energy pathway for (H2)BHNHNH2 (2) → BH2NH2NH2 (1) ...... 106 6.5 Calculated Geometry and Relative Energy of the stationary points on the + + minimum energy pathway for BH2NH2NH2 (1) → NH3BNH3 ...... 109 6.6 Comparison of Hydrogen-Hydrogen Distances and Stretching Frequencies of the Complexes Involving Electrostatic Bonding Between an H2 and a Boron-Nitrogen Moiety...... 112 6.7 Binding Energies of the Various Structures Involving Electrostatic Bonds Between a Dihydrogen Molecule and a Boron-Nitrogen Moiety Calculated at + the CCSD(T)/pVTZ(+) level of theory and relative to B + N2 + 3H2 ...... 113

vii 6.8 Comparison of Electrostatic and Covalent Boron-Hydrogen Distances and Stretching Frequencies of the Complexes Involving Electrostatic Bonding Between an H2 and a Boron-Nitrogen Moiety and the + + BH2NHNH and BH2NH2NH2 structures...... 114 6.9 Comparison of Electrostatic and Dative Sigma Covalent Boron-Nitrogen Bond Distances and BN Stretching Frequencies of Literature References and of the Boron Cation System...... 115 6.10 Comparison of Hybrid Dative/Ordinary and Ordinary Sigma Covalent Boron- Nitrogen Bond Distances and Stretching Frequencies of Literature References and the Boron Cation System ...... 116 6.11 Calculated Geometries, Relative Energies, and Stretching Frequencies of Trans 1,2-Diimide and the Eclipsed and Gauche forms of Hydrazine ...... 118 6.12 Comparison of Pi Boron-Nitrogen Bond Distances and Stretching Frequencies of the Boron Cation System...... 119 6.13 Comparison of a Subset of distances, calculated at the MP2/TZ+ level of theory and reported in angstroms, of TS(1), TS(6), TS(5), and TS(10) and Their Electrostatic Reactants and Products...... 121 7.1 Calculated Geometry and Relative Energy of the stationary points on the + + minimum energy pathway for BH2 + N2 → BHNNH (1)...... 187 7.2 Calculated Geometry and Relative Energy of the stationary points on the + + minimum energy pathway for BH2NH2NH2 (2) + H2 → NH3BH2NH3 ...... 188 7.3 Relative Energy of the stationary points on the minimum energy + + pathway for BH2 + N2 + 3H2 → BH2 + 2NH3 that are also on the + + B + N2 + 3H2 → B + 2NH3 minimum energy pathway...... 192 7.4 Comparison of a Subset of distances, calculated at the MP2/TZ+ level and reported in angstroms, of TS(1) of the B+ catalytic system and TS(12) of + the BH2 catalytic system...... 193 7.5 Comparison of the Calculated Geometries and Stretching Frequencies of the + BH3 Component of the BH3NH2NH3 Structure with the Isolated BH3 Structure and with Experimental Geometries (X-Ray Crystallographic, Infrared) and Stretching Frequencies (Infrared) of the Isolated BH3 Structure...194 7.6 Comparison of the Calculated Geometries and Stretching Frequencies of the + + + N2H5 Component of the BH3NH2NH3 Structure with an Isolated N2H5 Structure and with Experimental Geometries and Stretching Frequencies of the + Isolated the N2H5 Component of Three Salts...... 195 8.1 Calculated Geometry and Relative Energy of the Stationary Points on the Minimum Energy Pathway for BeH2 + N2 → BeHNNH(2)...... 239

viii 8.2 Calculated Geometry and Relative Energy of the Stationary Points on the Minimum Energy Pathway for BeHNNH(2) + H2 → BeHNHNH2 ...... 240 8.3 Calculated Geometry and Relative Energy of the Stationary Points on the Minimum Energy Pathway for BeHNHNH2 + H2 → NH2BeHNH3 ...... 242 8.4 Calculated Geometry and Relative Energy of the Stationary Points on the Minimum Energy Pathway for NH2BeHNH3 + H2 → (NH3)BeH2NH3 ...... 244 8.5 Comparison of Electrostatic or Van Der Waals Beryllium-Nitrogen Interaction and Dative Sigma Covalent Beryllium-Nitrogen Bond Distances and Stretching Frequencies of the BeH2 System ...... 247 8.6 Comparison of Pi Covalent Beryllium-Nitrogen Bond Distances and Stretching Frequencies of the Literature References and the BeH2 System...... 248

8.7 Comparison the Calculated Geometries and Stretching Frequencies of BeH2, NH3, BeH2NH3, and the BeH2NH3 components of NH3BeH2NH3 and (NH3)BeH2NH3...... 249

8.8 Binding Energies of Various Structures of the BeH2 + N2 + 3H2 Catalytic System...... 250 8.9 Comparison of a Subset of Distances of TS(1), TS(3), TS(4), TS(5), TS(6), and TS(7) and Their Electrostatic Reactants and Products and of the Activation Energies of These Transition States...... 251 9.1 Comparison of a Subset of Distances, calculated at the MP2/TZ+ level of + + theory and reported in angstroms, of TS(1) of the B , Be, BH2 , and BeH2 system ...... 296 9.2 Comparison of the Mechanisms, Activation Energies, and Coordination + + Numbers of the B , BH2 , Be, and BeH2 Catalytic Systems ...... 297 9.3 Activation Energies of One or Both Hydrazine Reduction Steps of the B+, Be, and BeH2 Catalytic Systems...... 299 9.4 Comparisons of Catalytic Systems ...... 300 + + A.1 Optimized Geometries for the Stationary Points of the B and BH2 Catalytic Systems ...... 304

A.2 Optimized Geometries for the Stationary Points of the BeH2 Catalytic Systems ...... 317

A.3 Optimized Geometry of CS Symmetry NH3BeNH3 Minimum...... 322 + B.1 Harmonic Frequencies for B (N2)(H2) through TS(2)...... 323 + + B.2 Harmonic Frequencies for BHNNH (2) through (H2)BHNNH (1) ...... 324 + B.3 Harmonic Frequencies for TS(4) through BH2NHNH ...... 325

ix + B.4 Harmonic Frequencies for BH2NHNH (H2) through TS(7)...... 326 + B.5 Harmonic Frequencies for (H2)BHNHNH2 (2) through TS(9) ...... 327 + B.6 Harmonic Frequencies for (H2)BHNHNH2 (4) through TS(11) ...... 328 + + B.7 Harmonic Frequencies for BH2NH2NH2 through NH2BHNH3 ...... 329 + B.8 Harmonic Frequencies for TS(12) and NH3BNH3 ...... 330 + + B.9 Harmonic Frequencies for BH2N2 and TS(1) of the BH2 System ...... 331 + + B.10 Harmonic Frequencies for (H2)BH2NH2NH2 through BH3NH2NH3 ...... 332 + + B.11 Harmonic Frequencies for TS(13) of the BH2 system through NH3BH2NH3 ..333 + B.12 Harmonic Frequencies for (H2) 2BN2 through TS(BH4-BH3) ...... 334 + B.13 Harmonic Frequencies for (H2)BHNNH (3) through TS(BH3(3) – BH2)...... 335

B.14 Harmonic Frequencies for BeH2(N2) through TS(2) ...... 336 B.15 Harmonic Frequencies for BHNNH(2) through TS(2)...... 336

B.16 Harmonic Frequencies for BeHNHNH2 through TS(6)...... 337

B.17 Harmonic Frequencies for NH2BeHNH3 through NH3BeH2NH3...... 338

B.18 Harmonic Frequencies for TS(8) through (NH3)BeH2NH3 ...... 339

B.19 Harmonic Frequencies for (H2)Be(N2), TS(1) of the Be System, TS(7) of the Be System, and the CS Symmetry NH3BeNH3 Minimum ...... 340

x LIST OF FIGURES

3.1 Modified Thorneley-Lowe kinetic scheme for the reduction of N2...... 48

3.2 Proposed intermediates in the reduction of dinitrogen at a [HIPTN3N]Mo center through the step-wise addition of protons and electrons...... 49 6.1 Optimized structures of the stationary points of the boron cation catalyzed reduction of dinitrogen...... 122 6.2 Energy of the stationary points of the first reduction of dinitrogen relative to + B + N2 + H2 calculated at the CCSD(T)/pVTZ(+)//MP2/pVTZ+ level of theory with harmonic ZPE added at the MP2/pVTZ+ level of theory ...... 130 6.3 Energy of the stationary points of the second reduction of dinitrogen relative + to B + N2 + 2H2 calculated at the CCSD(T) level of theory with harmonic ZPE added at the MP2 level of theory...... 131 6.4 Energy of the stationary points of the first reduction of diimide relative to + B + N2 + 3H2 calculated at the CCSD(T) level of theory with harmonic ZPE added at the MP2 level of theory ...... 132 6.5 Energy of the stationary points of the second reduction of diimide relative to + B + N2 + 3H2 calculated at the CCSD(T) level of theory with harmonic ZPE added at the MP2 level of theory ...... 134 6.6 Energy of the stationary points of the first and second reductions of + hydrazine relative to B + N2 + 3H2 calculated at the CCSD(T) level of theory with harmonic ZPE added at MP2 level of theory ...... 135 6.7 B+ Catalyzed Reduction of Dinitrogen to Ammonia ...... 136 6.8 Relative energy of stationary points along the minimum energy reaction path + + for B + N2 + H2 → BHNNH (1) calculated at the CCSD(T)/pVTZ(+)//MP2/pVTZ+ level of theory with MP2/pVTZ+ harmonic ZPE added...... 137

6.9 Structures of the C2V BH2NH2 molecule and of the transition state, ‘BH2NH2 (Cs – TS)’ ...... 138 6.10 Dipole Moment Plots for All of the Stationary Points of the B+ Catalytic System...... 139 6.11 Most plausible resonance structures of the various products of the B+ catalytic system based on bond lengths, HOMO pictures, and dipole moments ...... 147 + 6.12 Pictures of the HOMOs of BH2NH2 and BHNH2 ...... 152 6.13 Pictures of the LUMO, HOMO, HOMO-1, HOMO-2, and HOMO-3 of the various products of the B+ catalytic system...... 153

xi 7.1 Optimized structures of the stationary points of the boron dihydride cation catalyzed reduction of dinitrogen...... 196 7.2 Energy of the stationary points of the first reduction of dinitrogen relative + to BH2 + N2 calculated at the CCSD(T)/pVTZ(+)//MP2/pVTZ+ level of theory with harmonic ZPE added at the MP2/pVTZ+ level of theory ...... 198 7.3 Energy of the stationary points of the second reduction of dinitrogen relative + to BH2 + N2 + H2 calculated at the CCSD(T) level of theory with harmonic ZPE added at the MP2 level of theory...... 199 7.4 Energy of the stationary points of the first reduction of diimide relative to + BH2 + N2 + 2H2 calculated at the CCSD(T) level of theory with harmonic ZPE added at the MP2 level of theory...... 200 7.5 Energy of the stationary points of the second reduction of diimide relative to + BH2 + N2 + 2H2 calculated at the CCSD(T) level of theory with harmonic ZPE added at the MP2 level of theory...... 202 7.6 Energy of the stationary points of the first reduction of hydrazine relative to + BH2 + N2 + 3H2 calculated at the CCSD(T)/pVTZ(+)//MP2/pVTZ+ level + of theory, where the energies of the (H2)BH2NH2NH2 and TS(12) were estimated, with harmonic ZPE added at the MP2/pVTZ+ level of theory ...... 203 7.7 Energy of the stationary points of the first reduction of hydrazine relative + to BH2 + N2 + 3H2 calculated at the CCSD(T)/pVTZ(+)//MP2/pVTZ+ level of theory with harmonic ZPE added at the MP2/pVTZ+ level of theory ...204 + 7.8 BH2 Catalyzed Reduction of Dinitrogen to Ammonia...... 205 7.9 Relative energy of stationary points along the minimum energy reaction path + + BH2 + N2 -> BHNNH (1) calculated at the CCSD(T)/pVTZ(+)//MP2/pVTZ+ level of theory with MP2/pVTZ+ harmonic ZPE added ...... 206 7.10 Pictures of the LUMO, HOMO, HOMO-1, HOMO-2, and HOMO-3 of the + various products of the BH2 catalytic system...... 207 + 7.11 Dipole moment plots of stationary points of the BH2 Catalytic System...... 213 + 7.12 Most plausible resonance structures of the various products of the BH2 catalytic system based on bond lengths, HOMO pictures, and dipole moments...... 215 8.1 Optimized Structures of the Stationary Points of the Beryllium Dihydride Catalyzed Reduction of Dinitrogen...... 253 8.2 Energy of the stationary points of the reduction of dinitrogen to form Diimide relative to BeH2 + N2 + H2 calculated at the CCSD(T)/pVTZ(+)//MP2/pVTZ+ level of theory with harmonic ZPE added at the MP2/pVTZ+ level of theory ...... 259

xii 8.3 Energy of the stationary points of the reduction of diimide to form hydrazine relative to BeH2 + N2 + 2H2 calculated at the CCSD(T) level of theory with harmonic ZPE added at the MP2 level of theory...... 260 8.4 Energy of the stationary points of the reduction of hydrazine to form ammonia relative to BeH2 + N2 + 3H2 calculated at the CCSD(T)/pVTZ(+)//MP2/pVTZ+ level of theory with harmonic ZPE added at the MP2/pVTZ+ level of theory ...... 261

8.5 Energy of the stationary points of the conversion of NH3BeH2NH3 to (NH3)BeH2NH3 relative to BeH2 + N2 + 3H2 calculated at the CCSD(T)/pVTZ(+)//MP2/pVTZ+ level of theory with harmonic ZPE added at the MP2/pVTZ+ level of theory ...... 262

8.6 BeH2 Catalyzed Reduction of Dinitrogen to Ammonia...... 263 8.7 Relative energy of stationary points along the minimum energy reaction + path for BeH2 + N2 -> BHNNH (1) calculated at the CCSD(T)/pVTZ(+)//MP2/pVTZ+ level of theory with MP2/PVTZ+ harmonic ZPE added...... 264 8.8 Pictures of the LUMO, HOMO, HOMO-1, HOMO-2, and HOMO-3 of the various products of the BeH2 catalytic system ...... 265 8.9 Pictures of the occupied molecular orbitals illustrating the sigma and pi bonds of the example structures, BeH2NH3, BeHNH2, and BeNH ...... 274

8.10 Dipole moment plots for all of the stationary point of the BeH2 + N2 + 3H2 catalytic system...... 275

8.11 Most plausible resonance structures of the various products of the BeH2 catalytic system based on bond lengths, HOMO pictures, and dipole moments...... 280 9.1 Relative energy of stationary points along the minimum energy reaction path for Be + H2 + N2 → BeHNNH(1) calculated at the CCSD(T)/pVTZ(+)//MP2/pVTZ+ level of theory with MP2/pVTZ+ harmonic ZPE added...... 301 9.2 Energy of the stationary points along the energy reaction path for + + + B + N2 + 2H2 -> (H2)BHNNH relative to B + N2 + 2H2 and calculated at the CCSD(T)/pVTZ(+)//MP2/pVTZ+ level of theory with MP2/pVTZ+ harmonic ZPE added...... 302

xiii CHAPTER I INTRODUCTION

Nitrogen is an essential nutrient for plants and animals as it is a key component of the amino acids, proteins, DNA, and RNA, which are required for life and growth [1, 2, 3]. In agricultural systems, large quantities of this essential nutrient are removed by crops, livestock, gaseous emission, leaching, and offsite transport [1, 2]. Due to the deficiency in soil nitrogen, most agricultural systems require nitrogen input. Nitrogen fertilizers are, therefore, critical for maintaining crop yields. The increase in food production necessary for sustaining the needs of a growing world population will require increasing amounts of nitrogen fertilization [1, 2, 3]. As cultivation and fertilization increase throughout the world, more reactive nitrogen is being added to the environment. Although nitrogen is a nutrient, it is also a pollutant. Part of the nitrogen input by fertilizers is leached as nitrate, emitted as nitrous oxide or ammonia, or transported as runoff. The increase of these reactive forms of nitrogen in the environment has contributed to a cascade of effects, including acidification of aquatic and soil systems, eutrophication of surface waters, hypoxia, groundwater and air pollution, decreased biological diversity, and reduced forest and crop production [5, 6, 7] The loss of nitrogen from the soil of crop systems results in economic loss. For instance, it was estimated at one point that approximately 33% of the nitrogen fertilizer used for cereal crops was used efficiently or was actually used by these crops worldwide, and the 67% of nitrogen fertilizer that was lost equated to an economic loss of 15.9 billion US dollars worldwide. The efficiency of nitrogen fertilizer use must be improved to increase crop production, diminish the negative impacts of nitrogen pollution on the environment, and reduce economic loss [1]. In order to increase nitrogen use efficiencies, further investigations into the factors influencing nitrogen loss are necessary. With as much as 30% [8] of applied nitrogen being lost to ammonia volatilization, many studies [9 - 14] have been performed to understand the factors and processes that

1 contribute to emission of NH3. Understanding the volatilization process will enable the development of reliable methods for decreasing ammonia volatilization [15]. To better understand the ammonia volatilization process, models [9, 15, 16] have been developed

to simulate NH3 volatilization based on physical and chemical characteristics and processes. Mechanistic models of ammonia volatilization, particularly from fields to which slurry has been applied, are reviewed in Chapter II. An increase in the world’s population and the world’s need for nitrogen fertilizers will most likely lead to an increase in the production and use of industrially produced fertilizers. Ammonia and fertilizers made from ammonia, such as urea, ammonium nitrate and ammonium sulfate, comprise a large percentage of the total amount of nitrogen fertilizer used in agriculture. About 85% of industrially produced ammonia is used to make fertilizers [17]. Each year more than a hundred million tons of ammonia are produced through the Haber-Bosch process [18, 19]. It has been estimated that about 40% of the world’s population is sustained by fertilizer made from the ammonia produced by this process and that the source of between 40 to 60 percent of the nitrogen in the human body is from this ammonia [18]. In the Haber-Bosch process, severe temperatures, as o high as 400 C, and pressures of several hundred atmospheres, and a catalyst are used to reduce dinitrogen to ammonia [20]. Each year about one percent of the world’s total energy supply is consumed to produce the dihydrogen gas, high temperatures, and high pressures needed for this process [21]. In order to cut the large amounts of energy, and thus the cost and quantities of fossil fuels required to obtain the high temperatures and pressures of the Haber-Bosch process, scientists have been searching for a way to

catalyze the reduction of N2 at lower temperatures and pressures. Chapter III is devoted to a short review of the Haber-Bosch process and of other catalytic ammonia synthesis systems. In Chapters VI - VIII, high level ab initio electronic structure calculations, described in Chapter IV, are used to study the effectiveness of the boron cation, boron dihydride cation, and beryllium dihydride to activate N2 and reduce it to ammonia. A comparison of these three catalytic systems is

2 given in Chapter IX, as well as a comparison between these systems and the systems discussed in Chapter III.

3 1.1 References

[1] Delgado, J. A. J. Soil Water Conserv. 2002, 57, 387. [2] Tabachow, R. M.; Peirce, J. J.; Richter, D. D. Environ. Eng. Sci. 2001, 18, 81. [3] Follett, R. F. and Delgado, J. A. J. Soil Water Conserv. 2002, 57, 402. [4] Igarashi, R. Y.; Seefeldt, L. C. Crit. Rev. in Biochem. Mol. Biol. 2003, 38, 351. [5] Vitousek, P. M.; Aber, J. D.; Howarth, R. W.; Likens, G. E.; Matson, P.A.; Schindler, D. W.; Schlesinger, W. H.; and Tilman, D. G. Eco. Appl. 1997, 7, 737. [6] Vitousek, P. and Field, C. B. Input/Output Balances and Nitrogen Limitation in Terrestrial Ecosystems in Global Biogeochemical Cycles in the Climate System, edited by Schulze, E. Academic Press, Orlando, 2001, 217. [7] Mosier, A. R.; Bleken, M. A.; Chaiwanakupt, P.; Ellis, E. C.; Freney, J. R.; Howarth, R. B.; Matson, P. A.; Minami, K.; Naylor, R.; Weeks, K. N.; Zhu, Z-L. Biogeochem. 2002, 57, 477. [8] Kirk, G. J. D. and Nye, P. H. J. Soil Sci. 1991, 42, 103. [9] Sommer, S. G.; Génermont, S.; Cellier, P.; Hutchings, N.J.; Olesen, J. E.; Morvan, T. Europ. J. Agron. 2003, 19, 465. [10] Sommer, S. G.; Hutchings, N. J. Europ. J. Agron. 2001, 15, 1. [11] He, Z. L.; Alva, A. K.; Calvert, D. V.; Banks, D. J. Soil Sci. 1999, 164, 750. [12] Sommer, S. G.; Olesen, J. E.; Christensen, B. T. J. Agr. Sci. 1991, 117, 91. [13] Huijsmans, J. F. M.; Hol, J. M. G.; Hendriks, M. M. W. B. Neth. J. Agr. Sci. 2001, 49, 323. [14] Sommer, S. G.; Hansen, M. N.; Søgaard, H. T. Biosys. Eng. 2004, 88, 359. [15] Génermont, S.; Cellier, P. Agricultural and Forest Meteorology. 1997. 88, 145. [16] Ni, J. J. Agric. Eng. Res. 1999, 72, 1. [17] Appl, Max. Ammonia: Principles and Industrial Practice. Weinheim, Germany. 1999. 245. [18] Fryzuk, M. D. Nature. 2004. 427, 498. [19] Pool, J. A.; Lobkovsky, E.; Chirik, P. J. Nature. 2004, 427, 527. [20] Leigh, G. J. Science, 2003. 302, 55. [21] Smith, B. E. Science. 2002, 297, 1654.

4 CHAPTER II A REVIEW OF THE MECHANISTIC MODELS OF AMMONIA EMISSION FROM FIELD-APPLIED SLURRY

2.1 Introduction Ammonia volatilization from fertilizer is a major source of nitrogen loss from the soil of crop systems and is also a major source of atmospheric ammonia [1, 2, 3]. Although the volatilized ammonia is deposited on plants and soils that are fairly close to the source of the volatilized ammonia for the most part, some of the volatilized ammonia combines readily with nitrate and sulfate in the atmosphere to form particulates [1, 4]. Particulate formation prolongs the existence of ammonia, nitrate, and sulfate in the atmosphere and thus effects the geographical distribution of acidic depositions [4]. Ammonia contributes largely to soil acidification and water eutrophication [1]. Therefore, understanding the mechanisms that control ammonia volatilization is necessary [2]. Models can be used to study the chemical and physical factors and mechanisms that influence ammonia volatilization, to predict ammonia volatilization potential in relation to these factors and mechanisms, and to interpret the results of experiments [2, 5]. Empirical models, in which measured data are correlated statistically, have been developed to predict ammonia volatilization based on a few or several factors [6]. Empirical models are simple in structure, easy to use in estimating the ammonia volatilization potential in relation to a few given factors, and can explain a considerable amount of the variance in the data [2, 6]. However, empirical models often will give improbable results for combinations of data that are valid [2]. Also, empirical models fail to capture the complexity of mechanisms that control ammonia volatilizations, are not reliable for a wide range of conditions, and contribute very little to an understanding of the chemical and physical mechanisms of ammonia volatilization [2, 6]. Mechanistic models of ammonia volatilization, to some extent, capture the complexity of the mechanisms that control ammonia volatilizations and thus can be used

5 for a wider range of conditions. Also, mechanistic models greatly contribute to an understanding of the chemical and physical mechanisms of ammonia volatilization as well as provide a quantitative description of ammonia volatilization. However, some of the significant processes of ammonia volatilization are still difficult to describe in mechanistic models [2]. Also, because the amount of input data that are required in mechanistic models is large and often many of the values required in the input of these models are unknown, these models are not suitable for use in decision support systems that are used by farmers, advisors, or policy makers [2]. Thus, models that are hybrids between empirical and mechanistic models appear to be more useful because the demands for input data would be reduced while the reliability of model predictions over a wide range of conditions would be greater than that of empirical models [2]. However, development of these kinds of models still requires an understanding of the mechanisms controlling ammonia volatilization. In this chapter, mechanistic models of ammonia volatilization from field-applied slurry will be reviewed. These models are based on chemical and physical processes of ammonia volatilization such as the diffusion mass transfer of ammonia in slurry, the chemistry of ammonia in soil solution, and the convective mass transfer of gaseous ammonia from the soil or slurry surface into the free air stream [6].

2.2 Core Equation for Ammonia Volatilization Volatilization of ammonia from the soil or slurry surface is driven by the gradient between the concentration of ammonia at the surface of the slurry or soil, denoted as

[NH3,g], and the concentration of ammonia in the atmosphere, denoted as [NH3,a], above the field at a height where the concentration is unaffected by volatilization from the slurry or soil surface [1, 2, 6]. This height is dependent upon meteorological conditions [2]. The

flux of ammonia volatilization, Fv, is essentially a function of the convective mass

transfer or transport coefficient, denoted as hm, [NH3,g], and [NH3,a]:

Fv = hm([NH3,g] - [NH3,a]) [2, 6]. (2.1)

6 Therefore, in order to model ammonia volatilization, the ammonia concentration or partial pressure in the air above the field must be input and the convective mass transfer coefficient and the ammonia concentration or partial pressure at the surface must be determined [6]. As the symbols that represent the various variables and constants vary between different models, a set of symbols have been chosen to represent the various variables and constants throughout this review. For a compiled list of these symbols in the order in which they appear in the review, see Table 2.1.

2.3 Boundary Layer Theory Several theories have been proposed for interphase transport in systems involving many components, including: “Film theory”, “Penetration theory”, “Two-film theory”, and “Boundary layer theory” [6]. Of these theories, the “Boundary layer theory” has been applied in models of ammonia volatilization from field applied slurry. Based upon the boundary layer theory, volatilization of ammonia from the surface can be thought of as a two-step process [2, 6]. In the first step, the applied slurry infiltrates into the soil and in the second step ammonia volatilizes from the infiltrated slurry [2]. During the first step, different fractions of the slurry are separated. The liquid fractions of the slurry infiltrate the soil while the solid fractions remain at the soil surface unless the slurry is ploughed into the soil [2]. If any volatilization occurs during this first step, it is dependent upon the characteristics of the slurry and the processes of atmospheric transport [2]. In the second step, ammonia is volatilized from the soil surface or from within the soil surface through a pseudo-laminar boundary layer and an internal boundary layer [2]. Also in the second step, the infiltrated slurry can either be driven downward by rain or irrigation water or drawn upwards by evaporation [2]. Because the slurry has infiltrated the soil in the first step, ammonia volatilization is dependent upon the interaction between the slurry and the soil and not just upon the slurry in the second step [2]. Soil microbial processes also become important as time progresses [2]. The pseudo-laminar boundary layer is just above the soil surface [2]. This layer is not fully laminar because the description of the transfer process combines the

7 characteristics of the turbulence of the surface boundary layer and of molecular diffusion [2]. The internal boundary layer is just above the pseudo-laminar boundary layer and is the part of the atmosphere that is affected by the applied slurry [2]. The depth, δ, of this layer has been estimated using the following equation:

0.875 δ = 0.334zo(x/z 0) (2.2)

where x is the distance from the leading edge of the slurry-treated area in the direction of

the wind and z 0 is the aerodynamic roughness length for momentum [2, 5]. Another layer of the boundary layer theory is the surface boundary layer. This layer starts at the soil

surface and goes up to about one-tenth of the internal boundary layer. The depth, δs, of this layer has been described by the following equation:

2 δs{ln(δs/z 0) – 1} = κ x (2.3)

where κ is the von Karman constant (κ = 0.4(-)) [5].

2.4 Estimation of the Convective Mass Transfer Coefficient 2.4.1 Resistance Approach Another way to estimate the convective mass transfer coefficient is to use a resistance approach, 1 hm = ++ rrr cba (2.4)

where ra is the resistance in the surface boundary layer, rb is the resistance in the pseudo-

laminary boundary layer, and rc is the resistance within the crop canopy and the surface itself [2, 5, 7]. The models of van der Molen et al. [5] and Sommer and Olesen [7] both use the resistance approach to estimate the convective mass transfer coefficient. The

8 aerodynamic resistance, ra, relates to the transport of ammonia via atmospheric turbulence [2]. As can be seen in Table 2.2, the aerodynamic resistance can be calculated several different ways. One such method for calculating ra is to use the Monin-Obukhov theory,

⎛ z ⎞ ⎛ z ⎞ ψ ⎜ ⎟ − ψ ⎜ ⎟ ⎛ u(z) ⎞ H L M L )z(r = ⎜ ⎟ − ⎝ ⎠ ⎝ ⎠ a ⎜ 2 ⎟ κu ⎝ u* ⎠ * [2]. (2.5)

In this equation, u(z) is the wind velocity at height z, which z is the height above ground, u* is the friction wind velocity, ψH is the stability correction for heat, ψM is the stability correction for momentum, and L is the Monin-Obukhov length [2]. The displacement height, z, is relative to the zero plane displacement height, which is between ½ and ¾ of the vegetation height. The Monin-Obukhov length measures the thermal stability of the atmosphere, where L is positive under stable conditions and negative under unstable conditions [2]. Thermal conditions are stable when the temperature of the surface is lower than the temperature of the air [2]. Under unstable conditions, the stability correction for momentum is much smaller than that for heat, such that equation 2.5 may be reformulated to

⎛ z ⎞ z ⎜ ⎟ ⎛ ⎞ ln⎜ ⎟ − ψM ⎜ ⎟ ⎝ z0 ⎠ ⎝ L ⎠ a )z(r = κu* [2, 5]. (2.6)

Under neutral conditions, the heat stability correction becomes zero [2]. The resulting equation is very similar to the equation used for aerodynamic resistance by van der Molen et al. In the van der Molen et al. ammonia volatilization model, the aerodynamic resistance is calculated using the following equation:

ra(x) = ln(δs/z 0)/{κu*} (2.7)

9 where δs is the depth of the surface boundary layer [5]. Sommer and Olesen calculate the aerodynamic resistance using the following equation:

⎛ l d- ⎞ ln⎜ ⎟ ⎝ z0 ⎠ a t)(r = ζ κu* (2.8) where l is the height of the internal boundary layer, d is the zero plane displacement, and ζ is a correction for the atmospheric stability [7]. The internal boundary layer height is calculated [7] using

2 l{ln[(l-d)/z 0]- l} = κ x (2.9)

In this equation, the roughness length, z 0, and the zero plane displacement, d, are both functions of h, the crop or weed canopy height [7],

zo = 0.1h (2.10) d = 0.6h (2.11)

For bare soils, zo is 1mm and d is zero [7]. The stability correction for the atmospheric stability is calculated using the equations listed in Table 2.2. As can be seen in Table 2.2, all the aerodynamic resistance functions are functions of friction velocity, the von Karman constant, and height. Most of these functions are also dependent upon the aerodynamic roughness length for momentum.

Resistance in the pseudo-laminar boundary layer, rb, may be estimated using an equation that is similar to equations 2.7 and 2.8. The length ratio of δs or l-d to z 0 is replaced by a ratio of z 0 to z 0c, where the pseudo-laminar boundary layer begins at z 0c, the height where the ammonia concentration is equal to the ammonia concentration at

10 the surface or the roughness length of ammonia concentration, and ends at z 0. van der Molen et al. calculate the resistance of the pseudo-laminar boundary layer using

rb = ln(z 0/z 0c)/{κu*} (2.14)

where the ratio of z 0 and z 0c is estimated to be about 10, which means that

rb ~ 5.8/u* [5]. (2.15)

On the other hand, Sommer and Olesen calculate the resistance of the pseudo-laminar boundary layer as -0.67 rb = 6.2u* [7]. (2.16)

According to van der Molen et al., diffusion processes occuring within the soil and slurry layers control the resistance of the surface, rc [5]. The rate of diffusion, JD(t) is defined by

[TAN] [TAN]- ][NH-][NH tJ = D)( avgaq, aq + D avgg,3, g3, D aq 3 g,NH lc lc (2.17)

where Daq and DNH3,g are the coefficients for aqueous and gaseous diffusion, respectively, of ammoniacal nitrogen, [TAN]aq,avg and [NH3,g,avg] are the average ammoniacal nitrogen concentrations of the aqueous and gaseous phases in the soil, respectively, [TAN]aq and

[NH3,g] are the concentrations of ammoniacal nitrogen of the same phases at the surface of the soil, and lc is the average distance between the surface and the furthest point that ammoniacal nitrogen has traveled in the soil [5]. Ammoniacal nitrogen includes ammonia + and ammonium, TAN or total ammoniacal nitrogen = NH3 + NH4 [2]. Based on Henry’s law as defined by van der Molen et al., which is

11 KH = [NH3,aq]/[NH3,g,soil] (2.18)

where KH is the Henry’s law constant, [NH3,aq] is the concentration of ammonia in the soil solution, and [NH3,g,soil] is the concentration of ammonia in the soil gaseous phase, equation 2.17 can be rearranged to

][NH-][NH tJ += )DKD()( avgg,3, g3, D 3 g,NHHaq lc . (2.19)

By definition, Jd(t) is a function of rc and

Jd(t) = (1/rc)([NH3,g,avg] – [NH3,g]) (2.20)

The following equation is a result of the combination of equations 2.19 and 2.20 [5]:

rc = lc/(DaqKH + DNH3,g) (2.21)

where lc is estimated to be 0.5Ll, the Henry’s law constant is calculated using

-1 logKH = -1.69 + 1477.7T , (2.22)

and Daq and Dg are calculated using the equations listed in Table 2.2. In the model of Sommer and Olesen, the resistance of the slurry and soil surface as well as that of the crop canopy is estimated using

rc = β0 + β1h + β2(1-θ) [7]. (2.23)

In this equation, β0, β1, and β2 are empirical constants that are estimated from experimental data including different values of surface pH [7]. This equation is also a

12 function of the canopy height, h, and the water content of the slurry and soil surface layer, θ [7].

2.4.2 Advection Model With the exception of the equations for aerodynamic resistance, the models of van der Molen et al. [5] and Sommer and Olesen [7] are one dimensional in that they only account for height and do not account for the distance from the leading edge in the wind direction of the field. These one-dimensional models are only suitable for small plots, and require a large number of parameters or input data that must be measured specifically [1]. These problems and others that are associated with one-dimensional models can be avoided by using an advection model, in which concentration and the mass transfer coefficient are functions of both height and the distance of the field [2]. The volatilization models of Génermont and Cellier [1] and Wu et al. [3] both use advection models.

Génermont and Cellier calculate hm using

-bi hm = aiκu*(0.3X/zo) (2.24)

where X is the length of the field in the wind direction [1]. Constants ai and bi depend on the ratio of x/zo [1]. The values for ai and bi are given in Table 2.2. In the Wu et al. model, the mass transfer coefficient is calculated using

5/4 3/1 ⎛ θ ⎞ D air,NH ⎛ xu ⎞ ⎛ ν ⎞ h = ⎜ 0 ⎟ 3 ⎜ ∞ ⎟ ⎜ ⎟ m ⎜ φ ⎟ x ν ⎜ D ⎟ (2.25) ⎝ ⎠ ⎝ ⎠ ⎝ 3 air,NH ⎠

where θ is the soil water content at the surface, φ is the porosity of the soil, Lw is the width of the field strip, in the wind direction, that has been irrigated, u∞ is the wind speed across the irrigated strip, ν is the kinematic viscosity of the air, and D is the NH3,air diffusion coefficient of ammonia in free air. The D is estimated using NH3,air

13

Ref (T-TRef) DNH3,air = DNH3,air 1.03 (2.26) where D Ref is the reference value for the diffusion coefficient of gaseous ammonia, NH3,air -5 2 -1 which is 2.8 * 10 m s , T is the temperature, and TRef is the reference temperature [3].

2.5 Slurry and Soil Chemistry Ammonia volatilization is dependent on the concentration of gaseous ammonia at the surface of the slurry and soil, [NH3,g], and [NH3,g] is dependent on the speciation, or distribution of ammonium and ammonia, and concentration of the total ammoniacal nitrogen in slurry and soil [2]. Most of the ammoniacal nitrogen in slurry comes from urea in faeces [2]. The amount of urea and faecal nitrogen in slurry is affected by the species and diet of the animals from which it comes [2]. Urea quickly hydrolizes to ammoniacal nitrogen

Urease + - - CO(NH3)2 + 3H2O 2NH4 + HCO3 + OH [2, 10]. (2.27)

So, slurry is stored prior to application [2]. However, part of the ammoniacal nitrogen in slurry is still volatilized prior to application [2]. Consequently, the concentration of TAN in slurry may vary considerably, depending on slurry management and storage [2]. Speciation of TAN in slurry and soil depends on pH [2]. In slurry and soil solution, the equilibrium between ammonium and ammonia is

+ + NH4 (aq) + H2O NH3(aq) + H3O (2.28)

If the activity coefficients of all the species of involved in this reaction are assumed to be equal to unity, the concentrations of aqueous ammonium and ammonia in slurry and soil solution can be calculated using

14 [NH3,aq] Ka = [NH + ] [H O+] 4 ,aq 3 (2.29)

+ + where [NH4 ,aq], [NH3,aq], and [H3O ] are the concentrations of ammonium, ammonia, and hydronium ion in soil/slurry solution, respectively, and Ka is the equilibrium constant [2, 6]. The concentration of the hydronium ion is related to pH,

+ -pH [H3O ] = 10 . (2.30)

In the Sommer and Olesen model, the correlation between surface pH and the surface water content, θ, is the basis for the calculation of pH, where

pH = 7.87 – 0.52(ln θ)2 [7]. (2.31)

Génermont and Cellier simulate the change in pH in the soil over time, but the approach used did not take into account the Based on this equation, a decrease in soil water results + in the decline of surface pH and an increase in [H3O ] [7]. The equilibrium constant is temperature dependent and can be calculated several different ways, see Table 2.3. Most of the models use an empirical equation, the first equation listed in Table 2.3, to calculate Ka. Génermont and Cellier [1], Wu et al. [3], and Sommer and Olesen [7] all report that this equation is from Beutier and Renon [8]. However, the coefficients of this equation do not match up with those listed in ‘Table AII’ of the Beutier and Renon paper. In the model of van der Molen et al, Ka is calculated using an equation from Hales and Drewes [9], the last equation in Table 2.3. Based on the liquid-gas equilibrium of ammonia,

NH3(aq) NH3(g), (2.32)

15 the concentration of gaseous ammonia at the surface of the soil can be calculated from Henry’s law. The different Henry’s law equations and constants that have been reported in the literature are listed in Table 2.4. Equations 2.29 and 2.30 and the first equation in

Table 2.4 are combined in the Wu et al. model to calculate [NH3,g] from the concentration ammonium in slurry and in soil solution,

+ -pH [NH3,g] = KaKH[NH4 ,aq]/10 [3]. (2.33)

+ Since TAN = NH3 + NH4 , equation 2.29 can be reformulated using the equations in Table 2.4 to so that the concentration of gaseous ammonia at the surface of the slurry and soil can be calculated from the concentration of total ammoniacal nitrogen in slurry and in soil. In the models of Génermont and Cellier and Sommer and Olesen, [NH3,aq] is calculated using

TAN][K ][NH = H g3, + + )K]OH[(1 (2.34) a3 where [TAN] is the concentration of total ammoniacal nitrogen in slurry and in soil solution [1, 2, and 7]. In the van der Molen et al. model, [NH3,aq] is calculated using

TAN][ ][NH = g3, + + )K]OH[(1K a3H [5]. (2.35)

2.6 Convection and Diffusion in Soil The concentration of the gaseous ammonia at the surface, before slurry infiltration, is dependent on the concentration of TAN in the slurry. However, as the slurry infiltrates the soil, the ammonium and ammonia species in the slurry diffuse into the soil solution or adsorb to the soil, and ammonia is volatilized, the concentration of the gaseous ammonia at the surface becomes a function of the concentration of TAN in the

16 soil. In the soil, the concentration of TAN is the sum of the concentrations of adsorbed, aqueous, and gaseous ammonium and ammonia species. In the Wu et al. [3] and van der Molen et al. [5] models, the concentration of TAN in the soil is dependent on dry bulk density, ρb, soil water content, θ, porosity, φ, and adsorption,

[TAN] = Lc(ρb[TAN]s + θ[TAN]aq + (θ – φ)[NH3,g]), (2.36)

where Lc is the thickness of the soil compartment and is only in the van der Molen et al.

[TAN] function, [TAN]s is the total concentration of ammoniacal nitrogen that has adsorbed to the soil solid, and [TAN]aq is the total concentration of ammoniacal nitrogen + that is in the soil solution, [TAN]aq = [NH4 ,aq]+[NH3,aq] [3, 5]. [TAN]s is equal to the + + sum of [NH4 ,s] and [NH3,s] in the Wu et al. model [3], but is only equal to [NH4 ,s] in the van der Molen et al. model [5]. The calculation the total concentration of TAN in the soil in the Génermont and Cellier model is very similar to the calculation of [TAN] in the soil in the Wu et al. [3] and van der Molen et al. [5] models. However, the Génermont and Cellier model does not account for ammonical nitrogen adsorbed by the soil, where the dry bulk density and the concentration of ammonical nitrogen that has adsorbed to the soil solid are not included [1]. In the Sommer and Olesen model, the concentration of TAN in soil is determined empirically by measuring the [TAN] in the soil before and after a measuring period and interpolating linearly between measuring times [7]. Concentration of an adsorbed species is related to the concentration of the species in the aqueous phase by a linear isotherm, [3] and [5], a Freundlich isotherm, [1, 5], or a Langmuir isotherm [5]:

[species,s] = as[species,aq] (2.37)

bs [species,s] = as[species,aq] (2.38)

[species,s] = asbs[species,aq]/(1 + bs[species,aq]), (2.39)

17 where [species,s] and [species,aq] are the concentrations of ammonium or ammonia in the soil solid and soil aqueous phases, respectively, and as and bs are constants [1, 3, 5]. As ammonia is volatilized from the slurry and soil surface a concentration gradient develops between the surface layer and the layers of the soil [6]. This gradient drives TAN convection and diffusion in the soil [6]. Thus, the concentration of TAN in the soil is also related to convection and diffusion of ammoniacal nitrogen in the soil. In the Génermont and Cellier [1], Wu et al. [3], and van der Molen [5] models, convection and aqueous and gaseous ammoniacal nitrogen diffusion are included, whereas the Sommer and Olesen model [7] does not account for convection or diffusion. In all of the three models that account for convection and diffusion, Fick’s second law is used to calculate the convection and diffusion of TAN in the soil. Because Fick’s first law only applies to steady state conditions [11], Fick’s second law, which applies to non-steady state conditions and is a combination of Fick’s first law and the continuity equation [11, 12], is used. From Fick’s second law, the general equation used for convection and diffusion in these models is

∂[TAN] ∂J = t ∂t ∂zs , (2.40)

where t is time, Jt is the total flux of ammoniacal nitrogen through the soil, and zs is the depth of the ammonical nitrogen front starting from the surface [3, 5]. Wu et al. and Van der Molen et al. combine the gaseous, aqueous, and solid phases in equation 2.40 and solve equation 2.40 numerically using implicit finite difference schemes [3, 5]. However, Génermont and Cellier [1] separate equation 2.40 into two equations consisting of the aqueous and gaseous phases, do not include the soil solid phase in these two equations, and use an interative procedure to solve these equations. Van der Molen et al. [5] describe the finite difference scheme used to solve equation 2.40 in their model. In the van der Molen et al. model [5], the right and left sides of equation 2.40 are treated separately, where

18

∂[TAN] Δ[TAN] = ∂t Δt (2.41) and the right side is integrated such that

∂J Δ ΔJJ t = t = t ∂ s Δ s Lzz c . (2.42)

The Δ in equations 2.41 and 2.42 indicates the difference between [TAN], time, flux, and compartment depth before and after a time step has occurred. Also, the soil through which ammoniacal nitrogen travels is split into two compartments in the van der Molen et al. model. Ammonia volatilization takes place in the top compartment, which has a depth of L1, while no ammonia volatilization takes place in the second compartment, which acts as a reservoir and has a depth of L2 [5]. The bottom of the second compartment is the ammoniacal nitrogen front in the soil.

The total flux of ammoniacal nitrogen, Jt, is the sum of convective and diffusive fluxes,

Jt = Jc + Jd,aq + Jd,g, (2.43)

where Jc is the convective flux, Jd,aq is the aqueous diffusive flux, and Jd,g is the gaseous diffusive flux [5]. Convective flux is a function of the flux density of the soil solution, Jw, and the sum of the concentrations of the aqueous ammoniacal species, [TAN]aq,

Jc = Jw[TAN] aq [1, 3, 5]. (2.44)

As can be seen in Table 2.5, the flux density of the soil solution is calculated differently in the Génermont and Cellier [1] and van der Molen et al. [5] models and Wu et al. do not

19 include a description of how Jw is calculated. The aqueous and gaseous diffusive fluxes are functions of the aqueous and gaseous diffusion coefficients, respectively, the depth of ammoniacal nitrogen diffusion in the soil, and of the total concentration of the aqueous and gaseous ammoniacal species, respectively, see Table 2.5. Van der Molen et al. [5] describe aqueous and gaseous diffusive flux in terms of the finite difference scheme used to solve for these fluxes, where Δ[TAN]aq and Δ[NH3,g] are the differences between the aqueous and gaseous concentrations of ammonical nitrogen in the top compartment and those of the bottom compartment and Ld is the average of the lengths of the two compartments. The equations for convective and diffusive flux are then combined with equation 2.40 or the mass balance equation of ammoniacal nitrogen in the soil system [3] and the results of this combination are given in Table 2.5. Once the water and heat submodel equations are solved numerically by using implicit finite difference schemes or iterative procedures, the concentration of gaseous ammonia is calculated numerically from the mass balance equations for ammoniacal nitrogen in soil given in Table 2.6.

2.7 Summary and Conclusions Because volatilization of ammonia from the slurry or soil surface is driven by a concentration gradient, all of the models have very similar cores, where the core equation of ammonia volatilization flux, Fv, is a function of the convective mass transfer coefficient, the concentration of gaseous ammonia at the surface, [NH3,g], and the concentration of ammonia in the atmosphere, [NH3,a]. The convective mass transfer coefficient is generally expressed as a function of friction wind velocity, aerodynamic roughness length, the distance ammonia is estimated to travel in the air, and in the models employing the advection model method, the length of the field. The one-dimensional resistance models developed by van der Molen et al. [5] and Sommer and Olesen [7] require a large number of parameters or input data that must be measured specifically and slurry infilitration must be calibrated before each use [1]. Also, the van der Molen et al. model [5] is only suitable for small plots [1]. The two dimensional models of Génermont and Cellier [1] and Wu et al. [3] avoid these problems by using an advection model

20 method and using functions that are dependent on both the height of ammonia volatilization and the field length [1, 2]. The concentration of gaseous ammonia at the surface is dependent on pH, soil water content, porosity, bulk density, flux density, and concentration of total ammoniacal nitrogen of the slurry and soil. [NH3,g] is dependent on physical and chemical processes including: adsorption, convection, and diffusion. Also,

[NH3,g] is a function of the equilibrium constant, Henry’s Law constant, diffusion coefficients of ammoniacal nitrogen in the aqueous and gaseous phases in the soil, diffusion coefficients of ammoniacal nitrogen in free water and free air, time, and the depth of ammonia diffusion into the soil. Based on analysis of the sensitivity of the amount of ammonia volatilization predicted by the models to parameters of ammoniacal nitrogen transfer in the soil and atmosphere, pH, temperature, saturated hydraulic conductivity, roughness length, and wind speed are the most sensitive factors and significantly affect the simulated amount of ammonia volatilization [1, 3, 7]. These most sensitive factors as well as other sensitive factors must be input either from experimental data or from simulation submodels. Because most of these factors are required to be input in the van der Molen et al. [5] and Sommer and Olesen [7] models, these models would not be as useful as decision support systems as the Génermont and Cellier and Wu et al. models, which simulate several factors in submodels. However, the Génermont and Cellier and Wu et al. models also require a considerable amount of input data. In order to cut down on the amount of input data and develop easy to use decision support systems for farmers, policy makers, etc., hybrid models consisting of submodels using these mechanistic models and empirical models could be developed. In these hybrid models, farmers or policy makers could select climate, soil, and fertilizer type, and the amount of fertilizer and based on these selections the input data for the mechanistic submodels of ammonia volatilization could be determined from empirical submodels. The models reviewed in this chapter could be also used in models that simulate the dynamics of nitrogen in soil and plant systems, which provide useful estimates for managing nitrogen fertilizers [1].

21 Table 2.1: Symbols.

Calculated Symbol Notation Equation Unit or Input -2 -1 Fv Flux of ammonia volatilization 2.1 μg, g, or kg m s Calculated -1 hm Convective mass transfer or transport coefficient m s Calculated -3 [NH3,g] Concentration of ammonia at the surface of the slurry μg, g, or kg m , Calculated or soil mol L-1, or atm -3 [NH3,a] Concentration of ammonia in the atmosphere above the μg, g, or kg m or Input field at a height where the concentration is unaffected -1

22 mol L by volatilization from the slurry covered soil surface

δ Depth of the internal boundary layer 2.2 m Calculated

z0 Aerodynamic roughness length for momentum m Input x Distance from the leading edge of the slurry-treated m Input area in the direction of the wind

δs Depth of the surface boundary layer 2.3 m Calculated κ von Karman constant ( = 0.4) Dimensionless Input

Cd Drag coefficient 2.3 Dimensionless Input u Wind velocity m s-1 Input -1 ra Aerodynamic resistance 2.4, 2.5 - 2.8 s m Calculated -1 rb Resistance in the pseudo-laminary boundary layer 2.4, 2.14 - 2.16 s m Calculated -1 rc Resistance within the crop canopy and the surface itself 2.4 and 2.21 s m Calculated z Height above ground or displacement height m Calculated -1 u* Friction wind velocity m s Input Table 2.1: Continued.

Calculated Symbol Notation Equation Unit or Input

ψH Stability correction for heat 2.5 Dimensionless Calculated

ψM Stability correction for momentum 2.5 Dimensionless Calculated L Monin-Obukhov length 2.5 m Calculated l Height of the internal boundary layer 2.8 and 2.9 m Calculated d Zero plane displacement 2.8, 2.9, 2.11 m Calculated ζ Correction for the atmospheric stability 2.8 & Table 2.2 Dimensionless Calculated

23 h Crop or weed canopy height 2.10 and 2.11 m Input

z 0c Height where the ammonia concentration is equal to 2.14 & Table 2.2 m Input the ammonia concentration at the surface or the roughness length of ammonia concentration -2 -1 JD(t) Rate of Diffusion 2.17 μg m s Calculated 2 -1 Daq Diffusion coefficient of aqueous ammoniacal nitrogen m s Calculated in the soil 2 -1 DNH3,g Diffusion coefficient of ammonia in the gaseous phase m s Calculated of the soil -3 [TAN]aq,avg Average ammoniacal nitrogen concentration of the 2.17 μg m Calculated aqueous phase of the slurry and/or soil -3 [NH3,g,avg] Average ammoniacal nitrogen concentration of the 2.17 μg m Calculated gaseous phase of the slurry and/or soil -3 -1 [TAN]aq Ammoniacal nitrogen concentration of the aqueous 2.17 μg m or mol L Input or phase of the slurry and/or soil Calculated Table 2.1: Continued.

Calculated Symbol Notation Equation Unit or Input

l c Average distance between the surface and the furthest 2.17 m Calculated point that ammoniacal nitrogen has traveled in the soil -1 KH Henry’s law constant atm L mol Calculated -3 -1 [NH3,aq] Concentration of ammonia in the slurry and/or soil 2.18 μg m or mol L Calculated solution -3 -1 [NH3,g,soil] Concentration of ammonia in the soil gaseous phase 2.18 μg m or mol L Calculated o 24 T Absolute temperature 2.22 C or K Input

β0, β1, β2 Empirical constants 2.23 Calculated θ Water content of the soil 2.23 m3 m-3 Initial value is input, rest of values are calculated

ai, bi Coefficients of advection model 2.24 Dimensionless Input X Field length 2.24 m Input 2.25 3 -3 Calculated φ Porosity of the soil m m D 2 -1 NH3,air Diffusion coefficient of ammonia in free air m s Calculated 3 -3 θ0 Water content at the soil surface 2.25 m m Initial value is input, rest of values are calculated -1 u∞ Wind speed across the irrigated strip 2.25 ms Input Table 2.1: Continued.

Calculated Symbol Notation Equation Unit or Input ν Kinematic viscosity of the air 2.25 m2 s-1 Calculated Ref 2 -1 DNH3,air Diffusion coefficient of dissolved ammonia in water at m s Calculated a reference temperature o TRef Reference temperature 2.26, Table 2.5 C or K Input Concentration of ammonium in the slurry and/or soil 2.29 μg m-3 or mol L-1 Input or + [NH4 ,aq] solution Calculated

25 Ka Equilibrium constant Dimensionless Calculated Concentration of ammonium in the slurry and/or soil 2.29 and 2.30 mol L-1 Calculated + [H3O ] solution Total concentration of ammoniacal nitrogen in the μg or kg m-3 Calculated [TAN] gaseous, aqueous, and solid phases of the soil

Lc Thickness of the soil compartment 2.36 m Input and Calculated -3 ρb Dry bulk density 2.36 kg m Input -1 [TAN]s Total concentration of ammoniacal nitrogen that has 2.36 μg or kg kg Calculated adsorbed to the soil solid + -1 [NH4 ,s] Concentration of ammonium ion adsorbed to the soil μg or kg kg Calculated solid -1 [NH3,s] Concentration of ammonia adsorbed to the soil solid μg or kg kg Calculated -1 [species,s] Concentration of an ammonium or ammonia species in 2.37 to 2.39 μg or kg kg Calculated the soil solid phase -3 [species,aq] Concentration of an ammonium or ammonia species in 2.37 to 2.39 μg or kg m Input or the soil aqueous phase Calculated Table 2.1: Continued.

Calculated Symbol Notation Equation Unit or Input

as and bs Coefficients of the adsorption isotherms 2.37 to 2.39 Dimensionless Input t Time s Input -2 -1 J t Total flux of ammoniacal nitrogen through the soil μg or kg m s Calculated

zs Depth of the ammonical nitrogen front m Calculated

L1 Depth of the top compartment m Calculated

L2 Depth of the bottom compartment m Calculated

26 -2 -1 J c Convective flux 2.43, 2.44, Table μg or kg m s Calculated 2.5 -2 -1 J d,aq Aqueous diffusive flux 2.43, Table 2.5 μg or kg m s Calculated -2 -1 J d,g Gaseous diffusive flux 2.43, Table 2.5 μg or kg m s Calculated -1 J w Flux density of the soil solution 2.44, Table 2.5 m s Calculated Ri Richardson number Table 2.2 Dimensionless Calculated g Gravitational acceleration Table 2.2 m s-2 Not Specified o Ta Air temperature Table 2.2 C or K Input o Ts Soil surface temperature Table 2.2 C or K Input -1 Kw Hydraulic conductivity of the soil Table 2.5 m s Calculated

hw Soil water pressure head Table 2.5 Dimensionless Calculated E(t) Evaporation rate Table 2.5 m s-1 Input P(t) Rainfall rate Table 2.5 m s-1 Input

Ld Diffusion length Table 2.5 m Calculated R Gas constant Table 2.5 atm L mol-1 K-1 Input Table 2.1: Continued.

Calculated Symbol Notation Equation Unit or Input

λNH4+ Limiting equivalent conductance of ammonium ions Table 2.5 Not Specified Calculated

ZNH4+ Ionic charge of ammonium ions Table 2.5 C Input F Faraday constant Table 2.5 C mol-1 Input

rNH4+ Ionic radius of ammonium ion Table 2.5 m Input

αL Dispersivity of the soil Table 2.5 m Input

τw(θ) Impedance factor of the water flow path in the soil Table 2.5 Dimensionless Calculated 27 b Pore-size distribution parameter Table 2.5 Dimensionless Calculated

f clay Mass percentage of clay Table 2.5 Not Specified Input

f fs Mass percentage of fine sand Table 2.5 Not Specified Input 2 -1 Daq,water Diffusion coefficient for aqueous ammoniacal nitrogen Table 2.5 m s Calculated in water Ref 2 -1 Daq,water Diffusion coefficient of aqueous ammoniacal nitrogen Table 2.5 m s Calculated in water at a reference temperature

τa(θ) Impedance factor of the air flow path in the soil Table 2.5 Dimensionless Calculated

as,NH4+,aq Coefficient of the adsorption isotherm of liquid-phase Table 2.5 Dimensionless Input ammonium ion

as,NH3,aq Coefficient of the adsorption isotherm of liquid-phase Table 2.5 Dimensionless Input ammonia

as,NH3,g Coefficient of the adsorption isotherm of gas-phase Table 2.5 Dimensionless Input ammonia -2 [TAN]1' Total concentration of ammoniacal nitrogen in top Table 2.5 μg m Input or compartment prior to the time step Calculated Table 2.1: Continued.

Calculated Symbol Notation Equation Unit or Input -2 [TAN]2' Total concentration of ammoniacal nitrogen in bottom Table 2.5 μg m Input or 28 compartment prior to the time step Calculated -2 S1 and S2 Rate of loss of ammonical nitrogen due to biological Table 2.5 μg m Calculated processes in a compartment V Table 2.5 μg m-2 Calculated Rate of loss of ammonical nitrogen due to volatilization s(t) Rate of loss of ammonical nitrogen due to biological Table 2.5 μg m-2 s-1 Input processes in system -2 [TAN]1 Total concentration of ammoniacal nitrogen in top Table 2.5 μg m Input or compartment prior to the time step Calculated -2 [TAN]2 Total concentration of ammoniacal nitrogen in bottom Table 2.5 μg m Input or compartment prior to the time step Calculated Table 2.2: Mass Transfer Coefficients in Ammonia Volatilization Models. a For consistency throughout the review, many of the symbols have been modified from the original citing.

Number Equations, values, remarks, and references a 1 1 hm = ++ rrr cba

ra is the aerodynamic resistance and is calculated using one of the following:

from reference [2]:

- under stable conditions

⎛ z ⎞ ⎛ z ⎞ ψ ⎜ ⎟ − ψ ⎜ ⎟ ⎛ u(z) ⎞ H L M L )z(r = ⎜ ⎟ − ⎝ ⎠ ⎝ ⎠ a ⎜ 2 ⎟ κu ⎝ u* ⎠ * - under unstable conditions

⎛ z ⎞ ⎛ z ⎞ ln ⎜ ⎟ − ψM ⎜ ⎟ ⎝ z0 ⎠ ⎝ L ⎠ a )z(r = κu*

- under neutral conditions

r a(z) = ln(z/z0)/(κu*)

from reference [5]:

ra(z) = ln(δs/zo)/(κu*)

29 Table 2.2: Continued.

Number Equations, values, remarks, and references a 1 Continued from reference [7]:

⎛ l -( d) ⎞ ln ⎜ ⎟ ⎝ z0 ⎠ a )z(r = ζ κu*

u(z) is the wind velocity at height z, u* is the friction velocity, ψH is a

stability correction function for heat, ψH is a stability correction function for momentum, z is the height above the ground or the displacement height, L in the Monin-Obukhov length, κ is the von

Karman constant, zo is the aerodynamic roughness length for momentum and in reference [7] it is equal to 0.1h , where h is the

crop or weed canopy height, δs is the height of the surface boundary layer, for reference [7] l is the height of the internal boundary layer and is calculated by using

2 l {ln[(l - d)/z 0] - l} = κ x [7],

d is the zero plane displacement and d = 0.6h [7], and in reference [7] ζ is a correction for atmospheric stability and is calculated using

⎪⎧ 1( − Ri) 2- 1.0 ≤− Ri ζ = ⎨ -0.75 ⎩⎪(1-16Ri) Ri −< 1.0

g(z - d)(T )T- R = sa i 2 Tu a

u* ⎛ d-z ⎞ u = ln ⎜ ⎟ κ ⎝ z0 ⎠

where g is the gravitational acceleration, Ta is the air temperature,

and Ts is the soil surface temperature.

30 Table 2.2: Continued.

Number Equations, values, remarks, and references a

1 Continued rb is the laminar boundary layer resistance and is estimated in one of two ways:

from reference [5]:

rb = 5.8/u*

from reference [7]:

-0.67 rb = 6.2u*

rc is the laminar boundary layer resistance and is estimated in one of two ways:

from reference [5]:

rc = 0.5Ll /(DaqKH + DNH3,g)

0.5L l is a substitute for the average distance between the furthest point that ammoniacal nitrogen has traveled in

the soil and the soil surface, KH is Henry's law constant,

and Daq and DNH3,g are coefficients for soil-liquidand soil gas diffusion of ammoniacal nitrogen, respectively. Refer

to Table 2.5 for the calculation of Daq and DNH3,g.

from reference [7]:

rc = β0 + β1h + β2(1-θ)

β0, β1, and β2 are empirical constants, h is the canopy height, and θ is the water content of the soil and slurry

31 Table 2.2: Continued.

Number Equations, values, remarks, and references a -bi 2 hm = aiκu*(0.3X/zo)

X is the field length in the wind direction [1], ai and bi are coefficients

of the advection model and vary with the x/zo ratio [2],

3 a = 0.887, b = 0.19 10≤(x/zo)<10

3 5 a = 0.665, b = 0.15 10 ≤(x/zo)≤10

From references 1 and 2

3 5/4 3/1 ⎛ θ ⎞ DNH ,air ⎛ xu ⎞ ⎛ ν ⎞ h = ⎜ 0 ⎟ 3 ⎜ ∞ ⎟ ⎜ ⎟ m ⎜ φ ⎟ x ν ⎜ D ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ NH3,air ⎠

θ0 is the soil water content at the surface, DNH3,air is the diffusion

coefficient of dissolved ammonia in water, Lw is the width of the field

strip, in the wind direction, that has been irrigated, u∞ is the wind speed across the irrigated strip, and ν is the kinematic viscosity of the air. From reference [3].

32 Table 2.3: Equilibrium or Dissociation Constants, Ka.

33 References Equations

[1], [2], [3], [7] ln(Ka) = -177.95292 - (1843.22/T) + 31.4335 ln(T) - 0.0544843T

[8] ln(Ka) = 191.97 - (8451.61/T) - 31.4335 ln(T) + 0.0162123T

-1 [5], [9] log (Ka) = -0.09018 - 2729.92T Table 2.4: Henry's Law Equations.

34 References Equations

[1], [2], [3], [7] [NH3,g] = KH[NH3,aq]

[1] ln(KH) = 160.46 - (8621/T) + 25.677 ln(T) + 0.0354T

[2], [7], [8] ln(KH) = 160.559 - (8621.06/T) - 25.6767 ln(T) + 0.035388T

[3] ln(KH) = 158.17 - (8621/T) - 25.677 ln(T) + 0.0354T

[5] [NH3,g] = [NH3,aq]/KH -1 [5] log (KH) = -1.69 + 1477.7T Table 2.5: Convective and Diffusive Flux Equations.

Comments and References Equations

Convective Flux: J c = J w[TAN]aq References [1, 3, 5] + [TAN]aq = [NH4 ,aq] + [NH3,aq]

Flux density of the soil solution:

Reference [1] ⎛ ∂ w θ)(h ⎞ Jw θ)( = -K w θ)( ⎜ ⎟ + w θ)(K ⎝ ∂z ⎠

Kw is the hydraulic conductivity and hw is the

pressure head. J w,Kw, and hw are all functions of the water content of the soil.

Reference [5] J w = E(t) - P(t)

E(t) is the evaporation rate and P(t) is the rainfall rate

Aqueous Diffusion: Reference [1] ∂[TAN]aq θ Jd, = -Daqaq ∂zs

Reference [3] ∂[TAN]aq Jd,aq = -Daq ∂zs

-1 Reference [5] J d,aq = - DaqΔ[TAN]aqLd

Ld is the diffusion length and is calculated using

Ld = (L1 + L2)*0.5

35 Table 2.5: Continued.

Comments and References Equations Diffusion coefficients of aqueous ammoniacal nitrogen in soil solution: 10/3 2 References [1, 5] Daq = (θ /φ )Daq,water

Reference [3] Daq = αL|J w| + θτw(θ)Daq,water

αL is the dispersivity of the soil, τw(θ) is the impedance factor of the water flow path in the soil and can be expressed as

⎧ θ - 0.022b ⎪ .0 45 , θ > 0.022b τw = ⎨ φ - 0.022b ⎩⎪0, θ ≤ 0.022b b is the pore-size distribution parameter and is calculated using

1 b = 2 0.303- 0.093ln(ρb -) 0.0565ln(fclay ) + 0.00003ffs

f clay and f fs are the mass percentages of clay and fine sand

Diffusion coefficients of aqueous ammoniacal nitrogen in water:

Ref (T-TRef) References [1], [3], [5] Daq,water = Daq,water 1.03

o Ref -10 2 -1 References [1], [5] At TRef = 0 C, Daq,water = 9.8*10 m s

o Ref -9 2 -1 Reference [3] At TRef = 25 C, Daq,water = 1.96*10 m s

36 Table 2.5: Continued.

Comments and References Equations Diffusion coefficients of aqueous ammoniacal nitrogen in free water continued:

2 References [1, 2] Daq,water = (RTλNH4+)/(|ZNH4+|F )

R is the gas constant, T is the temperature, λNH4+ is the limiting equivalent conductance of ammonium ions and is calculated using

r + λ 10.56 90.72++= log(Z ) + 42.95 NH 4 NH + NH + 4 4 Z + NH 4

rNH4+ is the ionic radius, ZNH4+ is ionic charge of ammonium ions, and F is the Faraday constant and is 4 -1 equal to 9.648456*10 C mol .

Note: Génermont and Cellier state that the gas constant, R, is equal to 0.831 atm L mol-1 K-1. [1] However, R is equal to 0.08206 atm L mol-1 K-1.

Gaseous Diffusion: Reference [1] ∂[NH ](φ θ)- J = -D 3,g d,g NH 3 g, ∂zs Reference [3] ∂[NH ] J = -D 3,g d,g NH3 g, ∂zs

-1 Reference [5] J d,g = - DNH3,gΔ[NH3,g]Ld

37 Table 2.5: Continued.

Comments and References Equations Diffusion coefficients of gaseous ammonia in soil air 10/3 2 References [1] and [5] DNH3,g = ((φ−θ) /φ )DNH3,air

Reference [3] DNH3,g = (φ - θ)τa(θ)DNH3,air

+ /31 b ⎛φ -θ ⎞ τa(θ) = 0.45⎜ ⎟ ⎝ φ ⎠

Diffusion coefficients of gaseous ammonia in free air: Ref (T-TRef) References [1], [3], [5] DNH3,air = DNH3,air 1.03

o Ref -5 2 -1 References [1], [5] At TRef = 25 C, DNH3,air = 1.7*10 m s

o Ref -5 2 -1 Reference [3] At TRef = 25 C, DNH3,air = 2.8*10 m s

38 Table 2.6: Mass Balance Equations of Ammonical Nitrogen in Soil.

References Equations 1 ∂([TAN] θ) ∂(J [TAN] ) ∂ ⎛ ∂[TAN] θ ⎞ aq w aq ⎜ aq ⎟ −= + ⎜Daq ⎟ ∂t ∂zs ∂zs ⎝ ∂zs ⎠

∂([NH ](φ θ)- ∂ ⎛ ∂[NH ](φ θ)- ⎞ 3,g = ⎜D 3,g ⎟ ⎜ NH3 g, ⎟ ∂t ∂zs ⎝ ∂zs ⎠

3 ∂(ρ [TAN]sb + θ[TAN]aq + φ -( θ)[NH3,g ]) ) = ∂t ∂ ⎛ ∂[TAN] ∂[NH ]⎞ ⎜- J [TAN] + Daq aq + D 3,g ⎟ ⎜ w aq NH3 g, ⎟ ∂zs ⎝ ∂zs ∂zs ⎠

By using the relationships between the component species in equations 2.29, 2.30, and 2.37 in this equation and rearranging

∂ ⎡⎛ ⎛ K ⎞ KK ⎞ ⎤ ⎜ ρ K( 1 ++ a θ + φ -( θ) da ⎟[NH + ] = ⎢⎜ db ⎜ -pH ⎟ -pH ⎟ 4 ,aq ⎥ ∂t ⎣⎝ ⎝ 10 ⎠ 10 ⎠ ⎦ + ∂ ⎡ ∂[NH ,aq ] ⎛ K ⎞ ⎤ D 4 1+− a J [NH + ] ⎢ ⎜ -pH ⎟ 4w ,aq ⎥ ∂zs ⎣⎢ ∂zs ⎝ 10 ⎠ ⎦⎥

Ka KK Ha d = aa + + as,NH ,aq + as,NH g, s,NH 4 ,aq 3 10-pH 3 10-pH

as,NH4+,aq,as,NH3,aq, and as,NH3,g are coefficients of the adsorption isotherms of liquid-phase ammonium ion, liquid-phase ammonia, and gas-phase ammonia, respectively

⎛ Ka ⎞ KK Ha aq ⎜1DD += ⎟ + DNH g, ⎝ 10 -pH ⎠ 3 10 -pH

39 Table 2.6: Mass Balance Equations of Ammonical Nitrogen in Soil.

References Equations

5 L1(ρb[NH4+,s,1] + θ[TAN]aq,1 + (θ – φ)[NH3,g,1]) =

[TAN]1' - S1 + (J c+J d,aq+J d,g)Δt - V

L2(ρb[NH4+,s,2] + θ[TAN]aq,2 + (θ – φ)[NH3,g,2]) =

[TAN]2' - S2 - (J c+J d,aq+J d,g)Δt

1 and 2 denote which compartment, the prime denotes the total concentration of ammoniacal

nitrogen prior to the time step, S1 and S2 are the rates of loss of ammonical nitrogen due to biological processes in the two different compartments and is calculated using = s)t(S 11 (t)Δt

[TAN]1 1 )t(s = s(t) [TAN]1 +[TAN] 2

= sS 22 (t)Δt

[TAN] 2 2 )t(s = s(t) [TAN]1 +[TAN] 2 s(t) is the rate of loss of ammonical nitrogen due to biological processes from the system. V is the rate of volatilization and is calculated using

V = FvΔt

40 2.8 References [1] Génermont, S.; Cellier, P. Agr. Forest Meteorol. 1997. 88, 145. [2] Sommer, S. G.; Génermont, S.; Cellier, P.; Hutchings, N.J.; Olesen, J. E.; Morvan, T. Europ. J. Agron. 2003, 19, 465. [3] Wu, J.; Nofziger, D. L.; Warren, J. G.; Hattey, J. A. Soil Sci. Soc. Am. J. 2003, 67, 1. [4] Sommer, S. G.; Hutchings, N. J. Europ. J. Agron. 2001, 15, 1. [5] Van der Molen, J.; Beljaars, A. C. M.; Chardon, W. J.; Jury, W. A.; Faassen, H. G. Neth. J. of Agr. Sci. 1990, 38, 239. [6] Ni, J. J. Agric. Eng. Res. 1999, 72. [7] Sommer, S. G.; Olesen, J.E. Atm. Env. 2000, 34, 2361. [8] Beutier, D.; Renon, H. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 220. [9] Hales, J. M.; Drewes, D. R. Atm. Env. 1979, 13, 1133. [10] Rachhpal-Singh; Nye, P. H. J. Soil Sci. 1986, 37, 9. [11] Marshall, T. J.; Holmes, J. W. Soil Physics. Cambridge University Press, New York, 1988. [12] Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena. Wiley, New York, 1960.

41 CHAPTER III CATALYTIC REDUCTION OF DINITROGEN TO FORM AMMONIA

For more than a hundred years, scientists have been challenged to reduce dinitrogen to ammonia, or to fix dinitrogen, under mild reaction conditions [1]. The chemical inertness of dinitrogen makes this task difficult. Dinitrogen is relatively inert due to the strength of its triple bond, high ionization potential, negative electron affinity, nonpolarity, and weak alkalinity [1, 2]. The dissociation energy of the triply bonded dinitrogen molecule is high at 225 kcal/mol [2]. A catalytic process where the high activation energy required for dinitrogen dissociation is offset through the formation of surface atom bonds, or chemisorption, was developed by Fritz Haber and optimized for commercial production by Carl Bosch more than 70 years ago [3]. Almost 90% of the industrial production of ammonia relies on this process. The following reaction scheme for Haber-Bosch ammonia synthesis is based on experimental results:

H2 + * 2 Had

N2 + * N2,ad

N2,ad 2Nad

Nad + Had NHad

NHad + Had NH2,ad

NH2,ad + Had NH3,ad

NH3,ad NH3 + *

0.5 N2 + 1.5 H2 = NH3, ΔH298 = -11.05 kcal/mol where * denotes an ensemble of atoms forming an adsorption site [3, 4]. Dissociative dinitrogen adsorption, N2,ad 2Nad, is considered as the rate-determining step [3, 4]. Various metal catalysts have been studied for their ability to lower the dissociation energy of dinitrogen through chemisorption. Table 3.1 describes the viability

42 of different elements as ammonia formation catalysts. As can be seen in Table 3.1, an element is considered viable as an ammonia formation catalyst if it can absorb dinitrogen and does not form covalent bonds with nitrogen or hydrogen atoms [5]. Group 3B – 8B elements are considered viable as ammonia synthesis catalysts [5]. In particular, iron and ruthenium are the most promising. The Haber-Bosch process utilizes iron catalysts. The energy required for dissociative dinitrogen adsorption to industrial iron catalysts ranges from 0 kcal/mol, for Fe(111), to 6.5 kcal/mol, for Fe(110), at zero coverage of the surface to 23.9 kcal/mol when the surface is highly covered [3, 4]. These energies are much lower than the energy required for the dissociation of N2 without a catalyst. However, o high temperatures, 400 – 500 C, and pressures, in excess of 130 bar, are still necessary for the iron catalyzed synthesis of ammonia [3]. In the Kellogg Advanced Ammonia Process, KAAP, ruthenium on a graphite support is used as an ammonia synthesis catalyst [3]. This process is reported to be 10 to 20 times more active and requires less pressure, 50 bar, than the traditional iron catalyst [3, 6]. The synthesis of ammonia on ruthenium is similar to the synthesis of ammonia on iron [6]. The dissociative adsorption of dinitrogen on the ruthenium surface is regarded as the rate-determining step and has a dissociation barrier of at least 9.6 kcal/mol [5, 7, 8]. Ruthenium catalysts are less susceptible to poisoning by ammonia than iron catalytsts [3, 8] However, ruthenium catalysts are inhibited by hydrogen and thus work best at lower than stoichiometric H2/N2 ratios [3, 8]. Although the graphite supported ruthenium catalysts used in the KAAP process are much more active than the traditional iron catalysts, they are costly and have a short lifetime compared to the iron catalysts [9]. Studies have been conducted and are being conducted to find supports for ruthenium that will be more stable under ammonia synthesis conditions [9]. The problem with the processes involving iron and ruthenium catalysts and with surface processes in general is that high temperatures are required to remove hydrogen and nitrogen atoms that are strongly bound to the metal surfaces so that a clean and reactive surface is available for continued ammonia synthesis [8]. Thus, avoiding high temperatures in heterogeneous surface catalysis based on N2 and H2 dissociation requires a surface that binds sufficiently

43 with N2 to decrease the energy required for dissociative dinitrogen adsorption but does not bind too strongly to hydrogen and nitrogen atoms [8]. In contrast to industrial ammonia synthesis, biological ammonia synthesis occurs at ambient temperature and atmospheric pressure. The overall chemical reaction for biological reduction of dinitrogen to ammonia is

+ - N2 + 8H + 8e + 16MgATP → 2NH3 + H2 + 16MgADP + 16Pi (3.1)

[10, 11, 12]. Although the structures of quite a few of the proteins that form several of the nitrogenases have been determined through X-ray crystallography, such as the molybdenum-iron protein, iron protein, and the two of the complexes between these two proteins of molybdenum containing nitrogenases, the mechanisms of these systems are still unresolved [10, 11]. In the most commonly studied molybdenum-iron nitrogenase, the FeMo-cofactor in the MoFe protein is thought to be the active site or the site of binding and reduction of dinitrogen [10]. In the catalytic cycle of the reduction of dinitrogen to form ammonia by the Klebsiella pneumoniae nitrogenase proposed by

Lowe and Thorneley, the FeMo-cofactor (E0) is reduced successively by eight electrons - - - to give 1e , 2e , and 3e reduced states (E1, E2, and E3, etc.), see Figure 3.1 [10, 11]. Each + reduction of the FeMo-cofactor is coupled with the transfer of an H to give states E1H1,

E2H2, and E3H3, etc [10, 11]. The dinitrogen exchanges for an H2 of the E3H3 to form + + E3N2 (H ), then addition of electrons and H continues. According to the scheme proposed by Thorneley and Lowe, one nitrogen atom of the N2 is reduced to form ammonia at a time, where the intermediates of the reduction of the first nitrogen atom include E4N-NH2 and E5=N-NH3, and the intermediates of the reduction of the nitrogen atom include E6=NH and E7NH2 [11]. Thus, based on the Thorneley-Lowe kinetic scheme, ammonia molecules are thought to be formed one at a time and the bond between the nitrogen atoms is cleaved after hydrogenation not before in biological ammonia synthesis. Recently, several organometallic complexes have been found which activate and reduce dinitrogen to form ammonia under mild conditions in solution. One such complex,

44 5 is (η -C5Me4H)2ZrCl2, which consists of a zirconium ion and two substituted cyclopentadienyl rings [14]. When one atmosphere of dinitrogen is added, a binuclear dinitrogen complex is formed in which the N2 is bound side-on to the two zirconium 5 2 2 atoms in a planar Zr2N2 core, [(η -C5Me4H)2Zr]2(μ2,η ,η -N2) [13]. In this binuclear dinitrogen complex the bond between the nitrogen atoms has elongated considerably, where the NN bond length of 1.377 angstroms, Å, is much greater than the NN bond length of an isolated N2, 1.0975 Å [13]. This bond length is longer than the NN bond length of the trans isomer of diimide, 1.252 Å, but is shorter than the NN bond length of an isolated hydrazine, 1.460 Å, as well as other side-on bound zirconium dinitrogen complexes [13, 15]. Addition of one atmosphere of H2 gas yields a cis diimide complex, 5 2 2 [(η -C5Me4H)2ZrH]2(μ2,η ,η -N2H2) [13]. In this complex, the NN bond length, 1.457 Å [13], is close to that of hydrazine. All of this is accomplished at ambient temperature and 5 2 2 with only one atmosphere of pressure [13]. From the [(η -C5Me4H)2ZrH]2(μ2,η ,η -

N2H2) complex there are two ways in which ammonia is formed. One way in which 5 2 2 ammonia is formed involves gentle heating of the [(η -C5Me4H)2ZrH]2(μ2,η ,η -N2H2) in o a heptane solution to 85 C under one atmosphere of H2 gas, which results in a low 10 to 5 15% yield of ammonia and a 60% yield of (η -C5Me4H)2ZrH2 [13]. The other way in which ammonia is formed is a two-step process involving thermolysis and further 5 2 2 reaction with dihydrogen [14]. First, heating of the [(η -C5Me4H)2ZrH]2(μ2,η ,η -N2H2) o o in boiling heptane, about 100 C, to 85 C in the absence of H2 gas results in the loss of 5 one equivalent of H2 as well as cleavage of the NN bond to form [(η -C5Me4H)2Zr]2(μ2- 5 NH2)(μ2-N) [13]. Adding excess anhydrous HCl to [(η -C5Me4H)2Zr]2(μ2-NH2)(μ2-N) 5 yields two equivalents of NH4Cl and (η -C5Me4H)2ZrCl2 [13]. The yield of these 5 products is not reported. Because the (η -C5Me4H)2ZrCl2 is reformed in this two-step process of ammonia, NH4Cl, formation, this process is catalytic. Another organometallic complex which catalyzes the reduction of dinitrogen to ammonia has been found consists of molybdenum attached to a tetradentate triamidoamine ligand,[{3,5-(2,4,6-i-Pr3C6H2)2C6H3NCH2CH2}3N]Mo or [HIPTN3N]Mo

45 [16]. In this catalytic system, the proton source or the source of hydrogen is {2,6- lutidinium}{B(3,5-(CF3)2C6H3)4} or {LuH}{BAr’4} and the electron source is 5 decamethylchromocene, Cr(η -C5H5)2 or CrCp*2 [16]. First, dinitrogen is added to the

[HIPTN3N]Mo to form the [HIPTN3N]Mo(N2) intermediate [16]. Then, {LuH}{BAr’4} and CrCp*2 are added slowly so that the [HIPTN3N]Mo intermediates are maintained in + excess of both acid and reductant. The {[HIPTN3N]Mo=N-NH2} , + + {[HIPTN3N]Mo=NH} , and {[HIPTN3N]Mo(NH3)} intermediates that have been isolated agree with the proposed mechanism illustrated in Figure 3.2 [16]. The proposed catalytic cycle for the reduction of dinitrogen to ammonia by [HIPTN3N]Mo is very similar to the catalytic cycle proposed for biological dinitrogen reduction, in which the nitrogen atom that is distal to the metal is hydrogenated prior to cleavage of the NN bond.

Studies of the reduction of [HIPTN3N]Mo(NH3){BAr’4} under dinitrogen, where + {[HIPTN3N]Mo(NH3)} is reduced to [HIPTN3N]Mo(NH3) and the ammonia is exchanged for dinitrogen to yield [HIPTN3N]Mo(N2), indicate that the rate-determining or slowest step of the [HIPTN3N]Mo catalytic system is conversion of

[HIPTN3N]Mo(NH3) to [HIPTN3N]Mo(N2) [16]. The ammonia yield of this system at 63%, which is relative to the amount of ammonia expected by theory, based on reducing equivalents, is only 12% smaller than the 75% ammonia yield produced in MoFe nitrogenase catalyzed biological reduction of dinitrogen [16].

46 Table 3.1: Viability of Various Elements as Ammonia Synthesis Catalystsa. aReference [5].

Elements Viability of elements as NH3 synthesis catalysts 1 & 2 A Considered not viable since they form stable ionic nitrides and react o (Li – Cs) directly with N2 below 300 C with the exception of heavier elements. 47 (Be – Ba) Group 2 elements can chemisorb, but they form hydrides.

3A – 7A Considered not viable since they can form stable covalent nitrides, do not o (B, Al, C, Si, P, O) chemisorb N2 easily, elements listed react directly with N2 below 300 C.

3B – 8B (Ce, Mo, Mn, Considered most promising since they form interstitial nitrides, can o Fe, Ru, Co, Ni) chemisorb N2 readily, do not react directly with N2 below 300 C.

aReference [5].

a a Figure 3.1: Modified Thorneley-Lowe Kinetic Scheme for the reduction of N2. From reference [11].

48

a Figure 3.2: Proposed intermediates in the reduction at a [HIPTN3N]Mo center through the step-wise addition of protons and electrons. aReference [17].

49 3.1 References [1] Pool, J. A.; Lobkovsky, E.; Chirik, P. J. Nature. 2004, 427, 527. [2] Bazhenova, T. A.; Shilov, A. E. Coord. Chem. Rev. 1995, 144, 69. [3] Appl. M. Ammonia Principles and Industrial Practice. Wiley – VCH, Weinheim, 1999. [4] Ertl, G. Elementary Steps in Ammonia Synthesis in Catalytic Ammonia Synthesis, edited by Jennings, J. R. Plenum Press, New York, 1991, 109. [5] Aika, K; Tamaru, K. Ammonia Synthesis Over Non-Iron Catalysts and Related Phenomena in Ammonia – Catalysis and Manufacture, edited by Nielsen, W. A. Springer-Verlag, Heidelberg, 1995, 103. [6] Szmigiel, D.; Bielawa, H.; Kurtz, M.; Hinrichsen, O.; Muhler, M.; Raróg, W.; Jodzis, S.; Kowalczyk, Z.; Znak, L.; Zielinski, J. J. Catal. 2002, 205, 205. [7] Tautermann, C. S.; Clary, D. C. J. Chem. Phys. 2005, 122, 134702. [8] Rod, T. H.; Logadittir, A.; Nørskov, J. K. J. Chem. Phys. 2000,112, 5343. [9] Dahl, S.; Taylor, P. A.; Törnqvist, E.; Chorkendorff, I. J. Catal. 1998, 178, 679. [10] Noodleman, L.; Lovell, T.; Han W. G.; Li, J.; Himo, F. Chem. Rev. 2004, 104, 459. [11] Igarashi, R. Y.; Seefeldt, L. C. Critical Reviews in Biochemistry and Molecular Biology, 2003, 38, 351. [12] Rees, D. C.; Howard, J. B. Curr. Opin. Chem. Biol. 2000, 4, 559. [13] Pool, J. A.; Lobkovsky, E.; Chirik, P. J. Nature. 2004, 427, 527. [14] Fryzuk, M. D. Nature. 2004, 427, 498. [15] Carlotti, M.; Johns, W. C.; Trombetti, A. Can. J. Chem. 1974, 52, 1006. [16] Yandulov, D. V; Schrock, R. R. Science. 2003, 301, 76.

50 CHAPTER IV METHODS

The GAUSSIAN 98 suite of programs [1] was used to perform all calculations. The calculations were performed on a DEC alpha 433au workstation and on a Compaq AlphaServer ES40. Initially geometry optimizations and stationary point characterizations were performed using the aug-cc-pVDZ (augmented double zeta) basis + + set in the B + N2 + 3H2 and BH2 + N2 + 3H2 systems and the 6-31g* basis set in the Be

+ N2 + 3H2 and BeH2 + N2 + 3H2 systems [2, 3, 4, 5]. Final geometry optimizations and stationary point characterizations were performed using the aug-cc-pVTZ (augmented triple zeta) basis set for hydrogen, nitrogen, and boron, and the cc-pVTZ (triple zeta) basis set, augmented by a set of uncontracted (1s1p1d1f) diffuse functions previously developed by Sharp and Gellene, for beryllium [6]. The augmentation in the aug-cc- pVDZ and aug-cc-pVTZ basis sets consisted of a (1s1p1d) and a (1s1p1d1f) set of diffuse functions, respectively. Pure spherical harmonic functions were employed in the double and triple zeta basis sets. Stationary points were optimized and characterized using MP2 perturbation theory applied to a Hartree-Fock wave function with frozen core electrons. The geometries of the stationary points were optimized using analytical first derivatives. Characterization + + of the stationary points of the B and BH2 systems as a local minimum with all real frequencies or as a transition state with one imaginary frequency was performed using analytical second derivatives. Since the aug-cc-pVTZ basis set for beryllium was developed by Sharp and Gellene, analytical second derivatives were not available in

Gaussian. So, the characterization of the stationary points of the BeH2 system as a local minimum or as a transition state was performed using numerical second derivatives, which are less reliable than analytical second derivatives. The geometry of each transition state was displaced slightly toward the positive and negative directions of the eigenvector of the imaginary frequency and was then optimized to the subsequent stationary point to properly identify each transition state.

51 Coupled cluster with single and double substitutions and a perturbative treatment of triple substitutions, CCSD(T), calculations were performed on each of the previously identified stationary points. Since sufficient memory was not available to complete the required integral transforms of the aug-cc-pVTZ basis set, the CCSD(T) calculations were performed using hybrid basis sets. The hybrid basis set used in the boron and boron dihydride cation systems consisted of aug-cc-pVTZ for hydrogen and cc-pVTZ for the boron and nitrogen (abbreviated pVTZ(+)). The hybrid basis set in the beryllium dihydride system consisted of cc-pVTZ for hydrogen and nitrogen and the augmented cc- pVTZ basis set described above for beryllium (also abbreviated pVTZ(+)). Beryllium dihydride is a neutral species and augmentation is not necessary for neutral systems, where as the augmentation is necessary to accurately describe the polarizability involved + + in the cationic B and BH2 systems, in particular the many electrostatic complexes of these two systems.

52 4.1 References [1] Gaussian 98, Revision A.6, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, Jr., J. A.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T., Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A.Gaussian, Inc.: Pittsburgh PA, 1998. [2] Dunning, T. H., Jr. J Chem Phys. 1989, 90, 1007. [3] Kendal, R. A.; Dunning, T. H., Jr.; Harrison, R. J. J. Chem. Phys., 1992, 96, 6796. [4] Hariharan, P. C.; Pople, J. A. Chem. Phys. Lett. 1972, 66, 217. [5] Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. A. J. Chem. Phys., 1982, 77, 3654. [6] Sharp, S. B.; Gellene, G. I. J. Phys. Chem. A., 2000, 104, 10951.

53 CHAPTER V ORGANIZATION AND LABELING SYSTEM OF THE FIGURES AND TABLES OF THE BORON CATION, BORON DIHYDRIDE CATION, AND BERYLLIUM DIHYDRIDE CATALYTIC SYSTEMS

+ + The energies and geometric parameters that characterize the B , BH2 , BeH2, N2, H2 reactants and the ammonia product are summarized in Tables 5.1. Various stationary points of the boron cation, boron dihydride cation, and beryllium dihydride catalyzed reductions of dinitrogen are illustrated in Figures 6.1, 7.1, and 8.1, respectively. The illustrations of the various stationary points as well as illustrations of the LUMO (Lowest Unoccupied Molecular Orbital), HOMO (Highest Occupied Molecular Orbital), HOMO- 1, HOMO-2, HOMO-3 of various structures were generated using MOLDEN [1]. The energies and geometric parameters that characterize the various stationary points of the + + B , BH2 , and BeH2 catalytic systems are summarized in Tables 6.1 - 6.5, 7.1 – 7.3, and 8.1 – 8.4, respectively. The geometric parameters that will be discussed were calculated at the MP2/pVTZ+ level of theory. Only a subset of internal coordinates will be reported to facilitate comparisons between the properties of the various stationary points of the M + + + N2 + 3H2 -> M + 2NH3 systems, where M = B , BH2 , and BeH2. The labeling scheme of the subscripted text in Tables 6.1 – 6.5, 7.1 – 7.3, and 8.1 – 8.4 is based on the pictures of the various stationary points in Figures 6.1, 7.1, and 8.1. In this labeling scheme, the nitrogen atoms of the N2 are labeled as N(a) and N(b), the hydrogen atoms of the first H2 that reduces the dinitrogen are H(1) and H(2), the hydrogen atoms of the second H2 are

H(3) and H(4), the hydrogen atoms of the third H2 are H(5) and H(6), and the hydrogen atoms of the fourth H2 are H(7) and H(8). The hydrogen atoms are labeled such that H(1),

H(3), H(5), and H(7) are the first hydrogen atoms of their respective H2 molecules to be added to a nitrogen. The transition states are labeled TS(#). In the structures that contain

54 parentheses in their labels, the parentheses are indicative of electrostatic bonding. In the + (H2)B (N2) structure for instance, the parentheses around the H2 and N2 indicate that the dihydrogen and dinitrogen molecules are bound electrostatically to the boron cation.

The coordinates RH(1)H(2), RH(3)H(4), RH(5)H(6), RH(7)H(8), and RNN are the distances between B or Be and the midpoint of the distance between the hydrogen atoms of the first, second, third, and fourth H2 molecules and the nitrogen atoms of the N2 molecule respectively. The ratom1,atom2 coordinates will denote the bond lengths in angstroms, Å, between the atoms indicated by the subscripted text. The angle, θatom1,atom2,atom3, and dihedral, φatom1,atom2,atom3,atom4, coordinates are reported in degrees. The θRH(1)H(2)rH(1)H(2),

θRH(3)H(4)rH(3)H(4), θRH(5)H(6)rH(5)H(6), θRH(7)H(8)rH(7)H(8) and θRNNrN2 coordinates denote the angles formed by a line drawn from the B or Be to the midpoint of the indicated H2 or N2 molecule, and a line drawn from the midpoint of the H2 or N2 molecule to H(1), H(3), H(5), H(7), or N(a). The total energies and harmonic zero point energies (ZPEs) are reported relative to + + the infinitely separated M + N2 + 3H2, M = B , BeH2, or BH2 , reactants. The ZPEs were calculated using unscaled MP2 harmonic frequencies. The relative energies discussed in the results and discussion sections of Chapters VI-VIII, unless stated otherwise, were calculated at the CCSD(T)/pVTZ(+) level of theory, see Chapter IV for details concerning the hybrid basis sets. The zero point energies and frequencies that will be discussed were calculated at the MP2/pVTZ+ level. The energies of the stationary points along the pathways of diimide, hydrazine, and ammonia formation are illustrated in Figures 6.2 – 6.6, 7.2 – 7.7, and 8.2 – 8.5. Figures 6.7, 7.8, and 8.6 illustrate the minimum energy pathways, where only the lowest energy isomers are included, of the boron cation, beryllium dihydride, and boron dihydride cation catalytic cycles, respectively. The + + stationary points along the M + N2 + 3H2 -> M + 2NH3, M = B , BH2 , and BeH2, reaction pathways will be discussed in terms of the formation of diimide, hydrazine, and ammonia.

55 a + + Table 5.1: Calculated Geometries , Energies, and Stretching Frequencies of B , BH2 , and BeH2.

+ + Property B BeH2 BH2 Point Group D∞hD∞h b rMH (Å) 1.3319 1.1702 b θHMH (deg) 180.00 180.00 Energy in Hartrees MP2/pVDZ+ -24.27 -25.53 56 MP2/6-31g* -15.80 CCSD(T)/pVDZ+ -24.29 -25.55 MP2/pVTZ+ -24.27 -15.83 -25.55 CCSD(T)/pVTZ -24.30 -25.57 CCSD(T)/pVTZ(+) -24.30 -15.85 -25.57 Stretching Frequency (cm-1) 2056.5460c, 2265.6296d 2728.8866c, 3014.2729d

aThe geometries were optimized at the MP2/aug-cc-pVTZ level.

bM = B or Be. cBeH and BH stretching frequencies calculated at the MP2/aug-cc-pVTZ level.

cSymmetric BeH or BH stretch.

dAsymmetric BeH or BH stretch. a Table 5.2: Calculated Geometries , Energies, and Stretching Frequencies of N2, and H2 Reactants and the NH3 Product.

Property N2 H2 NH3

Point Group D∞hD∞h C3V

rNN (Å) 1.1141

rHH (Å) 0.7374

rNH (Å) 1.0121

57 θHNH (deg) 106.77

θHHH (deg) 60.00 Energy in Hartrees MP2/pVDZ+ -109.28 -1.16 -56.40 MP2/6-31g* -109.25 -1.14 -56.35 CCSD(T)/pVDZ+ -109.30 -1.16 -56.43 MP2/pVTZ+ -109.36 -1.17 -56.46 CCSD(T)/pVTZ -109.37 -1.17 -56.47 CCSD(T)/pVTZ(+) -109.37 -1.17 -56.48 Stretching Frequency (cm-1) 2186.8283 4517.6379 3480.4163 - 3635.3404 aThe geometries were optimized at the MP2/aug-cc-pVTZ level.

bNN, HH, and NH stretching frequencies calculated at the MP2/aug-cc-pVTZ level. 5.1 References [1] Schaftenaar, G.; Noordik, J.H. J. Comput. Aided Mol. Des., 2000, 14, 123.

58 CHAPTER VI CATALYTIC REDUCTION OF DINITROGEN TO AMMONIA BY B+

6.1 Introduction As can be seen in Table 3.1, boron was not previously considered a viable ammonia synthesis catalyst. Recent research, however, suggests that it might be possible to activate dinitrogen and that catalytic ammonia synthesis might be possible through a cooperative interaction sigma bond activation mechanism. In this mechanism, the energy required to + activate sigma bonds is lowered with increasing cooperative interactions. In the B + nH2, + n = 1 – 3, and B + nCH4, n = 1 and 2, systems, the activation energy (Ea) of breaking HH or CH bonds and forming BH or BC bonds was significantly lowered as the number of cooperative interactions of B+ with HH or CH sigma bonds increased [1,2]:

+ + B + 3H2 t BH2 + 2H2 Ea = -2.7 kcal/mol + + B + 2CH4 t CH3BH + CH4 Ea = 5.0 kcal/mol

Studies on other possible sigma bond activators (Al+, Be, and Li-) in dihydrogen systems determined that the boron cation as the most effective activator in the cooperative interaction mechanism of the activators studied [1,3-5]. Because the highest occupied molecular orbital, HOMO(Highest Occupied

Molecular Orbital), of dinitrogen is the 3σg orbital, it is feasible to apply the sigma bond + activation mechanism in a B + N2 + nH2, n = 1-3, system. In this system, it is possible to avoid the large energy requirement of dissociating the dinitrogen by sequentially hydrogenating N2, creating substituted diimide and hydrazine intermediates along the pathway to ammonia synthesis.

59

6.2 Results 6.2.1 Formation of Diimide Initially a dihydrogen molecule and a dinitrogen molecule come in from infinity to form an electrostatic complex with the boron cation, where the boron is 2.29 Å away from the midpoint of the HH distance and 2.77 Å away from the midpoint of the NN + distance. This (H2)B (N2) electrostatic complex is calculated to have CS symmetry, where o the H forms a near T-shape with the B+ ( = 92.97 ) and dinitrogen is nearly 2 θRH(1)H(2)rH2 o linear with the B+ ( = 3.80 ), see Figure 6.1. In the (H )B+(N ) structure, the θRN(P)N(D)rN2 2 2 bond between the atoms of the electrostatically bound H2, where rH(1)H(2) = 0.75 Å and the -1 HH stretching frequency is 4336 cm , is similar to the HH bond of an isolated H2 -1 molecule, where rHH = 0.74 Å and the HH stretching frequency is 4518 cm . Also, the + NN bond of the electrostatically bound N2 in the (H2)B (N2) complex, with a NN bond distance of 1.115 Å and a NN stretching frequency of 2187 cm-1, is very similar to the

NN bond of an isolated N2 molecule, which has a NN bond distance of 1.114 Å and a NN -1 stretching frequency of 2187 cm . The strong electrostatic binding of the N2 and H2 to the boron cation results in a -14.51 kcal/mol drop in energy and a 1.97 kcal/mol increase in the zero point energy relative to that of the infinitely separated reactants, see Figure 6.2. + + The initial transition state, which connects (H2)B (N2) and BHNNH (1) and is labeled

TS(1), involves the simultaneous breaking of the H2 bond and the formation of BH, NH, and BN bonds. In this transition state, which has CS symmetry, the H2 bond weakens as the distance between the two hydrogen atoms increases, where rH(1)H(2) lengthens to 0.90 Å and the H(1)H(2) stretching frequency decreases to 2390 wavenumbers or cm-1, which is down from the HH stretch of the electrostatic structure, 4336 cm-1, and from the HH -1 + stretch of an H2 molecule, 4518 cm . A bond begins to form between the B and H(2) as rBH(2) decreases to 1.42 Å down from 2.30 Å in the electrostatic complex, and a bond begins to form between the distal nitrogen atom or the atom furthest from the boron and

60 H(1) as rN(b)H(1) decreases to 1.57 Å down from the 3.20 Å (rNH(1)) distance in the + electrostatic complex. As the dinitrogen moves in closer to form bonds with the B , rBN(a)

= 1.72 Å and rBN(b) = 2.21 Å, and a hydrogen atom is added to the dinitrogen, one of the three N2 bonds begins to break, where the distance between the nitrogen atoms increases to 1.16 Å and the NN stretching frequency decreases from 2170 cm-1 in the electrostatic -1 -1 complex and 2187 cm in an isolated N2 molecule to 1765 cm in the transition state. o The BNN angle goes from being nearly linear, θBN(P)N(D) = 175.24 , in the electrostatic o complex to being nearly perpendicular, θBN(a)N(b) = 97.78 . The CCSD(T)/pVTZ(+) relative energy for this first transition state is 11.40 kcal mol-1 and the harmonic zero point energy (ZPE) predicts that the transition state energy is increased by 3.82 kcal mol-1. + The initial insertion intermediate, BHNNH (1), has CS symmetry and a cyclic o structure, θBN(a)N(b) = 76.13 , rBN(a) = 1.41 Å, and rBN(b) = 1.67 Å, where the H2 bond has been broken, rH(1)H(2) = 2.16 Å, H(1) has bonded with the distal nitrogen atom, rN(b)H(1) = + 1.12 Å, and H(2) has bonded with the boron, rBH(2) = 1.17 Å. The BHNNH (1) intermediate, which has a relative energy of -23.09 kcal/mol, isomerizes, through TS(2),

+ o to BHNNH (2) by opening up the BN(a)N(b) angle from θBN(a)N(b) = 76.13 to θBN(a)N(b) = o 166.25 , and BHNNH+(2) then isomerizes, through TS(3), to BHNNH+(3) by reducing o the BNN angle down to θBN(a)N(b) = 62.06 and decreasing the distance from N(b) to H(1) to 1.03 Å. An activation energy with ZPE added in of 5.13 kcal/mol relative to + + + BHNNH (1) is required for BHNNH (1) to isomerize to BHNNH (2) and an EA with ZPE added in of 16.87 kcal/mol is required for BHNNH+(2) to isomerize BHNNH+(3). The relative energy and relative zero point energy of TS(2) are -18.21 kcal/mol and 7.72 kcal/mol respectively and the relative energy and relative zero point energy of TS(3) are -30.83 kcal/mol and 8.20 kcal/mol respectively. The N(b)H(1) stretching frequency of the BHNNH+(3) isomer, 3381 cm-1, is nearly 900 cm-1 higher than the N(b)H(1) stretching frequency of the BHNNH+(1) isomer. The BHNNH+(3) isomer, which also has Cs o symmetry with dihedral angles, φH(1)N(b)N(a)B and φH(2)BN(a)N(b), of 180.00 , is the lowest in

61 energy of the three BHNNH+ isomers with a relative energy of -64.97 kcal/mol and a ZPE of 9.79 kcal/mol. In this isomer, the nitrogen atom that was closest to boron in + BHNNH (1) is now distal to the boron at rBN(a) = 1.47 Å and the nitrogen atom that was + farthest from the boron in BHNNH (1) is now proximal to the boron at rBN(b) = 1.43 Å, + such that H(1) is on the proximal nitrogen atom. The BHNNH (3) N2 bond distance is -1 1.28 Å and the N2 stretching frequency, 1491 cm , is almost 300 wavenumbers lower than the N2 stretching frequency of the initial transition state. + + A hydrogen molecule approaches the BHNNH (3) isomer to form (H2)BHNNH (1), + where the hydrogen atoms of the H2 are still far from the BHNNH component, RH(3)H(4)

= 2.45 Å. The H(3)H(4) distance is still H2 like, rH(3)H(4) = 0.74 Å, and the HH stretch, at -1 4426 cm , is very close to the HH stretch of an isolated H2 molecule. Very little change + occurs to the BHNNH as the H2 molecule moves in from infinity, rBN(a) = 1.47 Å, rBN(b) = o 1.43 Å, θBN(a)N(b) = 62.16 , rNN = 1.27 Å, and rN(b)H(1) = 1.03 Å. The addition of an H2 molecule to BHNNH+ results in a 2.62 kcal/mol decrease in relative energy and a 1.59 increase in zero point energy, such that the H2 is bound by approximately 1 kcal/mol. + Before diimide is formed, the H2 moves in closer still to the boron of the BHNNH + + component, as the (H2)BHNNH (1) structure isomerizes to (H2)BHNNH (2), where

RH(3)H(4) = 1.45 Å. The isomerization transition state, TS(4), has a small activation energy + of 0.95 kcal/mol relative to (H2)BHNNH (1) with ZPE included, where the relative energy is -67.24 kcal/mol and the zero point energy is 11.99 kcal/mol. In the + (H2)BHNNH (2) structure, the H(3)H(4) bond weakens as the distance between the hydrogen atoms increases slightly to 0.78 Å and the HH stretching frequency decreases -1 + by almost 540 wavenumbers to 3890 cm . The (H2)BHNNH (2) structure is lower in + relative energy at -68.76 kcal/mol than TS(4) and (H2)BHNNH (1) and is a minimum at the electronic level. However, harmonic zero point energy calculations predict that the + (H2)BHNNH (2) structure is higher in total energy, where the sum of the relative energy + + and the ZPE is -54.27 kcal/mol, than TS(4), (H2)BHNNH (1), and BHNNH (3). The ZPE + calculations suggest that (H2)BHNNH (2) is not a minimum.

62 Diimide, N2H2, is formed through TS(5) which involves the simultaneous breaking of an H2 bond and the formation of B-H(4) and N(a)H(3) bonds. In TS(5), the H2 continues + to move in closer to BHNNH , RH(3)H(4) = 1.14 Å, and the H2 bond begins to break, rH(3)H(4) elongates to 1.13 Å. A bond begins to form between H(3) and the distal nitrogen, rN(a)H(3) = 1.57 Å, and another bond begins to form between H(4) and the boron, rBH(4) = 1.24 Å. Although the transition state is still somewhat cyclic, the BN(b)N(a) angle begins o to open as θBN(b)N(a) increases to 82.11 and rBN(a) increases to 1.82 Å. The activation energy required to form the boron dihydride cation and diimide is 17.23 kcal/mol relative + to (H2)BHNNH (2) with ZPE added. The relative energy of TS(5) is -51.19 kcal/mol and the ZPE is 14.15 kcal/mol. + In the CS symmetry BH2NHNH structure, the H2 bond is completely broken, rH(3)H(4) = 2.26 Å, the bond that forms between N(a) and H(3) is only 6.03 x 10-3 Å longer than the bond between N(b) and H(1), and the B-H(4) bond is only 4.29 x 10-3 Å longer than o the B-H(2) bond. The BN(b)N(a) angle increases to 125.41 and the BN(a) bond lengthens to 2.49 Å. In the boron dihydride cation and diimide structure, the N(a)N(b) distance lengthens to 1.24 Å and the NN stretching frequency decreases to 1647 + wavenumbers. The relative energy of the BH2NHNH structure is -101.43 kcal/mol and the relative zero point energy is 17.67 kcal/mol.

6.2.2 Formation of Hydrazine + Initially, a dihydrogen molecule approaches BH2NHNH from infinity to form + + BH2NHNH (H2). The H2 is closer to the nitrogen end of the BH2NHNH , rN(a)H(5) = 3.12

Å, than the boron, rBH(5) = 3.93 Å and rBH(6) = 3.93 Å. In the CS symmetry + BH2NHNH (H2) structure, the bond between the hydrogen atoms of the H2, where -1 rH(5)H(6) = 0.74 Å and the HH stretching frequency is 4464 cm , is very similar to the bond between the hydrogen atoms of an isolated H2 bond. As can be seen in Tables 6.2 + and 6.3, the BH2NHNH moiety changes very little as the hydrogen molecule approaches. + The dihydrogen molecule is bound to the BH2NHNH by 0.89 kcal/mol, where the

63 + relative energy of the BH2NHNH (H2) structure is -103.55 kcal/mol and the ZPE is 18.91 kcal/mol. + + In TS(6), the H2 of the (H2)BH2NHNH moves in closer to the BH2NHNH to + form (H2)BHNHNH2 (1). The bond between the hydrogen atoms of the approaching H2 molecule weakens, rH(5)H(6) = 0.90 Å, as one hydrogen atom adds to the distal nitrogen atom, rN(a)H(5) = 1.35 Å, and the other hydrogen atom adds to one of the hydrogen atoms of the BH2 component to form an H2 molecule, rH(4)H(6) = 1.27 Å, simultaneously. Another bond between the two nitrogen atoms weakens as the distance between N(a) and N(b) lengthens to 1.31 Å and the NN stretching frequency decreases to 1490 cm-1. TS(6) has a relative energy of -64.79 kcal/mol and a relative zero point energy of 19.05 + kcal/mol. An activation energy of 38.90 kcal/mol relative to (H2)BH2NHNH , with ZPE + included, is required to form (H2)BHNHNH2 (1). + In the CS symmetry (H2)BHNHNH2 (1) structure, the distance between the H(5) and H(6) elongates to 2.43 Å and the distance between N(a) and H(5) decreases to 1.01

Å. The distance between the H(4) and H(6) of the newly formed H2 molecule is only

0.05 Å longer that the distance between the hydrogen atoms of an isolated H2 molecule. The BH(4) bond length, 1.46 Å, is 0.02 Å longer than the BH(6) bond length. Although the pictures in Figures 6.1 and 6.13 appear to indicate that there is an ordinary covalent bond between H(4) and the boron, H(4) and H(6) are either bound electrostatically to or form weak 3c-2e- covalent bonds with the boron. See section 6.3.1 for a discussion of + electrostatic hydrogen bonding. This (H2)BHNHNH2 (1) structure has a relative energy of -119.34 kcal/mol which increases to -96.03 kcal/mol when ZPE is included. By + breaking the CS symmetry, (H2)BHNHNH2 (1) isomerizes to two enantiomers of + (H2)BHNHNH2 (2). The relative energy of TS(7) is -119.24 kcal/mol and the ZPE is + 23.07 kcal/mol. While the relative energy of (H2)BHNHNH2 (1) is lower than the relative energy of TS(7), ZPE calculations predict that the total relative energy, or the summation + of the relative energy and the ZPE, of (H2)BHNHNH2 (1) is higher than the total relative + energy of TS(7), see Figure 6.4. Although the (H2)BHNHNH2 (1) structure is a minimum at the electronic level, ZPE calculations suggest that it is not a minimum.

64 + In the (H2)BHNHNH2 (2) enantiomers, the symmetry is broken, where the H2 is no longer planar with BN(b)N(a), φH(4)BN(b)N(a) and φH(6)BN(b)N(a) are no longer equal to zero, and both of the hydrogen atoms on the distal nitrogen atom are on the same side, o o

φH(3)N(a)N(b)B B = 16.51 and φH(5)N(a)N(b)B = 137.29 in one enantiomer and φH(3)N(a)N(b)B = o o -137.29 and φH(5)N(a)N(b)B = -16.51 in the other enantiomer. These enantiomers are minimums and have a relative energy of -121.07 kcal/mol and a ZPE of 23.80 kcal/mol. + Since there are two (H2)BHNHNH2 (2) enantiomers, there will be two enantiomers of each stationary point and transition state along the pathway until a higher symmetry + + structure, BH2NH2NH2 (1), is formed. Only the (H2)BHNHNH2 (2) enantiomer in which the dihedral angles of H(3) and H(5) are positive and the isomers and transition states connected with this enantiomer will be discussed and featured in Table 6.3 and Figure 6.1. The pictures in Figures 6.1 and 6.13 appear to indicate that there is a covalent bond between H(4) and H(6) and the boron, the BH(4) is in fact either an electrostatic bond or a 3c-2e- bond. See section 6.3.1 for a discussion of electrostatic hydrogen bonding. + + The (H2)BHNHNH2 (2) structures isomerize to (H2)BHNHNH2 (3) through

TS(8), in which the H2 is displaced outward, rBH(4) = 2.48 Å and rBH(6) = 2.51 Å, as the o BN(b)N(a) angle begins to close up, θBN(b)N(a) = 125.46 . TS(8) has an activation energy + of 5.31 kcal/mol with ZPE added relative to (H2)BHNHNH2 (2). The relative energy is -111.52 kcal/mol and the relative zero point energy is 19.56 kcal/mol. The + (H2)BHNHNH2 (3) isomer has the lowest relative energy, -134.81 kcal/mol, and the + lowest ZPE, 20.59 kcal/mol, of the (H2)BHNHNH2 isomers. This isomer is cyclic, o where the BN(b)N(a) decreases to 68.68 . With a HH bond length of 0.74 Å and an HH stretching frequency of 4456 cm-1, the bond between H(4) and H(6) is very similar to the bond of an isolated H2 molecule. In TS(9), an activation energy of 9.08 kcal/mol with ZPE added in relative to + + (H2)BHNHNH2 (3) is required to move the H2 closer to the boron of the BHNHNH2 + component, rBH(4) and rBH(6) = 1.71 Å, to form (H2)BHNHNH2 (4). TS(9) has a relative + energy of -127.58 kcal/mol and a ZPE of 22.44 kcal/mol. In the (H2)BHNHNH2 (4) structure, the rBH(4) is 1.56 Å and the rBH(6) is 1.55 Å. To reduce steric effects as the H2

65 + approaches the nearly CS symmetry HBNHNH2 component, H(1) and H(2) go from o being nearly planar with the boron and nitrogen atoms, φH(1)N(b)N(a)BB = 179.71 and

o + φH(2)BN(b)N(a) = 179.86 , in the (H2)BHNHNH2 (3) isomer to being non-planar with the o o boron and nitrogen atoms, φH(1)N(b)N(a)B = 113.31 and φH(2)BN(b)N(a) = 117.62 , in the + + (H2)BHNHNH2 (4) isomer. The relative energy of the (H2)BHNHNH2 (4) structure is -127.52 kcal/mol and the ZPE is 23.71. At the MP2 level of theory, the aug-cc-pVDZ and + aug-cc-pVTZ relative energies of the (H2)BHNHNH2 (4) structure are lower than the relative energies of TS(9). However, at the CCSD(T)/pVTZ(+) level of theory, the + relative energy of TS(9) is lower that the relative energy of (H2)BHNHNH2 (4). When the ZPE is added to the relative energies of both levels of theory, the resulting total + energies of the (H2)BHNHNH2 (4) structure are higher than the total energies of TS(9). + The ZPE calculations suggest that the (H2)BHNHNH2 (4) may not be a minimum. Hydrazine is formed in TS(10), where the H(4)H(6) bond length elongates to 1.01

Å as one hydrogen atom of the H2 adds to the distal nitrogen atom, rN(b)H(4) = 1.43 Å, and the other hydrogen atom adds to the boron, rBH(6) = 1.28 Å. The activation energy, + + relative to (H2)BHNHNH2 (4), required to form BH2NH2NH2 (1) is 14.31 kcal/mol, where the relative energy of TS(10) is -113.97 kcal/mol and the ZPE is 24.47 kcal/mol. In the C2V symmetry boron dihydride and hydrazine structure, the length of the newly formed N(b)H(4) bond is equal to the length of the other NH bonds, rN(b)H(4) = 1.02 Å, the

B-H(6) bond length, rBH(6), is equal to the B-H(2) bond length at 1.18 Å, and the H2 bond has been broken, rH(4)H(6) = 2.60 Å. With a relative energy of -165.68 kcal/mol and a ZPE + + of 28.33 kcal/mol, BH2NH2NH2 (1) is the lowest energy BH2NH2NH2 isomer.

6.2.3 Formation of Ammonia Before the hydrogen atoms are transferred from the boron to form ammonia and + + + retrieve the B catalyst, the BH2NH2NH2 (1) structure isomerizes to BH2NH2NH2 (2) through TS(11). In this transition state, one of the nitrogen atoms of the hydrazine moves + away from the boron. Due to the C2V symmetry of BH2NH2NH2 (1), the nitrogen atom that moves away from the boron could be either N(a) and N(b). The labeling scheme

66 featured in this section is based on N(b) being the migrating nitrogen atom. In the + transition state between the two BH2NH2NH2 isomers, the BN(a)N(b) angle opens, o + θBN(a)N(b) = 107.46 and rBN(b) = 2.42 Å. The C2V symmetry of the BH2NH2NH2 (1) structure is broken in TS(11), where the hydrogen atoms of the boron go from being

+ o somewhat perpendicular to the BNN plane in the BH2NH2NH2 (1), φH(2)BN(b)N(a) = 102.34 o and φH(6)BN(b)N(a) = -102.34 , to being neither perpendicular to the BNN plane nor planar o o in TS(11), φH(2)BN(b)N(a) = 68.971 and φH(6)BN(b)N(a) = -137.543 . Also, the hydrogen atoms of the hydrazine rotate from an eclipsed conformation to a more gauche conformation, o o

φH(1)N(b)N(a)B B = 178.29 and φH(4)N(b)N(a)B = -64.61 . An activation energy of 14.84 kcal/mol, + with ZPE added in and relative to BH2NH2NH2 (1), is required for this isomerization. TS(11) has a relative energy of -149.35 kcal/mol and a relative zero point energy of 26.84 + kcal/mol. In the BH2NH2NH2 (2) structure, the boron dihydride hydrogen atoms are o nearly planar with the boron and nitrogen atoms, φH(2)BN(b)N(a) = 18.11 and φH(6)BN(b)N(a) =

o + 12.94 . The BN(b) bond length of the BH2NH2NH2 (2), at 2.51 Å, is greater than the + BN(b) bond lengths of BH2NH2NH2 (1) and TS(11), while the BN(a) and NN bond + lengths of BH2NH2NH2 (2), at rBN(a) = 1.55 Å and rNN = 1.44 Å, are nearly the same as + + the BN(a) and NN bond lengths of BH2NH2NH2 (1) and TS(11). This BH2NH2NH2 (2) isomer has a relative energy of -149.76 kcal/mol and a ZPE of 26.82 kcal/mol and is + higher in total energy, including ZPE, than the BH2NH2NH2 (1) isomer by 14.41 kcal/mol. Ammonia is formed through TS(12), which involves the simultaneous transfer of a hydrogen atom from the boron to the distal nitrogen atom, N(b), and the breaking of the + NN bond. In TS(12), the B-H(6) bond of BH2NH2NH2 (2) weakens as the length increases 0.17 Å to 1.34 Å and the B-H(6) stretching frequency, 1655 cm-1, is decreased -1 by over a 1000 cm and is coupled with a N(b)H(6) stretch. The NN bond weakens, rNN = 2.11 Å and the NN stretch decreases to 448 cm-1, as the distal nitrogen atom, N(b), moves away from the proximal nitrogen atom, N(a), and moves toward the migrating hydrogen, + rN(b)H(6) = 1.59 Å. The activation energy, including ZPE and relative to BH2NH2NH2 (2), + needed to form NH2BHNH3 is 73.17 kcal/mol. TS(12) has a relative energy of -70.31

67 + kcal/mol and a ZPE of 20.54 kcal/mol. In the NH2BHNH3 intermediate, the bond between the boron and H(6) is broken, rBH(6) = 2.15 Å, and the bond length between N(b) and the recently transferred hydrogen, H(6), is equal to the N(b)H(1) bond length at 1.02 Å. The distance between N(a) and N(b) has elongated to 2.52 Å. The BN(a) bond length decreases to 1.37 Å and the BN(a) stretching frequency increases to 1445 cm-1. The + distance between the nitrogen atom of the ammonia, N(b), and boron of the HBNH2 -1 component is 1.57 Å and the BN(b) stretching frequency is almost 780 cm . In this CS + symmetry NH2BHNH3 structure, the N(b) and H(4) of the ammonia are planar, o + o φH(4)N(b)N(a)B B = 180.00 , with the planar HBNH2 component, φH(3)H(5)N(a)B B = 180.00 and

o + φH(2)BN(a)H(3) = 180.00 . The NH2BHNH3 intermediate has a low relative energy of -236.54 kcal/mol and a high ZPE of 28.69 kcal/mol. The second ammonia is formed as the H(2) migrates from the boron to N(a) in

TS(13). In this transition state, the B-H(2) bond breaks, rBH(2) = 1.46 Å, and the N(a)H(2) bond forms, rN(a)H(2) = 1.21 Å, simultaneously. As the H(2) is transferred, the BN(a) bond lengthens by 0.11 Å to 1.48 Å. An activation energy of 103.48 kcal/mol with ZPE added, + relative to NH2BHNH3 , is required to form the second ammonia. The relative energy of TS(13) is -129.49 kcal/mol and the relative zero point energy is 25.13 kcal/mol. In the + NH3BNH3 structure, the N(a)H(2) bond length is equal to the bond lengths of N(a)H(1), + N(a)H(6), and N(b)H(5) at 1.02 Å. The NH3BNH3 structure has C2V symmetry, where both the –NH3 groups are equidistant to the boron with BN bond lengths of 1.62 Å and the BN bonds stretch symmetrically at the 569 cm-1 frequency and asymmetrically at the -1 693 cm frequency. The NH bond lengths, rNH = 1.02 or 1.03 Å, of the ammonias of the + NH3BNH3 structure are slightly longer than the NH bond lengths of an isolated NH3 + molecule, rNH = 1.01 Å. The NH3BNH3 ammonias have CS symmetry and the angles o between two non-planar hydrogen atoms, such as H(1)N(b)H(6), are 104.02 and the angles between a non-planar hydrogen atom and a planar hydrogen atom, such as o H(1)N(a)H(4), are 108.16 . In an isolated ammonia molecule, which has C3V symmetry, + all the HNH angles are 106.77 degrees. It is interesting to note that the NH3BNH3 minimum geometry at the double zeta level of theory has C2 symmetry, where as the

68 + geometry calculated at the triple zeta level of theory has C2V symmetry. This NH3BNH3 structure has a relative energy of -148.77 kcal/mol and a ZPE of 27.50 kcal/mol. The combined relative energy of a boron cation and two separate ammonia molecules is -40.99 kcal/mol and the combined ZPE is 20.89 kcal/mol. There is no energy barrier between the infinitely separated boron cation and ammonia molecules and the + NH3BNH3 structure.

6.3 Discussion

The results demonstrate that the 3σg HOMO of N2 can be activated by the + + cooperative interaction mechanism, similar to that observed for B + nH2 and B + nCH4 [1, 2]. In particular, the transition state for + + B + N2 + H2 -> BHNNH Ea = 15.2 kcal/mol + + + resembles the transition state for B + 2H2. In both the B + N2 + H2 and B + 2H2 systems, the node between the boron cation and the other reactants in the HOMO of the electrostatic complex is maneuvered in the transition state to bisect the HH bonds causing them to weaken, see Figure 6.8 for the evolution of the HOMO along the path for + + BHNNH formation [1]. However, the transition state for the B + N2 + H2 system is + different than the transition state for the B + 2H2 system in that this node that is maneuvered to bisect the HH bond remains in place between the boron cation and the dinitrogen. It is one of the σg nodes of the N2 that retracts to bisect the N2. As in the boron cation and dihydrogen system, the transition state in the B+, dinitrogen, and dihydrogen system is pericyclic, where the process of breaking HH and NN bonds and forming BH, NH, and BN bonds is concerted and occurs through a cyclic transition state.

6.3.1 Electrostatic Hydrogen Bonding + + Half of the structures along the B + N2 + 3H2 -> B + 2NH3 hypersurface involve electrostatic bonds between a dihydrogen molecule and a boron-nitrogen component. The bonds between the electrostatically bound dihydrogen molecules and boron-nitrogen moieties can be classified into two types: weakly bound and strongly bound. The

69 structures in which the electrostatic bond between the H2 molecules and the boron- + + + nitrogen components is weak include: (H2)B (N2), (H2)BHNNH (1), BH2NHNH (H2), + and (H2)BHNHNH2 (3). The large distances between the dihydrogen molecules and boron-nitrogen components, the similarity between the bonds of the bound dihydrogen molecules and an isolated HH bond, and the small binding energies demonstrate that the

H2 molecules in these structures are very weakly bound. In these structures, the hydrogen atoms of the electrostatically bound H2 are at least 2.30 Å from the boron and at least 3.12 Å away from the closest nitrogen atom. The HH bond lengths of the weakly bound

H2 molecules, ranging from 0.7410 to 0.7489 Å, are very close to the distance between the hydrogen atoms of an isolated H2, rHH = 0.7374 Å. Also, the HH stretching frequencies of these structures range from 4336 to 4464 wavenumbers and are close to the HH stretch of an isolated dihydrogen molecule, 4518 cm-1. Table 6.6 is a compilation of the HH bond lengths and stretching frequencies of the all the structures involving electrostatic bonds between H2 molecules and boron-nitrogen components. As can be seen in Table 6.7, the binding of a dihydrogen molecule to a boron-nitrogen molecule in + + + the electrostatic complexes of (H2)B (N2), (H2)BHNNH (1), BH2NHNH (H2), and + (H2)BHNHNH2 (3) only lowers the total energy, including ZPE, by 2.25 kcal/mol or less. + + When the cyclic, CS symmetry BHNHNH2 moiety of the (H2)BHNHNH2 (3) complex was optimized without a dihydrogen molecule as an isolated structure and second derivative calculations were performed on the final optimized geometry, the + isolated BHNHNH2 was found to be a local minimum with all real frequencies. + + Although a transition state linking the isolated BH2NHNH and BHNHNH2 structures has been identified, the CCSD(T)/pVTZ(+) activation energy of 50.61 kcal/mol, + including ZPE and relative to the BH2NHNH structure, required to reach this transition state is 11.71 kcal/mol higher than the activation energy, including ZPE and relative to + the BH2NHNH (H2) structure, required to reach TS(6). Thus, both the transition state + + + linking the isolated BH2NHNH and BHNHNH2 structures and the BHNHNH2 structure are not on the minimum energy pathway to ammonia formation.

70 The bonds between the hydrogen atoms of the H2 molecules and the boron- + + nitrogen moieties in the (H2)BHNNH (2) and (H2)BHNHNH2 (1, 2, and 4) structures can be considered to be either very strongly electrostatic or weak 3c-2e- covalent bonds. The small BH bond lengths, large BH stretching frequencies, large differences between the

HH bonds of these structures and the HH bond of an isolated H2, and the large differences in geometry between the boron-nitrogen components of these structures and the isolated boron-nitrogen structures support the interpretation that the BH bonds between the dihydrogen molecules and the boron are either strongly electrostatic or - + + 3c-2e bonds. In the (H2)BHNNH (2) and (H2)BHNHNH2 (1, 2, and 4) structures, the distances between the hydrogen atoms of the H2 and the boron range from 1.43 to 1.56 Å and are at least 0.78 Å shorter than the electrostatic BH distances of the weakly bound electrostatic structures. However, the BH bond lengths between the hydrogen atoms of + + the H2 molecules and the boron in the (H2)BHNNH (2) and (H2)BHNHNH2 (1, 2, and 4) structures are at least 0.25 Å longer than the more strongly covalent BH distances in the + + + + BHNNH and BHNHNH2 components and in the BH2NHNH and BH2NH2NH2 structures. While the stretching frequencies of the BH bonds between the hydrogen atoms of the H2 molecules and the boron in the weakly bound electrostatic structures are non- -1 + existent except for the 184 cm BH stretch of the (H2)BHNNH (1) structure, the stretching frequencies of the BH bonds between the strongly bound dihydrogen molecules and the boron are 389 cm-1 or more. The bonds between the hydrogen atoms of + + the bound H2 molecules and the boron in the (H2)BHNNH (2) and (H2)BHNHNH2 (4) structures are weaker, with BH distances ranging between 1.50 and 1.56 Å and BH stretching frequencies ranging between 389 and 717 cm-1, than those in the + (H2)BHNHNH2 (1 and 2) structures, where the distances between the hydrogen atoms of the H2 and the boron range between 1.43 and 1.48 Å and the stretching frequencies range -1 + between 1033 and 1195 cm . In the (H2)BHNHNH2 (1, 2, and 4) structures the BH stretches between the hydrogen atoms of the H2 molecule and the boron are coupled asymmetrically, 1033 cm-1 for (1) and 1085 cm-1 for (2), and symmetrically, 1163 cm-1

71 for (1), 1195 cm-1 for (2), and 717 cm-1 for (4), with the NN stretch. The coupling of the BH stretches with the NN stretch is another indication that the dihydrogen molecules are + strongly bound to the boron in the (H2)BHNHNH2 (1, 2, and 4) structures. Also, the more + + strongly covalent BH stretching frequencies of the BHNNH and BHNHNH2 + + components and the BH2NHNH , and BH2NH2NH2 structures, which range from 2710 -1 to 2911 cm , are more than twice the BH stretching frequencies of the strongly bound H2 molecules. For a comparison of electrostatic and covalent BH distances and stretching frequencies see Table 6.8. Also, the HH bond lengths of the strongly bound dihydrogen molecules in the + + (H2)BHNNH (2) and (H2)BHNHNH2 (1, 2, and 4) structures are at least 0.03 Å longer + than the HH bond lengths of the weakly bound dihydrogen molecules in the (H2)B (N2), + + + (H2)BHNNH (1), (H2)BH2NHNH , and (H2)BHNHNH2 (3) structures discussed above and at least 0.04 Å longer than the HH bond of an isolated dihydrogen molecule. The HH stretching frequencies of the strongly bound dihydrogen molecules are at least 298 cm-1 less than the HH stretching frequencies of the weakly bound dihydrogen molecules and at -1 least 480 cm less than the HH stretching frequency of an isolated H2. There are large differences between the structures of the BHNNH+ and + + + BHNHNH2 components in the (H2)BHNNH (2) and (H2)BHNHNH2 (1, 2, and 4) + + structures and the isolated BHNNH (3) and BHNHNH2 structures. The main difference + + + between the BHNNH and BHNHNH2 components of the (H2)BHNNH (2) and + (H2)BHNHNH2 ( 4) structures and their isolated counterparts is the change in symmetry. The H(1) and H(2) go from being in the BNN plane in the isolated BHNNH+(3) and + + BHNHNH2 structures and nearly in the BNN plane in the (H2)BHNNH (1) and + (H2)BHNHNH2 (3) structures to being very much out of the plane in the + + (H2)BHNNH (2) and (H2)BHNHNH2 ( 4) structures so that the H2 can move in closer. In + + the (H2)BHNHNH2 (1 and 2) structures, the main difference between the BHNHNH2 + component and its isolated counterpart is that the structure of the BHNHNH2 component + of the (H2)BHNHNH2 (1 and 2) structures is not cyclic. The BN(b)N(a) angles of the + (H2)BHNHNH2 (1 and 2) structures are 129.69 degrees and 133.37 degrees, respectively,

72 + where as the BN(b)N(a) angle of the (H2)BHNHNH2 (3) structure is 68.68 degrees and + the BN(b)N(a) angle of the isolated BHNHNH2 structure is 68.91 degrees. It is + interesting to note that in the optimizations of the non-cyclic BHNHNH2 components of + the (H2)BHNHNH2 (1 and 2) by themselves, the BN(b)N(a) angle closes to form the CS + + symmetry, cyclic BHNHNH2 structure. Thus, an isolated, non-cyclic BHNHNH2 does + exist. The electrostatically bound dihydrogen molecule in the (H2)BHNHNH2 (1 and 2) + structures sterically hinders the BN(b)N(a) angle of the BHNHNH2 from closing.

6.3.2 Boron-Nitrogen Bonds Before the steps of the B+ catalyzed reduction of dinitrogen can be discussed, it is important to understand boron-nitrogen bonding. The weakest boron-nitrogen bond is an + electrostatic bond. In the (H2)B (N2) structure, the bond between the B and N(a) is electrostatic. The large BN(a) distance, the fact that none of the frequencies are BN(a) + stretching frequencies, the small difference between the NN bond of (H2)B (N2) and the

NN bond of an isolated N2 molecule as well as the small difference between the energy of + the B (N2) complex and the sum of the energies of an isolated boron cation and an + isolated N2 molecule all demonstrate that the BN(a) bond of the (H2)B (N2) structure is + electrostatic. In the (H2)B (N2), the BN distance of 2.21 Å is 0.56 Å longer than the dative σ bond of a BH3NH3 molecule, which will be discussed later in this section. The + similiarity between the NN bonds of the (H2)B (N2) and an isolated N2 molecule demonstrate that the effect of the BN(a) bond on the bond between the nitrogen atoms is + very small. The NN bond of the (H2)B (N2) complex is very similar to the NN bond of an + isolated dinitrogen molecule in that the NN bond distance in the (H2)B (N2) structure is -4 only 9.10 x 10 Å longer than the NN bond length of an isolated N2 and the NN + stretching frequency of the (H2)B (N2) is only 17 wavenumbers smaller than the stretching frequency of an isolated N2. Another indication that the bond between the boron cation and dinitrogen is electrostatic is the fact that dinitrogen is bound to the + boron cation by only 10.30 kcal/mol, where the energy, including ZPE, of the B (N2) complex is 10.30 kcal/mol lower than the sum of the energies of an isolated B+ and an

73 + + isolated N2. It is interesting to note that while the BN bonds of the B (N2) and (H2)B (N2) + complexes are very similar, the BN(a) bond of the B (N2) is slightly stronger than the + + BN(a) bond of (H2)B (N2), where the length of the BN(a) bond in the B (N2) complex is + + 0.02 Å shorter than the BN(a) bond in (H2)B (N2) and the B (N2) complex has a BN stretching frequency of 231 cm-1, whereas there is no BN stretching frequency for the + (H2)B (N2). In order to assess the accuracy of the computational method employed and establish reference values for the various types of covalent BN bonds, MP2/aug-cc-pVTZ calculations were carried out on simple boron-nitrogen molecules. In Tables 6.9 through 6.11, the MP2/aug-cc-pVTZ calculated BN distances and stretching frequencies of these sample molecules are compared with their experimentally determined values as well as with the experimentally determined BN distances and stretching frequencies of various other structures reported in the literature. All of these values are also compared with the BN distances and stretching frequencies of the structures of the B+ catalytic system in Tables 6.9 through 6.11.

6.3.2.1 Boron-Nitrogen Sigma Bonds The simplest covalent bond between a boron atom and a nitrogen atom is that of a sigma (σ) bond of which there are two types: an ordinary covalent bond and dative covalent bond. In an ordinary covalent σ bond, each atom donates an electron. One of the simplest examples of an ordinary covalent bond is the C-C bond of ethane, where the breaking of the C-C bond yields two methyl radicals. In a dative covalent σ bond, the two lone pair electrons of a donor atom, such as nitrogen, are donated to an acceptor atom, such as boron, to form a bond. For example, the BN bond of the BH3NH3 structure is a dative σ bond, where the breaking of the BN bond yields the closed shell species BH3 and NH3 [6, 7]. The calculated MP2/TZ+ and experimentally determined BN distances and frequencies of the BH3NH3 structure will be used as references for the dative BN σ bonds, which are labeled as ‘Dative σ’ bonds in Table 6.9, of the B+ catalytic system.

74 At the MP2/TZ+ level of theory, the BN distance of the BH3NH3 molecule is calculated to be 1.65 Å. This distance compares well with the experimental BN bond lengths of 1.6576(16) Å, which was determined for the rS structure, and 1.6722(5), which was determined for the rO structure, from a microwave study conducted by Thorne et al.

[8]. The MP2/TZ+ calculations predict that the BN stretching frequency for the BH3NH3 molecule is 684 wavenumbers. This frequency is around a 100 wavenumbers smaller than the BN stretching frequencies reported by Taylor et al. (787 cm-1) and Sawodny et al. (776 cm-1) [7]. In an argon-matrix study, Smith et.al. assign the BN stretching -1 frequency of the BH3NH3 molecule to 968 cm [7]. However, after comparing their HF/6-31G(d) calculations with the experimental studies conducted by Taylor et. al, Sawodny et. al, and Smith et al., Dillen and Verhoeven assign the 968 cm-1 frequency to -1 the BH3 rocking mode and assign the 603 cm , which Smith et al. assigns as the BH3 rocking mode, as the BN stretching frequency mode [7]. Assuming the Dillen and Verhoeven reassignment of the BN stretching frequency is correct, the MP2/TZ+ calculated BN stretching frequency is approximately 80 wavenumbers larger than the BN stretching frequency of the argon-matrix study and falls in the middle of all the experimentally determined BN stretching frequencies of the BH3NH3 molecule. The BN(b) bond of the BHNNH+(1) structure and both BN bonds of the + NH3BNH3 are very similar to the bond between the boron and the nitrogen atom of the

BH3NH3 molecule. As can be seen in Table 6.9, the distance between the boron and N(b) + in BHNNH (1) is only 0.02 Å longer than the BN distance of BH3NH3 and the distance + between the boron and the nitrogen atoms in NH3BNH3 is only 0.03 Å shorter than the + BN distance of BH3NH3. Also, the boron-nitrogen stretching frequencies of BHNNH (1), + + -1 NH3BNH3 , and BH3NH3 are all very similar. In the BHNNH (1), the 569 cm stretch between the boron and N(b) is 115 wavenumbers smaller than the BN stretch of the -1 BH3NH3 molecule and the 705 cm BN(b) stretch is only 21 wavenumbers larger than the BN stretch of the BH3NH3 molecule. Most likely the BN(b) stretch of the BHNNH+(1) occurs at two frequencies due to the coupling of the BN(b) stretch with the + bend of the hydrogen atom on the boron. In the NH3BNH3 , the frequency of the

75 symmetric BN stretches, 569 cm-1, is 115 wavenumbers smaller than the BN stretch of -1 the BH3NH3 molecule and the frequency of the asymmetric BN stretches, 693 cm , is only 9 wavenumbers greater than the BN stretch of BH3NH3 molecule.

Taking away a hydrogen atom from the boron of the BH3NH3 structure, results in + the positively charged BH2NH3 , in which the BN bond appears to be a hybrid between a dative σ bond and an ordinary covalent σ bond. As can be seen in Table 6.10, the + distance between the boron and the nitrogen atom of the BH2NH3 structure is 1.56 Å which is 0.10 Å less than the dative BN σ bond distance in the BH3NH3 structure and is

0.08 Å greater than the ordinary covalent BN σ bond length in the CS BH2NH2 transition state, which is labeled as ‘BH2NH2 (CS – TS)’ in Table 6.10 and will be discussed later in + -1 this section. The BN stretching frequency of BH2NH3 at 894 cm is 210 wavenumbers larger than the BN stretching frequency of the BH3NH3 and is 181 wavenumbers smaller than the BN stretching frequency of the BH2NH2 transition state structure. The BN bond + + of the BH2NH3 molecule will be used as a reference for the BN bonds of the B and + BH2 catalytic systems that will be referred to as ‘hybrid dative/ordinary σ‘ bonds. + Based upon BN bond lengths, the BN(a) bonds of (H2)BHNNH (2), + + + (H2)BHNHNH2 (4), and BH2NH2NH2 (2), the BN(b) bonds of BH2NHNH , + + BH2NHNH (H2), and NH2BHNH3 all appear to be hybrid dative/ordinary σ bonds, where the lengths of these BN bonds are at most 0.02 Å greater than or less than the BN + bond length of the BH2NH3 molecule. Also, as can be seen in Table 6.10, the BN + stretching frequencies between the B and N(a) of BH2NH2NH2 (2) and between the + + boron and N(b) of BH2NHNH and BH2NHNH (H2) are somewhat similar to the BN + stretching frequency of BH2NH3 . Although the lengths of the BN(a) bonds in the + + (H2)BHNNH (2) and (H2)BHNHNH2 (4) structures more closely resemble the BN bond + length of the BH2NH3 than that of the ‘BH2NH2 (Cs – TS)’, the stretches of the BN(a) + + bonds in (H2)BHNNH (2) and (H2)BHNHNH2 (4) occur symmetrically with the stretches of the BN(b) bonds and closely resemble the stretching frequency of the ordinary σ BN bond in the ‘BH2NH2 (Cs – TS)’. Since the BN(a) stretches are symmetric to the BN(b) + + stretches in the (H2)BHNNH (2) and (H2)BHNHNH2 (4), the BN(a) bonds of these

76 structures are placed in the ‘Ordinary s Bond’ columns of Table 6.10 along with the + BN(b) bonds. Whereas the BN(a) bond length of (H2)BHNHNH2 (3) more closely + resembles the BN bond length of BH2NH3 than that of BH3NH3, the stretching + frequency of the BN(a) bond of (H2)BHNHNH2 (3) is very similar to the BN stretching + frequency of the BH3NH3 molecule, where the BN(a) stretch of (H2)BHNHNH2 (3) is -1 only 22 cm less than the BN stretch of BH3NH3. The BN(b) stretching frequency of the + NH2BHNH3 is closer to the BN stretching frequency of the BH3NH3 molecule than to + that of the BH2NH3 . However, since the BN(b) bond distance is so close to the BN + + distance of the BH2NH3 , the BN(b) bond of the NH2BHNH3 is placed in the ‘Hybrid Dative/ Ordinary σ Bond’ columns of Table 6.10. + The BN bond lengths of BH2NH2NH2 (1) are nearly equidistant to the BN bond + lengths of BH3NH3 and BH2NH3 , but are slightly closer to the BN bond length of the + + -1 BH2NH3 . The symmetric BN stretching frequency of BH2NH2NH2 (1) is 123 cm less -1 than the BN stretch of BH3NH3, while the asymmetric BN stretch is 87 cm less than the + + BN stretch of BH2NH3 . Thus, the BN bonds of BH2NH2NH2 (1) can be considered to be either dative σ bonds or hybrids between dative σ bonds and ordinary σ bonds. Because the BN distances and the asymmetric BN stretching frequency are closer to those of the + + BH2NH3 , BN bonds of the BH2NH2NH2 (1) are placed in the ‘Hybrid Dative/Ordinary σ Bond’ columns of Table 6.10. Several structures have been optimized in an attempt to find a minimum energy structure which contains an ordinary σ bond. In almost every attempt to optimize a structure in which there is an ordinary σ bond between the boron and a nitrogen atom, the structure optimizes to a final geometry in which there is a double bond between the boron + and the nitrogen atom. For example, a bent HBNH2 structure, in which there is an ordinary bond between the boron and the nitrogen atom and the hydrogen atoms on the nitrogen atom are bent to avoid the lone pair of electrons on the nitrogen atom, optimizes to a planar structure, where the distance between the boron and the nitrogen atom shortens as the lone pair of the nitrogen atom are donated to the boron. The minimum + energy conformation of HBNH2 is one in which there is a double bond between the

77 boron and the nitrogen atom, not a single bond. The exceptions, where the bond between the boron and nitrogen atom remained an ordinary covalent σ bond, all had at least one imaginary frequency. For instance, the simplest example of an ordinary σ BN bond is that of the CS symmetry transition state for internal rotation about the BN bond of the C2V

BH2NH2 structure, which has a double bond between the boron and the nitrogen atom that Otsby et al. consider to be an ordinary covalent σ bond overlaid by a dative π bond

[9]. In the CS BH2NH2 transition state, the dative π bond of the C2V BH2NH2 molecule is broken as hydrogen atoms of the amino component, which are planar to the BH2 in the

BH2NH2 molecule, are rotated to an orientation where the hydrogen atoms of the NH2 component are orthogonal to the hydrogen atoms of the BH2 component, such that the bond between the boron and nitrogen atom of the transition state is an ordinary covalent

σ bond [9]. For pictures of the CS BH2NH2 transition state, which will now be referred to as ‘BH2NH2 (CS – TS)’ throughout this work, and the C2V BH2NH2 molecule, see Figure 6.9.

In BH2NH2 (CS – TS), the MP2/pVTZ+ calculated distance between the boron and the nitrogen atom is 1.48 Å. As can be seen in Table 6.10, this distance is in good agreement with the covalent BN bond lengths of the molecules labeled ‘1-o’, ‘3’, and ‘4’ in reference [6] as determined using gas electron diffraction and X-ray diffraction. The -3 BN distance of BH2NH2 (CS – TS) is only 1.88 x 10 Å longer than the B4N3 distance of structure 3, which has been determined by X-ray diffraction and has the shortest ordinary covalent σ bond of the structures of reference [6], and is 1.77 x 10-2 Å shorter than the B2N3 distance of structure 1-o, which has been determined by gas electron diffraction and has the largest ordinary covalent σ bond of the structures of reference [6]. The BN bond length and stretching frequency of the BH2NH2 (CS – TS) will be used as references for the ordinary covalent σ bonds, which are labeled as ‘Ordinary σ’ bonds in Table 6.10, + + for the B and BH2 systems. + + The BN(a) bonds of BHNNH (3) and (H2)BHNNH (1) and both BN bonds of + + (H2)BHNNH (2) and (H2)BHNHNH2 (4) all closely resemble the BN bond of the + BH2NH2 (CS – TS). The distances between the boron and N(a) of BHNNH (3) and

78 + + + (H2)BHNNH (1) and both nitrogen atoms of (H2)BHNNH (2) and (H2)BHNHNH2 (4) are at most 0.03 Å less than and 0.06 Å greater than the BN distance of BH2NH2 (CS – TS). There is less than 300 wavenumbers difference between the stretching frequencies + + for the BN(a) bond of BHNNH (3) and (H2)BHNNH (1) as well as both BN bonds of + + (H2)BHNNH (2) and (H2)BHNHNH2 (4) and the BN stretching frequency of the

BH2NH2 (CS – TS). Because of the similarities in BN bond lengths and stretching + + frequencies between the BN(a) bonds of BHNNH (3) and (H2)BHNNH (1), both BN + + bonds of (H2)BHNNH (2) and (H2)BHNHNH2 (4), and the BN bond of the BH2NH2 (CS + + – TS), the BN(a) bonds of BHNNH (3) and (H2)BHNNH (1) and both BN bonds of + + (H2)BHNNH (2) and (H2)BHNHNH2 (4) are considered ordinary sigma bonds. The covalent sigma BN bonds that are of particular interest in this system are + those of NH3BNH3 structure. The strength of the BN bond in this structure determines how easily ammonia can be removed from B+. Besides looking at the BN distances and stretching frequencies of this structure, the strength of the BN bonds in this structure can be evaluated by calculating the binding energy of B+ and two ammonia molecules and + comparing this binding energy with the binding energies of BH2 to diimide, eclipsed + hydrazine, and gauche hydrazine and with the binding energy of B to N2. The binding + + energies of the BH2 to diimide, eclipsed hydrazine, and gauche hydrazine and of B to two ammonias are large and thus demonstrate the strength of the BN bonds in the + + + + BH2NHNH , BH2NH2NH2 (1), BH2NH2NH2 (2), and NH3BNH3 structures. As can be + seen in Table 6.11, the BH2 is bound to the trans 1,2-diimide by 75.85 kcal/mol, to an eclipsed hydrazine by 114.54 kcal/mol, and to a gauche hydrazine by 92.68 kcal/mol. An ammonia molecule is bound to the boron cation by 68.51 kcal/mol. This difference + between the relative energy, including ZPE, of the BNH3 and the sum of the relative energies, including ZPE, of the infinitely separated boron cation and ammonia is only + 7.34 kcal/mol smaller than the difference in energy between the BH2NHNH and the + infinitely separated BH2 and trans diimide. Two ammonias are bound to a boron cation by 117.16 kcal/mol. This difference between the relative energy, with ZPE added in, of + the NH3BNH3 structure and the sum of the relative energies, with ZPE added, of the

79 infinitely separated boron cation and two ammonias is only slightly greater, by 2.62 + kcal/mol, than the energy difference between BH2NH2NH2 (1), in which the boron forms hybrid dative/ordinary σ bonds with both nitrogen atoms, and the infinitely separated + BH2 and eclipsed hydrazine. The addition of a second ammonia molecule to the boron only drops the relative energy, including ZPE, down by 48.65 kcal/mol, which is 71 percent of the drop in relative energy, including ZPE, after the addition of the first + + + + ammonia. In the BH2NHNH , BH2NH2NH2 (1), BH2NH2NH2 (2), BNH3 , and + NH3BNH3 , the boron is bound to the dinitrogen by at least 6 times more kcal/mol than + the boron is bound to the nitrogen atom in the previously discussed electrostatic B (N2) + structure. Because the bonds in the NH3BNH3 structure are covalent bonds and are not simply electrostatic, a lot of energy will be required to isolate the ammonias from the boron cation. It is interesting to note that while the boron is initially positively charged, + MP2/TZ+ calculations predict that it is negatively charged in the BH2NH2NH2 (1) and + NH3BNH3 intermediates. There are two ways to determine the charge of atoms from the output given by the Gaussian 98 program, Mulliken charges and the dipole moment. Since the Mulliken charges are calculated from the SCF (Self-Consistent Field) wavefunction and the dipole moment is calculated from the final MP2 wavefunction, Mulliken charges are less reliable than the dipole moment. Thus, only the dipole moment information will be used to determine the charge of the boron. In the Gaussian 98 program, the dipole moment goes from the negative charge toward the positive charge. For instance, in the MP2/TZ+ optimization of HF, the dipole moment points from the fluorine atom toward the hydrogen atom. As can be seen in Figure 6.10, the dipole + + moments of the BH2NH2NH2 (1) and NH3BNH3 structures point away from the boron toward the nitrogen atoms, indicating that the boron is negatively charged and the nitrogen end of the molecules is positively charged. The dipole moments of this chapter and those of Chapter VII and VIII were calculated at the MP2/pVTZ+ level of theory. These dipole moments are in agreement with the resonance structures of the + + BH2NH2NH2 (1) and NH3BNH3 in which there is a single bond between the boron and

80 the nitrogen atoms, the boron is negatively charged, and the nitrogen atoms are positively charged, see Figure 6.11.

6.3.2.2 Boron-Nitrogen Pi Bonds As mentioned previously, Otsby et al. consider the ordinary covalent σ bond between the boron and the nitrogen atom of the C2V BH2NH2 molecule to be overlaid by a dative π bond [9]. The π bond between the boron and the nitrogen atom of the BH2NH2 is considered to be dative because the rotation of the NH2 into an orthogonal orientation results in both the former π-electrons occupying an atomic orbital on the nitrogen atom

[9]. In the BH2NH2 molecule, a MP2/TZ+ calculation predicts that the distance between the boron and the nitrogen atom is 1.395 Å, which is only 4.08 x 10-3 Å greater than the BN distance observed experimentally for the molecule by Sugie et al. in a microwave study [9, 10]. The BN stretching frequency of BH2NH2 is calculated to be 1367 wavenumbers. When a hydrogen atom is taken away from the boron of the BH2NH2 to + form BHNH2 , the bond distance between the boron and the nitrogen atom shortens to 1.32 Å and the BN stretching frequency increases to 1450 and 1599 cm-1. The BN stretch + of the BHNH2 occurs at two frequencies due to coupling with bends of the hydrogen atoms on the nitrogen atom. As in the BH2NH2 molecule, the π bond between the B and + N of the BHNH2 can be considered to be dative since the breaking of the bond would result in both π-electrons occupying an atomic orbital on the nitrogen atom. It is + interesting to note that the BN distance of the BHNH2 is only 0.02 Å larger than the MP2/TZ+ predicted distance between the B and N of the bent BNH+, in which the bond between the B and N is a double bond, the boron is positively charged, and the angle between the B, N, and H is bent due to the lone pair on the nitrogen atom. The BN + -1 -1 stretching frequencies of the BHNH2 are only 19 cm less than and 130 cm greater + + + than the BN stretch of the BNH . The HOMOs of the BH2NH2, BHNH2 , and BNH structures are all similar, in that the out-of-plane p orbitals of the boron and nitrogen atom overlap, see Figure 6.12. Although the BN distances, stretching frequencies, and HOMOs + + + of the BHNH2 and BNH are very similar, the π bond between B and N of the BNH is

81 considered in this work to be ordinary because if the bond were to be broken one of the former π-electrons would occupy an atomic orbital on the nitrogen atom and the other π- electron would occupy an atomic orbital on the boron. Because the differences between + ordinary σ + dative π BN bonds of the BH2NH2 and BHNH2 and the ordinary σ + ordinary π BN bond of the BNH+ are not very large, there will be no hybrid category for the double bonds as there is for the single bonds. The BN distances and the BN + stretching frequencies of the BH2NH2 and BHNH2 are used as references for the BN bonds of the boron cation and boron dihydride cation catalytic systems that are referred to as ‘ordinary σ + dative π’ bonds. + + + Because the BN(a) bonds of the BHNNH (1), BHNNH (2), and NH2BHNH3 + + + and the BN(b) bonds of the BHNNH (3), (H2)BHNNH (1), (H2)BHNHNH2 (1), + + (H2)BHNHNH2 (2), and (H2)BHNHNH2 (3) are similar to the BN bonds of the BH2NH2 + and BHNH2 , they are classified in this work as ‘ordinary σ + dative π‘ bonds. As can be seen in Table 6.12, the distances and stretching frequencies of the BN(a) bonds of the + + + BHNNH (2) and NH2BHNH3 and the BN(b) bonds of the (H2)BHNHNH2 (1), + + (H2)BHNHNH2 (2), and (H2)BHNHNH2 (3) all fall within the range between the BN + distances and stretching frequencies of BH2NH2 and BHNH2 , with the exception of the + + 1185 and 1085 wavenumber frequencies of the BHNNH (2) and (H2)BHNHNH2 (2). The + + BN stretches of the BHNNH (2) and (H2)BHNHNH2 (2) occur at two or three frequencies due to coupling with the NN stretch, BH stretches, and the wag or frustrated + rotation of the H2 on the (H2)BHNHNH2 (2). The BN(a) bond distance of the + + + BHNNH (1) and the BN(b) bond distances of the BHNNH (3) and (H2)BHNNH (1) are only 0.01 and 0.03 Å greater than the BN bond distance of the BH2NH2. Also, the stretching frequencies BN(a) bond of the BHNNH+(1) and of the BN(b) bonds of the + + -1 -1 BHNNH (3) and (H2)BHNNH (1) alone, not including the 1130 cm and 1125 cm + + stretches of the BHNNH (3) and (H2)BHNNH (1) which are coupled asymmetrically with the BN(a) stretches, are at most 50 cm-1 larger than and 59 cm-1 smaller than the BN stretching frequency of the BH2NH2.

82 + + Also, the BN(a) bonds of the BHNNH (1) and NH2BHNH3 and the BN(b) bonds + + + + of the BHNNH (3), (H2)BHNNH (1), (H2)BHNHNH2 (1), (H2)BHNHNH2 (2), and + + (H2)BHNHNH2 (3) are similar to the BN bonds of the BH2NH2 and BHNH2 in that the out-of-plane p orbitals, or the p orbitals that are not in the plane formed by the boron and the nitrogen atoms, of the boron and the nitrogen atom overlap in either the HOMO or another occupied molecular orbital, see Figure 6.13. However, as can be seen in Figure 6.13, the out of plane p orbitals of the boron and both nitrogen atoms overlap in the HOMO-1 of the BHNNH+(1), the HOMO-1 of the BHNNH+(2), and the HOMO-2 of the BHNNH+(3). In the HOMO-2 of the BHNNH+(3), it is possible that the lone pair electrons from both nitrogen atoms are donated to an empty p orbital of the boron. The HOMO-1 of the BHNNH+(1) and HOMO-2 of the BHNNH+(3) indicate that any of the resonance structures depicted in Figure 6.11 are viable for the BHNNH+(1) and BHNNH+(3). Although the out-of-plane p orbitals of the boron and both nitrogen atoms overlap in HOMO-1 of the BHNNH+(1), the 1.67 Å BN(b) bond of the BHNNH+(1) is still considered to be a dative sigma bond in this work due to the similarity of the BN(b) bond length and stretching frequencies to the BN bond length and stretching frequency of + BH3NH3. Also, the 1.47 Å BN(a) bond of the BHNNH (3) is still considered to be an ordinary sigma bond in this work due to the similarity of the BN(a) bond length and stretching frequencies to the BN bond length and stretching frequency of ‘BH2NH2 (Cs- + TS)’. Although the illustration of the HOMO-3 of the (H2)BHNNH (1) in Figure 6.13 is very similar to the illustration of the HOMO-2 of the BHNNH+(3), where the out-of- plane p orbitals of the boron and both nitrogen atoms overlap, eigenvalues of these + orbitals indicate that the HOMO-3 of the (H2)BHNNH (1) is different than the HOMO-2 + + of the BHNNH (3). In the HOMO-2 of the BHNNH (3), only the pz orbitals of the boron + and the nitrogen atoms have eigenvalues. In the HOMO-3 of the (H2)BHNNH (1), however, the s and p orbitals of the boron have eigenvalues while only the p orbitals of the nitrogen atoms have eigenvalues. However, because the BN bond lengths and + stretching frequencies of the (H2)BHNNH (1) are very similar to those of the + + BHNNH (3), the BN(a) bond of the (H2)BHNNH (1) is still considered an ordinary

83 + sigma bond and the BN(b) bond of the (H2)BHNNH (1) is still considered an ordinary sigma + dative pi bond in this work.

6.3.3 Steps of the B+ Catalytic Reduction of Dinitrogen to Form Ammonia The boron cation catalytic reduction of dinitrogen to form ammonia occurs in three phases. The reduction of the boron cation and dinitrogen with two dihydrogen + molecules to form BH2NHNH is the first phase, Phase 1, and the reduction of the + + BH2NHNH with a dihydrogen molecule to form BH2NH2NH2 (1) is the second phase,

Phase 2. In the third phase, Phase 3, a hydrogen atom transfers from the boron of the BH2 + + component of BH2NH2NH2 (1) to reduce the hydrazine component to form NH2BHNH3 , + then a hydrogen atom transfers from the boron of the NH2BHNH3 structure to the NH2 + component to form NH3BNH3 . Phases 1 and 2 both occur in similar three-step mechanisms, whereas the three-step mechanism of Phase 3 is very different from the mechanisms of Phases 1 and 2. The mechanisms of Phases 1 and 2 will be compared in section 6.3.3.1 and Phase 3 will be discussed and contrasted with Phases 1 and 2 in section 6.3.3.2.

6.3.3.1 Steps of Dinitrogen and Diimide Reduction

In the first step of the mechanisms of Phases 1 and 2, an H2 molecule is added to + the boron cation and the dinitrogen in Phase 1 and to the BH2NHNH in Phase 2. Initially, the dihydrogen molecule approaches from infinity and forms weak electrostatic + + bonds with the boron and nitrogen species, (H2)B (N2) in Phase 1 and BH2NHNH (H2) in

Phase 2. Then the electrostatically bound H2 molecule continues to move in closer to the + + B (N2) and to the BH2NHNH . The bond between the hydrogen atoms breaks as one hydrogen atom of the H2 adds to the distal nitrogen atom while the other hydrogen atom adds elsewhere. In Phase 1 the other hydrogen atom adds to the boron to form BHNNH+(1), through TS(1), whereas in Phase 2 the other hydrogen atom adds to another hydrogen atom to form a new H2, which then binds electrostatically to form + (H2)BHNHNH2 (1), through TS(6).

84 The transition states of the first step of Phases 1 and 2, TS(1) and TS(6), are similar in that the bond of an H2 and a bond between the nitrogen atoms break simultaneously as a NH bond and a BH or HH bond are formed. As the H2 breaks apart, the angle between the boron, proximal nitrogen atom, and distal nitrogen atom closes, enabling the hydrogen atoms of the H2 molecule to form bonds with the distal nitrogen atom and the boron or H(4), simultaneously. Addition of a hydrogen atom to the distal nitrogen atom results in the breaking of one of the π bonds between the nitrogen atoms, where the NN distance of the intermediates of step one, BHNNH+(1) in Phase 1 and + + (H2)BHNHNH2 (1) in Phase 2, is 0.17 Å longer than the NN distance of the (H2)B (N2) + in Phase 1 and BH2NHNH (H2) in Phase 2. The activation energies of TS(1), Ea = 27.77 + kcal/mol relative to (H2)B (N2), and TS(6), Ea = 38.90 kcal/mol relative to + BH2NHNH (H2), are somewhat close. The 11 kcal/mol difference between the activation energies, including ZPEs, of TS(1) and TS(6) is due largely to the differences between the BN bonds of the + + (H2)B (N2) structure and those of BHNNH (1) being larger than the differences between + + the BN bonds of the BH2NHNH (H2) structure and those of (H2)BHNHNH2 (1). Since the formation of a BN bond helps to offset the energy required to break the HH bond of an H2 molecule and a bond between the nitrogen atoms, one can expect that the more BN bonds that are formed, the lower the activation energy needed to break HH and NN bonds + will be. In the (H2)B (N2), the bond between the B and N(a) is electrostatic, rBN(a) = 2.21 Å, and there is no bond between the B and N(b). Because the bond between the B and

N(a) is an ordinary σ + dative π bond, rBN(a) = 1.41 Å, and the BN(b) bond is a dative σ + bond, rBN(b) = 1.67 Å, in the BHNNH (1), TS(1) involves the formation of three covalent BN bonds, two sigma and one pi. While there is still no bond between the B and N(a) in + the BH2NHNH (H2), the bond between the B and N(b) is a hybrid between a dative sigma bond and an ordinary sigma bond, rBN(b) = 1.55 Å. Since the bond between the B + and N(b) is an ordinary σ + dative π bond in (H2)BHNHNH2 (1), rBN(b) = 1.35 Å, TS(6) only involves the formation of a dative π bond. Thus, more BN bonds are being formed

85 in TS(1) than in TS(6), which contributes to the activation energy, including ZPE, of TS(1) being 11 kcal/mol lower than the activation energy, including ZPE, of TS(6).

Also, the sterics and rotation involved in the addition of the H2 molecule to the + BH2NHNH contribute to the Ea of TS(6) being 11 kcal/mol higher than the Ea of TS(1). + The CS symmetry of the (H2)B (N2) structure is maintained in TS(1), but the CS + symmetry of the BH2NHNH (H2) structure is broken in TS(6). In the CS symmetry + + BH2NHNH component of the BH2NHNH (H2) structure, H(3) on the distal nitrogen atom and H(4) on the boron are in the same plane and are only 2.49 Å apart. Thus, the dihydrogen molecule is sterically hindered from coming closer to the CS symmetry + BH2NHNH . The hydrogen atoms on the boron and on the distal nitrogen atom must rotate out of the BNN plane in TS(6) to enable the H2 molecule to move in closer. Although the energy required for this rotation in TS(6) is small, no rotational energy is necessary in TS(1) for the H2 to move closer. The second step in the three-step mechanisms of both Phase 1 and Phase 2 involves the isomerization of the newly formed structures, BHNNH+(1) and + + (H2)BHNHNH2 (1), to lower energy cyclic geometries, BHNNH (3) and + + + (H2)BHNHNH2 (3). Initially, the BHNNH (1) and (H2)BHNHNH2 (1) isomerize to + + BHNNH (2) and (H2)BHNHNH2 (2), which are less strained and thus are lower in + + energy than the BHNNH (1) and (H2)BHNHNH2 (1) structures. The ring strain of the BHNNH+(1), in which there is a double bond between the B and N(a) and a dative single bond between the B and N(b), is non-existent in the BHNNH+(2), in which the double bond between the B and N(a) is shorter than it is in the BHNNH+(1), but there is no bond between the B and N(b). Due to the electrostatically bound H2 being out of the BNN + + plane, the (H2)BHNHNH2 (2) structure is less strained than the (H2)BHNHNH2 (1) structure, where the H2 is in the same plane as the borons and nitrogen atoms. The activation energies of this first isomerization are very low, where the Ea, including ZPE, of the isomerization between BHNNH+(1) and BHNNH+(2) through TS(2) is 5.13 kcal/mol relative to BHNNH+(1) and the Ea, including ZPE, of the isomerization between

86 + + (H2)BHNHNH2 (1) and (H2)BHNHNH2 (2) through TS(7) is -0.14 kcal/mol relative to + (H2)BHNHNH2 (1). + At the electronic level, (H2)BHNHNH2 (1) is a minimum and the Ea energy + + required for the isomerization of the (H2)BHNHNH2 (1) to (H2)BHNHNH2 (2) through TS(7) is positive, but ZPE calculations suggest that it is not a minimum and that Ea for TS(7) is negative. It could be that the harmonic approximation overestimates the ZPE of + + the (H2)BHNHNH2 (1) and that the (H2)BHNHNH2 (1) is actually a minimum. However, + + because the total relative energies of (H2)BHNHNH2 (1), TS(7), and (H2)BHNHNH2 (2) are so close, within 1.24 kcal/mol with ZPE included, and are all so much lower than the total relative energy of TS(6), by at least 50.29 kcal/mol, there is not much dynamical + significance in the differences between the energies of the (H2)BHNHNH2 (1), TS(7), + and (H2)BHNHNH2 (2) structures. There are most likely several different structures that + are very similar in structure and energy to (H2)BHNHNH2 (1), TS(7), and + + (H2)BHNHNH2 (2). Although the (H2)BHNHNH2 (1) structure might not be a local + minimum, it appears to be on the path toward forming BH2NH2NH2 . In the second isomerization of step two of Phases 1 and 2, the BNN angle closes and the distance between the boron and the distal nitrogen atom decreases to form a lower energy ring structure. In the BHNNH+(3) structure, the BN(a)N(b) angle of 104.20 degrees smaller than it is in BHNNH+(2) and the distance between the boron and N(b), the distal nitrogen atom, in the BHNNH+(3) isomer is 1.09 Å shorter than the BN(b) + + distance of the BHNNH (2). The BN(b)N(a) angle of the (H2)BHNHNH2 (3) is 64.70 + degrees smaller than the BN(b)N(a) angle of the (H2)BHNHNH2 (2) structure and the + distance between the boron and the distal nitrogen atom, N(a), of the (H2)BHNHNH2 (3) + is 0.95 Å shorter than it is in the (H2)BHNHNH2 (2). One might expect the relative + + energies, including ZPEs, of the BHNNH (3) and the (H2)BHNHNH2 (3) structures to be + + higher in energy than the BHNNH (2) and the (H2)BHNHNH2 (2) structures due to ring strain. However, the relative energy, including ZPE, of the BHNNH+(3) structure is almost 16 kcal/mol lower than that of the BHNNH+(2) structure and the relative energy, + including ZPE, of the (H2)BHNHNH2 (3) is almost 17 kcal/mol lower than that of the

87 + + (H2)BHNHNH2 (2). Most likely, the BHNNH (3) is lower in relative energy than the BHNNH+(2) due to the resonance stability of the BHNNH+(3) structure, where π electrons in the out-of-plane p orbitals are delocalized over the boron and nitrogen atoms, see the HOMO-2 picture of the BHNNH+(3) structure in Figure 6.13. As discussed + previously in section 6.3.1 of this chapter, the cyclic BHNHNH2 structure is a stable + minimum, while a non-cyclic BHNHNH2 minimum does not exist. The stability of the + cyclic BHNHNH2 structure most likely contributes to the relative energy of the + + (H2)BHNHNH2 (3) being lower than that of the (H2)BHNHNH2 (2). The decrease in + + relative energy between the (H2)BHNHNH2 (3) and (H2)BHNHNH2 (2) structures can also be attributed to the decrease in strain between the electrostatically bound H2 and the + + H(3) in the (H2)BHNHNH2 (3), where the rH(3)H(4) of the (H2)BHNHNH2 (3) is 3.73 Å + and the rH(3)H(4) of the (H2)BHNHNH2 (2) is 2.50 Å. The activation energy required for the isomerization of BHNNH+(2) to BHNNH+(3) through TS(3), Ea = 16.87 kcal/mol relative to BHNNH+(2) and including ZPE, is 11.56 kcal/mol larger than the activation energy required for the isomerization of + + (H2)BHNHNH2 (2) to (H2)BHNHNH2 (3) through TS(8), Ea = 5.31 kcal/mol relative to + (H2)BHNHNH2 (2) and including ZPE. Similarity between the structures of TS(8) and + (H2)BHNHNH2 (2) contribute to the activation energy of TS(8) being nearly 12 kcal/mol lower than the Ea of TS(3). TS(8) is an early transition state in that its structure more + + closely resembles the (H2)BHNHNH2 (2) isomer than the (H2)BHNHNH2 (3) intermediate. In particular, the bond between the boron and the distal nitrogen atom + changes very little between (H2)BHNHNH2 (2) and TS(8) with the rBN(a) of TS(8) being + only 0.07 Å smaller than the rBN(a) of (H2)BHNHNH2 (2), where as the rBN(a) is 0.88 Å + larger in TS(8) than it is in (H2)BHNHNH2 (3). In comparison, TS(3) is neither early nor late. The distance between the boron and N(b) is 0.43 Å smaller in TS(3) than it is in BHNNH+(2) and is 0.66 Å larger in TS(3) than it is in BHNNH+(3). Also, although the bonds between the boron and the hydrogen atoms of the H2 molecule weaken as the + dihydrogen molecule moves away from the BHNHNH2 , rBH(4) = 2.48 Å and rBH(6) = 2.51 + Å, the dihydrogen molecule is still slightly electrostatically bound to the BHNHNH2 in

88 TS(8). Because the BH bonds between the dihydrogen molecule and the boron in the + (H2)BHNHNH2 (2) are strongly electrostatic or weakly covalent, as discussed in section

6.3.1, and the H2 is still somewhat electrostatically bound to the boron in TS(8), not much energy is required to weaken the BH bonds between the dihydrogen molecule and the + boron. Thus, the energy required to reach TS(8) from (H2)BHNHNH2 (2) is less than the energy required to reach TS(3) from BHNNH+(2). Another possible contributor to the activation energy of TS(8) being low is the + stability of the cyclic, BHNHNH2 structure. As discussed previously in section 6.3.1, an + + isolated, non-cyclic BHNHNH2 structure similar to the BHNHNH2 component of the + (H2)BHNHNH2 (2) does not exist and optimizes to the stable, cyclic, CS symmetry + + + BHNHNH2 , which is similar to the BHNHNH2 component of the (H2)BHNHNH2 (3). Thus, one might expect that very little to no energy would be required for the + + (H2)BHNHNH2 (2) to isomerize to (H2)BHNHNH2 (3). However, the dihydrogen molecule, which sterically hinders the distal nitrogen atom from moving in closer to the + boron in the (H2)BHNHNH2 (2), must be moved and therefore the BH bonds between the boron and the H2 must be weakened and elongated so that the BN(b)N(a) angle can close + to form (H2)BHNHNH2 (3) and energy is required to weaken these BH bonds. + + The BHNNH (3) and (H2)BHNHNH2 (3) final intermediates of step two are + + somewhat similar. In the BHNNH (3) and BHNHNH2 structures, the bond between the boron and the N(b) is a double bond, rBN(b) = 1.43 and 1.34 Å, respectively, and the bond between the boron and the N(a) is a single bond, rBN(a) = 1.47 and 1.58 Å, respectively. The BN(a)N(b) angle of the BHNNH+(3) structure at 62.06 degrees is somewhat similar

+ o to the BN(a)N(b) angle of the BHNHNH2 structure, θBN(a)N(b) = 52.02 . Also, the

+ o o BHNNH (3) is planar, φH(1)N(b)N(a)B B = 180.00 and φH(2)BN(a)N(b) = 180.00 , and H(1) and

+ o H(2) of the BHNHNH2 structure are nearly planar, φH(1)N(b)N(a)BB = 179.71 and o φH(2)BN(a)N(b) = 179.86 . While the second steps of Phases 1 and 2 are fairly similar in that lower energy ring structures are formed, where the bond between the nitrogen atom to which a hydrogen atom is added in step three and the boron becomes a sigma bond, there are

89 some small differences between the second steps of Phases 1 and 2. One difference is that in Phase 1 the distal nitrogen atom of the BHNNH+(1) structure becomes the proximal nitrogen atom in the BHNNH+(3), where as in Phase 2 the distal nitrogen atom of the + + (H2)BHNHNH2 (1) is also the distal nitrogen atom in the (H2)BHNHNH2 (3) isomer.

Also, Phase 2 is different from Phase 1 in that throughout Phase 2 there is an H2 molecule + that is electrostatically bound to a BHNHNH2 moiety, which offsets the energy required to form a BNN ring. The last step of the three-step mechanism of Phase 1 is different from the last step of Phase2. In step three of Phase 1, a dihydrogen molecule approaches the + + BHNNH (3) structure from infinity to form (H2)BHNNH (1). In Phase 2, however, a dihydrogen molecule does not need to be added because a dihydrogen molecule is formed + in TS(6) and is already electrostatically bound in the (H2)BHNHNH2 (3) structure. The rest of step three of Phase 1 is similar to the third step of Phase 2. In the second part of step three of Phase 1 and the first part of step three of Phase 2, the electrostatically bound + + dihydrogen molecules of the (H2)BHNNH (1) and (H2)BHNHNH2 (3) structures move in + + + closer to the BHNNH and BHNHNH2 structures to form the (H2)BHNNH (2) and + (H2)BHNHNH2 (4) isomers. Then, as the H2 molecules continue to move in closer, the bond between the hydrogen atoms breaks and atom adds to the distal nitrogen atom while + + the other hydrogen atom adds to the boron to form BH2NHNH and BH2NH2NH2 (1). + + The isomerization of the (H2)BHNNH (1) to (H2)BHNNH (2) in Phase1 is + + similar to the isomerization of the (H2)BHNHNH2 (3) to the (H2)BHNHNH2 (4) in Phase + 2. The dihydrogen goes from being weakly bound in the (H2)BHNNH (1) and + + (H2)BHNHNH2 (3) structures to being very strongly bound in the (H2)BHNNH (2) and + + (H2)BHNHNH2 (4) structures. As the H2 molecule gets closer to the BHNNH and + + BHNHNH2 components, the nearly planar hydrogen atoms of the BHNNH and + + BHNHNH2 rotate away from the incoming H2 and the symmetry of the BHNNH and + BHNHNH2 moieties distorts. The dihedral angles between H(1) and H(2) and the plane of the boron and nitrogen atoms, which are somewhat close to 180 or -180 degrees in the + + (H2)BHNNH (1) and (H2)BHNHNH2 (3) structures, decrease or increase, respectively,

90 o o significantly, where φH(1)N(b)N(a)B B = 175.39 and φH(2)BN(a)N(b) = -115.79 in the

+ o o (H2)BHNNH (2) and φH(1)N(b)N(a)BB = 113.31 and φH(2)BN(a)N(b) = 117.62 in the + + (H2)BHNHNH2 (4). Also, as the dihydrogen molecule moves in closer to the BHNNH + and BHNHNH2 components, the distance between the boron and nitrogen atoms + increases, with the exception of the BN(a) bond in the (H2)BHNHNH2 (4), which decreases by 0.04 Å. In TS(4) and TS(9), the dative π bonds between the B and N(b) in + + the (H2)BHNNH (1) and (H2)BHNHNH2 (3) structures, rBN(b) = 1.43 Å in + + (H2)BHNNH (1) and rBN(b) = 1.34 Å in (H2)BHNHNH2 (3), break. In the + + (H2)BHNNH (2) and (H2)BHNHNH2 (4) structures, the bonds between the B and N(b) + are ordinary sigma bonds, rBN(b) = 1.48 Å in (H2)BHNNH (2) and rBN(b) = 1.44 Å in + (H2)BHNHNH2 (4). Very little activation energy, Ea = 0.95 kcal/mol relative to + (H2)BHNNH (1) and including ZPE, is required be required for an H2 to move in closer to the BHNNH+. The activation energy, Ea = 9.08 kcal/mol relative to + (H2)BHNHNH2 (3) and including ZPE, required for the H2 to move in closer to the + BHNHNH2 is somewhat small as well. Most likely, the activation energy of TS(4) is 8.12 kcal/mol lower than the Ea of

TS(9) due to the large difference in the way that the H2 molecule is bound to the + + BHNHNH2 component in (H2)BHNHNH2 (3) and the way that it is bound in TS(9) and + + (H2)BHNHNH2 (4). In the (H2)BHNHNH2 (3) structure, as discussed previously, the electrostatic bonds between the boron and the hydrogen atoms of the H2 are weakly electrostatic, rBH(4) = 3.88 Å and rBH(6) = 3.91 Å. In TS(9), the dihydrogen molecule is much more strongly bound to the boron, where rBH(4) and rBH(6) = 1.71 Å and the B-H(4) and B-H(6) distances are 2.17 and 2.20 Å longer, respectively, than the B-H(4) and B- + + H(6) distances of (H2)BHNHNH2 (3). Also as discussed previously, the BHNHNH2 + moiety is very similar to the isolated CS BHNHNH2 structure. In TS(9), however, the

H(1) and H(2) rotate away from the incoming dihydrogen molecule. So φH(1)N(b)N(a)B B and

o o + φH(2)BN(a)N(b) go from being 179.7 and 179.9 , respectively, in the (H2)BHNHNH2 (3) to o o being 118.9 and 124.9 , respectively, in TS(9). These large differences as well as others + between the (H2)BHNHNH2 (3) and TS(9) and the similarities between TS(9) and the

91 + (H2)BHNHNH2 (4), see Table 6.4, indicate that TS(9) is a late transition state. In comparison, the changes in the electrostatic bonding of the dihydrogen molecule to the + + boron and in the BHNNH moiety are much less severe between the (H2)BHNNH (1), + TS(4), and (H2)BHNNH (2) structures, indicating that TS(4) is neither early nor late. The BH distances between the boron and the hydrogen atoms of the weakly bound + dihydrogen molecule in TS(4) are almost 0.50 Å shorter than those of (H2)BHNNH (1) + and are 0.50 Å longer than the strong electrostatic BH bonds of (H2)BHNNH (2). Also, + o the change in the BHNNH component is gradual, where φH(1)N(b)N(a)B B = 179.8 and

o + o φH(2)BN(a)N(b) = -165.7 in (H2)BHNNH (1), φH(1)N(b)N(a)B B = 178.7 and φH(2)BN(a)N(b) = -

o o o + 138.7 in TS(4), and φH(1)N(b)N(a)B = 175.4 and φH(2)BN(a)N(b) = -115.8 in (H2)BHNNH (2). Because TS(9) is a late transition state, where a significant amount energy is required for the H2 to go from being weakly bound to strongly bound and for the rotation of H(1) and + H(2) of the BHNHNH2 moiety, and TS(4) is neither early nor late, the Ea of TS(9) is larger than the Ea of TS(4). + The CCSD(T) and MP2 relative electronic energies of (H2)BHNNH (2) are lower than the CCSD(T) and MP2 relative electronic energies of TS(4) and the MP2 relative + electronic energies of the (H2)BHNHNH2 (4) are lower than the MP2 relative electronic energies of TS(9). Based on these electronic energies alone, at least at the MP2 level of + + theory, the (H2)BHNNH (2) and (H2)BHNHNH2 (4) structures are minima. It is + interesting to note that while the MP2 relative energies of (H2)BHNHNH2 (4) are lower than the MP2 relative energies of TS(9), the CCSD(T) relative energies of + (H2)BHNHNH2 (4) are higher than the CCSD(T) relative energies of TS(9). As the CCSD(T) calculations were carried out on single MP2 points and the relative energies of + (H2)BHNHNH2 (4) and TS(9) are very close, complete CCSD(T) optimization calculations might perhaps find that the CCSD(T) relative energies of the + (H2)BHNHNH2 (4) might indeed be lower than the CCSD(T) relative energies of TS(9). However, since complete CCSD(T) optimizations would consume vast amounts of time and memory, these calculations are too costly to run using our current resources at this time. The ZPE calculations predict that the MP2 and CCSD(T) total relative energies of

92 + + the (H2)BHNNH (2) and (H2)BHNHNH2 (4) structures will be higher than the total relative energies of their respective transition states, TS(4) and TS(9), and thus suggest + + that the (H2)BHNNH (2) and (H2)BHNHNH2 (4) structures are not minima. The + harmonic approximation might be overestimating the ZPE of the (H2)BHNNH (2) and + + (H2)BHNHNH2 (4) structures. Because the total relative energies of (H2)BHNNH (1 and 2) isomers, TS(4), and BHNNH+(3) are so close, within 1.94 kcal/mol with ZPE included, and are all so much lower than the total relative energy of TS(3), by at least 31.64 kcal/mol, there is not much dynamical significance in the differences between the energies these structures. Also, there is not much dynamical significance in the difference + between the energies of TS(9) and (H2)BHNHNH2 (4), because TS(9) is only 1.33 + kcal/mol lower in total relative energy, including ZPE, than (H2)BHNHNH2 (4) and because there is at least a 9.08 kcal/mol difference in total relative energy, including ZPE, between these structures and the total relative energies, including ZPE, of the neighboring + (H2)BHNHNH2 (4) and TS(11) structures. It is likely that there are several different + structures that are very similar in structure and energy to the (H2)BHNNH (1 and 2) + + isomers and TS(4) and to TS(9) and (H2)BHNHNH2 (4). Although the (H2)BHNNH (2) + + and (H2)BHNHNH2 (4) structures might not be a local minima, the (H2)BHNNH (2) + + appears to be on the path toward forming BH2NHNH and the (H2)BHNHNH2 (4) + appears to be on the path toward forming BH2NH2NH2 . Finally in the last step of both Phases 1 and 2, the bond between the hydrogen atoms of the electrostatically bound dihydrogen molecule breaks as one hydrogen atom adds to the distal nitrogen atom while the other hydrogen atom adds to the boron to form + + BH2NHNH through TS(5) in Phase 1 and to form BH2NH2NH2 (1) through TS(10) in Phase 2. TS(5) and TS(10) are similar in structure. In both TS(5) of Phase1 and TS(10) of Phase 2, the nitrogen atom with the least hydrogen atoms or the nitrogen atom to which a hydrogen atom is to be added is the distal nitrogen atom. The distance between the boron and the distal nitrogen atom in TS(5) is 1.82 Å and the distance between the boron and the distal nitrogen atom in TS(10) is 1.60 Å. In both TS(5) and TS(10), the bond between the bond between the hydrogen atoms of the H2 is elongated and weak, where rH(3)H(4) =

93 1.13 Å in TS(5) and rH(4)H(6) = 1.01 Å in TS(10). Another similarity between TS(5) and

TS(10) is the proximity of the hydrogen atoms of the H2 to the boron, where rBH(3) = 1.30

Å and rBH(4) = 1.24 Å in TS (5) and rBH(4) = 1.32 Å and rBH(6) = 1.28 Å in TS(10). The structures of both TS(5) and TS(10) are cyclic, where the BN(b)N(a) angle of TS(5) is 57.56 degrees and the BN(a)N(b) angle of TS(10) is 64.84 degrees. The activation + + energies required to form BH2NHNH in Phase 1 and BH2NH2NH2 (1) in Phase 2 are + similar, Ea = 17.23 kcal/mol for TS(5) relative to (H2)BHNNH (2), including ZPE, and + Ea = 14.31 kcal/mol for TS(10) relative to (H2)BHNHNH2 (4), including ZPE. Although TS(1) and TS(6) of step 1 and TS(5) and TS(10) of step 3 of the three step mechanisms of Phases 1 and 2 all involve simultaneous breaking of a HH bond and formation of BH, NH, or HH bonds, the activation energies needed to reach TS(5) and TS(10) are about half of those of TS(1) and TS(6). A possible explanation for the lower activation energies of TS(5) and TS(10) can be found in a comparison of the structures of the transition states. Because the energies required to reach TS(5) and TS(10) from the + + (H2)BHNNH (2) and (H2)BHNHNH2 (4) reactants are somewhat low, at least in comparison to TS(1) and TS(6), one might expect that the change in geometry between these two transition states and the intermediates preceding them to be somewhat small. However, TS(1), TS(5), TS(6), and TS(10) are neither early nor late, that is to say that their structures do not resemble the intermediates preceding them more closely than the intermediates following them or vice versa, as can be seen in Table 6.13. The key to the lower activation energies of TS(5) and TS(10) lies in the proximity of both hydrogen atoms of the bound H2 molecule to the boron. As can be see in Table 6.13, the hydrogen atom that adds to the distal nitrogen atom is closer to the nitrogen atom than the boron in TS(1) and TS(6), where as the hydrogen atom that adds to the distal nitrogen atom is closer to the boron than the nitrogen atom in TS(5) and TS(10). The cyclic structure of TS(5) and TS(10) allows this hydrogen atom to be close to the boron and the distal nitrogen atom at the same time. In TS(5), the B-H(3) bond length is 1.30 Å, the N(b)H(3) bond length is 1.57 Å, and the B-H(3) stretching frequency is 204 cm-1 less than the B-H(4) stretching frequency. In TS(10), the B-H(4) bond length is 1.32

94 Å, the N(a)H(4) bond length is 1.43 Å, and the B-H(4) stretching frequency is 170 cm-1 less than the B-H(6) stretching frequency in TS(10). The three center-two electron bonding ability of the boron allows the hydrogen atom that adds to the distal nitrogen atom to bridge between the boron and the nitrogen atom. The increase in the number of BH bonds offsets the energy requirement of breaking an HH bond in TS(5) and TS(10). Thus, the cooperative interaction mechanism contributes to the activation energies of TS(5) and TS(10) being lower than the activation energies of TS(1) and TS(6).

6.3.3.2 Steps of Hydrazine Reduction Phase 3 of the boron cation catalytic system also occurs through a three-step mechanism. However, this mechanism is very different from the three-step mechanisms of Phases 1 and 2. Because dihydrogen is being added in Phases 1 and 2, the boron is reduced in Phase 1 and is neither reduced nor oxidized in Phase 2. However, in Phase 3, the boron is oxidized because the hydrogen atoms on the boron are transferred to the nitrogen atoms. The boron is oxidized again when the boron cation catalyst is recovered or separated from the two ammonias. The first step in the three-step mechanism of Phase 3 involves the isomerization + + of BH2NH2NH2 (1) to BH2NH2NH2 (2). In contrast, the first steps of Phases 1 and 2 + involve the addition of an H2 molecule. The isomerization of BH2NH2NH2 (1) to + BH2NH2NH2 (2) occurs through a late transition state, TS(11), which closely resembles + the BH2NH2NH2 (1) in structure and energy. In TS(11), the BN(a)N(b) angle is only 6.68 + degrees larger than the BN(a)N(b) angle of the BH2NH2NH2 (2) isomer and the BN(b) + distance is only 0.09 Å shorter than it is in the BH2NH2NH2 (2). The hydrazine + o components of TS(11) and BH2NH2NH2 (2) are very similar, where there is only a 10.98 + difference between the H(1)N(b)N(a)B dihedrals of TS(11) and BH2NH2NH2 (2) and o + only a 11.43 difference between the φH(4)N(b)N(a)B B of TS(11) and that of BH2NH2NH2 (2). + The first step of Phase 3 is endothermic as the BH2NH2NH2 (1) is 14.41 kcal/mol lower + in total relative energy, including ZPE, than the BH2NH2NH2 (2).

95 It is interesting to note that at the CCSD(T)/pVTZ(+) level of calculation, the gauche form of an isolated hydrazine, which is similar to the hydrazine component of the + BH2NH2NH2 (2), has an energy of 7.97 kcal/mol, including ZPE, relative to N2 + 2H2 and that the eclipsed form of an isolated hydrazine, which is similar to the hydrazine + component of the BH2NH2NH2 (1), has an energy of 16.2 kcal/mol, including ZPE, relative to N2 + 2H2. Although the gauche conformation is the more stable form of + + hydrazine, the BH2NH2NH2 (1) isomer is more stable than the BH2NH2NH2 (2) isomer. + Increased BN bonding in the BH2NH2NH2 (1) structure contributes to the relative energy, + including ZPE, of the BH2NH2NH2 (1) isomer being lower than the relative energy, + including ZPE, of the BH2NH2NH2 (2) isomer. As can be seen in Table 6.7, the BH2 is + bound to the eclipsed hydrazine in the BH2NH2NH2 (1) by 114.5 kcal/mol and is bound + to the gauche hydrazine in the BH2NH2NH2 (2) by 92.7 kcal/mol. The additional bond between the boron and a nitrogen atom atom of the hydrazine results in the energy of the + + BH2NH2NH2 (1) isomer being lower than the energy of the BH2NH2NH2 (2) isomer. As discussed previously, steps 2 and 3 of Phase 3 are different than steps 2 and 3 of Phases 1 and 2, in that hydrogen atoms are removed from the boron. The process of removing a hydrogen atom from the boron of a BH2 or BH component is very costly, where the activation energy required to remove the first hydrogen atom through TS(12) is + 73.17 kcal/mol, relative to BH2NH2NH2 (2), and the Ea required to remove the second + hydrogen atom through TS(13) is 103.48 kcal/mol, relative to NH2BHNH3 . In TS(12), the elongation of the B-H(6) bond and the breaking of the bond between the nitrogen atoms of the hydrazine contribute to the high energy of TS(12). The breaking of the BH(6) and NN bonds is only offset a little by the formation of the N(b)H(6) bond. The formation of the BN(b) bond does not occur until well after TS(12). At one point during the optimization of the geometry of TS(12) displaced slightly toward the negative direction of the eigenvector of the imaginary frequency, the newly formed ammonia + + moves away from the HBNH2 component, rBN(b) = 2.70 Å, while the HBNH2 becomes o o nearly planar, φH(2)BH(5)H(3) = 172.461 and θH(2)BN(a) = 179.986 . However, the ammonia + eventually begins to move toward the HBNH2 until the nitrogen atom of the ammonia

96 + forms a covalent bond with the boron, rBN(b) = 1.57 Å, in the NH2BHNH3 intermediate. + + The NH2BHNH3 is very stable and it is the global minimum of the B catalytic system with the lowest total energy, which includes ZPE, of -207.85 kcal/mol. The third step, in which the last hydrogen atom is transferred from the boron, is + highly endothermic, where the energy difference between the NH2BHNH3 and the + NH3BNH3 is 86.89 kcal/mol, when ZPE is included. Although the change in geometry required to reach TS(13) appears minimal in Figure 6.1, Table 6.5 reveals the considerable geometry change that is required to reach TS(13). In TS(13), the B-H(2) bond elongates by 0.28 Å and the H(2) is closer to the N(a), rN(a)H(2) decreases by 1.06 Å, than the boron. As can be seen from the proximity of the H(2) to both the boron and N(a) and from the B-H(2) stretch occurring at the same frequency as the N(a)H(2) stretch, 2081 cm-1, the H(2) is bridging between the boron and the nitrogen atom. In order for the H(2) to transfer from the boron to N(a), the H(2) and H(5) must rotate out of the BNN plane, wherein the H(2)N(a)N(b)B and the H(5)N(a)N(b)B dihedrals transition from 0 + degrees in the NH2BHNH3 structure to 54.71 degrees and -35.74 degrees, respectively, + in TS(13). The stability and low energy of the NH2BHNH3 , the breaking of the BH bond, and the breaking of the CS symmetry as H(2) and H(5) twist out of the BNN plane result in the energy of TS(13) being large. This transition state is a late transition state; the geometry and thus the energy of TS(13) closely resemble the geometry and energy of + + NH3BNH3 . The NH3BNH3 is fairly stable, where the boron cation is bound to the two ammonias by 101.2 kcal/mol of energy, including ZPE. Thus, a significant amount of energy will be required to recover the boron cation catalyst.

6.3.4 Overall Trends of the B+ Catalytic System Reduction of a nitrogen species or component results in the breaking of a NN bond, where the NN bond length increases and the NN stretching frequency decreases. In + the BH2NHNH final intermediate of Phase 1, the distance between the nitrogen atoms of the diimide component is 0.13 Å longer than the NN distance of an isolated triply bonded

N2 molecule, and the NN stretching frequency is almost 540 wavenumbers less than the

97 NN stretching frequency of a N2 molecule. The distance between the nitrogen atoms of + the BH2NH2NH2 (1), the final intermediate of Phase 2, is 0.22 Å longer than the NN + + bond length of BH2NHNH and the NN stretching frequency of the BH2NH2NH2 (1) is -1 + almost 660 cm less than the NN stretching frequency of the BH2NHNH structure. In the final intermediate of Phase 3, there are no bonds between the nitrogen atoms and the + distance between the nitrogen atoms of the NH3BNH3 is 1.10 Å longer than the NN + distance in the BH2NH2NH2 (1). Because there are no bonds between the nitrogen atoms, + none of the frequencies of the NH3BNH3 structure are NN stretches, where as the NN + stretching frequency of the BH2NH2NH2 (1) structure is 987 wavenumbers. Throughout the boron cation cycle, the reduction of a nitrogen species or component takes place at the distal nitrogen atom, or the nitrogen atom farthest from the boron, with the exception of the last step of Phase 3, where a hydrogen atom is + transferred to the proximal nitrogen atom in TS(13) to form NH3BNH3 . With the exception of the last two steps of Phase 3, the activation energy required to reduce a nitrogen species or component is very low, nearly zero kcal/mol for TS(7), to moderate, + almost 28 kcal/mol for TS(1) and almost 39 kcal/mol for TS(6). The B + N2 + 3H2 catalytic system is effective at activating the dinitrogen and is capable of producing ammonia. However, due to the large amount of energy required to recover the boron cation catalyst, the system becomes less effective towards the end of the cycle. For a comparison of the efficiency of the boron cation in reducing dinitrogen to form ammonia with the efficiency of other ammonia synthesis catalysts, see subsequent chapters.

98 Table 6.1: Calculated Geometrya and Relative Energy of the Stationary Points on the MinimumEnergy Pathway for B+ + + N2 + H2 → BHNNH (3) (Steps 1 and 2 of Phase 1).

+ + + + Property (H2)B (N2) TS(1) HBNNH (1) TS(2) BHNNH (2) TS(3) BHNNH (3)

Point Group CS CS CS CS CS CS CS

RH(1)H(2) (Å) 2.2929 1.5649 0.8444 1.0043 1.0154 0.9997 0.8054

rBH(1) (Å) 2.3040 1.8101 1.5468 2.1060 3.1317 3.0167 2.4434

rBH(2) (Å) 2.3423 1.4224 1.1725 1.1731 1.1664 1.1711 1.1670

rH(1)H(2) (Å) 0.7489 0.8962 2.1640 2.7547 4.2676 4.1165 3.4742 99 RNN (Å) 2.7708 1.8914 1.4060 1.6625 1.9133 1.6527 1.3000

rBN(a) (Å) 2.2148 1.7224 1.4137 1.3923 1.3153 1.3953 1.4705

rBN(b) (Å) 3.3272 2.2060 1.6684 2.1053 2.5171 2.0843 1.4263

rNN (Å) 1.1150 1.1646 1.2875 1.2983 1.2200 1.2871 1.2781

rN(b)H(1) (Å) 3.4731 1.5690 1.1231 1.0519 1.0405 1.0345 1.0307

rN(a)H(2) (Å) 3.2008 2.5075 2.5677 2.5645 2.4796 2.5654 2.5824

θH(1)BH(2) (deg) 18.53 29.17 104.62 111.08 164.63 156.38 146.18

θR H(1)H(2) r H(1)H(2) (deg) 87.03 116.54 106.17 123.57 167.09 159.88 145.44

θNBN (deg) 1.59 31.54 48.52 36.95 6.61 37.17 52.34

θR NN r N2 (deg) 3.80 64.46 77.48 54.71 9.40 55.70 92.21

θBN(a)N(b) (deg) 175.24 97.78 76.13 102.92 166.25 101.91 62.06

θH(1)N(b)N(a) (deg) 37.06 104.85 119.19 115.71 110.00 107.80 126.61

θH(2)BN(a) (deg) 90.17 105.36 166.20 176.95 175.21 176.71 156.37 aGeometry optimized at MP2/aug-cc-pVTZ level. Table 6.1: Continued.

+ 100 + + + Property (H2)B (N2) TS(1) HBNNH (1) TS(2) BHNNH (2) TS(3) BHNNH (3) Relative Energy MP2/pVDZ+ -13.68 8.95 -21.62 -15.51 -43.07 -29.10 -61.47 CCSD(T)/pVDZ+ -12.98 15.31 -14.73 -11.85 -39.50 -24.33 -54.55 MP2/pVTZ+ -14.52 6.68 -27.96 -20.20 -49.63 -33.80 -69.45 CCSD(T)/pVTZ(+) -14.51 11.40 -23.09 -18.21 -47.98 -30.83 -64.97 Relative ZPE MP2/pVDZ+ 1.95 3.96 7.50 7.75 8.46 8.26 9.74 MP2/pVTZ+ 1.97 3.82 7.48 7.72 8.48 8.20 9.79 Table 6.2: Calculated Geometrya and Relative Energy of the Stationary Points on the Minimum Energy Pathway for + + BHNNH (3) + H2 → BH2NHNH (Step 3 of Phase 1).

+ + + Property (H2)BHNNH (1) TS(4) (H2)BHNNH (2) TS(5) BH2NHNH

Point Group C1 C1 C1 C1 CS

RH(1)H(2) (Å) 0.8096 0.8508 0.9775 1.1030 1.2501

RH(3)H(4) (Å) 2.4476 1.9620 1.4456 1.1374 1.5896

rBH(1) (Å) 2.4458 2.4571 2.4840 2.4705 2.2723

rBH(2) (Å) 1.1656 1.1656 1.1684 1.1682 1.1736

101 rBH(3) (Å) 2.4775 1.9999 1.4952 1.3019 2.4932

rBH(4) (Å) 2.4738 1.9955 1.5003 1.2390 1.1779

rH(1)H(2) (Å) 3.4727 3.4491 3.3539 3.1732 2.6135

rH(3)H(4) (Å) 0.7434 0.7522 0.7839 1.1337 2.2583

RNN (Å) 1.3051 1.3213 1.3703 1.5648 1.9814

rBN(a) (Å) 1.4748 1.4880 1.5339 1.8200 2.4909

rBN(b) (Å) 1.4297 1.4426 1.4767 1.5269 1.5556

rNN (Å) 1.2747 1.2676 1.2475 1.2221 1.2432

rN(b)H(1) (Å) 1.0305 1.0299 1.0297 1.0305 1.0271

rN(a)H(2) (Å) 2.5822 2.5881 2.2854 1.5703 1.0331

θH(1)BH(2) (deg) 145.86 141.78 129.77 116.79 93.11

θH(3)BH(4) (deg) 17.27 21.70 30.34 52.93 64.77

θR H(1)H(2) r H(1)H(2) (deg) 145.31 142.86 137.12 132.60 125.41

θR H(3)H(4) r H(3)H(4) (deg) 90.29 90.34 89.61 93.55 132.27 a Geometry optimized at MP2/aug-cc-pVTZ level. Table 6.2: Continued.

+ + + Property (H2)BHNNH (1) TS(4) (H2)BHNNH (2) TS(5) BH2NHNH

θNBN (deg) 52.04 51.23 48.91 41.69 24.01

θR NN r N2 (deg) 92.25 92.28 92.89 104.86 140.20

θBN(a)N(b) (deg) 62.16 66.24 67.94 82.11 125.38

θH(1)N(b)N(a) (deg) 126.77 126.70 127.13 125.75 112.73

θH(2)BN(a) (deg) 155.73 150.38 135.04 118.66 139.70

102 θH(3)BN(a) (deg) 89.38 94.67 97.95 57.56 23.93

θH(3)N(a)N(b) (deg) 86.36 84.08 82.01 92.24 108.77

θH(4)BN(a) (deg) 101.67 109.14 118.16 99.78 88.70

φH(1)N(b)N(a)B (deg) 179.84 178.68 175.39 166.22 180.00

φH(2)BN(a)N(b) (deg) -165.74 -138.67 -115.79 -109.22 0.00

φH(3)BN(b)N(a) (deg) -81.40 106.24 110.77 138.62 180.00

φH(4)BN(a)N(b) (deg) 90.82 89.66 86.78 105.17 180.00 Relative Energy MP2/pVDZ+ -64.15 -63.80 -65.48 -50.03 -97.68 CCSD(T)/pVDZ+ -57.16 -56.76 -58.26 -42.37 -92.99 MP2/pVTZ+ -72.13 -71.78 -73.50 -56.94 -103.13 CCSD(T)/pVTZ(+) -67.59 -67.24 -68.76 -51.19 -101.43 Relative ZPE MP2/pVDZ+ 11.28 11.93 14.38 14.04 17.66 MP2/pVTZ+ 11.38 11.99 14.49 14.15 17.67 Table 6.3: Calculated Geometrya and Relative Energy of the Stationary Points on the Minimum Energy Pathway for + + BH2NHNH + H2→ (H2)BHNHNH2 (2) (Step 1 and Part of Step 2 of Phase 2).

+ + + Property BH2NHNH (H2) TS(6) (H2)BHNHNH2 (1) TS(7) (H2)BHNHNH2 (2)

Point Group CS C1 CS C1 C1

RH(1)H(2) (Å) 1.2495 0.8392 0.9494 0.9590 0.9895

RH(3)H(4) (Å) 1.5901 1.4945 1.6303 1.6387 1.7636

RH(5)H(6) (Å) 3.9101 2.3662 1.9247 1.8723 1.7045

rBH(1) (Å) 2.2693 2.1597 2.0422 2.0301 2.0172 103 rBH(2) (Å) 1.1738 1.1737 1.1722 1.1708 1.1683

rBH(3) (Å) 2.4980 2.4953 2.8568 2.7381 2.7042

rBH(4) (Å) 1.1775 1.2844 1.4599 1.4632 1.4280

rBH(5) (Å) 3.9276 2.5696 2.8568 3.0149 3.2208

rBH(6) (Å) 3.9276 2.2360 1.4825 1.4789 1.4358

rH(1)H(2) (Å) 2.6096 3.0441 2.7357 2.7029 2.6365

rH(3)H(4) (Å) 2.2670 2.6112 3.1550 2.9214 2.5023

rH(5)H(6) (Å) 0.7410 0.8997 2.4291 2.9210 3.6399

RNN (Å) 1.9801 1.8515 1.8848 1.8965 1.9063

rBN(a) (Å) 2.4899 2.3662 2.5030 2.5202 2.5265

rBN(b) (Å) 1.5540 1.4542 1.3545 1.3547 1.3608

rNN (Å) 1.2433 1.3092 1.4106 1.4093 1.3903

rN(b)H(1) (Å) 1.0270 1.0241 1.0172 1.0182 1.0194 aGeometry optimized at MP2/aug-cc-pVTZ level. Table 6.3: Continued.

+ + + Property BH2NHNH (H2) TS(6) (H2)BHNHNH2 (1) TS(7) (H2)BHNHNH2 (2)

rN(a)H(3) (Å) 1.0347 1.0285 1.0110 1.0115 1.0141

rN(a)H(5) (Å) 3.1175 1.3548 1.0110 1.0137 1.0156

rH(4)H(6) (Å) 3.0697 1.2737 0.7869 0.7869 0.8026

θH(1)BH(2) (deg) 93.04 129.50 113.89 112.43 108.78

θH(3)BH(4) (deg) 64.99 80.50 87.67 82.08 66.41

θH(5)BH(6) (deg) 10.83 20.08 58.24 72.07 95.05 104 θR H(1)H(2) r H(1)H(2) (deg) 125.34 130.04 122.57 122.04 121.21

θR H(3)H(4) r H(3)H(4) (deg) 132.32 125.90 125.88 124.02 126.69

θR H(5)H(6) r H(5)H(6) (deg) 90.00 112.12 129.62 129.13 132.06

θNBN (deg) 24.02 29.33 25.70 24.76 23.58

θR NN r N2 (deg) 140.24 135.94 146.43 147.66 148.74

θBN(b)N(a) (deg) 125.41 117.70 129.69 131.51 133.37

θH(1)N(b)N(a) (deg) 112.83 112.46 112.13 111.17 110.70

θH(2)BN(b) (deg) 115.67 134.56 139.93 138.90 136.00

θH(2)BN(a) (deg) 139.68 145.30 165.64 163.26 158.86

θH(3)N(a)N(b) (deg) 109.04 108.82 111.85 111.76 111.08

θH(4)BN(a) (deg) 88.93 78.55 98.60 97.38 88.07

θH(4)BN(b) (deg) 112.95 98.05 124.30 121.13 109.26

θH(5)N(a)N(b) (deg) 118.52 104.48 111.85 110.28 109.37

θH(5)N(a)H(3) (deg) 11.85 90.59 113.98 111.94 109.34 Table 6.3: Continued.

+ + + Property BH2NHNH (H2) TS(6) (H2)BHNHNH2 (1) TS(7) (H2)BHNHNH2 (2)

θH(6)BN(b) (deg) 76.38 75.00 93.29 96.88 84.39

θH(6)BH(4) (deg) 36.97 28.93 31.01 31.02 32.55

φH(1)N(b)N(a)B (deg) 180.00 -146.39 180.00 172.46 168.96

105 φH(2)BN(b)N(a) (deg) 180.00 127.09 180.00 172.40 169.76

φH(3)N(a)N(b)B (deg) 0.00 -45.81 -64.62 -32.54 16.51

φH(4)BN(b)N(a) (deg) 0.00 -48.65 0.00 -17.96 -27.14

φH(5)N(a)N(b)B (deg) 7.77 49.88 64.62 92.65 137.29

φH(6)BN(b)N(a) (deg) 5.57 -31.01 0.00 2.73 7.21 Relative Energy MP2/pVDZ+ -99.87 -64.44 -118.17 -118.05 -119.40 CCSD(T)/pVDZ+ -95.21 -56.90 -109.06 -109.06 -110.93 MP2/pVTZ+ -105.15 -69.40 -125.53 -125.15 -126.53 CCSD(T)/pVTZ(+) -103.55 -64.79 -119.34 -119.24 -121.07 Relative ZPE MP2/pVDZ+ 18.91 19.12 23.25 23.03 23.81 MP2/pVTZ+ 18.91 19.05 23.31 23.07 23.80 Table 6.4: Calculated Geometrya and Relative Energy of the Stationary Points on the Minimum Energy Pathway for + + (H2)BHNHNH2 (2) → BH2NH2NH2 (1) (Rest of Step 2 and Step 3 of Phase 2).

+ + + Property TS(8) (H2)BHNHNH2 (3) TS(9) (H2)BHNHNH2 (4) TS(10) BH2NH2NH2 (1)

Point Group C1 C1 C1 C1 C1 C2V

RH(1)H(2) (Å) 0.6003 0.7112 0.9006 0.9585 1.1178 1.2879

RH(3)H(4) (Å) 2.0012 2.5809 0.9064 0.8601 0.9841 1.8287

RH(5)H(6) (Å) 2.2960 3.0311 1.4836 1.3946 1.3129 1.2879

rBH(1) (Å) 2.0589 2.3255 2.1651 2.1357 2.2042 2.3049 106 rBH(2) (Å) 1.1663 1.1676 1.1702 1.1723 1.1702 1.1768

rBH(3) (Å) 2.7052 2.2792 2.2030 2.1945 2.1564 2.3049

rBH(4) (Å) 2.4780 3.8838 1.7146 1.5591 1.3234 2.3049

rBH(5) (Å) 2.7688 2.2790 2.2901 2.2905 2.2866 2.3049

rBH(6) (Å) 2.5124 3.9076 1.7099 1.5545 1.2803 1.1768

rH(1)H(2) (Å) 3.1237 3.3940 2.9782 2.8628 2.7308 2.6001

rH(3)H(4) (Å) 3.3014 3.7299 3.5071 3.3962 2.9882 2.8062

rH(5)H(6) (Å) 2.6211 2.0439 2.7446 2.7470 2.6154 2.6001

RNN (Å) 1.8403 1.2671 1.2803 1.2915 1.3829 1.4231

rBN(a) (Å) 2.4571 1.5777 1.5393 1.5353 1.5250 1.5994

rBN(b) (Å) 1.3288 1.3351 1.4154 1.4415 1.5987 1.5994

rNN (Å) 1.4351 1.4563 1.4796 1.4827 1.4539 1.4598

rN(b)H(1) (Å) 1.0185 1.0093 1.0142 1.0158 1.0182 1.0162 aGeometry optimized at MP2/aug-cc-pVTZ level. Table 6.4: Continued.

+ + + Property TS(8) (H2)BHNHNH2 (3) TS(9) (H2)BHNHNH2 (4) TS(10) BH2NH2NH2 (1)

rN(a)H(3) (Å) 1.0139 1.0170 1.0178 1.0175 1.0182 1.0162

rN(b)H(4) (Å) 3.0490 3.5765 2.2866 2.1706 1.4261 1.0162

rN(a)H(5) (Å) 1.0144 1.0194 1.0156 1.0153 1.0168 1.0162

rH(4)H(6) (Å) 0.7439 0.7416 0.7617 0.7732 1.0112 2.6001

θH(1)BH(2) (deg) 149.97 150.97 123.71 116.83 103.79 90.6647

θH(3)BH(4) (deg) 78.99 68.92 126.63 128.80 116.29 74.9960 107 θH(5)BH(6) (deg) 59.28 23.88 85.35 89.06 89.73 90.6647

θR H(1)H(2) r H(1)H(2) (deg) 140.14 146.91 128.21 125.50 124.86 125.91

θR H(3)H(4) r H(3)H(4) (deg) 95.11 59.09 107.51 114.10 119.53 90.00

θR H(5)H(6) r H(5)H(6) (deg) 96.46 35.59 106.56 111.68 121.51 125.91

θNBN (deg) 28.41 59.30 59.93 59.65 55.42 54.31

θR NN r N2 (deg) 143.98 101.04 95.55 94.18 86.72 90.00

θBN(a)N(b) (deg) 26.14 52.02 55.88 57.03 64.86 62.85

θBN(b)N(a) (deg) 125.46 68.68 64.20 63.32 59.72 62.85

θH(1)N(b)N(a) (deg) 112.46 126.00 114.47 110.91 111.98 112.50

θH(2)BN(b) (deg) 174.32 157.28 145.12 130.12 126.63 112.62

θH(3)N(a)N(b) (deg) 109.06 115.15 117.46 117.37 114.58 112.50

θH(4)BN(b) (deg) 102.19 66.86 93.37 92.59 94.03 21.96

θH(4)N(b)N(a) (deg) 80.54 56.44 82.25 82.06 92.95 112.50

θH(4)N(b)H(1) (deg) 151.35 96.15 158.76 154.22 138.25 112.86 Table 6.4: Continued.

+ + + Property TS(8) (H2)BHNHNH2 (3) TS(9) (H2)BHNHNH2 (4) TS(10) BH2NH2NH2 (1)

θH(5)N(a)N(b) (deg) 108.78 114.89 112.02 111.67 113.01 112.50

θH(5)N(a)H(3) (deg) 110.44 115.23 113.68 113.50 113.14 112.86

θH(6)BN(b) (deg) 101.52 76.61 117.01 119.62 100.69 112.62

θH(6)BH(4) (deg) 17.13 10.92 25.70 28.76 45.67 90.66

φH(1)N(b)N(a)B (deg) 177.66 179.71 118.93 113.31 104.47 115.59

φH(2)BN(b)N(a) (deg) 152.55 179.86 124.87 117.62 112.09 102.34 108 φH(3)N(a)N(b)B (deg) -54.38 -111.31 -106.07 -106.00 -106.80 -115.59

φH(4)BN(b)N(a) (deg) -37.01 -52.03 -103.18 -105.80 -122.72 -100.77

φH(4)N(b)N(a)B (deg) -29.00 -109.14 -47.36 -44.20 -41.25 -115.59

φH(5)N(a)N(b)B (deg) 66.13 111.22 119.62 120.45 121.60 115.59

φH(6)BN(b)N(a) (deg) -19.52 -46.85 -92.65 -95.46 -107.18 -102.34 Relative Energy MP2/pVDZ+ -110.28 -131.95 -125.16 -125.35 -112.86 -163.27 CCSD(T)/pVDZ+ -101.91 -122.31 -115.52 -115.50 -101.91 -153.68 MP2/pVTZ+ -117.16 -141.38 -134.15 -134.29 -121.82 -171.92 CCSD(T)/pVTZ(+) -111.52 -134.81 -127.58 -127.52 -113.97 -165.68 Relative ZPE MP2/pVDZ+ 19.64 20.57 22.27 23.62 24.38 28.17 MP2/pVTZ+ 19.56 20.59 22.44 23.71 24.47 28.33 Table 6.5: Calculated Geometrya and Relative Energy of the Stationary Points on the Minimum Energy Pathway for + + BH2NH2NH2 (1) → NH3BNH3 (Phase 3).

+ + + Property TS(11) BH2NH2NH2 (2) TS(12) NH2BHNH3 TS(13) NH3BNH3

Point Group C1 C1 C1 CS C1 C2V

RH(1)H(2) (Å) 1.3444 1.3291 1.1670 1.1342 0.6044 0.7190

RH(3)H(4) (Å) 1.9266 1.9237 1.9157 1.7641 1.8889 2.0234

RH(5)H(6) (Å) 1.0750 0.8688 1.1518 0.5687 0.7901 0.7190

rBH(1) (Å) 3.3167 3.3708 3.4668 2.1501 2.1275 2.1396 109 rBH(2) (Å) 1.1754 1.1769 1.1782 1.1776 1.4625 2.1396

rBH(3) (Å) 2.1419 2.1040 2.1489 2.1298 2.2824 2.3570

rBH(4) (Å) 2.6149 2.6401 2.6329 2.1994 2.2593 2.3570

rBH(5) (Å) 2.1516 2.1084 2.1784 2.0705 2.1307 2.1396

rBH(6) (Å) 1.1766 1.1757 1.3411 2.1501 2.1353 2.1396

rH(1)H(2) (Å) 4.1874 4.2929 4.6224 2.6217 3.4452 4.0303

rH(3)H(4) (Å) 2.8291 2.8269 2.9016 2.5097 2.5212 2.4176

rH(5)H(6) (Å) 2.7212 2.9388 2.7896 4.0652 3.9626 4.0303

RNN (Å) 1.9036 1.9562 1.6950 0.7599 0.8884 0.9993

rBN(a) (Å) 1.5558 1.5473 1.4275 1.3673 1.4814 1.6249

rBN(b) (Å) 2.4247 2.5098 2.4365 1.5671 1.5784 1.6249

rNN (Å) 1.4505 1.4421 2.1109 2.5181 2.4929 2.5624

rN(b)H(1) (Å) 1.0166 1.0160 1.0430 1.0228 1.0227 1.0247

rN(a)H(2) (Å) 2.3332 2.2978 2.3806 2.2758 1.2113 1.0247 aGeometry optimized at MP2/aug-cc-pVTZ level. Table 6.5: Continued.

+ + + Property TS(11) BH2NH2NH2 (2) TS(12) NH2BHNH3 TS(13) NH3BNH3

rN(a)H(3) (Å) 1.0219 1.0265 1.0217 1.0086 1.0312 1.0266

rN(b)H(4) (Å) 1.0164 1.0153 1.0333 1.0201 1.0272 1.0266

rN(a)H(5) (Å) 1.0290 1.0314 1.0217 1.0099 1.0193 1.0247

rH(4)H(6) (Å) 2.4163 2.4492 1.8702 1.6471 1.6660 1.6613

rN(b)H(6) (Å) 2.6766 2.6789 1.5938 1.0228 1.0259 1.0247

θH(1)BH(2) (deg) 131.37 135.73 167.00 99.82 146.75 140.73 110

θH(3)BH(4) (deg) 72.21 72.15 73.94 70.84 67.43 61.71

θH(5)BH(6) (deg) 105.95 124.51 102.23 148.80 136.52 140.73

θR H(1)H(2) r H(1)H(2) (deg) 148.69 150.96 170.19 122.97 124.98 90.00

θR H(3)H(4) r H(3)H(4) (deg) 78.09 76.48 77.98 88.05 90.63 90.00

θR H(5)H(6) r H(5)H(6) (deg) 123.69 126.86 117.30 85.83 89.82 90.00

θNBN (deg) 34.80 31.62 59.62 118.06 109.08 104.09

θR NN r N2 (deg) 51.23 46.20 56.99 81.19 86.16 90.00

θBN(a)N(b) (deg) 107.46 114.14 84.69 33.31 36.75 37.95

θH(1)N(b)N(a) (deg) 108.31 108.65 144.57 122.87 134.69 123.46

θH(2)BN(a) (deg) 116.67 114.33 131.79 126.66 48.59 27.49

θH(2)N(a)N(b) (deg) 124.31 141.21 106.32 57.84 84.24 123.46

θH(3)N(a)N(b) (deg) 107.08 107.11 88.87 93.40 92.95 85.96

θH(4)N(b)N(a) (deg) 107.32 107.65 91.20 86.16 87.05 85.96

θH(4)N(b)H(1) (deg) 108.62 108.70 101.25 107.47 107.91 108.16 Table 6.5: Continued.

+ + + Property TS(11) BH2NH2NH2 (2) TS(12) NH2BHNH3 TS(13) NH3BNH3

θH(5)N(a)N(b) (deg) 113.75 114.17 105.03 153.71 148.73 123.46

θH(5)N(a)H(3) (deg) 106.76 104.88 112.78 112.89 112.09 108.16

θH(6)N(b)N(a) (deg) 59.21 59.83 66.39 122.87 110.55 123.46

θH(6)BN(b) (deg) 89.01 85.10 37.35 26.47 27.14 27.49

φH(1)N(b)N(a)B (deg) 178.29 -170.73 161.61 71.65 46.36 70.86 111 φH(2)BN(b)N(a) (deg) 68.97 18.11 169.90 180.00 -52.47 -25.38

φH(2)N(a)N(b)B (deg) -23.28 -8.38 -1.04 0.00 54.71 70.86

φH(3)N(a)N(b)B (deg) -118.95 -119.42 -122.06 180.00 -179.84 180.00

φH(4)N(b)N(a)B (deg) -64.61 -53.18 -86.93 180.00 158.82 180.00

φH(5)N(a)N(b)B (deg) 123.35 124.94 124.63 0.00 -35.74 -70.86

φH(6)BN(b)N(a) (deg) -137.54 -168.35 179.17 -121.68 -99.88 -125.15

φH(6)N(b)N(a)B (deg) -20.20 -5.86 0.46 -71.65 -92.53 -70.86 Relative Energy MP2/pVDZ+ -148.12 -148.62 -65.23 -235.71 -126.46 -144.36 CCSD(T)/pVDZ+ -139.72 -140.14 -63.97 -224.63 -118.90 -139.42 MP2/pVTZ+ -154.62 -155.07 -69.14 -243.48 -133.53 -150.52 CCSD(T)/pVTZ(+) -149.35 -149.76 -70.31 -236.54 -129.49 -148.77 Relative ZPE MP2/pVDZ+ 26.80 26.83 20.58 28.62 25.07 27.31 MP2/pVTZ+ 26.84 26.82 20.54 28.69 25.13 27.50 Table 6.6: Comparison of Hydrogen-Hydrogen Distances and Stretching

Frequencies of the Complexes Involving Electrostatic Bonding Between an H2 + + + and a Boron-Nitrogen Moiety (B (N2), BHNNH ,BH2NHNH and + BHNHNH2 )

HH Stretching Structure HH Distances (Å) Frequencies (cm-1)

H2 0.7374 4518 + (H2)B (N2) 0.7489 4336 + (H2)BHNNH (1) 0.7434 4426 + (H2)BHNNH (2) 0.7839 3890 + BH2NHNH (H2) 0.7410 4464 + (H2)BHNHNH2 (1) 0.7869 3870 + (H2)BHNHNH2 (2) 0.8026 3615, 3618 + (H2)BHNHNH2 (3) 0.7416 4456 + (H2)BHNHNH2 (4) 0.7732 4038

112 Table 6.7: Binding Energies of the Various Structures Involving Electrostatic Bonds Between a Dihydrogen Molecule and a + a Boron-Nitrogen Moiety Calculated at the CCSD(T)/pVTZ(+) level of theory and relative to B +N2 +3H2. Sum of the + + + + relative energies, including ZPE, of the B (N2), BHNNH (3), BH2NHNH , and BHNHNH2 structures and an infinitely b c separated H2. Relative energy, including ZPE, of the electrostatic complexes listed in the structure column. The binding energies are the differences in energy between the first two columns. 113

Total Energy when the H2 Total Energy when Binding Energies a b c Structure is at infinity in kcal/mol H2 is bound in kcal/mol in kcal/mol + (H2)B (N2) -10.30 -12.55 2.25 + (H2)BHNNH (1) -55.18 -56.21 1.03 + BH2NHNH (H2) -83.75 -84.64 0.89 + (H2)BHNHNH2 (3) -113.17 -114.22 1.05 a + + + + Sum of the relative energies, including ZPE, of the B(N2), BHNNH (3), BH2NHNH , and BHNHNH2 structures and an

infinitely separated H2.

bRelative energy, including ZPE, of the electrostatic complexes listed in the structure column.

cThe binding energies are the differences in energy between the first two columns. Table 6.8: Comparison of Electrostatic or 3c-2e- and Covalent Boron-Hydrogen Distances and Stretching Frequencies of the - + + Complexes Involving Electrostatic or 3c-2e Bonding Between an H2 and a Boron-Nitrogen Moiety (B (N2), BHNNH , + + + + BH2NHNH , and BHNHNH2 ) and the BH2NHNH and BH2NH2NH2 structures.

Electrostatic or 3c-2e- Covalent Electrostatic or 3c-2e- BH Stretching Covalent BH Stretching -1 -1 114 Structure BH Distances (Å) Frequencies (cm ) BH Distances (Å) Frequencies (cm ) + (H2)B (N2) 2.30 and 2.34 + (H2)BHNNH (1) 2.47 and 2.48 184 1.17 2911 + (H2)BHNNH (2) 1.50 624 1.17 2862 + BH2NHNH 1.17 and 1.18 2723 and 2888 + BH2NHNH (H2) 3.93 1.17 and 1.18 2726 and 2888 + (H2)BHNHNH2 (1) 1.46 and 1.48 1033 & 1163 1.17 2848 + (H2)BHNHNH2 (2) 1.43 and 1.44 1085 & 1195 1.17 2870 + (H2)BHNHNH2 (3) 3.88 and 3.91 1.17 2897 + (H2)BHNHNH2 (4) 1.55 and 1.56 389 & 717 1.17 2831 + BH2NH2NH2 1.18 2710 - 2875 Table 6.9: Comparison of Electrostatic and Dative Sigma Covalent Boron-Nitrogen Bond Distances and Stretching Frequencies of Literature References and the Boron Cation Systema. Dative σ Bond Electrostatic Dative σ Bond BN Stretching Structure BN Distances (Å) BN Distances (Å) Frequencies (cm-1) Literature 1.62b, 1.64c, 1.66d, 1.67d, 1.72e 603f, 776f, 787f

BH3NH3 1.65 684 + B (N2) 2.19 + (H2)B (N2) 2.21 BHNNH+(1) 1.67 569, 705 + NH3BNH3 1.62 569 and 693 aCalculated at the MP2/TZ+ level of theory.

b For the (ClMesB)2NNMe2 molecule using X-ray diffraction from reference [6].

c For the the (ClMesB)2NNMe2 molecule using gas electron diffraction from reference [6].

dReference [8].

eFor 2,2,6,6-tetramethylpiperidino[(dibromoboryl)-tert-butylamino]bromoborane using X-ray diffraction from reference [6].

fReference [7].

115 Table 6.10: Comparison of Hybrid Dative/Ordinary and Ordinary Sigma Covalent Boron-Nitrogen Bond Distances and Stretching Frequencies of Literature References and the Boron Cation Systema.

Hybrid Dative/ Hybrid Dative/Ordinary σ Ordinary σ Bond Ordinary σ Bond Bond BN Stretching Ordinary σ Bond BN Stretching -1 -1 Structure BN Distances (Å) Frequencies (cm ) BN Distances (Å) Frequencies (cm ) Literature 1.47b, 1.48c, 1.49d,e

BH2NH2 (CS - TS) 1.48 1075 + BH2NH3 1.56 894 116 BHNNH+(3) 1.47 1130 + (H2)BHNNH (1) 1.47 1125 + (H2)BHNNH (2) 1.48, 1.53 1022 and 1291 + BH2NHNH 1.56 816 + BH2NHNH (H2) 1.55 819

aCalculated at the MP2/TZ+ level of theory.

bFor 2,2,6,6-tetramethylpiperidino[(dibromoboryl)-tert-butylamino]bromoborane using X-ray diffraction from reference [6].

c For the (ClMesB)2NNMe2 molecule using X-ray diffraction from reference [6].

d For the the (ClMesB)2NNMe2 molecule using gas electron diffraction from reference [6].

e For the Me2NBMeNMeBMe2 molecule using gas electron diffraction from reference [6]. Table 6.10: Continued.

117 Hybrid Dative/ Hybrid Dative/Ordinary σ Ordinary σ Bond Ordinary σ Bond Bond BN Stretching Ordinary σ Bond BN Stretching Structure BN Distances (Å) Frequencies (cm-1) BN Distances (Å) Frequencies (cm-1) + (H2)BHNHNH2 (3) 1.58 662 + (H2)BHNHNH2 (4) 1.44, 1.54 1224 and 1366 + BH2NH2NH2 (1) 1.60 551 and 807 + BH2NH2NH2 (2) 1.55 794 and 932 + NH2BHNH3 1.57 779 Table 6.11: Calculated Geometriesa, Relative Energies, and Stretching Frequenciesa of Trans 1,2-Diimide (Trans) and the Eclipsed (Ecl) and Gauche (Gau) froms of Hydrazine.

Property NHNH (Trans) NH2NH2 (Ecl) NH2NH2 (Gau)

Point Group C2H C2V C2

rNN (Å) 1.2550 1.4736 1.4352

rNH (Å) 1.0293 1.0150 1.0103 & 1.0134

θHNN (deg) 105.84 107.9742 107.08 & 108.82

118 θHNH (deg) 104.262 107.6726 Energy in kcal/mol CCSD(T)/pVTZ(+) b -7.90 -22.81 -30.26 CCSD(T)/pVTZ(+) c -83.75 -137.35 -122.94 Difference 75.85 114.54 92.68 NN Stretching Frequency (cm-1) 1506 929.8328 1128.8292 NH Stretching Frequencies (cm-1) 3315 & 3350 3469 - 3603 3508 - 3624

aCalculated at the MP2/TZ+ level of theory.

b The sum of the CCSD(T)/pVTZ(+) energies, including ZPE calculated at the MP2/pVTZ+ level, of the nitrogen species + + + listed and BH2 relative to B + N2 + 2H2 for the diimide species and to B + N2 + 3H2 for the hydrazine species.

c + + The CCSD(T)/pVTZ(+) energies, including ZPE calculated at the MP2/pVTZ+ level, of BH2NHNH , BH2NH2NH2 (1), + + + and BH2NH2NH2 (2) relative to B + N2 + 2H2 for the diimide species and to B + N2 + 3H2 for the hydrazine species. Table 6.12: Comparison of Pi Boron-Nitrogen Bond Distances and Stretching Frequencies of the Boron Cation Systema.

Ordinary σ Bond + Ordinary σ Bond + Ordinary σ Bond + Ordinary σ + Ordinary Dative π Bond Dative π Bond BN Stretch Ordinary π Bond π Bond BN Stretching Structure BN Distances (Å) Frequencies (cm-1) BN Distances (Å) Frequencies (cm-1) Literature 1.34b, 1.38c, 1.39d,e 1.41f,f 1556.9j BNH+ (bent) 1.30 1469 + BHNH2 (planar) 1.32 1450 & 1599 BH NH (C ) 1.40 1367

119 2 2 2V BHNNH+(1) 1.41 1418 BHNNH+(2) 1.32 1185 and 1952

aCalculated at the MP2/TZ+ level of theory.

bFor 2,2,6,6-tetramethylpiperidino[(dibromoboryl)-tert-butylamino]bromoborane using X-ray diffraction from reference [6].

c For the (ClMesB)2NNMe2 molecule using X-ray diffraction from reference [6].

d For the the (ClMesB)2NNMe2 molecule using gas electron diffraction from reference [6].

e For the H2BNH2 molecule from reference [9, 10].

f For the HB(NH2)2 molecule using microwave spectroscopy from reference [9]. Table 6.12: Comparison of Pi Boron-Nitrogen Bond Distances and Stretching Frequencies of the Boron Cation Systema.

Ordinary σ Bond + Ordinary σ Bond + Ordinary σ Bond + Ordinary σ + Ordinary 120 Dative π Bond Dative π Bond BN Stretch Ordinary π Bond π Bond BN Stretching Structure BN Distances (Å) Frequencies (cm-1) BN Distances (Å) Frequencies (cm-1) BHNNH+(3) 1.43 1130 and 1309 + (H2)BHNNH (1) 1.43 1125 and 1309 + (H2)BHNHNH2 (1) 1.35 1597 + (H2)BHNHNH2 (2) 1.36 1085, 1393, 1603 + (H2)BHNHNH2 (3) 1.34 1512 + NH2BHNH3 1.37 1445 Table 6.13: Comparison of a Subset of distances, calculated at the MP2/TZ+ level of theory and reported in angstroms, of TS(1), TS(6), TS(5), and TS(10) and Their Electrostatic Reactants and Products.

a b c Structure rBN(a) rBN(b) rNN rHH rNH rBH + (H2)B (N2) 2.2148 3.3272 1.1150 0.7489 3.4731 2.3040

TS(1) 1.7224 2.2060 1.1646 0.8962 1.5690 1.8101 BHNNH+(1) 1.4137 1.6684 1.2875 2.1640 1.1231 1.5468 +

121 BH2NHNH (H2) 2.4899 1.5540 1.2433 0.7410 3.1175 3.9276 TS(6) 2.3662 1.4542 1.3092 0.8997 1.3548 2.5696 + (H2)BHNHNH2 (1) 2.5030 1.3545 1.4106 2.4291 1.0110 2.8568 + (H2)BHNNH (2) 1.5339 1.4767 1.2475 0.7839 2.2854 1.4952 TS(5) 1.8200 1.5269 1.2221 1.1337 1.5703 1.3019 + BH2NHNH 2.4909 1.5556 1.2432 2.2583 1.0331 2.4932 + (H2)BHNHNH2 (4) 1.5353 1.4415 1.4827 0.7732 2.1706 1.5591 TS(10) 1.5250 1.5987 1.4539 1.0112 1.4261 1.3234 + BH2NH2NH2 (1) 1.5994 1.5994 1.4598 2.6001 1.0162 2.3049

aThe distance between the hydrogens of the electrostatically bound hydrogen molecule.

bThe distance between the hydrogen and the distal nitrogen to which it adds.

cThe distance between the boron and the hydrogen that adds to the distal nitrogen. B N(a)

B N(a) N(b) N(b) (2) (1) (2) (1)

+ (H2)B (N2) TS(1)

N(a) N(a)

B N(b) N(b) B

(2) (1) (2) (1)

BHNNH+(1) TS(2)

N(b)

(2) B N(a)

(1)

BHNNH+(2)

Figure 6.1: Optimized structures of the stationary points of the boron cation catalyzed reduction of dinitrogen. These structures were optimized at the MP2/aug-cc-pVTZ level of theory. This figure does not illustrate double or triple bonds between atoms. For a + more accurate illustration of the bonding involved in the various structures of the BH2 catalytic system refer to Figure 6.11.

122 N(a) (1)

B N(b)

(2) TS(3)

N(a) N(a)

B (2) (3) N(b) B N(b) (1) (1) (4)

(2) + + BHNNH (3) (H2)BHNNH (1)

N(a) N(a)

(1) (1) N(b) N(b)

B (3) (3) B

(4) (4) (2) (2) + TS(4) (H2)BHNNH (2)

Figure 6.1: Continued.

123 (3)

(4) N(a)

B N(b) (2)

(1) TS(5) (6)

(3) (5) (4) N(a) (4) (3)

B N(b) B N(a) N(b)

(1) (2) (2) (1) + + BH2NHNH BH2NHNH (H2)

(3) (4) (6) (3) (5) (5) (6) N(a) (4) N(a) B N(b) B N(b) (2)

(2) (1) (1) + TS(6) (H2)BHNHNH2 (1) Figure 6.1: Continued.

124 (6) (3) (4) (5) N(a)

B N(b)

(2) (1) TS(7)

(6) (3) (4) N(a)

(5) B N(b)

(2) (1) + (H2)BHNHNH2 (2)

(6)

(4) (5) (3)

N(a)

(2) B N(b)

(6) (1) TS(8) Figure 6.1: Continued.

125 (6)

(3) (5) (4)

N(a)

B N(b) (2) (1) + (H2)BHNHNH2 (3)

(3)

(5) N(a)

(1) (2) B N(b)

(6) (4)

TS(9)

Figure 6.1: Continued.

126 (3) (3) (5) (5) N(a) N(a)

(1) (2) B N(b) (1) B N(b) (2) (6) (4) (6) (4)

+ (H2)BHNHNH2 (4) TS(10)

(3) (5) N(a)

(2) B N(b) (1) (4) (6) + BH2NH2NH2 (1)

Figure 6.1: Continued.

127 (3) (5)

N(a) (2) (1)

B N(b)

(4) (6) TS(11)

(3) (5)

(2) N(a) (1)

N(b) B

(4)

(6) + BH2NH2NH2 (2)

(3) (5) N(a)

(2) B (1) N(b)

(6) (4)

TS(12)

Figure 6.1: Continued.

128 (3) (5) (3) (5) N(a) N(a)

(4) (4) (2) B B N(b) N(b) (2) (1) (6) (6) (1)

+ NH2BHNH3 TS(13)

(3) (4)

N(a) N(b) (5) (1) (6) (2) B

+ NH3BNH3

Figure 6.1: Continued.

129 + (3) +

-55.2

BHNNH

-22.6 TS(3)

(2) +

-39.5

BHNNH

-10.5 TS(2)

(1) +

-15.6

BHNNH

15.2 TS(1) ) 2 )(H

2 -12.5 (N +

B

2 + H

2 0.0

+ N +

B

calculatedat the CCSD(T)/pVTZ(+)//MP2/pVTZ+ level with harmonic of theory theZPE added at

2 0.0 20.0 10.0

-10.0 -20.0 -30.0 -40.0 -50.0 -60.0 + H

2 (kcal/mol) Energy FigureEnergy6.2: of the stationary points of the first reductionof dinitrogen (steps 2 1 and of Phase 1) relative to B + N MP2/pVTZ+ levelMP2/pVTZ+ of theory.

130

+ +

2

+ N + NHNH -83.8 2 BH

-37.0 TS(5)

(2) +

-54.3 )BHNNH

2 (H

-55.3 TS(4)

(1) +

-56.2

)BHNNH 2

(H 2

(3) + H +

-55.2

BHNNH

0.0 20.0

-20.0 -40.0 -60.0 -80.0 -100.0

calculated at the CCSD(T) level of theory with harmonic ZPE added at the MP2 level of theory.

2 Energy (kcal/mol) Energy Figure 6.3: Energy of the stationary points of the second reduction of dinitrogen (step 3 of Phase 2) relative to B 2H

131

(2) +

2

-97.3 )BHNHNH 2 (H

TS(7) -96.2

(1) + 2

-96.0 )BHNHNH 2 (H

TS(6) -45.7

) 2 (H +

-84.6

NHNH 2

BH

2

+ H +

-83.8 calculated harmonic of with theory level the theory. CCSD(T) at of ZPE added the MP2 level at NHNH

2 2

BH + 3H 2 + N

+ 0.00 20.00

-20.00 -40.00 -60.00 -80.00 -100.00 -120.00 (kcal/mol) Energy Figure 6.4: Energy of the stationary points of the first reduction of diimide (steps 1 and 2 and part of step 3 of Phase 2) diimide 2) of Phase 3 of reduction step of first the part of and 2 and 1 points (steps stationary the of Energy 6.4: Figure relative to B

132

(4) + 2

-103.8 )BHNHNH 2

(H

TS(9) -105.1

(3) + 2

-114.2 )BHNHNH 2 (H

Figure 6.4: Continued. TS(8) -92.0

(2) + 2

-97.3 )BHNHNH 2 (H

0 20

-20 -40 -60 -80 -100 -120 -140 Energy (kcal/mol) Energy

133

(2)

+ 2

NH 2

-122.9 NH 2

BH

3 of Phase 2 and step 1 of TS(11) -122.5

(1) +

2

NH 2 NH

-137.3 2

BH duction of diimide (rest of step

.5 -89 TS(10)

calculated at the level CCSD(T) of theory with harmonic ZPE added at the MP2 (4) 2 + 2 + 3H

2 -103.8

+ N + )BHNHNH 2 (H

0 20

-20 -40 -60 -80 -100 -120 -140 -160

Energy (kcal/mol) Energy Energy (kcal/mol) Energy level of theory. level of Phase 3) relative to B Figure 6.5: Energy of the stationary points of the second re

134

3

+ 2NH -20.1

+ B

+ 3

1.3 BNH 3

-12 NH

TS(13) -104.4

+ 3

BHNH 2 -207.9-207.9 cond reductions of hydrazine (steps 2 and 3 of Phase 3) relative NH NH

-49.8 TS(12)

(2) + 2 NH 2 -122.9 -122.9 NH 2 BH BH calculated at the CCSD(T) level of theory with harmonic ZPE added at the MP2 level of theory.

2

+ 3H 2 20.00 -30.00 -80.00

-130.00 -180.00 -230.00

+ N

+ Energy (kcal/mol) Energy Figure 6.6: Energy of the stationary points of the first and se to B

135 3 4

5 1 2 6 2 NH3 N2 + H2 3 + B 2 1 5 + NH3BNH3 -207.8 TS(1) 4 15.2 2 2 + 1 TS(12) BHNNH (3) 6 1 3 -104.3 -55.2 5 H2 4 + NH2BHNH3 1 3 2 6 -207.8 + (H2)BHNNH (1) + -56.2 1 B Catalyzed 2 4 136 3 Reduction of Dinitrogen to Ammonia 5 TS(12) 3 2 -49.7 TS(5) 4 1 -37.2 6 4 2 1 All energies are reported at the CCSD(T)/pVTZ(+)//MP2/pVTZ+ BH NH NH +(1) + 2 2 2 + level of theory relative to B + N + nH in kcal/mol with 3 BH NHNH 3 2 2 -137.3 2 5 -83.7 4 harmonic ZPE added at the MP2/aug-cc-pVTZ level of theory.

2 1 4 2 1 The geometries were optimized at the MP2/pVTZ+. 6 TS(10) -89.5 TS(6) 3 + -45.7 H 5 (H )BHNHNH (3) 2 2 2 3 -114.2 6 5

6 2 1 4 3 6 4 5 4 2 1

2 1 Figure 6.7: B+ Catalyzed reduction of dinitrogen to ammonia. All energies are reported at the + CCSD(T)/pVTZ(+)//MP2/pVTZ+ level of theory relative to B + N2 + nH2 in kcal/mol with harmonic ZPE added at the MP2/aug-cc-pVTZ level of theory. The geometries were optimized at the MP2/pVTZ+ level of theory. Only the lowest energy isomers are illustrated.

20.00 TS(1)

15.00 15.2

10.00

5.00 + B + N2 + H2 137 0.00 0.0

Energy (kcal/mol) Energy -5.00

-10.00 + B (N2 )(H2) -12.5 BHNNH+(1) -15.00 -15.6 -20.00

+ Figure 6.8: Relative energy of stationary points along the minimum energy reaction path for B + N2 + H2 -> BHNNH+(1) calculated at the CCSD(T)/pVTZ(+)//MP2/pVTZ+ level of theory with MP2/aug-cc-pvtz harmonic ZPE added. The orbitals pictured show the evolution of the HOMO along the reaction path. BH2NH2 BH2NH2 (CS –TS)

138 H H H .. B N B N H H H H H

Figure 6.9: Structures of the C2V BH2NH2 molecule and of the transition state, ‘BH2NH2 (Cs – TS)’. 2 1 + "bh2n2es" "ts1" N(b) B (H2)(N2) N(a) 1 TS(1) 0.5 N(a) 0 0 N(b)

-1 B -0.5 B y -2 Dipole Moment y Dipole Moment -1 -3

-1.5 -4

-5 -2 139

-6 -2.5 -0.5 0 0.5 1 1.5 2 2.5 3 -1 -0.5 0 0.5 1 1.5 2 x x

3.5 1 "bhnnh1" "ts2" BHNNH(1) N(a) TS(2) 3 0.5

0 2.5 N(b) B -0.5 2

-1 y 1.5 y Dipole Moment -1.5

1 N(a) Dipole Moment -2 0.5 -2.5

0 -3 N(b) B -0.5 -3.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 -1 0 1 2 3 4 5 x x

+ Figure 6.10: Dipole moment plots for all of the stationary points of the B + N2 + 3H2 catalytic system. 2.5 0.6 "bhnnh2" N(a) "ts3" TS(3) BHNNH+(2) 0.4 2

0.2 1.5 0

1 -0.2 B B y y

-0.4 N(b) 0.5 Dipole Moment Dipole Moment

N(a) -0.6 0

-0.8

-0.5 -1 140 N(b) -1 -1.2 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 -1 -0.5 0 0.5 1 1.5 2 2.5 3 x x "h2bhnnh1" 1.6 "bhnnh3" 1.4 BHNNH(3) + z (H2)BHNNH (1) 1.2

1 1.4 1.2 0.8 1 B N(b) 0.8 0.6 0.6 0.4 y z 0.2 0.4 0 N(b) Dipole Moment -0.2 0.2 -0.4 -0.6 0 N(a) 2 -0.2 1.5 1 -0.4 N(a) -0.6 -0.4 0.5 -0.2 y B 0 0 -0.6 0.2 -1 -0.5 0 0.5 1 1.5 2 0.4 -0.5 x 0.6 x 0.8 -1 Figure 6.10: Continued. "ts4" "h2bhnnh2" + z TS(4) (H )BHNNH (2) z 2 N(a) 0.2 1.6 0.1 Dipole Moment 1.4 Dipole Moment 0 N(b) 1.2 1 -0.1 B z 0.8 N(a) -0.2 z 0.6 0.4 B N(b) -0.3 0.2 -0.4 0 -0.2 -0.5 -0.4 1 1 0.5 0.5 0 0 -0.8 -0.5 -0.6 -2 -0.5 -0.4 -1 y -1.5

141 -1 -0.2 -1.5 -1 y 0 -1.5 0.2 -2 -0.5 x 0.4 0 -2 0.6 -2.5 x 0.5 1 -2.5 "ts5"

0.5 "bh2nhnh" z N(b) + TS(5) 0.4 BH2NHNH

0.3 1.2 1 Dipole Moment 0.2 0.8 0.6 0.1 z B N(a) 0.4 Dipole Moment

y 0 0.2 N(a) 0 N(b) -0.1 -0.2 -0.2 0.8 0.6 0.4 -0.3 0.2 0 -1 -0.2 -0.8 -0.4 -0.6 -0.4 -0.4 -0.6 y -0.2 -0.8 B 0 -1 -0.5 0.2 -1.2 x 0.4 -1.4 -1.5 -1 -0.5 0 0.5 1 1.5 0.6 x

Figure 6.10: Continued. "ts6"

0.8 + BH2NHNH (H2) z TS(6) 0.7 N(b) N(a) 0.6 0.2 0.15 0.1 0.5 Dipole Moment 0.05 B z 0

y 0.4 -0.05 Dipole Moment -0.1 0.3 -0.15 N(b) 0.2 1 0.8 0.6 0.4 0.1 N(a) -1.5 0.2 142 -1 -0.5 0 y B 0 -0.2 0 0.5 -0.4 -1.5 -1 -0.5 0 0.5 1 1.5 x 1 1.5 -0.6 x "ts7" 1 "h2bhnhnh21" (H )BHNHNH +(1) z 0.5 2 2 N(b) Dipole Moment TS(7)

0.7 B 0 0.6 N(a) 0.5 0.4 -0.5 z 0.3

y 0.2 -1 0.1 0 -0.1 B -1.5 Dipole Moment 3 N(b) N(a) 2.5 2 -2 1.5 -3.5 -3 -2.5 -2 1 y -1.5 -1 0.5 -2.5 -0.5 0 0 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 0.5 x 1 -0.5 x 1.5 Figure 6.10: Continued. "h2bhnhnh22"

+ "ts8" z (H2)BHNHNH2 (2) TS(8) Dipole Moment z 1.4 1.2 0.4 N(a) 1 0.35 0.8 0.3 Dipole Moment 0.25 z 0.6 0.2 0.4 0.15 B z 0.1 0.2 0.05 0 0 B -0.05 -0.2 -0.1 -0.15 N(b) N(b) N(a) 2 0.3 1.5 0.2 0.1 1 0 143 -3 -0.1 -2.5 -1.5 -2 -1 -0.2 -1.5 0.5 y -0.5 0 -0.3 y -1 0.5 -0.4 -0.5 1 0 0 1.5 2 -0.5 0.5 2.5 -0.6 x 1 "h2bhnhnh23" x 3 3.5 1.5 -0.5 4 -0.7

z + "ts9" (H2)BHNHNH2 (3) TS(9)

z 1 B 0.8 0.6 N(b) 0.5 Dipole Moment 0.4 N(a) 0.4 z 0.2 0.3 0.2 0 0.1 N(b) -0.2 z B 0 N(a) -0.4 -0.1 -0.2 0.8 -0.3 0.6 0.4 1 0.2 -1 0.5 -0.8 0 0 -0.6 -0.2 y -0.8 -0.4 Dipole Moment -0.6 -0.5 -0.2 -0.4 -0.4 -0.2 -1 y 0 -0.6 0 x 0.2 0.2 0.4 -0.8 0.4 -1.5 x 0.6 0.8 -2

Figure 6.10: Continued. "h2bhnhnh24" "ts10" + (H2)BHNHNH2 (4) TS(10) z B z

B 0.35 0.14 0.3 0.12 0.25 0.1 0.2 Dipole Moment 0.08 0.15 0.06 Dipole Moment 0.1 z 0.04 z 0.05 0.02 0 N(b) N(b) -0.05 N(a) 0 -0.1 -0.02 -0.15 -0.04 -0.2 -0.06

1 N(a) 1 0.8 0.5 0.6 0.4 0 0.2 -1 0 -0.8 -0.5 -0.8 -0.6 -0.6 -0.2 144 -0.4 y -0.4 -0.4 y -0.2 -1 -0.2 0 0 -0.6 0.2 0.2 -0.8 0.4 -1.5 0.4 -1 x 0.6 x 0.6 0.8 -2 0.8 -1.2 "ts11" 1.5 "bh2nh2nh21" 1 B + TS(11) BH2NH2NH2 (1) z 0.5

0 1.8 Dipole Moment 1.6 -0.5 N(a) N(b) 1.4 1.2 1 z -1 z 0.8 N(b)

y 0.6 N(a) -1.5 0.4 B 0.2 -2 0 Dipole Moment -0.2 -2.5 0.5 0 -3 -0.5 -1.5 -1 -3.5 -1 -0.5 -1.5 y 0 0.5 -2 -4 x 1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.5 -2.5 yx

Figure 6.10: Continued. "bh2nh2nh22" "ts12" BH NH NH +(2) z 2 2 2 z TS(12) Dipole Moment 1.6 0.9 1.4 0.8 1.2 0.7 1 0.6 0.5 0.8 N(b) z z 0.4 N(a) Dipole Moment 0.6 0.3 0.4 N(a) 0.2 0.2 B 0.1 0 0 B -0.2 -0.1 N(b) 0.5 1.5 0 1 -0.5 0.5 -1.5 -1 -1.5 -1 -1 0 -0.5 -1.5 y -0.5 y 145 0 0 0.5 -2 0.5 -0.5 x 1 x 1 1.5 -2.5 1.5 -1

1 "ts13" "nh2bhnh3" + NH2BHNH3 TS(13) 0.5 B z

N(a) 0 0.6 0.5 0.4 -0.5 N(b) 0.3 Dipole Moment y 0.2 Dipole Moment z -1 0.1 0 N(a) -0.1 -0.2 -1.5 N(b) B 4 3.5 3 -2 2.5 2 -1.5 1.5 -1 1 y -0.5 0.5 -2.5 0 0 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 0.5 x 1 -0.5 x 1.5 -1

Figure 6.10: Continued. 1 B "nh3bnh3yzxy" + NH3BNH3

0 N(b) N(a)

-1 146

z y -2 Dipole Moment

-3

-4

-5 -1.5 -1 -0.5 0 0.5 1 1.5 xy

Figure 6.10: Continued. .. .. N(a) +

+ .. N(a) N(a)

B N(b) .. H H B N(b) H B N(b) + H H H BHNNH+(1)

+ .. + H B N(a) N(b) H B N(a) N(b) H H

BHNNH+(2)

.. + .. N(a) N(a) + N(a) + - + B N(b) B N(b) - + H H H H B N(b) H H BHNNH+(3)

Figure 6.11: Most plausible resonance structures of the various products of the B+ catalytic system based on bond lengths, HOMO pictures, and dipole moments.

147 .. N(a) + .. + + N(a) N(a) B N(b) + H H - N(b) - + B B N(b) H H H H H H H H H H + (H2)BHNNH (1)

.. + .. N(a) N(a) + + N(a) N(b) + B - N(b) - + H H H B H B N(b) H H H H H H H H

+ (H2)BHNNH (2)

H H H H H B + .. N(a) B + N(a) N(b) .. H N(b) .. H H

+ BH2NHNH

Figure 6.11: Continued.

148 HH HH

H H H H

B + N(a) B + N(a) H H .. N(b) .. N(b) ..

H H

+ BH2NHNH (H2)

HH H H H H HH + + N(a) B .. N(a) B H H N(b) .. N(b) .. H H

+ (H2)BHNHNH2 (1)

H H H H H H + B .. N(a) H H B + N(a) H N(b) .. H N(b) ..

H H

+ (H2)BHNHNH2 (2)

Figure 6.11: Continued.

149 H H H H H H H H H H H H N(a) + N(a) + N(a) + .. + + - B N(b) - B N(b) B N(b) H H H H H .. H

+ (H2)BHNHNH2 (3)

H H H H H H N(a) + + N(a) N(a) + .. + - B N(b) - + H H B N(b) B N(b) H H H H .. H H H H H H

+ (H2)BHNHNH2 (4)

H H H H + N(a) . . N(a) - + N(b) + . B B . N(b) H H H H H H H H

+ BH2NH2NH2 (1)

Figure 6.11: Continued.

150 H H H H N(a) H H N(a) + H .. H B .N(b) + . B .N(b). H H H H

+ BH2NH2NH2 (2)

H H H H N(a) + N(a) H + - B H N(b) B .. + N(b) H H H H H H

+ NH2BHNH3 (1)

H H H H

N(a) N(a) N(b) H N(b) H .. .. H + B + H + H H H H - ..B

+ NH3BNH3

Figure 6.11: Continued.

151 BH2NH2

+ BHNH2

BNH+(bent)

Figure 6.12. Pictures of the HOMOs (Highest Occupied Molecular + + Orbital) of the BH2NH2, BHNH2 , and BNH (bent) structures.

152 BHNNH+(1)

LUMO

HOMO HOMO-1

HOMO-2 HOMO-3

Figure 6.13: Pictures of the LUMO (lowest unoccupied molecular orbital), HOMO (highest occupied molecular orbital), HOMO-1, HOMO-2, and HOMO-3 of the various products of the B+ catalytic system.

153 BHNNH+(2)

LUMO

HOMO HOMO-1

HOMO-2 HOMO-3

Figure 6.13: Continued.

154 BHNNH+(3)

LUMO

HOMO HOMO-1

HOMO-2 HOMO-3

Figure 6.13: Continued.

155 + (H2)BHNNH (1)

LUMO

HOMO HOMO-1

HOMO-2 HOMO-3

Figure 6.13: Continued.

156 + (H2)BHNNH (2)

LUMO

HOMO HOMO-1

HOMO-2 HOMO-3

Figure 6.13: Continued.

157 + BH2NHNH

LUMO

HOMO HOMO-1

HOMO-2 HOMO-3

Figure 6.13: Continued.

158 + (H2)BH2NHNH

LUMO

HOMO HOMO-1

HOMO-2 HOMO-3

Figure 6.13: Continued.

159 + (H2)BHNHNH2 (1)

LUMO

HOMO HOMO-1

HOMO-2 HOMO-3

Figure 6.13: Continued.

160 + (H2)BHNHNH2 (2)

LUMO

HOMO HOMO-1

HOMO-2 HOMO-3

Figure 6.13: Continued.

161 + (H2)BHNHNH2 (3)

LUMO

HOMO HOMO-1

HOMO-2 HOMO-3

Figure 6.13: Continued.

162 + (H2)BHNHNH2 (4)

LUMO

HOMO HOMO-1

HOMO-2 HOMO-3

Figure 6.13: Continued.

163 + BH2NH2NH2 (1)

LUMO

HOMO HOMO-1

HOMO-2 HOMO-3

Figure 6.13: Continued.

164 + BH2NH2NH2 (2)

LUMO

HOMO HOMO-1

HOMO-2 HOMO-3

Figure 6.13: Continued.

165 + NH2BHNH3

LUMO

HOMO HOMO-1

HOMO-2 HOMO-3

Figure 6.13: Continued.

166 + NH3BNH3

LUMO

HOMO HOMO-1

HOMO-2 HOMO-3

Figure 6.13: Continued.

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