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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: [email protected]
bDepartment of Chemistry, Supercomputing Institute, and ChemicalTheory Center, University of Minnesota, 207 Pleasant St. SE,Minneapolis, MN 55455-0431, USA. E-mail: [email protected]
w Electronic supplementary information (ESI) available. See DOI:10.1039/c2cp41996c
PCCP Dynamic Article Links
www.rsc.org/pccp PAPER
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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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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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