Electronic Structure and Bonding of Lanthanoid(III) Carbonatesw

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Electronic structure and bonding of lanthanoid(III) carbonatesw

Yannick Jeanvoine,a Pere Miro´,b Fausto Martelli,a Christopher J. Cramer*b and Riccardo Spezia*a

Received 14th June 2012, Accepted 31st July 2012 DOI: 10.1039/c2cp41996c

Quantum chemical calculations were employed to elucidate the structural and bonding properties of La(III) and Lu(III) carbonates. These elements are found at the beginning and end of the lanthanoid series, respectively, and we investigate two possible metal-carbonate stoichiometries (tri- and tetracarbonates) considering all possible carbonate binding motifs, i.e., combinations of mono- and bidentate coordination. In the gas phase, the most stable tricarbonate complexes coordinate all carbonates in a bidentate fashion, while the most stable tetracarbonate complexes incorporate entirely monodentate carbonate ligands. When continuum aqueous solvation eﬀects are included, structures having fully bidentate coordination are the most favorable in each instance. Investigation of the electronic structures of these species reveals the metal–ligand interactions to be essentially devoid of covalent character.

1. Introduction They concluded that light Ln(III) ions coordinate four carbonate ligands while heavier ones coordinate only three ligands. In The hydration properties of lanthanoids (Ln) in aqueous contrast, considering available crystallographic and spectroscopic solution have been widely studied both experimentally and data (including UV-vis, near infrared, and infrared), Janicki et al. theoretically.1–5 Such studies have primarily focused on concluded that in aqueous solution all Ln(III) ions form tetra- lanthanoids in their 3+ oxidation state, which are important carbonates when carbonate ions are not limited.16 These authors in nuclear waste remediation and medical imaging.6–8 In the also performed a set of theoretical calculations that suggest that context of nuclear waste, these ions are relevant because of the there is partial charge transfer between the Ln(III) ion and the challenge associated with separating them from actinide ions Published on 01 August 2012. Downloaded by Princeton University 07/07/2014 22:25:29. 9 carbonate ligand that introduces a degree of covalency to the (An). Ln(III) ions in deposited nuclear waste are expected to metal–ligand bonding. Another recent theoretical contribution in interact with carbonate as a counterion in so far as the presence of this area was a report by Sinha et al. on [Nd(CO ) ]5 using carbonates in geological media is ubiquitous. Interestingly, reliance 3 4 the Parameterized Model 3 (PM3) semi-empirical method.17 on diﬀerential lanthanide-carbonate interactions has been Notwithstanding these two studies, no systematic, quantitative proposed as a possible separation procedure for Ln(III)and 10 theoretical study has been undertaken in order to characterize An(III) ions in solution. Consequently, the characterization of the structures and bonding of lanthanoid(III) tri- and tetra- lanthanoid carbonate structures is central to understanding how carbonates, while, e.g., such kinds of studies were performed lanthanoid ions will behave in aqueous solutions with available on actinyl carbonate complexes.18,19 Among the questions that carbonate counterions that may act as supporting ligands. remain open: (i) what is the coordination geometry of the Crystallographic data for Ln3+ carbonate hydrates are 11 carbonate ligands for Ln(III) complexes in water?; (ii) which available for tri-carbonate ligands, and for Nd(III) Runde 12 5 stoichiometry dominates? and (iii) what is the degree of ionic et al. have suggested the formation of a [Nd(CO3)4H2O] vs. covalent bonding for the Ln(III)-carbonate interaction? structure at high carbonate concentrations. Recently Philippini Electronic structure methods, and in particular density- et al. have studied several Ln(III)-carbonate complexes in functional theory (DFT), have proven to be valuable tools solution using electrophoretic mobility measurements and time- for the study of heavy elements. Increasingly accurate lantha- resolved laser-induced ﬂuorescence spectroscopy (TRLFS).13–15 noid and actinoid pseudo-potentials20 have been particularly

a useful in this regard. In the present study, we focus on tri- and Universite´ d’Evry Val d’Essonne, CNRS UMR 8587 LAMBE, 3 5 Bd F. Mitterrand, 91025 Evry Cedex, France. tetracarbonates ([Ln(CO3)3] and [Ln(CO3)4] , respectively) E-mail: [email protected] considering the Ln(III) ions lanthanum (La) and lutetium (Lu). b Department of Chemistry, Supercomputing Institute, and Chemical As these two elements begin and end the lanthanoid series, Theory Center, University of Minnesota, 207 Pleasant St. SE, respectively, they should establish limiting behavior with Minneapolis, MN 55455-0431, USA. E-mail: [email protected] w Electronic supplementary information (ESI) available. See DOI: respect to forming complexes with carbonates. In aqueous 10.1039/c2cp41996c solution with non-coordinating counterions, the diﬀerence in

14822 Phys. Chem. Chem. Phys., 2012, 14, 14822–14831 This journal is c the Owner Societies 2012 View Article Online

ionic radius for these two elements gives rise to a difference B3LYP optimized geometries, single-point energies were in hydration number (9-fold vs. 8-fold for La and Lu, calculated in a vacuum and implicit solvent with several other 21,22 respectively). Ln(III)-aquo interactions have been deter- functionals to evaluate sensitivity of results to choice of mined to be mainly electrostatic in nature, as one might expect functional, including: BLYP,31,32 M05,33 M05-2X,34 PBE0,35 36 37 38 given the ‘‘hard’’ characters of both Ln(III) ions and water. As BHandH, TPSS, and VSXC. These functionals are of such, the variation in ionic radius is the main physical quantity different constructions: generalized gradient approximation, that affects hydration properties.22,23 The fact that ionic radii GGA (BLYP), meta-GGA (TPSS and VSXC), hybrid GGA can dictate the complexation properties has also been pointed (B3LYP and PBE0), meta-hybrid GGA (M05) and two hybrids out for the case of ligands that are potentially less hard than with a higher percentage of Hartree–Fock exchange: the hybrid water, like hexacyanoferrate.24 Nevertheless, carbonates are GGA BHandH and the meta-hybrid GGA M05-2X. MP2 softer ligands than water, and it is also possible that the single point calculations were also performed in both gas phase metal–ligand interaction may change across the spectrum of and continuum aqueous solution to have results from a wave the lanthanoid series. The difference between La and Lu offers function theory model against which to compare. insight into the extrema for the whole series if the interaction is In general, molecular geometries are not especially sensitive mainly electrostatic and/or if the contribution of 4f orbitals is to choice of (modern) density functional.39 We have verified negligible to Ln/carbonate interaction. This last situation is to that geometry optimizations with various functionals lead to be expected since 4f orbitals are compact around lanthanoids changes in geometries and energy orderings that are minimal and rarely invoked as contributing to valence bonding; indeed (relative energy differences are below 1 kcal mol1, see this behavior rationalizes the key role that ionic radius plays in Table S17 in ESIw). In the interest of brevity, we thus report dictating interactions with water as a ligand.25 As we will show below only results obtained with B3LYP geometries. in the present study, this is indeed the case for carbonate as We also examined all-electron calculations including relati- well and thus the difference between La and Lu complexes vistic effects. In particular, using the geometries optimized at does likely span the lanthanoid spectrum. the B3LYP/ECP/6-31+G(d) level of theory, single-point calcu- We study differences in Ln-carbonate interactions as a lations on all species were performed using the Amsterdam function of the lanthanoid, focusing on the number and Density Functional program (ADF 2010.02) developed by coordination geometries of the carbonate ligands. The influ- Baerends, Ziegler, and co-workers.40 For these computations ence of aqueous solvation has been included through the use the B3LYP functional was employed with an all-electron of implicit solvation methods, which are useful for predicting triple-z plus two polarization functions basis set on all atoms. the electrostatic component that dominates the free energies of Relativistic corrections were introduced by the scalar-relativistic solvation for these highly charged species. Finally, topological zero-order regular approximation (ZORA).41,42 Gas-phase analysis of the electron density and examination of valence and implicit aqueous solution calculations were performed, natural orbitals are undertaken to address the nature of the with continuum solvent effects included via the COSMO43 various Ln-carbonate bonds. solvent model with standard radii except for La (R = 2.42 A˚ ) and Lu (R = 2.24 A˚ ) centres.44 2. Computational details Published on 01 August 2012. Downloaded by Princeton University 07/07/2014 22:25:29. All geometries were fully optimized at the density functional 3. Results and discussion theory level with the Gaussian 03 electronic structure program 3.1 Structure of lanthanum and lutetium carbonates suite26 using the hybrid three parameter functional incorpor- ating Becke exchange and Lee–Yang–Parr correlation, also Structures of lanthanum(III) and lutetium(III) tri- and tetra- known as B3LYP.27 For La and Lu atoms, we have used the carbonates have been fully optimized at the B3LYP/ECP/ energy-consistent pseudopotentials (ECP) of the Stuttgart/ 6-31+G(d) level of theory (Fig. 1 and 2). The carbonate Cologne group which are semi-local pseudopotentials adjusted ligands can coordinate the metal centre in either a mono- 28,29 1 2 2 2 to reproduce atomic valence-energy spectra. Amongst the dentate (Z -CO3 ) or bidentate (Z -CO3 ) fashion. In con- available pseudopotentials, we have chosen the ECP28MWB sequence, we optimized all possible combinations of these two small core with 28 core electrons, multi electron fit (M) and coordination motifs in all of the studied species (see ESIw quasi relativistic reference data (WB) and we have used the for the complete set of optimized structures). As expected, ECP28MWB_SEG basis set for La and Lu. For carbon and metal–oxygen distances are shorter in Lu-carbonates than in oxygen atoms, we employ the 6-31+G(d) basis set and we have their analogous La-carbonates with an average difference of + ˚ checked, by exploring the [LnCO3] energy surface, the utility 0.19 A. This difference is in good agreement with the ionic of this basis (increasing the basis set to near triple zeta radius difference for these two metals (0.18–0.26 A˚ depending 6-311+G(d), adding polarization functions 6-311++G(3df), on experimental conditions).45,46 or going to the still more complete basis set aug-cc-pVTZ all The gas-phase energies of all of the studied species relative failed to significantly change the character of the surface (see to the most stable geometry are presented in Table 1. For the Fig. S1 in ESIw)). Integral evaluation made use of the grid tricarbonate species, the fully bidentate structure is the most defined as ultrafine in the Gaussian 03 program. The natures stable one at all levels of DFT, with a monotonic (and indeed of all stationary points were verified by analytic computa- nearly linear) increase of relative energy from the fully 2 3 tion of vibrational frequencies. Aqueous solvation effects were bidentate ([Ln(Z -CO3)3] ) structures to the fully monodentate 30 1 3 included with the PCM continuum solvation model. For the ([Ln(Z -CO3)3] ) ones with each ‘‘decoordination’’ change.

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3 Fig. 1 Lanthanoid(III)-carbonate structures [Ln(CO3)3] showing the diﬀerent possible ligand coordination motifs. Ln atoms are at centre, O atoms are red and C atoms are gray.

Sensitivity to DFT is for the most part modest, although larger various species including aqueous solvent eﬀects by means of 1 3 for [Ln(Z -CO3)3] . Qualitatively, however, all functionals the PCM model (Table 2), the most striking feature is that now provide the same picture, and MP2 calculations predict rela- for both tri- and tetracarbonate species the fully bidentate tive energies similar to those from M05-2X and BHandH coordination mode is predicted to be the most favorable, functionals, consistent with the larger contribution of thereby reversing the order predicted for the gas phase for Hartree–Fock exchange to these functionals. The observation the La and Lu tetracarbonate species. Solvation plays a typical that local functionals, and in particular BLYP, provide results role in leveling energy separations, but in the tetracarbonate in generally good agreement with the other models validates case also appears to eliminate intracomplex electrostatic the use of such computationally more eﬃcient functionals for repulsions that lead to expanded, monodentate structures in

Published on 01 August 2012. Downloaded by Princeton University 07/07/2014 22:25:29. DFT-based molecular dynamics, as recently undertaken for the gas phase (vide infra). other Ln3+ containing systems.47–49 The same trends presented in Tables 1 and 2 are observed For the tetracarbonates, there is more variation in relative from relativistic all-electron B3LYP calculations in both the energies as a function of theoretical level. From a qualitative gas phase and in aqueous solution (COSMO) as shown in standpoint, VSXC is a significant outlier, and seems untrust- Table 3. This increases our confidence in the robust nature of worthy. For La, most other models predict the fully mono- our qualitative predictions since isomer energy ordering does dentate and the singly bidentate structures in the gas phase to not depend on the solvation model, the functional, or the basis be similar in energy, with variation in which is lower as a set employed. The leveling effect of aqueous solvation for the function of model; for Lu, the fully monodentate species is tricarbonate relative energies is not present with COSMO as lowest in the gas phase. MP2 predicts the relative energies it is for PCM, likely owing to a smaller atomic radius being for different binding motifs to be closer to one another than used for the lanthanoid atoms in the latter model than the do most of the DFT methods. Increasing Hartree–Fock former, given the significant exposure of the lanthanoids in the exchange in the DFT functionals generally seems to stabilize tricarbonates compared to the tetracarbonates. 1 2 2 2 5 1 2 5 [La(Z -CO3 )3(Z -CO3 )] compared to [La(Z -CO3 )4] While specific interactions with the first solvation as also found in MP2 calculations where exchange is 100% shell—which are not modeled here—may give rise to effects Hartree–Fock. not captured in the continuum model, a significant component Irrespective of quantitative variations as a function of of the solvation effect is associated with long range electro- specific theoretical model, we find that in the gas phase for statics (because of the large charges on the ions) so we expect both studied lanthanoids the fully bidentate coordination mode the continuum model to capture dominant trends. Never- 1 2 3 is the most favored for the tricarbonates [Ln(Z -CO3 )3] theless, it will be interesting to use the present results for the while the fully monodentate coordination mode is preferred construction of force-field models with which explicit solva- 1 2 5 for the tetracarbonates [Ln(Z -CO3 )4] (or is very close in tion effects can be probed in order to explore this point further. energy to an instead preferred, singly bidentate congener). In order to better understand the inversion in the energy However, when equivalent calculations are performed for the ordering of the tetracarbonate structures we examined the

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5 Fig. 2 Lanthanoid(III)-carbonate structures [Ln(CO3)4] showing the diﬀerent possible ligand coordination motifs. Ln atoms are at centre, O atoms are red and C atoms are gray.

2n dissociation energy (D0), interaction energy (Eint), and repul- [(CO3)n] complex and all of the constituent carbonate ions sion energy per carbonate for the various complexes. D0 is the optimized at infinite separation, divided by the number of m difference in energy between a [Ln(CO3)n] complex and its carbonate molecules present. This can be expressed also as fully separated (optimized) constituents. Eint is the interaction (D0 Eint)/n. All these energies are presented in Table 4. We 3+ 2n energy between a Ln ion and its pre-formed [(CO3)n] report energies in the gas phase in order to clearly decompose m complex, i.e., the energy difference between a [Ln(CO3)n] the effect of different contributions to the total dissociation 3+ 2n complex and the corresponding Ln and [(CO3)n] frag- energy. ments infinitely separated but held at the original complex The dissociation energy, D0, is of course simply the energy geometry. Finally, the repulsion energy per carbonate is calcu- of the different isomers relative to a different zero than that lated from the difference in energy between the structure-specific used in Table 1, so again for the tricarbonate species the

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1 m Table 1 Relative gas-phase energies (kcal mol ) for the diﬀerent [Ln(CO3)n] species (Ln = La, Lu; n =3,4;m = 3, 5), at diﬀerent levels of theory. The carbonate coordination motifs are designated as number monodentate (m) or bidentate (b)

B3LYP MP2 BLYP M05 M05-2X PBE0 BHandH TPSS VSXC

3 Lanthanum tricarbonate ([La(CO3)3] ) 3m 43.8 55.6 37.9 46.0 54.7 48.3 57.3 43.2 54.3 2m1b 24.6 32.5 21.0 26.3 31.4 27.4 32.9 24.4 32.3 1m2b 10.2 14.2 8.6 11.2 13.5 11.6 14.0 10.2 14.4 3b 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3 Lutetium tricarbonate ([Lu(CO3)3] ) 3m 49.9 60.6 44.0 53.9 61.4 55.0 63.9 49.5 66.2 2m1b 25.2 32.3 21.5 28.3 32.7 28.5 33.9 25.0 37.7 1m2b 9.5 13.0 7.7 11.1 13.1 11.0 13.6 9.3 16.7 3b 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5 Lanthanum tetracarbonate ([La(CO3)4] ) 4m 0.0 0.7 0.0 0.0 0.0 0.0 0.2 0.0 7.1 3m1b 2.8 0.0 3.9 1.6 0.04 1.7 0.0 2.7 3.9 2m2b 6.9 0.4 9.0 4.5 1.5 4.8 1.5 6.7 1.3 1m3b 14.5 4.2 17.4 10.8 6.4 11.4 6.6 14.2 0.0 4b 23.9 9.9 27.4 18.8 13.5 19.9 14.0 23.5 0.8 5 Lutetium tetracarbonate ([Lu(CO3)4] ) 4m 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 9.0 3m1b 5.3 2.0 6.3 3.7 2.2 3.8 2.0 4.8 5.4 2m2b 11.5 4.4 13.6 8.4 5.3 8.6 5.2 10.7 1.4 1m3b 22.7 12.1 25.6 18.1 13.6 18.4 13.6 21.2 0.0 4b 36.2 22.1 39.6 29.9 24.5 30.7 24.9 34.1 0.3

1 m Table 2 Relative aqueous solution energies (kcal mol ) for the diﬀerent [Ln(CO3)n] species (Ln = La, Lu; n =3,4;m = 3, 5), at diﬀerent levels of theory with PCM solvation. The carbonate coordination motifs are designated as number monodentate (m) or bidentate (b)

B3LYP MP2 BLYP M05 M05-2X PBE0 BHandH TPSS VSXC

3 Lanthanum tricarbonate ([La(CO3)3] ) 3m 10.2 8.5 8.9 11.1 16.4 14.2 18.7 13.9 21.2 2m1b 5.4 4.3 4.8 6.2 9.5 8.0 10.7 7.9 13.3 1m2b 1.5 0.7 1.3 1.8 3.4 2.7 3.9 2.7 5.6 3b 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3 Lutetium tricarbonate ([Lu(CO3)3] ) 3m 40.1 39.9 37.4 41.7 48.7 44.4 51.1 42.1 57.9 2m1b 24.3 25.4 22.3 25.8 30.3 27.1 31.4 25.3 37.8 1m2b 11.4 12.3 10.3 12.3 14.6 12.8 14.9 11.7 19.3 3b 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5 Lanthanum tetracarbonate ([La(CO3)4] ) Published on 01 August 2012. Downloaded by Princeton University 07/07/2014 22:25:29. 4m 10.9 12.2 9.3 14.6 19.7 14.7 19.3 13.2 42.9 3m1b 9.1 10.2 7.8 11.9 15.8 11.8 15.1 10.6 34.9 2m2b 7.1 8.6 6.1 9.1 11.7 8.9 11.2 7.8 25.7 1m3b 4.6 5.8 4.0 5.7 6.81 5.3 6.5 4.6 13.8 4b 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5 Lutetium tetracarbonate ([Lu(CO3)4] ) 4m 24.1 28.7 20.6 28.8 36.5 29.6 35.8 26.3 70.8 3m1b 17.5 21.2 14.9 21.2 26.8 21.5 26.0 19.1 54.9 2m2b 10.2 13.1 8.4 12.9 16.4 12.9 15.7 11.2 36.5 1m3b 4.4 6.2 3.5 6.0 7.4 5.7 6.9 4.8 17.8 4b 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

2 3 [Ln(Z -CO3)3] structures are the most stable while for the a preference for that coordination motif for both the tri- 1 5 tetracarbonate complexes the [Ln(Z -CO3)4] structures are and tetracarbonate species with either La or Lu central lower in energy. Focusing on Eint, however, reveals that the lanthanoid ions. 3 fully bidentate structures have a larger metal–ligand inter- We next consider the energy of the reactions Ln(CO3)3 + 2 5 action for both the tri- and tetracarbonate stoichiometries. CO3 - Ln(CO3)4 for both La and Lu as reported in 5 Consequently the difference in the behaviour of the tri- and Table 5. For Ln(CO3)4 structures we considered both tetra- tetracarbonate gas-phase species must be attributed to a monodentate and tetra-bidentate structures that are the difference in the repulsion energies for the different carbo- minimum energy structure in gas phase and in solution 3 nates. In tetracarbonates, the carbonate ligands are closer and respectively. On the other hand, for Ln(CO3)3 structures in consequence the repulsive interactions between them are we considered only the tri-bidentate structures since they are larger than in the case of the tricarbonate analogs. In aqueous the minimum energy ones in both gas phase and solution. In solution, the intercarbonate repulsion is dielectrically screened the gas phase, the strong electrostatic repulsion between the leading to stabilization of the fully bidentate species and negatively charged species strongly disfavors coordination,

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Table 3 Relative energies (kcal mol1) in the gas phase and in tetracoordinated structures. This is probably why crystallo- m 11 aqueous solution (COSMO) for the different [Ln(CO3)n] species graphic studies mainly report tri-coordinated structures while (Ln = La, Lu; n =3,4;m = 3, 5) at a relativistic all-electron B3LYP/ 14,16 TZP level of theory. The carbonate coordination motifs are designated in solution studies the tetracoordinated ones are suggested. as number monodentate (m) or bidentate (b) In the gas phase, the tri-coordinate structure is preferred to the tetracoordinate one for Lu by 12.6 kcal mol1 more than for La Gas phase Aqueous solution while in continuum aqueous solution they are almost equivalent 3 1 Lanthanum tricarbonate ([La(CO3)3] ) (with a small preference for La by about 1 kcal mol ). Note a 3m 44.5 — that some experiments have suggested that across the series the 2m1b 25.3 27.5 3 1m2b 10.6 12.6 Ln(CO2)3 stoichiometry becomes more favorable for heavier 13–15 3b 0.0 0.0 elements. This is in line with our results for the gas phase 3 Lutetium tricarbonate ([Lu(CO3)3] ) while in continuum aqueous solution our results cannot provide 3m 51.6 57.4 a definitive answer. 2m1b 26.3 33.4 1m2b 10.0 14.8 3b 0.0 0.0 5 3.2 Topological analysis of the electron density Lanthanum tetracarbonate ([La(CO3)4] ) 4m 0.0 28.7 In order to further characterize the nature of Ln-carbonate 3m1b 2.9 20.5 2m2b 7.1 13.1 interactions, we performed single-point calculations on the 1m3b 14.6 6.0 B3LYP optimized structures with a relativistic all-electron 4b 23.8 0.0 5 basis set and performed a topological analysis of the electron Lutetium tetracarbonate ([Lu(CO3)4] ) 4m 0.0 29.3 density according to the quantum theory of atoms in mole- 50 3m1b 5.4 21.2 cules (AIM). In this theory, a chemical bond exists if a line of 2m2b 11.7 12.6 locally maximum electron density links two neighboring atoms 1m3b 22.8 6.1 and a bond critical point (BCP) is present. A BCP is defined as 4b 36.0 0.0 a minimum in the density along the locally maximal line. At a a SCF convergence failure. BCP, the gradient of the electron density (rr) is zero while the Laplacian (r2r) is the sum of two negative and one positive eigenvalues of the density Hessian matrix, and thus may have Table 4 Dissociation energy (D0), interaction energy (Eint) and either a net positive or net negative value. A positive Laplacian repulsion energy per carbonate (kcal mol1) for different m indicates a local depletion of charge (closed-shell/ionic inter- [Ln(CO3)n] species (Ln = La, Lu; n =3,4;m = 3, 5). The carbonate coordination motifs are designated as number monodentate action), while a negative value is a sign of a local concentration (m) or bidentate (b) of charge (shared/covalent interaction). However a positive Laplacian alone could be misleading e.g. F molecule.51 La Lu 2 Consequently, Cremer and Kraka52 and Bianchi et al.53 have a a D0 Eint Repulsion D0 Eint Repulsion suggested the classification of the bond between two ‘‘closed- 3 Tricarbonate ([Ln(CO3)3] ) shell’’ interacting atoms according also to a second condition, 3m 1202.0 1867.7 221.9 1300.4 1997.2 232.3 e Published on 01 August 2012. Downloaded by Princeton University 07/07/2014 22:25:29. the total electronic energy density at the BCP, Eb . This term is 2m1b 1221.2 1913.2 230.7 1325.1 2053.7 242.9 1m2b 1235.6 1956.6 240.3 1340.9 2103.1 254.1 defined as the sum of the kinetic energy density, Gb, which 3b 1245.8 1997.4 250.5 1350.3 2147.3 265.6 usually dominates in a non-covalent bond, and the potential 5 Tetracarbonate ([Ln(CO3)4] ) energy density Vb, which is usually negative and associated 4m 985.7 2263.5 319.4 1077.6 2409.3 332.9 with accumulation of charge between the nuclei. In clear 3m1b 982.9 2294.8 328.0 1072.4 2441.1 342.2 e 2m2b 978.8 2326.1 336.8 1066.1 2473.4 351.8 covalent bonds both the Laplacian and Eb are negative. In 1m3b 971.2 2356.4 346.3 1054.9 2502.4 361.9 less clear cases, where the Laplacian is slightly positive, the 4b 961.9 2384.8 355.7 1041.5 2528.9 371.9 e value of Eb can be used to make a further classification of the a Per carbonate. bond, from being slightly covalent to purely ionic/non- 2 e bonded. In this classification, with r r >0,ifEb is negative, e the bond is called dative; if Eb is positive, the bond is ionic. 1 Table 5 Reaction free energies (DG, kcal mol ) at the B3LYP/ECP/ The Gb/rb ratio is generally accepted to be less than unity for 6-31+G(d) level of theory in both vacuum and water (described with shared interactions and greater than unity for closed-shell the PCM continuum solvation model). In bold we highlight the DG corresponding to the most favorable product in vacuum or water interactions. Analogously, this topological analysis can be used to identify critical points within ring and cage structures Reaction DG(vacuum) DG(PCM) denoted as ring critical points (RCPs) or cage critical points, 2 3 2 1 5 respectively. In Table 6 calculated properties at the BCPs and [La(Z -CO3)3] +CO3 - [La(Z -CO3)4] 266.78 12.10 2 3 2 2 5 [La(Z -CO3)3] +CO3 - [La(Z -CO3)4] 294.71 5.29 RCPs for selected species are presented (see ESIw for other 2 3 2 1 5 1 2 3 [Lu(Z -CO3)3] +CO3 - [Lu(Z -CO3)4] 278.51 23.46 2 3 2 2 5 species). We have selected [Ln(Z -CO2)2(Z -CO2)] and [Lu(Z -CO3)3] +CO3 - [Lu(Z -CO3)4] 319.17 3.91 1 2 5 [Ln(Z -CO2)3(Z -CO2)] as representative of tri- and tetracarbonate species, chosen specifically as isomers that have but inclusion of aqueous solvation effects lowers drastically both carbonate coordination motifs (mono- and bidentate). the free energy difference between tri- and tetracoordina- BCPs are found for both coordination motifs and RCPs are tion. This indicates that a polar solvent strongly stabilizes also found for the bidentate ligands due to the four-membered

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Table 6 Properties computed at bond and ring critical points for selected species in gas phase. All values are expressed in atomic units

2 e Species Ligand Type rb r rb Gb Gb/rb Vb Eb 1 2 3 1 2 La [La(Z -CO3)2(Z -CO3)] Z -CO3 (3,1) 0.0794 0.3887 0.0964 1.2148 0.0957 0.0008 2 2 Z -CO3 (3,1) 0.0620 0.2395 0.0586 0.9453 0.0574 0.0012 2 2 Z -CO3 (3,+1) 0.0343 0.1844 0.0427 1.2460 0.0392 0.0034 1 2 5 1 2 [La(Z -CO3)3(Z -CO3)] Z -CO3 (3,1) 0.0546 0.2746 0.0621 1.1378 0.0555 0.0066 2 2 Z -CO3 (3,1) 0.0405 0.1601 0.0357 0.8809 0.0313 0.0044 2 2 Z -CO3 (3,+1) 0.0272 0.1349 0.0306 1.1215 0.0274 0.0032 1 2 3 1 2 Lu [Lu(Z -CO3)2(Z -CO3)] Z -CO3 (3,1) 0.0957 0.6069 0.1505 1.5720 0.0143 0.0012 2 2 Z -CO3 (3,1) 0.0754 0.3851 0.0954 1.2644 0.0944 0.0009 2 2 Z -CO3 (3,+1) 0.0408 0.2427 0.0576 1.4112 0.0544 0.0031 1 2 5 1 2 [Lu(Z -CO3)3(Z -CO3)] Z -CO3 (3,1) 0.0682 0.4202 0.0974 1.4279 0.0898 0.0076 2 2 Z -CO3 (3,1) 0.0705 0.4472 0.1019 1.4456 0.0920 0.0099 2 2 Z -CO3 (3,+1) 0.0319 0.1724 0.0401 1.2586 0.0371 0.0030

Rauk and Ziegler and implemented in ADF that has proven to be a very useful tool for discussing bonding in a number of systems.54–58 The bonding energy (DE) between two fragments

is deﬁned as the sum of three terms: DE = DEPauli + DEelectrostatic + DEorbitalic. The ﬁrst two terms are computed by considering the unperturbed fragments and account for the

Pauli (steric) repulsion (DEPauli) and electrostatic interaction (DEelectrostatic), while the third term (DEorbitalic) is the energy released when the densities are allowed to relax. In covalent

bonds the absolute value of DEorbitalic is larger than DEelectrostatic, meanwhile the opposite holds true for ionic bonds. The reader 2 1 Fig. 3 The Laplacian of the electron density (r r) of [La(Z -CO3)2- 2 3 1 2 3 has to be aware that the energy decomposition analysis is (Z -CO3)] (top) and [Lu(Z -CO3)2(Z -CO3)] (bottom): perpendicular 2 2 highly dependent on the chosen fragments, especially for to the ligand coordination plane (right), side view of an Z -CO3 1 2 charged species (see Tables S2–S5 in the ESIw). On one hand, ligand (centre) and side view of an Z -CO3 ligand (right). Negative values of the Laplacian are included in the red regions. in our study this analysis can be used to evaluate changes between lutetium- and lanthanum-carbonate bonds and to shed some light into the nature of the minor covalent con- ring-like structure including the lanthanoid. The Laplacian at tributions to the bond (since the Ln(III)-carbonate bond is all of the BCPs and RCPs is positive indicating an ionic mainly ionic as the topological analysis of the electron density interaction between the lanthanoid ions and the carbonate indicate). On the other hand, the interaction energies are ligands. In both cases the E e are slightly positive being also b strongly biased by the nature of the fragments and the charge in agreement with an ionic interaction. Furthermore, the Published on 01 August 2012. Downloaded by Princeton University 07/07/2014 22:25:29. transfer between them, being unreliable to determine the Laplacian is always larger in the Lu complex than in the La ionicity/covalency of the Ln(III)-carbonate bond. complexes, showing higher ionicity in the Lu-carbonate bonds The energy-decomposition results obtained using this than in the corresponding La case. The Laplacian of the approach are reported in Table 7 for the same selected electron density (r2r) for [La(Z1-CO ) (Z2-CO )]3 and 3 2 3 structures chosen in Section 3.2, while in the ESIw we report [Lu(Z1-CO ) (Z2-CO )]3 is plotted from several perspectives 3 2 3 results for all other structures. The orbitalic and electrostatic to give three dimensional insight into the metal-carbonate interactions are always similar in magnitude for the tricarbonate bonds (Fig. 3). The Laplacian has a positive value around species with the former being slightly larger than the latter. On the metal-carbonate bonds that is larger for the monodentate one hand, when the carbonate is coordinated in a bidentate ligand than for the bidentate ligands. Additionally, the Laplacian manner, both the orbitalic and the electrostatic interactions is less dense on the bidentate carbonate ligand. Finally, the G /r b b increase with respect to monodentate coordination; however, ratios are in agreement with a closed-shell interaction in both the orbitalic interaction increases by ca. 20 kcal mol1 while La- and Lu-carbonate bonds; however, the lutetium bonds are the increase in the electrostatic interaction is almost three predicted to be more ionic which is in agreement with our times larger (ca. 60 kcal mol1). Consequently, the bidentate previous results. The G /r ratio values below unity for some b b metal-carbonate bonds are slightly more ionic than the mono- of the bidentate ligands are associated with the bidentate dentate ones. The comparison between lutetium tricarbonates nature of the coordination. No qualitative changes are and their lanthanum equivalents reveals that both orbitalic observed when topological analysis of the electron density and electrostatic contributions are increased by ca. 10 and is performed including continuum aqueous solvation eﬀects 30 kcal mol1, respectively, leading to a more ionic metal– (see ESIw). ligand interaction in the lutetium species than in the lanthanum ones. (Note that the interaction energies for the ‘‘fourth’’ 3.3 Natural orbitals for chemical valence carbonate in the tetracarbonates of Table 7 cannot be compared To further characterize the Ln-carbonate interaction we have directly to the small endergonic complexation energies listed performed the energy decomposition analysis introduced by in Table 5 because the tricarbonates in Table 5 are relaxed,

14828 Phys. Chem. Chem. Phys., 2012, 14, 14822–14831 This journal is c the Owner Societies 2012 View Article Online

Table 7 Energy decomposition analysis (EDA, kcal mol1) of metal–ligand interaction for selected species. All energies are with respect to the isolated fragmentsa

Species Ligand Pauli rep. Orbitalic int. Electrostatic int. Solvation Total interaction

1 2 3 1 2 La [La( Z-CO3)2( Z-CO3)] Z-CO3 104.4 81.0 (50.61%) 79.1 (49.39%) 46.1 9.6 2 2 Z-CO3 130.2 95.9 (42.33%) 130.7 (57.67%) 78.6 17.8 1 2 5 1 2 [La( Z-CO3)3( Z-CO3)] Z-CO3 60.4 54.3 — 187.8 — 203.1 9.2 2 2 Z-CO3 80.6 69.4 — 161.7 — 189.6 16.7 1 2 3 1 2 Lu [Lu( Z-CO3)2( Z-CO3)] Z-CO3 106.2 79.5 (45.87%) 93.8 (54.13%) 38.4 28.7 2 2 Z-CO3 149.5 104.4 (38.84%) 164.3 (61.16%) 74.9 44.3 1 2 5 1 2 [Lu( Z-CO3)3( Z-CO3)] Z-CO3 67.0 56.5 — 190.3 — 226.5 25.7 2 2 Z-CO3 87.4 72.3 — 161.7 — 215.0 38.2 a One carbonate ligand was chosen as one fragment and the rest of the molecule as the other. No relaxation of the fragments was allowed.

Fig. 4 Natural Orbitals for the Chemical Valence (NOCV) with the largest contribution to the orbitalic interaction energy (contribution presented as percentage of the total orbitalic interaction energy). Colour code: lanthanum/lutetium obscured at center, carbon in gray, and oxygen in red.

while those implicit in Table 7 are not (rather, they maintain the occupied 2p orbitals of the carbonate oxygen to the empty

Published on 01 August 2012. Downloaded by Princeton University 07/07/2014 22:25:29. the tetracarbonate geometry)). 5d metal orbitals. This is consistent with 5d orbitals being In the tetracarbonate species, the electrostatic interaction more extended in space than 4f orbitals, such that the latter 3 between a carbonate ligand and the [Ln(CO3)3] fragment is essentially never contribute to bonding, similarly to what has always strongly repulsive (>150 kcal mol1) independently of been found for La3+ in water.47 the coordination motif. This is a consequence of the highly A complementary picture can be obtained also from Natural charged nature of the chosen fragments and it is compensated Bond Orbitals (NBO) analysis of Weinhold and co-workers63–65 by the solvation energy. The same increase in the orbitalic and that we have performed by means of NBO5.9 code.66 Even in the electrostatic interactions for the lanthanum and lutetium this case the interaction between Ln and carbonates results tricarbonate species is observed in the tetracarbonate ones highly ionic since when Ln and ligand are in the same fragment as well. the percentage of ionicity of Ln–O bond is more than 95%. In order to analyze the nature of the small covalent con- Second-order perturbative estimates of donor–acceptor tributions of the metal–ligand bond, we used the extended interactions in the NBO basis, can provide the presence and transition state (ETS) method combined with natural orbitals the nature of the interaction and results for prototypical 1 2 3 1 2 5 for the chemical valence (NOCV) theory, a combined charge [Ln(Z -CO3)2(Z -CO3)] and [Ln(Z -CO3)3(Z -CO3)] systems and energy decomposition scheme for bond analysis.59–62 are reported in ESIw (Table S18). We found that the inter- ETS–NOCV has been used, together with the fragment calcu- action is mainly between occupied lone pairs of oxygen and lations presented in Table 7, to give the contributions from empty orbitals of Ln, with an energy in the 10–35 kcal mol1 diﬀerent natural orbitals (constructed from the fragment range. Ln acceptor orbitals are mostly empty 5d orbitals. orbitals) to the orbitalic contribution. The natural orbitals Then, empty 6s orbitals are also involved, alone, as for Lu with the largest contribution to the metal–ligand bond are with tri-carbonates, or with participation of 5d and 4f orbitals presented in Fig. 4. (this lasts only for La). Note that NBO analysis ﬁnds a In all the species studied, the major contributions to the contribution of 4f orbitals but this is always small (between small covalent contribution to the bond energy between the 22 and 34% of the given interaction) and associated with lanthanides and the carbonate ligands are donations from charge transfer, not covalent bonding.

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Vreven, carbonate interactions highlighted by the present analysis K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, paves the way for developing classical force fields for these G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, systems. Simulations of lanthanoid solutions by means of R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, finite temperature molecular dynamics with explicit solvent will O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, Published on 01 August 2012. Downloaded by Princeton University 07/07/2014 22:25:29. J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, be crucial to address questions related to the formation and R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, equilibrium of these complexes as a function of salt concen- J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. 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