Structural, Energetic, and Electronic Properties of La(III)–Dimethyl Sulfoxide Clusters

Structural, Energetic, and Electronic Properties of La(III)−DimethylSulfoxide ClustersEnrico Bodo,† Mara Chiricotto,†,§ and Riccardo Spezia*,‡

†Department of Chemistry, University of Rome “La Sapienza”, 00185 Rome, Italy‡CNRS, Laboratoire Analyse et Modelisation pour la Biologie et l’Environnement, Universite d’Evry-Val-d’Essonne, 91025 EvryCedex, France

*S Supporting Information

ABSTRACT: By using accurate density functional theorycalculations, we have studied the cluster complexes of a La3+

ion interacting with a small number of dimethyl sulfoxide(DMSO) molecules of growing size (from 1 to 12). Extendedstructural, energetic, and electronic structure analyses havebeen performed to provide a complete picture of the physicalproperties that are the basis of the interaction of La(III) withDMSO. Recent experimental data in the solid and liquid phasehave suggested a coordination number of 8 DMSO moleculeswith a square antiprism geometry arranged similarly in theliquid and crystalline phases. By using a cluster approach onthe La3+(DMSO)n gas phase isolated structures, we have found that the 8-fold geometry, albeit less regular than in the crystal, isprobably the most stable cluster. Furthermore, we provide new evidence of a 9-fold complexation geometric arrangement that iscompetitive (at least energetically) with the 8-fold one and that might suggest the existence of transient structures with highercoordination numbers in the liquid phase.

■ INTRODUCTION

Complexation of lanthanoid (Ln) and actinoid (An) ions byorganic molecules is a very useful tool for their separation, anda thorough characterization of their solvation structure indifferent liquids is mandatory for selecting the best performingsolvents.1 Solvation is a phenomenon that is the basis of thechemical behavior of almost every element and compound:from tuning chemical reactions and thus organic synthesis todetermining the structure of large flexible molecules and frombeing the basis of dissolving and diffusing species in theenvironment to impacting industrial processes. These chemicalprocesses ultimately depend on solvent−solute interactions,and thus fundamental studies are necessary to develop an in-depth understanding of the phenomena involved.For example, industrial processes are normally conducted in

specific solvents that can be changed, modified, and designed toimprove the efficiency of the processes. One importantindustrial process involving Ln and An is their separationfrom nuclear waste; this work is currently done by employingorganic solvents to extract them from the aqueous phases withdifferent techniques and operating conditions.2−7 Furthermore,lanthanoids are extensively used in organic synthesis to catalyzeseveral reactions because of the ability to change their oxidationstate under nonaqueous conditions.8,9

Interaction of Ln and An with water was largely studiedtheoretically and experimentally in gas, solid, and liquidphases.10−13 In particular, the combination of theoreticalstudies in both gas and liquid phases was able to rationalize

the coordination number behavior across the series.14−30 As anexample of the importance of these studies in the gas and liquidphases, we mention the recent works of Williams and co-workers. From experimental studies in the gas phase of Ln(III)ions in water clusters of different sizes, it was possible todirectly relate absolute reduction energies of gaseous nano-drops containing Ln(III) ions to the absolute reductionenthalpy of the ion in bulk solution and then obtain anabsolute standard hydrogen electrode potential.31 Furthermore,by extrapolating recombination enthalpies to infinite size, theywere able to obtain the bulk hydration enthalpy of theelectron.32 While many experimental and theoretical studies arepresent for interaction of Ln(III) with water, much lesstheoretical work has been reported for nonaqueous sol-vents.33−38

In the work presented here, we describe the complexation ofthe prototype La3+ ion by a nonaqueous solvent, dimethylsulfoxide (DMSO). To the best of our knowledge, this is thefirst theoretical study of Ln ions interacting with DMSO. Theelectron pair donor ability is greater than that for water,39 andDMSO is more sterically demanding as a ligand. The fullyDMSO-solvated lanthanoid(III) ion crystal structures arereported, showing octakis(DMSO)lanthanoid(III) complexeswith iodide, bromide, and perchlorate salts, often with

Received: July 22, 2014Revised: November 16, 2014Published: November 18, 2014

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disordered DMSO ligands.40−48 All octakis(DMSO)lanthanoid-(III) iodides display an 8-fold coordination with a distributionof Ln−O bond distances with alternative positions for at leastone of the ligands.48 The coordination state of Ln3+ ions inDMSO solution is still controversial; spectroscopic andcrystallographic studies of lanthanoid iodides revealed thatlanthanoid(III) ions have a similar eight-coordinated config-uration both in liquid DMSO and in the solid state.48−50

According to these studies, the coordination number in DMSOseems to be constant across the series, an observation differentfrom that in water,51 although the decrease in the mean Ln−Obond distance is greater than expected on the basis of existingionic radius data for eight-coordination.48 However, otherstudies suggest some changes in the average coordinationnumber along the series.52,53 These results were confirmed in avery recent investigation dealing with apparent molar volumesand compressibilities of Ln3+ trifluoromethanesulfonates inDMSO.54

A recent X-ray absorption near edge structure (XANES)study reports accurate Ln−DMSO distances and suggests thatthe coordination motif is 8-fold,55 although the presence of aninth DMSO molecule in an intermediate solvation shell (i.e.,between the first and second) cannot be ruled out, because X-ray absorption is mainly sensitive to atoms in the first shell ofthe photo-absorber (here the Ln). In this work, we have studiedstructural, energetic, and bonding properties of La3+−DMSOclusters of growing size (up to 12 DMSO molecules), by meansof extended density functional theory (DFT) calculations. Inthis way, we were able to provide a basic understanding of thephysicochemical nature of ion−solvent interactions that are atthe heart of the observed properties.

■ COMPUTATIONAL DETAILSReasonable initial structures for the clusters of La3+ and nmolecules of DMSO (n ∈ [1,12]) were created using the MM3force field.56 In particular, the Monte Carlo-driven minimumsearch contained in the Tinker package57 was used inconjunction with annealing molecular dynamics. Once a reliableset of initial starting structures had been obtained, we usedDFT to obtain the cluster internal energy and vibrational zero-point energy (ZPE) in the harmonic approximation.DFT calculations were performed by using both the

B3LYP58 and M06-2X59 functional, with the 6-31G*60 basisset for the light elements and the Small Core ECP and basis61

for La3+. A preliminary test of the effect of basis set andpseudopotential was performed as reported below. Dispersioneffects were considered by the D3 Grimme method62 for theB3LYP functional. The M06-2X energies were left uncor-rected.59

We considered clusters composed of one La3+ ion and agrowing number of DMSO molecules {[La(DMSO)n]

3+ with n= 1−12}. For n > 8, we considered three possible structuralpatterns around La3+ that are generated by imposing (a) 10DMSO molecules in the first shell and the remainder in thesecond shell (the 10 + m series), (b) 9 molecules of DMSO inthe first shell and the remainder in the second shell (the 9 + mseries), and (c) 8 molecules of DMSO in the first shell and theremainder in the second shell (the 8 + m series). Theoptimization of each structure was done initially using theB3LYP functional without dispersion correction and thenfollowed by a refining run with its dispersion-corrected version(D-B3LYP)62 followed by a frequency evaluation. A second setof calculations were repeated with the M06-2X functional to

test the reliability of the different correlation models. For allfinal structures, a natural bonding orbital (NBO) analysis63 wasalso conducted. All calculations were conducted usingGaussian09.64

Initial assessments of the performances of different computa-tional settings (method, basis set, and dispersion) wereconducted out extensively on the simple monomeric [La-(DMSO)]3+ structure and partially on the [La(DMSO)2]

3+

dimeric structure. Most of the results of our tests are reportedin the Supporting Information. Here we shall limit ourselves toa few important considerations.The two different functionals used in this work were first

tested against wave function-based methods (MP2 andCoupled Cluster) on the monomer and the dimer (resultsreported in Tables 1 and 2 of the Supporting Information).This analysis shows that the DFT geometries are in excellentagreement with correlated calculations. The match between theadiabatic interaction energies obtained with DFT andcorrelated methods is also very good. In particular, theinteraction energy provided by M06-2X is very close to thatprovided by CCSD(T) and MP2 for the monomer, while forthe dimer, both D-B3LYP and M06-2X are able to provideenergies similar to those obtained with MP2.

Role of Dispersion Forces. While in the monomer thedispersion corrections of the B3LYP functional are ratherlimited, van der Waals forces are added to the number ofmolecules, and therefore, their importance deserves a moredetailed analysis. Obviously, the total correction due to theinclusion of empirical dispersion corrections grows with clustersize (see Table 3 of the Supporting Information). What wehave found is that the dispersion corrections have a sizable butminor effect on the structural properties of small clusters. Mostof the clusters do not show substantial geometry changes whenthe dispersion correction is switched on. Some examples arereported in Figure 1 of the Supporting Information. In the n =3 cluster, for example, the final structures obtained with B3LYPand D-B3LYP differ by a total root-mean-square deviation(rmsd) of 0.19 Å and the energy gain due to dispersion is only0.6 eV. Dispersion corrections are much more important whenthe number of DMSO molecules increases and the “crowding”of the solvation shell makes the average distance between theneutral solvent molecules shorter. For example, in the case ofthe structure with 6 DMSO molecules (Figure 1 of theSupporting Information), we find a slightly more sizablegeometric alteration. The total rmsd between the structuresobtained with B3LYP and D-B3LYP is now 1.68 Å. The totalgain due to dispersion interaction is 1.6 eV.The La−O distance as a function of cluster size calculated

with and without dispersion corrections for the B3LYPfunctional is reported in Figure 1. A small sample of La−Odistances with and without dispersion correction is alsoreported in Table 1. Figure 1 clearly shows that while thegeometry of the clusters is essentially insensitive to dispersionup to 4 DMSO molecules, for larger clusters the dispersioncorrections have an effect that is mainly that of compacting theresulting cluster. The general trend, as expected, is that the La−O distance is approximately 1% shorter when dispersioncorrections are switched on (see Table 1).

Functional Performance. As one can see in Figure 1, theuse of the M06-2X functional does not alter substantially thegeometry or shape of the cluster. The M06-2X functional, in itsnoncorrected expression, already has a better description oflong-range forces with respect to B3LYP.59 It therefore

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provides slightly more compact cluster geometries, even if wedo not detect any substantial change in the arrangement of thesolvent molecules. The rmsds between the structures obtainedwith M06-2X are very small, and only for a few structures doesit exceed 1 Å (the rmsd between all the various optimizedstructures coming from various methods is reported in Table 3of the Supporting Information). The similarity between theM06-2X and D-B3LYP structures is clearly shown by alsolooking at Figure 3 of the Supporting Information where therotational constants of the optimized geometries are reportedas a function of cluster growth for both D-B3LYP and M06-2X.The cluster series essentially maintain the same shaperegardless of the functional used.Pseudopotential. Another important approximation in-

volved in our calculations is the use of an effective potential atthe La3+ core. As mentioned in the previous section, a series ofstructural optimizations and energy calculations (includingZPE) were performed using also the LANL2DZ ECP on theclusters with n ranging from 1 to 10. The resulting LANL2DZstructures remain almost unchanged with respect to the RSCECP ones. Their mutual rmsd remains below 1 Å except forthose for n = 5 and 8. The rmsds between the optimized

structures are reported in Table 3 of the SupportingInformation.

■ STRUCTURAL PROPERTIESThe geometries of [Ln(DMSO)n]

3+ clusters obtained from D-B3LYP/RSC geometry optimization are shown in Figure 2(very similar structures are obtained with M06-2X). Here weshow the first series, which we call 10 + m, where we fill theLa3+ first shell with a maximum number of 10, and only for n >10 do we place the additional DMSO molecule(s) in a secondshell. In the same figure, we highlight the O−O contactswhenever their mutual distance falls below 4.0 Å to show thecage formed by the ligands around the La3+ ion. The cage startsforming at n = 4 with a clearly shaped tetrahedron geometrythat encloses the lanthanide ion. The average distance betweenLa and O is 2.28 Å. The tetrahedron is not perfectly regular,and the O−O distances range from 3.67 to 3.76 Å (O−La−Oangles ranging between 110° and 111°). The five-DMSOgeometry is instead that of a distorted triangular bipyramid withtwo “apical” oxygens at 2.36 Å and three equatorial oneslocated at distances ranging from 2.32 to 2.34 Å. The n = 6cluster is a slightly distorted octahedron with La−O distancesranging from 2.38 to 2.44 Å. The O−O distances are shown(together with La−O ones) in Figure 3 to clearly show theregularity of the structures. Evidently, because of the stericrepulsion between the methyl terminals and the progressivecrowding of the first sphere of solvation, the possibility ofhaving regular symmetric (Euclidean) structures is lost beyondn = 4. For a larger number of DMSO molecules, the network ofO−O contacts is no longer regular. Of particular interest here isthe structure with n = 8 because it seems to be the mostabundant solvation shell structure in solution at least as it hasbeen probed by XANES experiments.55 The structure is that ofan irregular square antiprism that is the favored geometry wheneight solvent molecules are distributed on the surface of asphere to maximize the distances among them. The La−Odistance in this structure is fairly regular and has an averagevalue of 2.52 Å with a very small dispersion (0.01 Å standarddeviation). The addition of a ninth DMSO molecule provides a“cap” for the structure with n = 8 giving rise to a distortedmonocapped square antiprism as if a vertex had been added tothe previous structure. This structure is slightly less regular thanthe previous one: the average La−O distance is 2.58 Å with astandard deviation of 0.03 Å.As shown in Figure 2, it is possible to obtain a minimum

energy structure that has a complete first shell made by 10DMSO molecule all arranged in a unique solvation sphere.Starting from n = 10, we found it was impossible toaccommodate any further molecule into the first shell andthe second shell began to be filled. As we will see below, thesubstantial crowding of the n = 10 solvation sphere makes thisconfiguration relatively unstable with respect to the accretionpattern that sees the growth of a second shell around a core of8 or 9 DMSO molecules.To further assess the shape and size of the cluster growth, we

have also calculated the rotational constants of the systems(they are shown in Figure 3 of the Supporting Information).The nearly “spherical” structures correspond to n = 4, n = 9,and n = 10. All the other clusters have a prolate shape. In Table1, we compare La−O distances obtained from geometryoptimization of different clusters with the available exper-imental data. The agreement is excellent, especially for the n =8 structures with both D-B3LYP and M06-2X substantially

Figure 1. La−O distances obtained by B3LYP, D-B3LYP, and M06-2Xin the 10 + n series.

Table 1. La−O Distances and Their Standard Deviations (inparentheses) for La3+ Binding DMSO As Obtained fromExperiments and Calculations

method La−O (Å) system ref

X-ray crystal 2.49 [La(DMSO)8]I 48EXAFS crystal 2.507 [La(DMSO)8]I 49XANES crystal 2.49(2) [La(DMSO)8]I 55EXAFS 2.503 La3+ in liquid DMSO 49XANES 2.492 La3+ in liquid DMSO 55D-B3LYP/RSC 2.52 (0.01) [La(DMSO)8]

3+ this workD-B3LYP/RSC 2.58 (0.03) [La(DMSO)9]

3+ this workD-B3LYP/RSC 2.65 (0.07) [La(DMSO)10]

3+ this workB3LYP/RSC 2.55 (0.02) [La(DMSO)8]



3+ this workM06-2X/RSC 2.50 (0.01) [La(DMSO)8]



3+ this work



reproducing the experimental data. From the data reported inTable 1, it seems fair to conclude, solely on the basis ofgeometrical considerations, that the likely candidate forrepresenting the structure of the “solvated” La3+ is the one inwhich the ion binds 8 DMSO molecules.As we shall see below, however, the pattern of the relative

energies of the possible structures obtained by using differentstructuring of the first shell of solvation makes the pictureslightly more complex and less certain. It is indeed possible todevise an accretion scheme in which, instead of filling up a firstshell using 10 DMSO molecules, we can add a second shell ofsolvent molecules to a first shell made of 8 or 9 DMSOmolecules. The calculations were extended to such geometries,and we report them in Figure 4. All the reported structureshave the topology of minimum energy structures and representan alternative pathway for cluster growth. In these structures,

the inner shell of 8 or 9 DMSO molecules is not perturbed bythe addition of new solvent molecules and can be seen tosurvive the additional solvation and maintain the same initialgeometry.

■ ENERGETIC PROPERTIESFrom an energetic point of view, the addition of one DMSOmolecule corresponds to adding ∼550 au in electronic energy.Because the total electronic energy does not yield appreciableinformation, we focus on the adiabatic interaction energy that iscalculated as

= − × − +E n E n n E E( ) ( ) (DMSO) (La )int3

(1)

In Figure 5, we report four kinds of interaction energiesalong the 10 + m series of clusters: (i) the one obtained usingD-B3LYP corrected for ZPE effects, (ii) the one obtained withD-B3LYP only, (iii) the one obtained using the plain B3LYPresults, and (iv) the M06-2X energies corrected for the ZPEeffects. As one can see, dispersion corrections play a rathersignificant role in terms of the cohesive energy. The main effectis to provide a sizable additional stabilization of the largercluster where the crowding of the DMSO molecules increasesthe level of steric repulsion that makes less stable the plainB3LYP results. ZPE correction seems to be less important, andits contribution to the interaction energy is small and positiveand grows with cluster size.One important question that we want to address here is the

competition between the various growth models that thecluster can undergo. In particular, it is important to comparevarious geometric configurations in which the inner shell ofDMSO presents different coordination numbers. The energeticdata we have shown up to this point concern clusters in whichthe first shell consists of 10 DMSO molecules and for n > 10the successive molecules are placed in the second shell. Todetermine the preferential number of DMSO molecules in La3+

Figure 2. Pictorial representation of the cluster growth around the La3+ center for the 10 + m series. Wireframe is used for carbons and hydrogensand CPK for sulfurs and oxygens. Connections between oxygen atoms are drawn using red sticks for distances from La3+ of <4.0 Å.

Figure 3. La−O (red) and O−O (black) distances as a function ofcluster growth in the 10 + n series for the D-B3LYP functional.



first shell, we studied the stability of the three series of clustersdefined previously: 10 + m, 9 + m, and 8 + m (shown in Figures2 and 4).Instead of the total binding energy reported above, it is

possible to characterize the progressive structuring around thecentral ion by looking at the incremental binding energy (orevaporation energy) that corresponds to the following process:

= − − +E n E n E n E( ) ( 1) ( ) (DMSO)inc (2)

The Einc values normally show a decreasing trend as the clusterwith n molecules requires less energy to evaporate one solventmolecule with respect to the cluster with n − 1 solventmolecules. Stable clusters can be spotted by looking at thechanges of the slope of Einc. The resulting values of Einc arereported in Figure 6 for the 10 + m, 9 + m, and 8 + m serieswith both D-B3LYP and M06-2X. The trend is similar alongthe three series, and the main energetic features that we seeduring the accretion of the cluster are equally described by thetwo functionals. We clearly see stable structures forming up to

Figure 4. Pictorial representation of the “second-shell” cluster growth around the La3+ center for the 9 + m and 8 + n models (see the text fordetails). Wireframe is used for carbons and hydrogens and CPK for sulfurs and oxygens. Connections between oxygen atoms are drawn using redsticks for distances of <3.5 Å.

Figure 5. Adiabatic interaction energy as a function of the number ofDMSO molecules.

Figure 6. Incremental interaction energy as a function of the number of DMSO molecules for M06-2X (right) and D-B3LYP (left).



5 DMSO molecules where the evaporation of one DMSOmolecule costs from 140 to 50 kcal. From 6 to 8 molecules, theevaporation energy decreases much less and remains around 40kcal. The configuration with 8 molecules seems to provide thelast of a series of stable clusters because the energy that isnecessary to remove one DMSO molecule from theconfigurations with n = 9 and n = 10 is approximately two-thirds and half of its value, respectively. Very similar results areobtained by looking at the same quantity but using the Gibbsfree energy that is reported for completeness in Figure 4 of theSupporting Information.We can further quantify the relative stability of a specific

cluster configuration with n DMSO molecules with respect toits parent (n − 1) and its offspring (n + 1) by taking the secondderivative (i.e., the central difference) of the total cluster energyas a function of n.

= + − + −S n E n E n E n( ) ( 1) 2 ( ) ( 1) (3)

Results for 10 + m, 9 + m, and 8 + m series are shown inFigure 7. We report both the central difference in the totalcluster energy and the Gibbs free energy. The larger S(n) is fora configuration, the more stable it is with respect to theadjacent ones. The most stable clusters in the 10 + m series areclearly those with n = 8 and 9. A single solvation shell made by10 DMSO molecules is greatly penalized. As we have pointedout before, this series of cluster sees the filling of a first shell of10 DMSO molecules whereby the 11th and 12th molecules areplaced in the second shell. The same happens with the 9 + mseries where again the configurations with 8 and 9 moleculesare clearly the most stable ones, although there are differencesbetween the results for the two functionals. In particular, the D-B3LYP functional clearly shows that the structure with 8molecules is the favored one, while the M06-2X functional putsthem on the same ground. For the 8 + m series, in which thefirst solvation shell consists of 8 DMSO molecules and theothers are added in a second shell, the most stableconfiguration during cluster growth clearly remains that withn = 8.

In view of the results described above, we conclude that thereis an evident energetic competition between the clusters having8 and 9 molecules in the first shell. The evaporation energypoints to the n = 8 structure as a natural closure of the first shellof solvation, which is consistent with experimental determi-nations. An analysis of the relative stability (eq 3), however,makes us think that the structure with 9 DMSO molecules isenergetically almost as stable as that with 8 and may present aviable configuration even in solution where it may represent atleast a transient structure.

■ BONDING FEATURES

For each cluster, at the equilibrium geometry, we havecalculated the NBOs and the corresponding populations toelucidate the nature of the interaction between the central ion

Figure 7. Second derivative of the total cluster energy (left) and the free energy (right) as a function of cluster size. S(n) values are in atomic units.

Table 2. Natural Charges and Valence Populations of theCentral La3+ Ion

cluster type charge valence population

1 2.64 0.42 2.45 0.63 2.28 0.84 2.11 0.95 1.94 1.16 1.75 1.37 1.58 1.48 1.41 1.59 1.29 1.610 1.26 1.711 1.26 1.712 1.25 1.78 + 1 1.41 1.58 + 2 1.40 1.68 + 3 1.40 1.69 + 1 1.29 1.79 + 2 1.30 1.79 + 3 1.30 1.7



and the surrounding solvent molecules. The interaction is dueto the electronic “donation” from the lone pairs of the O atoms

to the empty (one-center) nonbonding orbitals of the centralion. The strength of the resulting interaction is very high andleads to a substantial transfer of negative charge to the centralion from the ligands. The NBO charge65 on the La3+ decreasesfrom 2.64 in n = 1 to the “bulk”, stable value of 1.25 for n = 10.The total natural charge of the La3+ and its electronicpopulation (valence states only) are listed in Table 2. Theempty orbitals on La3+ are formally filled with 1.7 electronsduring cluster growth. For the 10 + m series, each DMSO adds0.2 valence population at the beginning and then 0.1, while for8 + m and 9 + m series, the results are almost constant, showingthat the second shell has no direct effect (as expected). Thisshows that there is no particular difference in the nature of theinteraction as a function of the number of DMSO molecules.We can then use one cluster to examine in detail the

electronic configuration of such complexes. As an example, wehave chosen the n = 8 cluster that seems to be the most likelypresent in solution. The lanthanum ion natural occupancy is[core]6s0.14f0.25d0.86p0.45f06d0. Because there is no back-donation (at least at our calculation level), the occupancy inthe lanthanum ion is entirely due to ligand-center donation.Most of it is due to “dative” bonds from the lone pairs of theoxygen atoms to the spd hybrids of the lathanum ion. The 4fshell is only marginally involved and accounts for only 0.2

Table 3. Natural Bond Orbitals Involved in Ligand−IonBondinga

orbital s p d f occupation

1d 0.01% 0.01% 98.56% 1.42% 0.192382d 0.09% 0.15% 98.06% 1.70% 0.188913df 1.21% 0.09% 94.13% 4.57% 0.171184df 0.54% 0.05% 94.49% 4.92% 0.168475s 95.83% 1.69% 2.32% 0.15% 0.155286pd 0.71% 6.66% 92.50% 0.12% 0.141337p 1.00% 94.89% 0.08% 4.01% 0.135788p 0.33% 98.51% 0.32% 0.83% 0.131529pd 0.06% 91.27% 6.91% 1.75% 0.1300810df 0.01% 0.02% 14.98% 84.96% 0.0333411df 0.01% 0.03% 16.73% 83.20% 0.0302812df 0.01% 0.02% 30.41% 69.51% 0.0258713df 0.05% 0.05% 32.87% 66.97% 0.0239214f 0.53% 3.55% 0.75% 94.66% 0.0191715f 0.10% 1.43% 0.69% 97.64% 0.0174116f 0.13% 0.56% 1.92% 97.32% 0.01535

aThey are reported in order of decreasing occupation number.

Figure 8. Empty molecular natural orbitals localized on the central ion. Referring to Table 3, we report starting from the top left panel, in readingorder, orbitals 3, 9, 10, and 15, respectively. The surface is plotted at 0.03 isovalue.



occupancy. The mixing of the 6s, 4f, 5d, and 6p orbitals givesrise to 16 empty natural localized orbitals whose composition isreported in Table 3. As an example, we report in Figure 8 fourof these orbitals: the numbers 3, 9, 10, and 15 that are a dfhybrid (d dominant), a pd hybrid (d dominant), a df hybrid (fdominant), and an f nonbonding atomic orbital, respectively.These orbitals are extended, like those of La(III) in water,25

suggesting that the interaction with DMSO is similar to thatwith water molecules.

■ CONCLUSIONS

In this work, we have studied structures, energetics, and bindingproperties of La3+−DMSO clusters by means of extended DFTcalculations. The different functionals and basis sets do notseem to be crucial in determining their geometric properties,while dispersion correction plays an important role. With anincrease in the number of ligands and consequently the extentof crowding of the outer solvation shell, the total contributionof the dispersion energy increases while, at the same time, thegeometric symmetry of the cage of oxygen atoms around thecentral ion decreases.One of the main objectives of this study was to characterize

the geometry and the structure of the clusters that build up byadding DMSO molecules around the central ion. Ourcalculations suggest that, probably, the 8-fold structure is themost stable cluster in the gas phase in terms of energy but thatthe 9-fold structure is close enough and can be easily populatedat room temperature in the liquid phase. Moreover, we havefound that the gas phase structures provide ligand cages that,although they resemble regular geometric structures, arenevertheless slightly distorted. The geometrical irregularity iscertainly due to the “bulkiness” of the solvent molecule. Theseresults can be used as the starting point for a dynamical andthermodynamical study of La3+ in liquid DMSO. This isactually the direction of our present research. Finally, NBOanalysis provided the details of the nature of the bonds betweenthe La3+ and the DMSO molecules. The donation from thelone pairs of O to the empty nonbonding orbitals of La, and theabsence of any back-donation, determine a charge transfer tothe central ion. This charge transfer is more important as thecluster grows in size. The f orbitals are only marginallyinvolved, and the donation involves mainly d orbitals, which issimilar to what has been observed in other systems containingLn3+ or An3+ binding water and carbonates.25,66,67 The maininteracting orbital is the 5d orbital that is available for bondingin all the series, thus suggesting that, as reportedexperimentally, other lanthanoid ions will behave similarly inDMSO.

■ ASSOCIATED CONTENT

*S Supporting InformationGeometries and energies of n = 1 and n = 2 clusters as obtainedby different DFT functionals, pseudopotentials, and post-HFmethods [MP2 and CCSD(T)], compared with post-HF,rmsds of dispersion-corrected and uncorrected clusters, rota-tional constants, and incremental free energies. This material isavailable free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected].

Present Address§M.C.: Laboratoire de Biochimie Theorique, IBPC, CNRS,UPR9080, Universite Paris Diderot, 13 rue Pierre et MarieCurie, 75005 Paris, France.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

Financial support of the Scientific Committee of the Universityof Rome through Grant “Ricerca 2012” and of ANR 2010 JCJC080701 ACLASOLV (Actinoids and Lanthanoids Solvation) isacknowledged. The support through Grant “IscrB_METIL” ofCINECA supercomputing centers and GENCI (Grantsx20131870 and x20141870) are also acknowledged.

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Structural, Energetic, and Electronic Properties of La(III)–Dimethyl Sulfoxide Clusters