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

Cite this: Phys. Chem. Chem. Phys., 2012, 14, 14822–14831

Electronic structure and bonding of lanthanoid(III) carbonatesw

Yannick Jeanvoine,aPere Miro,

bFausto Martelli,

aChristopher J. Cramer*

band

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

The hydration properties of lanthanoids (Ln) in aqueous

solution have been widely studied both experimentally and

theoretically.1–5 Such studies have primarily focused on

lanthanoids in their 3+ oxidation state, which are important

in nuclear waste remediation and medical imaging.6–8 In the

context of nuclear waste, these ions are relevant because of the

challenge associated with separating them from actinide ions

(An).9 Ln(III) ions in deposited nuclear waste are expected to

interact with carbonate as a counterion in so far as the presence of

carbonates in geological media is ubiquitous. Interestingly, reliance

on differential lanthanide-carbonate interactions has been

proposed as a possible separation procedure for Ln(III) and

An(III) ions in solution.10 Consequently, the characterization of

lanthanoid carbonate structures is central to understanding how

lanthanoid ions will behave in aqueous solutions with available

carbonate counterions that may act as supporting ligands.

Crystallographic data for Ln3+ carbonate hydrates are

available for tri-carbonate ligands,11 and for Nd(III) Runde

et al.12 have suggested the formation of a [Nd(CO3)4H2O]5�

structure at high carbonate concentrations. Recently Philippini

et al. have studied several Ln(III)-carbonate complexes in

solution using electrophoretic mobility measurements and time-

resolved laser-induced fluorescence spectroscopy (TRLFS).13–15

They concluded that light Ln(III) ions coordinate four carbonate

ligands while heavier ones coordinate only three ligands. In

contrast, considering available crystallographic and spectroscopic

data (including UV-vis, near infrared, and infrared), Janicki et al.

concluded that in aqueous solution all Ln(III) ions form tetra-

carbonates when carbonate ions are not limited.16 These authors

also performed a set of theoretical calculations that suggest that

there is partial charge transfer between the Ln(III) ion and the

carbonate ligand that introduces a degree of covalency to the

metal–ligand bonding. Another recent theoretical contribution in

this area was a report by Sinha et al. on [Nd(CO3)4]5� using

the Parameterized Model 3 (PM3) semi-empirical method.17

Notwithstanding these two studies, no systematic, quantitative

theoretical study has been undertaken in order to characterize

the structures and bonding of lanthanoid(III) tri- and tetra-

carbonates, while, e.g., such kinds of studies were performed

on actinyl carbonate complexes.18,19 Among the questions that

remain open: (i) what is the coordination geometry of the

carbonate ligands for Ln(III) complexes in water?; (ii) which

stoichiometry dominates? and (iii) what is the degree of ionic

vs. covalent bonding for the Ln(III)-carbonate interaction?

Electronic structure methods, and in particular density-

functional theory (DFT), have proven to be valuable tools

for the study of heavy elements. Increasingly accurate lantha-

noid and actinoid pseudo-potentials20 have been particularly

useful in this regard. In the present study, we focus on tri- and

tetracarbonates ([Ln(CO3)3]3� and [Ln(CO3)4]

5�, respectively)

considering the Ln(III) ions lanthanum (La) and lutetium (Lu).

As these two elements begin and end the lanthanoid series,

respectively, they should establish limiting behavior with

respect to forming complexes with carbonates. In aqueous

solution with non-coordinating counterions, the difference in

aUniversite d’Evry Val d’Essonne, CNRS UMR 8587 LAMBE,Bd F. Mitterrand, 91025 Evry Cedex, France.E-mail: riccardo.spezia@univ-evry.fr

bDepartment of Chemistry, Supercomputing Institute, and ChemicalTheory Center, University of Minnesota, 207 Pleasant St. SE,Minneapolis, MN 55455-0431, USA. E-mail: cramer@umn.edu

w Electronic supplementary information (ESI) available. See DOI:10.1039/c2cp41996c

PCCP Dynamic Article Links

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ionic radius for these two elements gives rise to a difference

in hydration number (9-fold vs. 8-fold for La and Lu,

respectively).21,22 Ln(III)-aquo interactions have been deter-

mined to be mainly electrostatic in nature, as one might expect

given the ‘‘hard’’ characters of both Ln(III) ions and water. As

such, the variation in ionic radius is the main physical quantity

that affects hydration properties.22,23 The fact that ionic radii

can dictate the complexation properties has also been pointed

out for the case of ligands that are potentially less hard than

water, like hexacyanoferrate.24 Nevertheless, carbonates are

softer ligands than water, and it is also possible that the

metal–ligand interaction may change across the spectrum of

the lanthanoid series. The difference between La and Lu offers

insight into the extrema for the whole series if the interaction is

mainly electrostatic and/or if the contribution of 4f orbitals is

negligible to Ln/carbonate interaction. This last situation is to

be expected since 4f orbitals are compact around lanthanoids

and rarely invoked as contributing to valence bonding; indeed

this behavior rationalizes the key role that ionic radius plays in

dictating interactions with water as a ligand.25 As we will show

in the present study, this is indeed the case for carbonate as

well and thus the difference between La and Lu complexes

does likely span the lanthanoid spectrum.

We study differences in Ln-carbonate interactions as a

function of the lanthanoid, focusing on the number and

coordination geometries of the carbonate ligands. The influ-

ence of aqueous solvation has been included through the use

of implicit solvation methods, which are useful for predicting

the electrostatic component that dominates the free energies of

solvation for these highly charged species. Finally, topological

analysis of the electron density and examination of valence

natural orbitals are undertaken to address the nature of the

various Ln-carbonate bonds.

2. Computational details

All geometries were fully optimized at the density functional

theory level with the Gaussian 03 electronic structure program

suite26 using the hybrid three parameter functional incorpor-

ating Becke exchange and Lee–Yang–Parr correlation, also

known as B3LYP.27 For La and Lu atoms, we have used the

energy-consistent pseudopotentials (ECP) of the Stuttgart/

Cologne group which are semi-local pseudopotentials adjusted

to reproduce atomic valence-energy spectra.28,29 Amongst the

available pseudopotentials, we have chosen the ECP28MWB

small core with 28 core electrons, multi electron fit (M) and

quasi relativistic reference data (WB) and we have used the

ECP28MWB_SEG basis set for La and Lu. For carbon and

oxygen atoms, we employ the 6-31+G(d) basis set and we have

checked, by exploring the [LnCO3]+ energy surface, the utility

of this basis (increasing the basis set to near triple zeta

6-311+G(d), adding polarization functions 6-311++G(3df),

or going to the still more complete basis set aug-cc-pVTZ all

failed to significantly change the character of the surface (see

Fig. S1 in ESIw)). Integral evaluation made use of the grid

defined as ultrafine in the Gaussian 03 program. The natures

of all stationary points were verified by analytic computa-

tion of vibrational frequencies. Aqueous solvation effects were

included with the PCM continuum solvation model.30 For the

B3LYP optimized geometries, single-point energies were

calculated in a vacuum and implicit solvent with several other

functionals to evaluate sensitivity of results to choice of

functional, including: BLYP,31,32 M05,33 M05-2X,34 PBE0,35

BHandH,36 TPSS,37 and VSXC.38 These functionals are of

different constructions: generalized gradient approximation,

GGA (BLYP), meta-GGA (TPSS and VSXC), hybrid GGA

(B3LYP and PBE0), meta-hybrid GGA (M05) and two hybrids

with a higher percentage of Hartree–Fock exchange: the hybrid

GGA BHandH and the meta-hybrid GGA M05-2X. MP2

single point calculations were also performed in both gas phase

and continuum aqueous solution to have results from a wave

function theory model against which to compare.

In general, molecular geometries are not especially sensitive

to choice of (modern) density functional.39 We have verified

that geometry optimizations with various functionals lead to

changes in geometries and energy orderings that are minimal

(relative energy differences are below 1 kcal mol�1, see

Table S17 in ESIw). In the interest of brevity, we thus report

below only results obtained with B3LYP geometries.

We also examined all-electron calculations including relati-

vistic effects. In particular, using the geometries optimized at

the B3LYP/ECP/6-31+G(d) level of theory, single-point calcu-

lations on all species were performed using the Amsterdam

Density Functional program (ADF 2010.02) developed by

Baerends, Ziegler, and co-workers.40 For these computations

the B3LYP functional was employed with an all-electron

triple-z plus two polarization functions basis set on all atoms.

Relativistic corrections were introduced by the scalar-relativistic

zero-order regular approximation (ZORA).41,42 Gas-phase

and implicit aqueous solution calculations were performed,

with continuum solvent effects included via the COSMO43

solvent model with standard radii except for La (R = 2.42 A)

and Lu (R = 2.24 A) centres.44

3. Results and discussion

3.1 Structure of lanthanum and lutetium carbonates

Structures of lanthanum(III) and lutetium(III) tri- and tetra-

carbonates have been fully optimized at the B3LYP/ECP/

6-31+G(d) level of theory (Fig. 1 and 2). The carbonate

ligands can coordinate the metal centre in either a mono-

dentate (Z1-CO32�) or bidentate (Z2-CO3

2�) fashion. In con-

sequence, we optimized all possible combinations of these two

coordination motifs in all of the studied species (see ESIwfor the complete set of optimized structures). As expected,

metal–oxygen distances are shorter in Lu-carbonates than in

their analogous La-carbonates with an average difference of

0.19 A. This difference is in good agreement with the ionic

radius difference for these two metals (0.18–0.26 A depending

on experimental conditions).45,46

The gas-phase energies of all of the studied species relative

to the most stable geometry are presented in Table 1. For the

tricarbonate species, the fully bidentate structure is the most

stable one at all levels of DFT, with a monotonic (and indeed

nearly linear) increase of relative energy from the fully

bidentate ([Ln(Z2-CO3)3]3�) structures to the fully monodentate

([Ln(Z1-CO3)3]3�) ones with each ‘‘decoordination’’ change.

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Sensitivity to DFT is for the most part modest, although larger

for [Ln(Z1-CO3)3]3�. Qualitatively, however, all functionals

provide the same picture, and MP2 calculations predict rela-

tive energies similar to those from M05-2X and BHandH

functionals, consistent with the larger contribution of

Hartree–Fock exchange to these functionals. The observation

that local functionals, and in particular BLYP, provide results

in generally good agreement with the other models validates

the use of such computationally more efficient functionals for

DFT-based molecular dynamics, as recently undertaken for

other Ln3+ containing systems.47–49

For the tetracarbonates, there is more variation in relative

energies as a function of theoretical level. From a qualitative

standpoint, VSXC is a significant outlier, and seems untrust-

worthy. For La, most other models predict the fully mono-

dentate and the singly bidentate structures in the gas phase to

be similar in energy, with variation in which is lower as a

function of model; for Lu, the fully monodentate species is

lowest in the gas phase. MP2 predicts the relative energies

for different binding motifs to be closer to one another than

do most of the DFT methods. Increasing Hartree–Fock

exchange in the DFT functionals generally seems to stabilize

[La(Z1-CO32�)3(Z

2-CO32�)]5� compared to [La(Z1-CO3

2�)4]5�

as also found in MP2 calculations where exchange is 100%

Hartree–Fock.

Irrespective of quantitative variations as a function of

specific theoretical model, we find that in the gas phase for

both studied lanthanoids the fully bidentate coordination mode

is the most favored for the tricarbonates [Ln(Z1-CO32�)3]

3�

while the fully monodentate coordination mode is preferred

for the tetracarbonates [Ln(Z1-CO32�)4]

5� (or is very close in

energy to an instead preferred, singly bidentate congener).

However, when equivalent calculations are performed for the

various species including aqueous solvent effects by means of

the PCMmodel (Table 2), the most striking feature is that now

for both tri- and tetracarbonate species the fully bidentate

coordination mode is predicted to be the most favorable,

thereby reversing the order predicted for the gas phase for

the La and Lu tetracarbonate species. Solvation plays a typical

role in leveling energy separations, but in the tetracarbonate

case also appears to eliminate intracomplex electrostatic

repulsions that lead to expanded, monodentate structures in

the gas phase (vide infra).

The same trends presented in Tables 1 and 2 are observed

from relativistic all-electron B3LYP calculations in both the

gas phase and in aqueous solution (COSMO) as shown in

Table 3. This increases our confidence in the robust nature of

our qualitative predictions since isomer energy ordering does

not depend on the solvation model, the functional, or the basis

set employed. The leveling effect of aqueous solvation for the

tricarbonate relative energies is not present with COSMO as

it is for PCM, likely owing to a smaller atomic radius being

used for the lanthanoid atoms in the latter model than the

former, given the significant exposure of the lanthanoids in the

tricarbonates compared to the tetracarbonates.

While specific interactions with the first solvation

shell—which are not modeled here—may give rise to effects

not captured in the continuum model, a significant component

of the solvation effect is associated with long range electro-

statics (because of the large charges on the ions) so we expect

the continuum model to capture dominant trends. Never-

theless, it will be interesting to use the present results for the

construction of force-field models with which explicit solva-

tion effects can be probed in order to explore this point further.

In order to better understand the inversion in the energy

ordering of the tetracarbonate structures we examined the

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

O atoms are red and C atoms are gray.

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dissociation energy (D0), interaction energy (Eint), and repul-

sion energy per carbonate for the various complexes. D0 is the

difference in energy between a [Ln(CO3)n]m� complex and its

fully separated (optimized) constituents. Eint is the interaction

energy between a Ln3+ ion and its pre-formed [(CO3)n]2n�

complex, i.e., the energy difference between a [Ln(CO3)n]m�

complex and the corresponding Ln3+ and [(CO3)n]2n� frag-

ments infinitely separated but held at the original complex

geometry. Finally, the repulsion energy per carbonate is calcu-

lated from the difference in energy between the structure-specific

[(CO3)n]2n� complex and all of the constituent carbonate ions

optimized at infinite separation, divided by the number of

carbonate molecules present. This can be expressed also as

(D0 � Eint)/n. All these energies are presented in Table 4. We

report energies in the gas phase in order to clearly decompose

the effect of different contributions to the total dissociation

energy.

The dissociation energy, D0, is of course simply the energy

of the different isomers relative to a different zero than that

used in Table 1, so again for the tricarbonate species the

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

O atoms are red and C atoms are gray.

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[Ln(Z2-CO3)3]3� structures are the most stable while for the

tetracarbonate complexes the [Ln(Z1-CO3)4]5� structures are

lower in energy. Focusing on Eint, however, reveals that the

fully bidentate structures have a larger metal–ligand inter-

action for both the tri- and tetracarbonate stoichiometries.

Consequently the difference in the behaviour of the tri- and

tetracarbonate gas-phase species must be attributed to a

difference in the repulsion energies for the different carbo-

nates. In tetracarbonates, the carbonate ligands are closer and

in consequence the repulsive interactions between them are

larger than in the case of the tricarbonate analogs. In aqueous

solution, the intercarbonate repulsion is dielectrically screened

leading to stabilization of the fully bidentate species and

a preference for that coordination motif for both the tri-

and tetracarbonate species with either La or Lu central

lanthanoid ions.

We next consider the energy of the reactions Ln(CO3)33�+

CO32� - Ln(CO3)4

5� for both La and Lu as reported in

Table 5. For Ln(CO3)45� structures we considered both tetra-

monodentate and tetra-bidentate structures that are the

minimum energy structure in gas phase and in solution

respectively. On the other hand, for Ln(CO3)33� structures

we considered only the tri-bidentate structures since they are

the minimum energy ones in both gas phase and solution. In

the gas phase, the strong electrostatic repulsion between the

negatively charged species strongly disfavors coordination,

Table 1 Relative gas-phase energies (kcal mol�1) for the different [Ln(CO3)n]m� 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

Lanthanum tricarbonate ([La(CO3)3]3�)

3m 43.8 55.6 37.9 46.0 54.7 48.3 57.3 43.2 54.32m1b 24.6 32.5 21.0 26.3 31.4 27.4 32.9 24.4 32.31m2b 10.2 14.2 8.6 11.2 13.5 11.6 14.0 10.2 14.43b 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0Lutetium tricarbonate ([Lu(CO3)3]

3�)3m 49.9 60.6 44.0 53.9 61.4 55.0 63.9 49.5 66.22m1b 25.2 32.3 21.5 28.3 32.7 28.5 33.9 25.0 37.71m2b 9.5 13.0 7.7 11.1 13.1 11.0 13.6 9.3 16.73b 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0Lanthanum tetracarbonate ([La(CO3)4]

5�)4m 0.0 0.7 0.0 0.0 0.0 0.0 0.2 0.0 7.13m1b 2.8 0.0 3.9 1.6 0.04 1.7 0.0 2.7 3.92m2b 6.9 0.4 9.0 4.5 1.5 4.8 1.5 6.7 1.31m3b 14.5 4.2 17.4 10.8 6.4 11.4 6.6 14.2 0.04b 23.9 9.9 27.4 18.8 13.5 19.9 14.0 23.5 0.8Lutetium tetracarbonate ([Lu(CO3)4]

5�)4m 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 9.03m1b 5.3 2.0 6.3 3.7 2.2 3.8 2.0 4.8 5.42m2b 11.5 4.4 13.6 8.4 5.3 8.6 5.2 10.7 1.41m3b 22.7 12.1 25.6 18.1 13.6 18.4 13.6 21.2 0.04b 36.2 22.1 39.6 29.9 24.5 30.7 24.9 34.1 0.3

Table 2 Relative aqueous solution energies (kcal mol�1) for the different [Ln(CO3)n]m� 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

Lanthanum tricarbonate ([La(CO3)3]3�)

3m 10.2 8.5 8.9 11.1 16.4 14.2 18.7 13.9 21.22m1b 5.4 4.3 4.8 6.2 9.5 8.0 10.7 7.9 13.31m2b 1.5 0.7 1.3 1.8 3.4 2.7 3.9 2.7 5.63b 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0Lutetium tricarbonate ([Lu(CO3)3]

3�)3m 40.1 39.9 37.4 41.7 48.7 44.4 51.1 42.1 57.92m1b 24.3 25.4 22.3 25.8 30.3 27.1 31.4 25.3 37.81m2b 11.4 12.3 10.3 12.3 14.6 12.8 14.9 11.7 19.33b 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0Lanthanum tetracarbonate ([La(CO3)4]

5�)4m 10.9 12.2 9.3 14.6 19.7 14.7 19.3 13.2 42.93m1b 9.1 10.2 7.8 11.9 15.8 11.8 15.1 10.6 34.92m2b 7.1 8.6 6.1 9.1 11.7 8.9 11.2 7.8 25.71m3b 4.6 5.8 4.0 5.7 6.81 5.3 6.5 4.6 13.84b 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0Lutetium tetracarbonate ([Lu(CO3)4]

5�)4m 24.1 28.7 20.6 28.8 36.5 29.6 35.8 26.3 70.83m1b 17.5 21.2 14.9 21.2 26.8 21.5 26.0 19.1 54.92m2b 10.2 13.1 8.4 12.9 16.4 12.9 15.7 11.2 36.51m3b 4.4 6.2 3.5 6.0 7.4 5.7 6.9 4.8 17.84b 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

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but inclusion of aqueous solvation effects lowers drastically

the free energy difference between tri- and tetracoordina-

tion. This indicates that a polar solvent strongly stabilizes

tetracoordinated structures. This is probably why crystallo-

graphic studies mainly report tri-coordinated structures11 while

in solution studies the tetracoordinated ones are suggested.14,16

In the gas phase, the tri-coordinate structure is preferred to the

tetracoordinate one for Lu by 12.6 kcal mol�1 more than for La

while in continuum aqueous solution they are almost equivalent

(with a small preference for La by about 1 kcal mol�1). Note

that some experiments have suggested that across the series the

Ln(CO2)33� stoichiometry becomes more favorable for heavier

elements.13–15 This is in line with our results for the gas phase

while in continuum aqueous solution our results cannot provide

a definitive answer.

3.2 Topological analysis of the electron density

In order to further characterize the nature of Ln-carbonate

interactions, we performed single-point calculations on the

B3LYP optimized structures with a relativistic all-electron

basis set and performed a topological analysis of the electron

density according to the quantum theory of atoms in mole-

cules (AIM).50 In this theory, a chemical bond exists if a line of

locally maximum electron density links two neighboring atoms

and a bond critical point (BCP) is present. A BCP is defined as

a minimum in the density along the locally maximal line. At a

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

either a net positive or net negative value. A positive Laplacian

indicates a local depletion of charge (closed-shell/ionic inter-

action), while a negative value is a sign of a local concentration

of charge (shared/covalent interaction). However a positive

Laplacian alone could be misleading e.g. F2 molecule.51

Consequently, Cremer and Kraka52 and Bianchi et al.53 have

suggested the classification of the bond between two ‘‘closed-

shell’’ interacting atoms according also to a second condition,

the total electronic energy density at the BCP, Ebe. This term is

defined as the sum of the kinetic energy density, Gb, which

usually dominates in a non-covalent bond, and the potential

energy density Vb, which is usually negative and associated

with accumulation of charge between the nuclei. In clear

covalent bonds both the Laplacian and Ebe are negative. In

less clear cases, where the Laplacian is slightly positive, the

value of Ebe can be used to make a further classification of the

bond, from being slightly covalent to purely ionic/non-

bonded. In this classification, with r2r > 0, if Ebe is negative,

the bond is called dative; if Ebe is positive, the bond is ionic.

The Gb/rb ratio is generally accepted to be less than unity for

shared interactions and greater than unity for closed-shell

interactions. Analogously, this topological analysis can be

used to identify critical points within ring and cage structures

denoted as ring critical points (RCPs) or cage critical points,

respectively. In Table 6 calculated properties at the BCPs and

RCPs for selected species are presented (see ESIw for other

species). We have selected [Ln(Z1-CO2)2(Z2-CO2)]

3� and

[Ln(Z1-CO2)3(Z2-CO2)]

5� as representative of tri- and tetra-

carbonate species, chosen specifically as isomers that have

both carbonate coordination motifs (mono- and bidentate).

BCPs are found for both coordination motifs and RCPs are

also found for the bidentate ligands due to the four-membered

Table 3 Relative energies (kcal mol�1) in the gas phase and inaqueous solution (COSMO) for the different [Ln(CO3)n]

m� species(Ln = La, Lu; n= 3, 4; m= 3, 5) at a relativistic all-electron B3LYP/TZP level of theory. The carbonate coordination motifs are designatedas number monodentate (m) or bidentate (b)

Gas phase Aqueous solution

Lanthanum tricarbonate ([La(CO3)3]3�)

3m 44.5 —a

2m1b 25.3 27.51m2b 10.6 12.63b 0.0 0.0Lutetium tricarbonate ([Lu(CO3)3]

3�)3m 51.6 57.42m1b 26.3 33.41m2b 10.0 14.83b 0.0 0.0Lanthanum tetracarbonate ([La(CO3)4]

5�)4m 0.0 28.73m1b 2.9 20.52m2b 7.1 13.11m3b 14.6 6.04b 23.8 0.0Lutetium tetracarbonate ([Lu(CO3)4]

5�)4m 0.0 29.33m1b 5.4 21.22m2b 11.7 12.61m3b 22.8 6.14b 36.0 0.0

a SCF convergence failure.

Table 4 Dissociation energy (D0), interaction energy (Eint) andrepulsion energy per carbonate (kcal mol�1) for different[Ln(CO3)n]

m� species (Ln = La, Lu; n = 3, 4; m = 3, 5). Thecarbonate coordination motifs are designated as number monodentate(m) or bidentate (b)

La Lu

D0 Eint Repulsiona D0 Eint Repulsiona

Tricarbonate ([Ln(CO3)3]3�)

3m �1202.0 �1867.7 221.9 �1300.4 �1997.2 232.32m1b �1221.2 �1913.2 230.7 �1325.1 �2053.7 242.91m2b �1235.6 �1956.6 240.3 �1340.9 �2103.1 254.13b �1245.8 �1997.4 250.5 �1350.3 �2147.3 265.6Tetracarbonate ([Ln(CO3)4]

5�)4m �985.7 �2263.5 319.4 �1077.6 �2409.3 332.93m1b �982.9 �2294.8 328.0 �1072.4 �2441.1 342.22m2b �978.8 �2326.1 336.8 �1066.1 �2473.4 351.81m3b �971.2 �2356.4 346.3 �1054.9 �2502.4 361.94b �961.9 �2384.8 355.7 �1041.5 �2528.9 371.9

a Per carbonate.

Table 5 Reaction free energies (DG, kcal mol�1) at the B3LYP/ECP/6-31+G(d) level of theory in both vacuum and water (described withthe PCM continuum solvation model). In bold we highlight the DGcorresponding to the most favorable product in vacuum or water

Reaction DG(vacuum) DG(PCM)

[La(Z2-CO3)3]3� + CO3

2� - [La(Z1-CO3)4]5�

266.78 12.10[La(Z2-CO3)3]

3� + CO32� - [La(Z2-CO3)4]

5� 294.71 5.29

[Lu(Z2-CO3)3]3� + CO3

2� - [Lu(Z1-CO3)4]5�

278.51 23.46[Lu(Z2-CO3)3]

3� + CO32� - [Lu(Z2-CO3)4]

5� 319.17 3.91

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

ring-like structure including the lanthanoid. The Laplacian at

all of the BCPs and RCPs is positive indicating an ionic

interaction between the lanthanoid ions and the carbonate

ligands. In both cases the Ebe are slightly positive being also

in agreement with an ionic interaction. Furthermore, the

Laplacian is always larger in the Lu complex than in the La

complexes, showing higher ionicity in the Lu-carbonate bonds

than in the corresponding La case. The Laplacian of the

electron density (r2r) for [La(Z1-CO3)2(Z2-CO3)]

3� and

[Lu(Z1-CO3)2(Z2-CO3)]

3� is plotted from several perspectives

to give three dimensional insight into the metal-carbonate

bonds (Fig. 3). The Laplacian has a positive value around

the metal-carbonate bonds that is larger for the monodentate

ligand than for the bidentate ligands. Additionally, the Laplacian

is less dense on the bidentate carbonate ligand. Finally, the Gb/rbratios are in agreement with a closed-shell interaction in both

La- and Lu-carbonate bonds; however, the lutetium bonds are

predicted to be more ionic which is in agreement with our

previous results. The Gb/rb ratio values below unity for some

of the bidentate ligands are associated with the bidentate

nature of the coordination. No qualitative changes are

observed when topological analysis of the electron density

is performed including continuum aqueous solvation effects

(see ESIw).

3.3 Natural orbitals for chemical valence

To further characterize the Ln-carbonate interaction we have

performed the energy decomposition analysis introduced by

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

has to be aware that the energy decomposition analysis is

highly dependent on the chosen fragments, especially for

charged species (see Tables S2–S5 in the ESIw). On one hand,

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-

tributions to the bond (since the Ln(III)-carbonate bond is

mainly ionic as the topological analysis of the electron density

indicate). On the other hand, the interaction energies are

strongly biased by the nature of the fragments and the charge

transfer between them, being unreliable to determine the

ionicity/covalency of the Ln(III)-carbonate bond.

The energy-decomposition results obtained using this

approach are reported in Table 7 for the same selected

structures chosen in Section 3.2, while in the ESIw we report

results for all other structures. The orbitalic and electrostatic

interactions are always similar in magnitude for the tricarbonate

species with the former being slightly larger than the latter. On

one hand, when the carbonate is coordinated in a bidentate

manner, both the orbitalic and the electrostatic interactions

increase with respect to monodentate coordination; however,

the orbitalic interaction increases by ca. 20 kcal mol�1 while

the increase in the electrostatic interaction is almost three

times larger (ca. 60 kcal mol�1). Consequently, the bidentate

metal-carbonate bonds are slightly more ionic than the mono-

dentate ones. The comparison between lutetium tricarbonates

and their lanthanum equivalents reveals that both orbitalic

and electrostatic contributions are increased by ca. 10 and

30 kcal mol�1, respectively, leading to a more ionic metal–

ligand interaction in the lutetium species than in the lantha-

num ones. (Note that the interaction energies for the ‘‘fourth’’

carbonate in the tetracarbonates of Table 7 cannot be compared

directly to the small endergonic complexation energies listed

in Table 5 because the tricarbonates in Table 5 are relaxed,

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

Species Ligand Type rb r2rb Gb Gb/rb Vb Ebe

La [La(Z1-CO3)2(Z2-CO3)]

3� Z1-CO32� (3,�1) 0.0794 0.3887 0.0964 1.2148 �0.0957 0.0008

Z2-CO32� (3,�1) 0.0620 0.2395 0.0586 0.9453 �0.0574 0.0012

Z2-CO32� (3,+1) 0.0343 0.1844 0.0427 1.2460 �0.0392 0.0034

[La(Z1-CO3)3(Z2-CO3)]

5� Z1-CO32� (3,�1) 0.0546 0.2746 0.0621 1.1378 �0.0555 0.0066

Z2-CO32� (3,�1) 0.0405 0.1601 0.0357 0.8809 �0.0313 0.0044

Z2-CO32� (3,+1) 0.0272 0.1349 0.0306 1.1215 �0.0274 0.0032

Lu [Lu(Z1-CO3)2(Z2-CO3)]

3� Z1-CO32� (3,�1) 0.0957 0.6069 0.1505 1.5720 �0.0143 0.0012

Z2-CO32� (3,�1) 0.0754 0.3851 0.0954 1.2644 �0.0944 0.0009

Z2-CO32� (3,+1) 0.0408 0.2427 0.0576 1.4112 �0.0544 0.0031

[Lu(Z1-CO3)3(Z2-CO3)]

5� Z1-CO32� (3,�1) 0.0682 0.4202 0.0974 1.4279 �0.0898 0.0076

Z2-CO32� (3,�1) 0.0705 0.4472 0.1019 1.4456 �0.0920 0.0099

Z2-CO32� (3,+1) 0.0319 0.1724 0.0401 1.2586 �0.0371 0.0030

Fig. 3 The Laplacian of the electron density (r2r) of [La(Z1-CO3)2-

(Z2-CO3)]3� (top) and [Lu(Z1-CO3)2(Z

2-CO3)]3� (bottom): perpendicular

to the ligand coordination plane (right), side view of an Z2-CO32�

ligand (centre) and side view of an Z1-CO32� ligand (right). Negative

values of the Laplacian are included in the red regions.

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while those implicit in Table 7 are not (rather, they maintain

the tetracarbonate geometry)).

In the tetracarbonate species, the electrostatic interaction

between a carbonate ligand and the [Ln(CO3)3]3� fragment is

always strongly repulsive (>150 kcal mol�1) independently of

the coordination motif. This is a consequence of the highly

charged nature of the chosen fragments and it is compensated

by the solvation energy. The same increase in the orbitalic and

the electrostatic interactions for the lanthanum and lutetium

tricarbonate species is observed in the tetracarbonate ones

as well.

In order to analyze the nature of the small covalent con-

tributions of the metal–ligand bond, we used the extended

transition state (ETS) method combined with natural orbitals

for the chemical valence (NOCV) theory, a combined charge

and energy decomposition scheme for bond analysis.59–62

ETS–NOCV has been used, together with the fragment calcu-

lations presented in Table 7, to give the contributions from

different natural orbitals (constructed from the fragment

orbitals) to the orbitalic contribution. The natural orbitals

with the largest contribution to the metal–ligand bond are

presented in Fig. 4.

In all the species studied, the major contributions to the

small covalent contribution to the bond energy between the

lanthanides and the carbonate ligands are donations from

the occupied 2p orbitals of the carbonate oxygen to the empty

5d metal orbitals. This is consistent with 5d orbitals being

more extended in space than 4f orbitals, such that the latter

essentially never contribute to bonding, similarly to what has

been found for La3+ in water.47

A complementary picture can be obtained also from Natural

Bond Orbitals (NBO) analysis of Weinhold and co-workers63–65

that we have performed by means of NBO5.9 code.66 Even in

this case the interaction between Ln and carbonates results

highly ionic since when Ln and ligand are in the same fragment

the percentage of ionicity of Ln–O bond is more than 95%.

Second-order perturbative estimates of donor–acceptor

interactions in the NBO basis, can provide the presence and

the nature of the interaction and results for prototypical

[Ln(Z1-CO3)2(Z2-CO3)]

3� and [Ln(Z1-CO3)3(Z2-CO3)]

5� systems

are reported in ESIw (Table S18). We found that the inter-

action is mainly between occupied lone pairs of oxygen and

empty orbitals of Ln, with an energy in the 10–35 kcal mol�1

range. Ln acceptor orbitals are mostly empty 5d orbitals.

Then, empty 6s orbitals are also involved, alone, as for Lu

with tri-carbonates, or with participation of 5d and 4f orbitals

(this lasts only for La). Note that NBO analysis finds a

contribution of 4f orbitals but this is always small (between

22 and 34% of the given interaction) and associated with

charge transfer, not covalent bonding.

Table 7 Energy decomposition analysis (EDA, kcal mol�1) of metal–ligand interaction for selected species. All energies are with respect to theisolated fragmentsa

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

La [La(1Z-CO3)2(2Z-CO3)]

3� 1Z-CO32� 104.4 �81.0 (50.61%) �79.1 (49.39%) 46.1 �9.6

2Z-CO32� 130.2 �95.9 (42.33%) �130.7 (57.67%) 78.6 �17.8

[La(1Z-CO3)3(2Z-CO3)]

5� 1Z-CO32� 60.4 �54.3 — 187.8 — �203.1 �9.2

2Z-CO32� 80.6 �69.4 — 161.7 — �189.6 �16.7

Lu [Lu(1Z-CO3)2(2Z-CO3)]

3� 1Z-CO32� 106.2 �79.5 (45.87%) �93.8 (54.13%) 38.4 �28.7

2Z-CO32� 149.5 �104.4 (38.84%) �164.3 (61.16%) 74.9 �44.3

[Lu(1Z-CO3)3(2Z-CO3)]

5� 1Z-CO32� 67.0 �56.5 — 190.3 — �226.5 �25.7

2Z-CO32� 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.

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4. Conclusions

Fully bidentate binding of carbonate ligands is preferred both

in the gas phase and water for tricarbonates of lanthanum(III)

and lutetium(III). By contrast, for the corresponding tetra-

carbonates fully monodentate binding is preferred in the gas

phase and fully bidentate binding in aqueous solution. The

stronger repulsion energy associated with four carbonate

ligands drives the different behavior for the tetracarbonate in

the gas phase compared to the tricarbonate, but aqueous

solvation effectively compensates for this effect. The energy

of the tri-carbonate structure relative to the tetra-carbonate

alternative is thus lower for Lu than La in the gas phase, in line

with some experimental suggestions,13–15 while in solution

La and Lu behave similarly. This deserves further studies

and developments, in particular to have access to free energy

differences in liquid systems explicitly considering the solvent

and the experimental conditions (pH, ionic strength, etc.). This

is the direction of our current research.

Topological analysis of the electron density, energy decom-

position analysis, and natural orbitals for the chemical valence

analysis all agree that the Ln-carbonate interaction is predo-

minantly closed shell/ionic in nature. Thus, the known differ-

ence in ionic radii across the lanthanoid series should be

the key physical quantity determining the properties of

Ln/carbonate complexes. A contrasting, and certainly inter-

esting situation could arise for the case of An(III)/carbonate

complexes, where the 5f orbitals, which have more valence

character than do 4f analogs, could determine differences in

binding through covalent interactions, as recently shown by

Gagliardi, Albrecht-Schmitt and co-workers.67,68

Finally, the highly closed-shell/ionic nature of lanthanoid(III)-

carbonate interactions highlighted by the present analysis

paves the way for developing classical force fields for these

systems. Simulations of lanthanoid solutions by means of

finite temperature molecular dynamics with explicit solvent will

be crucial to address questions related to the formation and

equilibrium of these complexes as a function of salt concen-

tration, as has recently been shown for lanthanoid-chloride,

thorium-chloride and thorium boride salts.69,70 The present

study suggests that the extension of such techniques to

Ln/carbonate salts in explicit water should be feasible to study

statistically the equilibrium between different complexes.

Acknowledgements

We would like to acknowledge Thomas Vercouter and Pierre

Vitorge for interesting discussions. This work was partially

supported by the French National Research Agency (ANR)

on project ACLASOLV (ANR-10-JCJC-0807-01) (Y.J., F.M.

and R.S.). PM and CJC acknowledge the National Science

Foundation (grant CHE-0952054).

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