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

Article pubs.acs.org/JPCA

Structural, Energetic, and Electronic Properties of La(III)−Dimethyl Sulfoxide Clusters Enrico Bodo,† Mara Chiricotto,†,§ and Riccardo Spezia*,‡ †

Department of Chemistry, University of Rome “La Sapienza”, 00185 Rome, Italy CNRS, Laboratoire Analyse et Modélisation pour la Biologie et l’Environnement, Université d’Evry-Val-d’Essonne, 91025 Évry Cedex, France

‡

S Supporting Information *

ABSTRACT: By using accurate density functional theory calculations, 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). Extended structural, energetic, and electronic structure analyses have been performed to provide a complete picture of the physical properties that are the basis of the interaction of La(III) with DMSO. Recent experimental data in the solid and liquid phase have suggested a coordination number of 8 DMSO molecules with a square antiprism geometry arranged similarly in the liquid and crystalline phases. By using a cluster approach on the La3+(DMSO)n gas phase isolated structures, we have found that the 8-fold geometry, albeit less regular than in the crystal, is probably the most stable cluster. Furthermore, we provide new evidence of a 9-fold complexation geometric arrangement that is competitive (at least energetically) with the 8-fold one and that might suggest the existence of transient structures with higher coordination numbers in the liquid phase.

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the coordination number behavior across the series.14−30 As an example of the importance of these studies in the gas and liquid phases, we mention the recent works of Williams and coworkers. From experimental studies in the gas phase of Ln(III) ions in water clusters of different sizes, it was possible to directly relate absolute reduction energies of gaseous nanodrops containing Ln(III) ions to the absolute reduction enthalpy of the ion in bulk solution and then obtain an absolute standard hydrogen electrode potential.31 Furthermore, by extrapolating recombination enthalpies to infinite size, they were able to obtain the bulk hydration enthalpy of the electron.32 While many experimental and theoretical studies are present for interaction of Ln(III) with water, much less theoretical work has been reported for nonaqueous solvents.33−38 In the work presented here, we describe the complexation of the prototype La3+ ion by a nonaqueous solvent, dimethyl sulfoxide (DMSO). To the best of our knowledge, this is the first theoretical study of Ln ions interacting with DMSO. The electron pair donor ability is greater than that for water,39 and DMSO is more sterically demanding as a ligand. The fully DMSO-solvated lanthanoid(III) ion crystal structures are reported, showing octakis(DMSO)lanthanoid(III) complexes with iodide, bromide, and perchlorate salts, often with

INTRODUCTION Complexation of lanthanoid (Ln) and actinoid (An) ions by organic molecules is a very useful tool for their separation, and a thorough characterization of their solvation structure in different liquids is mandatory for selecting the best performing solvents.1 Solvation is a phenomenon that is the basis of the chemical behavior of almost every element and compound: from tuning chemical reactions and thus organic synthesis to determining the structure of large flexible molecules and from being the basis of dissolving and diffusing species in the environment to impacting industrial processes. These chemical processes ultimately depend on solvent−solute interactions, and thus fundamental studies are necessary to develop an indepth understanding of the phenomena involved. For example, industrial processes are normally conducted in specific solvents that can be changed, modified, and designed to improve the efficiency of the processes. One important industrial process involving Ln and An is their separation from nuclear waste; this work is currently done by employing organic solvents to extract them from the aqueous phases with different techniques and operating conditions.2−7 Furthermore, lanthanoids are extensively used in organic synthesis to catalyze several reactions because of the ability to change their oxidation state under nonaqueous conditions.8,9 Interaction of Ln and An with water was largely studied theoretically and experimentally in gas, solid, and liquid phases.10−13 In particular, the combination of theoretical studies in both gas and liquid phases was able to rationalize © 2014 American Chemical Society

Received: July 22, 2014 Revised: November 16, 2014 Published: November 18, 2014 11602

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disordered DMSO ligands.40−48 All octakis(DMSO)lanthanoid(III) iodides display an 8-fold coordination with a distribution of Ln−O bond distances with alternative positions for at least one of the ligands.48 The coordination state of Ln3+ ions in DMSO solution is still controversial; spectroscopic and crystallographic studies of lanthanoid iodides revealed that lanthanoid(III) ions have a similar eight-coordinated configuration both in liquid DMSO and in the solid state.48−50 According to these studies, the coordination number in DMSO seems to be constant across the series, an observation different from that in water,51 although the decrease in the mean Ln−O bond distance is greater than expected on the basis of existing ionic radius data for eight-coordination.48 However, other studies suggest some changes in the average coordination number along the series.52,53 These results were confirmed in a very recent investigation dealing with apparent molar volumes and compressibilities of Ln3+ trifluoromethanesulfonates in DMSO.54 A recent X-ray absorption near edge structure (XANES) study reports accurate Ln−DMSO distances and suggests that the coordination motif is 8-fold,55 although the presence of a ninth DMSO molecule in an intermediate solvation shell (i.e., between the first and second) cannot be ruled out, because Xray absorption is mainly sensitive to atoms in the first shell of the photo-absorber (here the Ln). In this work, we have studied structural, energetic, and bonding properties of La3+−DMSO clusters of growing size (up to 12 DMSO molecules), by means of extended density functional theory (DFT) calculations. In this way, we were able to provide a basic understanding of the physicochemical nature of ion−solvent interactions that are at the heart of the observed properties.

test the reliability of the different correlation models. For all final structures, a natural bonding orbital (NBO) analysis63 was also conducted. All calculations were conducted using Gaussian09.64 Initial assessments of the performances of different computational settings (method, basis set, and dispersion) were conducted 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 reported in the Supporting Information. Here we shall limit ourselves to a few important considerations. The two different functionals used in this work were first tested against wave function-based methods (MP2 and Coupled Cluster) on the monomer and the dimer (results reported in Tables 1 and 2 of the Supporting Information). This analysis shows that the DFT geometries are in excellent agreement with correlated calculations. The match between the adiabatic interaction energies obtained with DFT and correlated methods is also very good. In particular, the interaction energy provided by M06-2X is very close to that provided by CCSD(T) and MP2 for the monomer, while for the dimer, both D-B3LYP and M06-2X are able to provide energies similar to those obtained with MP2. Role of Dispersion Forces. While in the monomer the dispersion corrections of the B3LYP functional are rather limited, van der Waals forces are added to the number of molecules, and therefore, their importance deserves a more detailed analysis. Obviously, the total correction due to the inclusion of empirical dispersion corrections grows with cluster size (see Table 3 of the Supporting Information). What we have found is that the dispersion corrections have a sizable but minor effect on the structural properties of small clusters. Most of the clusters do not show substantial geometry changes when the dispersion correction is switched on. Some examples are reported in Figure 1 of the Supporting Information. In the n = 3 cluster, for example, the final structures obtained with B3LYP and D-B3LYP differ by a total root-mean-square deviation (rmsd) of 0.19 Å and the energy gain due to dispersion is only 0.6 eV. Dispersion corrections are much more important when the number of DMSO molecules increases and the “crowding” of the solvation shell makes the average distance between the neutral solvent molecules shorter. For example, in the case of the structure with 6 DMSO molecules (Figure 1 of the Supporting Information), we find a slightly more sizable geometric alteration. The total rmsd between the structures obtained with B3LYP and D-B3LYP is now 1.68 Å. The total gain 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 B3LYP functional is reported in Figure 1. A small sample of La−O distances with and without dispersion correction is also reported in Table 1. Figure 1 clearly shows that while the geometry of the clusters is essentially insensitive to dispersion up to 4 DMSO molecules, for larger clusters the dispersion corrections have an effect that is mainly that of compacting the resulting cluster. The general trend, as expected, is that the La− O distance is approximately 1% shorter when dispersion corrections are switched on (see Table 1). Functional Performance. As one can see in Figure 1, the use of the M06-2X functional does not alter substantially the geometry or shape of the cluster. The M06-2X functional, in its noncorrected expression, already has a better description of long-range forces with respect to B3LYP.59 It therefore

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COMPUTATIONAL DETAILS Reasonable initial structures for the clusters of La3+ and n molecules of DMSO (n ∈ [1,12]) were created using the MM3 force field.56 In particular, the Monte Carlo-driven minimum search contained in the Tinker package57 was used in conjunction with annealing molecular dynamics. Once a reliable set of initial starting structures had been obtained, we used DFT to obtain the cluster internal energy and vibrational zeropoint energy (ZPE) in the harmonic approximation. DFT calculations were performed by using both the B3LYP58 and M06-2X59 functional, with the 6-31G*60 basis set for the light elements and the Small Core ECP and basis61 for La3+. A preliminary test of the effect of basis set and pseudopotential was performed as reported below. Dispersion effects were considered by the D3 Grimme method62 for the B3LYP functional. The M06-2X energies were left uncorrected.59 We considered clusters composed of one La3+ ion and a growing number of DMSO molecules {[La(DMSO)n]3+ with n = 1−12}. For n > 8, we considered three possible structural patterns around La3+ that are generated by imposing (a) 10 DMSO molecules in the first shell and the remainder in the second shell (the 10 + m series), (b) 9 molecules of DMSO in the first shell and the remainder in the second shell (the 9 + m series), and (c) 8 molecules of DMSO in the first shell and the remainder in the second shell (the 8 + m series). The optimization of each structure was done initially using the B3LYP functional without dispersion correction and then followed by a refining run with its dispersion-corrected version (D-B3LYP)62 followed by a frequency evaluation. A second set of calculations were repeated with the M06-2X functional to 11603

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structures are reported in Table 3 of the Supporting Information.

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STRUCTURAL PROPERTIES The geometries of [Ln(DMSO)n]3+ clusters obtained from DB3LYP/RSC geometry optimization are shown in Figure 2 (very similar structures are obtained with M06-2X). Here we show the first series, which we call 10 + m, where we fill the La3+ first shell with a maximum number of 10, and only for n > 10 do we place the additional DMSO molecule(s) in a second shell. In the same figure, we highlight the O−O contacts whenever their mutual distance falls below 4.0 Å to show the cage formed by the ligands around the La3+ ion. The cage starts forming at n = 4 with a clearly shaped tetrahedron geometry that encloses the lanthanide ion. The average distance between La 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−O angles ranging between 110° and 111°). The five-DMSO geometry is instead that of a distorted triangular bipyramid with two “apical” oxygens at 2.36 Å and three equatorial ones located at distances ranging from 2.32 to 2.34 Å. The n = 6 cluster is a slightly distorted octahedron with La−O distances ranging from 2.38 to 2.44 Å. The O−O distances are shown (together with La−O ones) in Figure 3 to clearly show the regularity of the structures. Evidently, because of the steric repulsion between the methyl terminals and the progressive crowding of the first sphere of solvation, the possibility of having regular symmetric (Euclidean) structures is lost beyond n = 4. For a larger number of DMSO molecules, the network of O−O contacts is no longer regular. Of particular interest here is the structure with n = 8 because it seems to be the most abundant solvation shell structure in solution at least as it has been probed by XANES experiments.55 The structure is that of an irregular square antiprism that is the favored geometry when eight solvent molecules are distributed on the surface of a sphere to maximize the distances among them. The La−O distance in this structure is fairly regular and has an average value of 2.52 Å with a very small dispersion (0.01 Å standard deviation). The addition of a ninth DMSO molecule provides a “cap” for the structure with n = 8 giving rise to a distorted monocapped square antiprism as if a vertex had been added to the previous structure. This structure is slightly less regular than the previous one: the average La−O distance is 2.58 Å with a standard 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 10 DMSO molecule all arranged in a unique solvation sphere. Starting from n = 10, we found it was impossible to accommodate any further molecule into the first shell and the second shell began to be filled. As we will see below, the substantial crowding of the n = 10 solvation sphere makes this configuration relatively unstable with respect to the accretion pattern that sees the growth of a second shell around a core of 8 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 Table 1, we compare La−O distances obtained from geometry optimization of different clusters with the available experimental 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 M06-2X in the 10 + n series.

Table 1. La−O Distances and Their Standard Deviations (in parentheses) for La3+ Binding DMSO As Obtained from Experiments and Calculations method

La−O (Å)

system

X-ray crystal EXAFS crystal XANES crystal EXAFS XANES D-B3LYP/RSC D-B3LYP/RSC D-B3LYP/RSC B3LYP/RSC B3LYP/RSC B3LYP/RSC M06-2X/RSC M06-2X/RSC M06-2X/RSC

2.49 2.507 2.49(2) 2.503 2.492 2.52 (0.01) 2.58 (0.03) 2.65 (0.07) 2.55 (0.02) 2.61 (0.03) 2.69 (0.07) 2.50 (0.01) 2.56 (0.02) 2.62 (0.05)

[La(DMSO)8]I [La(DMSO)8]I [La(DMSO)8]I La3+ in liquid DMSO La3+ in liquid DMSO [La(DMSO)8]3+ [La(DMSO)9]3+ [La(DMSO)10]3+ [La(DMSO)8]3+ [La(DMSO)9]3+ [La(DMSO)10]3+ [La(DMSO)8]3+ [La(DMSO)9]3+ [La(DMSO)10]3+

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provides slightly more compact cluster geometries, even if we do not detect any substantial change in the arrangement of the solvent molecules. The rmsds between the structures obtained with M06-2X are very small, and only for a few structures does it exceed 1 Å (the rmsd between all the various optimized structures coming from various methods is reported in Table 3 of the Supporting Information). The similarity between the M06-2X and D-B3LYP structures is clearly shown by also looking at Figure 3 of the Supporting Information where the rotational constants of the optimized geometries are reported as a function of cluster growth for both D-B3LYP and M06-2X. The cluster series essentially maintain the same shape regardless of the functional used. Pseudopotential. Another important approximation involved in our calculations is the use of an effective potential at the La3+ core. As mentioned in the previous section, a series of structural optimizations and energy calculations (including ZPE) were performed using also the LANL2DZ ECP on the clusters with n ranging from 1 to 10. The resulting LANL2DZ structures remain almost unchanged with respect to the RSC ECP ones. Their mutual rmsd remains below 1 Å except for those for n = 5 and 8. The rmsds between the optimized 11604

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Figure 2. Pictorial representation of the cluster growth around the La3+ center for the 10 + m series. Wireframe is used for carbons and hydrogens and CPK for sulfurs and oxygens. Connections between oxygen atoms are drawn using red sticks for distances from La3+ of 10 the successive molecules are placed in the second shell. To determine the preferential number of DMSO molecules in La3+

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

reproducing the experimental data. From the data reported in Table 1, it seems fair to conclude, solely on the basis of geometrical considerations, that the likely candidate for representing the structure of the “solvated” La3+ is the one in which 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 different structuring of the first shell of solvation makes the picture slightly more complex and less certain. It is indeed possible to devise an accretion scheme in which, instead of filling up a first shell using 10 DMSO molecules, we can add a second shell of solvent molecules to a first shell made of 8 or 9 DMSO molecules. The calculations were extended to such geometries, and we report them in Figure 4. All the reported structures have the topology of minimum energy structures and represent an alternative pathway for cluster growth. In these structures, 11605

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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 for details). Wireframe is used for carbons and hydrogens and CPK for sulfurs and oxygens. Connections between oxygen atoms are drawn using red sticks for distances of