Electronic Structure of Cesium Butyratouranylate(VI) as Derived from

Article pubs.acs.org/JPCA

Electronic Structure of Cesium Butyratouranylate(VI) as Derived from DFT-assisted Powder X‑ray Diffraction Data Anna V. Vologzhanina,*,† Anton V. Savchenkov,‡ Artem O. Dmitrienko,† Alexander A. Korlyukov,†,§ Ivan S. Bushmarinov,† Denis V. Pushkin,‡ and Larisa B. Serezhkina‡ †

Nesmeyanov Institute of Organoelement Compounds of Russian Academy of Sciences, 119991 Moscow, Russia Samara State University, 443011 Samara, Russia § Pirogov Russian National Research Medical University, 117997 Moscow, Russia ‡

S Supporting Information *

ABSTRACT: Investigation of chemical bonding and electronic structure of coordination polymers that do not form high-quality single crystals requires special techniques. Here, we report the molecular and electronic structure of the first cesium butyratouranylate, Cs[UO2(n-C3H7COO)3][UO2(n-C3H7COO)(OH)(H2O)], as obtained from DFTassisted powder X-ray diffraction data because of the low quality of crystalline sample. The topological analysis of the charge distribution within the quantum theory of atomsin-molecules (QTAIM) space partitioning and the distribution of electron localization function (ELF) is reported. The constancy of atomic domain of the uranium(VI) atom at different coordination numbers (7 and 8) and the presence of three ELF maxima in equatorial plane of an uranyl cation attributed to the 6s and 6p electrons were demonstrated for the first time. Details of methodologies applied for additional verification of the correctness of powder XRD refinement (Voronoi atomic descriptors and the Morse restraints) are discussed. diphenylmethylenediphosphinate),18 thus further comparison is of interest. PW-DFT calculations are not limited by the atomic weight of elements, and allow obtaining of the charge distribution even for actinides. At the same time, periodic calculations can also serve as validation for refinements using poor quality data or the structures solved from powder XRD data.19−21 Herein we present investigation of chemical bonding in a novel uranylcontaining compound, Cs[UO 2 (n-C 3 H 7 COO) 3 ][UO 2 (nC3H7COO)(OH)(H2O)] (1), based on comparison of theoretical QTAIM data, the Voronoi tessellation, and powder XRD data.

1. INTRODUCTION The search for quantitative structure−property relationship for crystalline materials requires, in general case, both description of peculiarities of the electron density distribution function ρ(r), and simultaneous analysis of a large number of similar compounds. These requirements are contradictory to some extent, due to experimental and theoretical restrictions on obtaining ρ(r) (particularly for compounds of heavy elements) on the one hand, and restrictions of approaches applicable to quantitative investigation of large data sets, on the other. Particularly, the ρ(r) in a crystal was obtained and analyzed within the Bader’s quantum theory of atoms-in-molecules (QTAIM)1 approach for a limited number of f-containing compounds.2−5 Vice versa, the topological analysis of crystal structures based on the Voronoi tessellation from the very beginning took actinide-6,7 and lanthanide-containing8,9 compounds as investigation objects, and nowadays gains widespread use for investigation of MOFs, zeolites and solid state conductors.10−12 Both QTAIM approach and the Voronoi tessellation divide crystal space into atomic and molecular basins, using, however, different principles. Similarity of atomic domains obtained within both approaches was demonstrated for some alkali and binary halogenides.13,14 Blatov suggested in 200615 that they would be similar for more complex substances. Recently, correlation between some atomic and molecular descriptors within these approaches was obtained for Sn2(OCH2CH2NMe2)2(OPh)2,16 (C4H11N2)2(C4H12N2)[Mo(CN)8],17 and [Cu(ppc)(MeOH)]·MeOH (ppc = P,P′© XXXX American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Synthetic Procedures. The commercially available (Panreac) reagents, UO2(NO3)2·6H2O, Cs2CO3, and nC3H7COOH were used. Cs2CO3 (97 mg, 0.3 mmol) was dissolved in butyric acid (53 mg, 0.6 mmol), and the mixture was diluted with 20 mL of H2O. The mixture was heated with a water bath until the end of CO2 effervescence. Then the uranyl dinitrate hexahydrate (150 mg, 0.3 mmol) was added to a reaction mixture. The molar ratio of UO2(NO3)2·6H2O:nC3H7COOH:Cs2CO3 was 1:2:1. The yellow solution (pH = 4) was left under room temperature. Yellow plate crystals were Received: July 23, 2014 Revised: September 18, 2014

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dx.doi.org/10.1021/jp507386j | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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bond lengths in the restrained refinement was defined as follows:

obtained after 5 days (yield 95 mg, 60%). Anal. Calcd for C16H31CsO14U2: U, 45.08. Found: U, 45.11%. IR (KBr disk): νs(H2O), νas(H2O) 3417 (m.br), νas(CH3) 2966 (m), νs(CH3) 2936 (w), νs(CH2) 2876 (w), δ(H2O) 1624 (w), νas(COO) 1534 (v.str), δas(CH3) 1466 (str), νs(COO) 1426 (m), δ(CαH2) 1414 (sh), δs(CH3) 1378 (w), ω(CαH2) 1347 (w), ω(CβH2) 1316 (w) and 1300 (sh), tw(CαH2) 1262 (w), tw(CβH2) 1211 (w), ν(CβCα) 1097 (w), γ(CH3) 1081 (sh) and 1048 (w), ν(CγCβ) 953 (w), νas(UO2) 927 (str), ν(CαC) 917 (m), 907 (m) and 879 (sh), γ(CαH2) 801 (w), γ(CβH2) 758 (w) and 725 (w) cm−1. 2.2. Crystallography. The single crystal of 1 was obtained from reaction mixture. The crystal system of C16H31CsO14U2 (M = 1056.38) is monoclinic; at 100.0(2) K: a = 14.779(1), b = 21.152(2), c = 8.3971(8) Å, β = 95.071(5)°, V = 2614.8(4) Å3, space group P21/c, Z = 4, Dcalc = 2.683 g cm−3, and μ = 45.849 mm−1. The intensities of 12352 reflections were measured with a Bruker Apex 2 CCD diffractometer using Cu Kα radiation (λ = 1.54178 Å) monochromated with microfocus tube with multilayer optics. The weak reflection ability of the compound did not allow application of Mo Kα radiation. Refinement of 1 was performed using the SHELXTL package. 22 4132 independent reflections (R(int) = 0.069) were used for the solution and the refinement. The structure was solved by the direct method and refined by full-matrix least-squares against F2. Non-hydrogen atoms were found on difference Fourier maps and were refined in anisotropic approximation. Although all non-hydrogen atoms were located and found to be ordered, the structure converged to inappropriate convergence factors (R1(F) = 0.122 for 3586 reflections with I > 2σ(I), wR2 = 0.298 and GOF = 2.14 for all independent reflections). Besides, high residual peaks of 10.4/−4.1 e Å−3 and doubtful interatomic distances were obtained. High absorption effects, low quality of the air-sensitive crystal or the presence of unresolved twinning could be among the reasons of above-mentioned problems. Thus, we tried to refine the structure using PXRD and used the single crystal refinement (1-cry model) only as the starting model for PW-DFT calculations. The powder pattern of 1 was measured on a Bruker D8 Advance Vario diffractometer at room temperature with LynxEye detector and Ge(111) monochromator, λ(Cu Kα1) = 1.54060 Å, θ/2θ scan from 3° to 90°, stepsize 0.0104788°. The measurement was performed in transmission mode, with the sample deposited between two Kapton films. The pattern proved itself of too low quality to index directly; instead, the unit cell parameters were obtained by fitting to it the 1-cry model with frozen atomic coordinates. Spherical harmonics23 were applied to line intensities to compensate the changes in structural factors. Afterward, the atomic coordinates were gradually relaxed, with restraints applied to all covalent and metal−O bonds. The anisotropic line broadening correction using a different set of spherical harmonics was essential for a reasonable fit. The unit cell parameters at RT deviated strongly from 1-cry (a = 15.2838(13) Å, b = 21.9156(8) Å, c = 8.4144(3) Å, β = 88.970(7)°, V = 2818.0(3) Å3), with ΔV of 202 Å3 (7.2%), Δa = 0.505 Å, Δb = 0.764 Å, Δc = 0.017 Å and Δβ = −6.1° upon heating. The b direction corresponds to one of the dimensions of the coordination polymer, so significant changes in U−O and Cs−O bond lengths were expected. The modified “Morse” restraint model24 using a symmetrized version of Morse potential for restraints, was applied during the Rietveld refinement in TOPAS.25 The penalty function P for

P = K1 ∑ κi{1 − exp[ −ai|Di − di|]}2 i

Here K1 is a global penalty function weighting, κi is the weighting of the individual bond penalty, ai is a coefficient corresponding to the bond force constant, Di is the defined length of a given bond, and di is its refined length at current minimization step. Sequential refinement with decreasing K1 was used to obtain the refined atomic coordinates; during the refinement, the bond lengths were checked for outliers using the approach described in ref 24. The bond length standard deviations were taken into account in determining the outlying bonds (a bond was not considered an outlier unless it exceeded the outlier threshold by more than 2σ, Figure 1). The restraints for U−O and Cs−O

Figure 1. Bond length deviations (Δd) in Rietveld refinement of 1 at varied values of global penalty function weighting (K1). The gray area denotes the limits of the “acceptable” bond lengths range according to the structure verification criterion, with average bond error taken into account.

bonds showing outliers in the Δd plots were adjusted within the range obtained for similar compounds taken from the Cambridge Structural Database until the plot contained zero outliers. The O−U−O angles were set to idealized values (ligand O atoms evenly spaced, OUO perpendicular to the ligands plane) with deviation of ±2° allowed with no penalty. The C−C−C−C torsion angles of the butyrate residues were restrained to either 180° or 65° during initial refinement and allowed to refine freely afterward. The resulting values of the torsion angles agreed with the distribution observed in CSD. The absorption was accounted for using a scaling factor according to eq 2.3.1.20 in ref 57. The final R values for the model with K1 = 3 (chosen to represent the refinement) are listed in Table 1 along with corresponding values of Pawley fit with free hkl intensities. The difference curve was reasonably smooth (Figure 2) despite strong preferred orientation (texture index 1.835). The resulting structure (1-pow model) significantly differs from the starting single crystal model (Figure 3). Not only butyrate anions are shifted, the positions of uranium and cesium atoms also deviate from the low temperature phase, as well as the unit cell is distorted. Unfortunately the quality of the powder data did not allow us to obtain precise bond lengths. Because of inherent restrictions of DFT calculations in solid B



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distribution function in terms of AIM theory a dense (360 × 240 × 336 points) FFT (fast Fourier transformation) grid was used. The latter was obtained by a separate single point calculation of optimized geometry with small core PAWs for each atom type. The topological analysis of electron density distribution function was carried out using AIM program − part of ABINIT software package.30 The average deviation of nonhydrogen atom coordinates between 1-calc and 1-cry was 0.063 Å, unambiguously confirming correctness of the structure according to the van de Streek criterion.21 Although we did not refine the unit cell parameters, even allowing for their relaxation the difference between calculated and measured structures did not exceed the 0.25 Å proposed as the cutoff value for correct single-crystal structures.

Table 1. R Values of Rietveld Refinement of 1-pow and Pawley Fit of the Same Pattern K1 RMS Δd, Å Rwp, % Rwp′, % Rp, % Rp′, % RBragg, % χ2

Pawley fit

Rietveld fit

− − 2.66 5.20 2.00 4.40 − 2.11

3 0.0127 3.90 7.61 2.98 6.53 1.50 2.73

3. RESULTS AND DISCUSSION The asymmetric unit of 1 contains two independent uranium(VI) atoms and a cesium cation (Figure 4). The U1 atom

Figure 2. Experimental and calculated powder patterns for 1 at K1 = 15 and their difference.

Figure 3. Fragment of crystal packing of (a) 1-cry and (b) 1-pow models (view along the crystallographic b axis). Cesium atoms are depicted with magenta, and uranium atoms are violet.

Figure 4. Asymmetric unit obtained from PW-DFT calculations (1calc model) with the Voronoi polyhedra of metal atoms. The Voronoi polyhedra faces corresponding to the agostic Cs···H interactions are filled with yellow.

state (performed by definition at 0 K) the high-temperature structure also could not be reliably modeled by calculations. Still, we can suggest that the propyl groups at room temperature are disordered, since the changes in carbon atom coordinates lead to essentially zero changes in Rwp. Nevertheless, peculiarities of electronic structure of 1 were investigated based on PW-DFT calculated ρ(r) obtained for the low temperature structure. 2.3. PW-DFT Calculations (1-calc Model). The quantum chemical calculations of 1 in the crystal were carried out using the Vienna ab-initio simulation package (VASP) 5.28 code.26−28 Conjugated gradient technique was used for optimizations of the atomic positions (started from experimental data) and minimization of total energy. Projected augmented wave (PAW) method was applied to account for core electrons while valence electrons were approximated by plane-wave (PW) expansion with 545 eV cutoffs. Exchange and correlation terms of total energy were described in terms of density functional theory (DFT). PBE exchange-correlation functional was used for this purpose.29 In the final (converged) step of our calculations atom displacements were less than 0.01 eV·Å−1, and energy changes were less than 10−3 eV. In order to carry out the topological analysis of electron density

coordinates three n-butyrates to form the [UO 2 (nC3H7COO)3]− anion which is typical of uranyl complexes with monocarboxylate anions. The U1O 8 coordination polyhedron adopts hexagonal bipyramidal geometry with uranyl oxygen atoms situated at axial positions. All three n-butyrates act as bidentate-chelate ligands and the crystal-chemical formula of the [UO2(n-C3H7COO)3]− anion can be written in terms of notation given in ref 31 as AB013 (where A = UO22+). The second uranyl coordinates two hydroxide anions, two n-butyrate anions and a water molecule. Crystallization of heteroligand uranyl complexes with aqua, hydroxide and acidic ligands is typical of dilute aqueous uranyl solutions.32,33 The U2O7 polyhedron is a pentagonal bipyramid with alternated U2−O equatorial distances. The U2−O11(aqua) distance is the longest one, the U2−O12(hydroxo) is the shortest (Table 2). The U2−O(butyrate) distances are intermediate between them. The mean deviations of oxygen atoms from equatorial planes of U1 and U2 in 1-calc are equal to 0.08(15) and 0.13(17) Å. Bond-valence sums at corresponding sites, calculated by using the bond-valence parameters Rij = 2.051 Å and b = 0.519 Å of Burns et al.,34 are 6.25 and 5.94 valence units, in accordance with valence state of uranium(VI). The OH− group acts as a bridge ligand (M2 in terms of ref 31), nC3H7COO− acts as a bidentate bridge ligand (B2), and H2O C



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Table 2. Topological Parameters of ρ(r) for Selected Bonds in 1-calc.a bond

d(A−X), Å

d1, Å

d2, Å

ρ(r), e Å−3

∇2ρ(r), e Å−5

Ge(r), au

Ve(r), au

he(r), au

U1−O1 U1−O2 U1−O3 U1−O4 U1−O5 U1−O6 U1−O7 U1−O8 U2−O9 U2−O10 U2−O11 U2−O12 U2−O12′ U2−O13 U2−O14 Cs1−O1 Cs1−O2 Cs1−O3 Cs1−O7 Cs1−O8 Cs1−O9 Cs1−O10 Cs1−O11 Cs1−O12 Cs1−H6B Cs1−H11C O11−H11A···O6 O11−H11B···O6 O12−H···O7

1.815 1.819 2.420 2.451 2.500 2.537 2.491 2.494 1.823 1.819 2.596 2.364 2.302 2.459 2.317 3.445 3.207 2.988 3.465 3.027 3.039 3.343 3.229 3.667 3.323 3.228 1.783 1.798 1.680

1.081 1.083 1.389 1.405 1.431 1.452 1.427 1.428 1.085 1.083 1.487 1.363 1.331 1.413 1.344 1.968 1.847 1.736 1.973 1.754 1.762 1.907 1.834 2.074 2.082 2.087 0.700 0.674 0.630

0.734 0.736 1.031 1.046 1.069 1.086 1.064 1.066 0.738 0.736 1.110 1.001 0.971 1.047 0.973 1.478 1.361 1.257 1.493 1.247 1.277 1.438 1.395 1.593 1.307 1.143 1.113 1.124 1.050

2.46 2.44 0.60 0.56 0.49 0.45 0.50 0.50 2.42 2.44 0.36 0.66 0.77 0.52 0.70 0.06 0.10 0.16 0.06 0.15 0.15 0.08 0.11 0.04 0.04 0.04 0.04 0.04 0.05

11.28 10.82 7.10 6.75 6.22 5.81 6.34 6.32 11.19 11.10 5.23 7.96 8.54 6.90 8.82 0.93 1.22 0.45 0.92 1.70 1.65 1.09 1.27 0.64 0.51 0.45 0.10 0.10 0.15

0.61 0.60 0.10 0.09 0.08 0.07 0.08 0.08 0.60 0.60 0.06 0.11 0.14 0.09 0.13 0.01 0.01 0.02 0.01 0.02 0.02 0.01 0.01 0.005 0.004 0.004 0.03 0.03 0.04

−1.11 −1.09 −0.13 −0.11 −0.09 −0.08 −0.10 −0.10 −1.08 −1.09 −0.06 −0.15 −0.18 −0.10 −0.16 −0.01 −0.01 −0.02 −0.01 −0.02 −0.02 −0.01 −0.01 −0.01 >−0.01 >−0.01 −0.03 −0.03 −0.05

−0.50 −0.49 −0.03 −0.02 −0.02 −0.01 −0.02 −0.02 −0.48 −0.49 −0.01 −0.03 −0.05 −0.02 −0.04 0.002 0.002 0.001 0.002 0.001 0.001 0.002 0.001 0.002 0.001 0.001 −0.003 −0.003 −0.006

For all bonds, d1 and d2 are the distances from atoms A and X to the bcp; ρ(r) is the ED at the bcp; ∇2ρ(r) is the corresponding Laplacian; Ge(r), kinetic energy density; Ve(r), potential energy density; he(r), local energy density.

a

properties of ρ(r) and the associated Laplacian (∇2ρ(r)). According to the QTAIM approach, information on chemical bonding can be obtained analyzing the local minima, maxima and saddle points of ρ(r). The electron density of a system of atoms typically exhibits bond paths (and related bond critical points, bcp) linking adjacent atoms to form the molecular graph. Results of PW-DFT calculations unambiguously indicate presence of all expected C−C, C−O, C−H, O−H, and U−O bonds as well as nine Cs−O and two Cs−H interactions (Table 2) and a number of intermolecular bonds (Table S1 in Supporting Information). The cesium acts with both complex anions as a cross-linker and, hence, makes their cocrystallization possible. The resulting cesium-connected 2D polymer is situated in the (100) plane and is additionally stabilized by intralayer hydrogen O11−H···O6 and O12−H···O7 bonds (r(O···O) = 2.68−2.78 Å, OHO = 171−173°). Thus, the interlayer interactions are represented by weak C−H···O hydrogen bonds and dispersion C−H···H−C interactions (Table S1, Supporting Information), and the main temperature effect can be regarded as the disorder of alkyl chains followed by the significant increase in their volume and the slide of 2D complexes along the crystallographic c axis (Figure 3). We obtained positive values of ∇2ρ(r) and high values of ρ(r) for all U−O interactions. Thus, the bonds formed by uranium atoms belong to interatomic interactions of intermediate type, e.g., highly polar covalent bonds with significant ionic contribution. In terms of Espinosa/Gatti43,44 classification, the U−O bonding interactions should be characterized as

acts as a terminal group (M1). The resulting neutral complex of the [UO2(n-C3H7COO)(OH)(H2O)] composition has a crystal-chemical formula AB2M2M1 and forms infinite chains parallel with crystallographic c axis. Besides this complex, there exist only three 1D and two 2D uranyl-containing polymers with the same AB2M2M1 crystal chemical formula. The chain complexes are K2[(UO2)SO4F2]·H2O,35 (C6H16N2)[(UO2)SO4F2],36 and Rb[(UO2)(SeO4)(OH)(H2O)].37 The layer structures are (C6H16N2)[(UO2)2(SO4)2F2(H2O)2]36 and [UO2(HCOO)(OH)(H2O)].38 Co-crystallization of an anion and neutral complex is also unusual. Complex 1 is the first cesium-containing compound with uranyl monocarboxylates with long alkyl chains. To date only the structures of cesium uranylcarboxylates with acetate and propionate anions have been published.39−41 The assignment of the vibrations in the IR spectrum was carried out with ref 42. The IR spectrum coincides with the results of X-ray analysis. The intense band at 927 cm−1 is assigned to the νas(UO22+) vibration. Both symmetrical and antisymmetrical vibrations of the nC3H7COO− groups arise in the region which is characteristic for a bidentate-chelate carboxylate anion (the B01 coordination type). In contrast with uranium atoms, coordination environment of cesium atom is not obvious. In accordance with element radii, a number of Cs−O, Cs−H, Cs−C and even Cs−U interactions can be suggested. This problem can be overcome within the QTAIM theory, which characterizes the chemical interactions between atoms on the basis of the topological D



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temperature phases is referred mainly to the proposed disorder of n-butyrate anions. The atomic charges of uranium atoms integrated over atomic basins are +3.31 and +3.39 e̅ (Table S4, Supporting Information), which are close to the QTAIM value of +3.20 e̅ calculated by Michelini et al. for the “naked” UO22+ ion.45 The Cs1 atom bears positive charge (0.23 e), ̅ the charges of the U1O2 and U2O2 species (1.74 and 1.82 e)̅ are very close to their formal charge (+2 e), ̅ and butyrate anions are negative (their charges vary from −0.66 to −0.61 e). ̅ The analysis of the distribution of valence electrons around the Cs and U atoms was carried out using the electron localization function (ELF). ELF is a measure of the likelihood of finding an electron in the neighborhood space of a reference electron located at a given point and with the same spin. Physically, this measures the extent of spatial localization of the reference electron and provides a method for the mapping of electron pair probability in multielectronic systems. As it was shown by Zhurov et al.4 in the case of Cs2UO2Cl4 the ELF distribution around the uranium atom has complex character with two maxima in plane passed through UO2 group and Cl atoms. At the same time, in plane of four equatorial chlorine atoms the distribution of ELF demonstrates the absence of clearly visible maxima. In the case of 1 the situation is quite different. Both 2D maps (Figure 5a,b) and 3D surfaces (Figure 6) demonstrate the presence of three maxima of ELF in

incipient covalent with bond order close to three for uranyl oxygens and one for equatorial bonds. The positive ∇2ρ(r) and he(r) values at Cs−O, Cs−H, C−H···O, and C−H···H−C bcp’s are typical for closed-shell interactions (Table S1, Supporting Information). It is worth mentioning that bcp’s are ≈10% shifted from the middles of U − O and Cs − O bond paths (Table 2). The position of the bcp in the UO bond (Table 2) is similar to that found for the free uranyl dication from theory (d1 = 0.940 Å, d2 = 0.757 Å)45 and those obtained from multipole refinement of Cs2UO2Cl4.4 In other words, the position of intersection between the atomic zero-flux surface and bonding path for heavy atoms depends on the nature of interacting atoms. Nevertheless, in our opinion, the Voronoi tesselation, which divides a crystal space into atomic domains consisting of all points closer to a given atom than to any other atom, can be applied to uranium- and cesium-containing compounds. The results of calculation of CN(U) and CN(Cs) using the method of intersecting spheres46 and sector’s47 algorithms implemented onto TOPOS code48 are listed in Tables S2 and S3. The latter model gives the same molecular graph as the QTAIM approach. Not only are all expected U−O and C −O bonds present, but also Cs···H6B and Cs···H11C interactions with high solid angles can be distinguished among other Cs···H contacts as agostic ones in terms of ref 49. The Hbonds can also be obtained within both approaches: these are strong bonds of intermediate type of interactions (∇2ρ(r) > 0 and he(r) < 0) characterized by the energies of 9.3−15.5 kcal/ mol estimated from the correlation proposed by Espinosa, Molins and Lecomte,50 and the solid angles Ω(O/O) > 10%.51 Vice versa, the bcp’s at U−Cs lines are absent, and the Voronoi polyhedra of metal atoms have no common faces, edges or vertices (Figure 4); thus, in terms of both approaches metal− metal interactions do not appear. The shift of bcp from the metal atom should be accompanied by expansion of atomic volume. Indeed, VAIM (the volumes of atomic domain obtained with the QTAIM approach) for U1, U2, and Cs1 atoms (19.1, 18.9, and 42.8 Å3) exceed corresponding VVP (the volume of atomic domain calculated with the Voronoi tesselation) values (9.8, 9.6, and 26.0 Å3). Notwithstanding the difference in equatorial U1−O and U2−O distances, the atomic volumes for eight- and seven-coordinated uranium(VI) atoms are almost equal; the same fact was previously obtained for the volumes of Voronoi polyhedra of metal atoms with large sets of coordination numbers.7,9,52,53 Moreover, in the 1-pow model, the VVP(U1) = 9.4, VVP(U2) = 9.3, and VVP(Cs1) = 25.6 Å3 are very close with those in the 1calc model, and both are in accord with the average values obtained for UVIOn (n = 6−10, 12) and CsOm (m = 6−20) coordination polyhedra (9.3(2)52 and 27.7(2)53 Å3, respectively). The VVP and VAIM values for carbon, oxygen, and hydrogen atoms in 1-calc differ from each other (Table S4, Supporting Information); nevertheless, the volumes of the four independent n-butyrate anions calculated within these approaches vary in narrow ranges. In 1-calc, the average nbutyrate volumes calculated with the Voronoi tessellation (123(4) Å3) and the QTAIM approach (117(2) Å3) are equal within 2σ. The VVP(C3H7COO) values in 1-pow vary from 124 to 144 Å3, and are enlarged in comparison with 1-calc. Thus, the values of the VVP of metal atoms and the constancy of anion volumes also indicate the correctness of the structure refinement. Besides, based on the VVP values, one can conclude, that the 7% volume difference between the low- and high-

Figure 5. ELF maps drawn in (a) U1−O5−O6, (b) U2−O12−O13, and (c) and O9−O10−Cs1 planes. Contours corresponding to the electron delocalization (0 < ELF 0.5). Contour intervals are equal to 0.05. E



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equatorial bonds. The charge density concentration corresponding to UO bond formation is strongly shifted toward the oxygen position. Methodological aspects of our work can be summarized as (i) The “Morse” restraints and a structure verification criterion developed for Rietveld refinement of simple organic compounds can be applied to metal−organic compounds, albeit with correction for individual bond uncertainties. (ii) Previously, the atomic volumes of metal atoms calculated within the Voronoi tessellation were found to be highly sensitive to the nature of surrounding atoms, nature and valence state of the metal,54,55 and errors in atomic coordinates,56 although independent of the coordination number.7,9,52,53 We demonstrated that the VVP of the metal as compared with the average value for the same metal in similar coordination environment can be used as additional criterion of accuracy of solving and refinement using powder XRD data. (iii) Quantum chemical calculations have been proved to be useful tool for structural model improvement even in the case of complex crystal structure containing heavy elements (uranium and cesium) and branched networks of H-bonds. Furthermore, the use of theoretical calculations provided the basis for improved understanding of the chemical bonding of actinides. (iv) There exists qualitative agreement between the QTAIM partitioning and the Voronoi tessellation of crystal space. The sector’s algorithm47 allows estimation of all chemical bonds, agostic Cs···H interactions and hydrogen bonds, that were obtained within the QTAIM approach. The atomic volumes of uranium atoms where found to be independent of coordination number, although the VAIM volumes significantly differ from the corresponding VVP values.

Figure 6. 3D isosurface of ELF function (0.85) illustrating the position of maxima corresponding to valence electrons around the (a) U1 and (b) U2 atoms versus electron pairs localized at adjacent oxygen atoms.

equatorial planes of both uranium atoms. There is no doubt, that the ELF maxima correspond to the electrons of outer shells. The PAW potential of uranium atom used for calculation corresponds to the 6s26p66d25f27s2 configuration of valence electrons. According to Zhurov et al.,4 the maxima of ELF around the U atoms most probably correspond to the electrons of 6s and 6p shells. It is reasonable to assume that mutual position of electron pairs of oxygen atoms and the localized 6s and 6p electrons should maintain the minimal electrostatic repulsion. Indeed, the centers of these maxima are located at the line bisecting the OUO angles (Figure 5). The only exception is the maximum directed toward the O11 atom of coordinated water. However, the U1−O11 bond is longer than the other U−O bonds. The distribution along UO bonds of uranyl moiety is characterized by two regions of ELF concentration (Figure 5c): the first one near the U atom and the second one near the oxygen atoms. No clearly visible maxima is observed along the UO bond line. These regions are separated by the area characterized by low ELF values (less than 0.5). The region of electron concentration around the oxygen atom (ELF > 0.5) demonstrates pronounced polarization toward the uranium atom. Such a picture is common for compounds where a uranium atom participates in multiple bonds with elements like oxygen or carbon. The regions of ELF concentration around oxygen atoms of uranyl cation are located on outer side of this moiety (“on the top and at the bottom of UO2 group”, Figure 6).

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ASSOCIATED CONTENT

S Supporting Information *

Tables of intermolecular contacts revealed in 1-calc using the QTAIM approach, calculation of uranium and cesium coordination numbers with various algorithms, the atomic integrated descriptors, and atomic coordinates for the 1-cry model and an X-ray crystallographic information file (.cif) is available for the 1-pow model. This material is available free of charge via the Internet at http://pubs.acs.org. The .cif file is also available from the Cambridge Crystallographic Data Center (CCDC) upon request (http://www.ccdc.cam.ac.uk, deposition number 1010932).

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AUTHOR INFORMATION

Corresponding Author

*(A.V.V.) E-mail: [email protected]. Fax: +7 49 91 35 50 85. Telephone: +7 49 91 35 93 43. Notes

The authors declare no competing financial interest.

4. CONCLUSIONS Chemical bonding in this uranyl- and cesium-containing compound has been investigated by means of the QTAIM approach and ELF function. Both axial and equatorial U−O bonds belong to the intermediate type of interactions, and cesium coordination bonds are closed-shell (ionic) interactions. The electron density distribution is in agreement with a triple uranyl bonds and significant covalence in both axial and

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ACKNOWLEDGMENTS A.V.V., A.O.D., A.A.K., and I.S.B. gratefully acknowledge support of the RFBR (Grant 12-03-00878) and the Council of the President of the Russian Federation (Grants MK5181.2013.3 and MD-3589.2014.3). The work of A.V.S., D.V.P., and L.B.S. was financially supported by the base part F



Article

Complex by the Theory of Atoms in Molecules and the Voronoi Tessellation. Mendeleev Commun. 2014, 24, 216−218. (19) Kaduk, J. A. Terephthalate Salts of Dipositive Cations. Acta Crystallogr., Sect. B 2002, 58, 815−822. (20) Brüning, J.; Alig, E.; van de Streek, J.; Schmidt, M. U. The Use of Dispersion-Corrected DFT Calculations to Prevent an Incorrect Structure Determination from Powder Data: the Case of Acetolone, C11H11N3O3. Z. Kristallogr.: Cryst. Mater. 2011, 226, 476−482. (21) van de Streek, J.; Neumann, M. A. Validation of Experimental Molecular Crystal Structures with Dispersion-Corrected Density Functional Theory Calculations. Acta Crystallogr., Sect. B 2010, 66, 544−558. (22) Sheldrick, G. M. A Short History of SHELX. Acta Crystallogr., Sect. A 2008, 64, 112−122. (23) Järvinen, M. Application of Symmetrized Harmonics Expansion to Correction of the Preferred Orientation Effect. J. Appl. Crystallogr. 1993, 26, 525−531. (24) Bushmarinov, I. S.; Dmitrienko, A. O.; Korlyukov, A. A.; Antipin, M. Y. Rietveld Refinement and Structure Verification Using Morse’ Restraints. J. Appl. Crystallogr. 2012, 45, 1187−1197. ̀ (25) TOPAS 4.2 UserManual; BrukerAXS GmbH: Karlsruhe, Germany, 2009. (26) Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals. Phys. Rev. B 1993, 47, 558−561. (27) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169−11186. (28) Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (29) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (30) Gonze, X.; Beuken, J.-M.; Caracas, R.; Detraux, F.; Fuchs, M.; Rignanese, G.-M.; Sindic, L.; Verstraete, M.; Zerah, G.; Jollet, F.; et al. First-Principles Computation of Material Properties: the ABINIT Software Project. Comput. Mater. Sci. 2002, 25, 478−492. (31) Serezhkin, V. N.; Vologzhanina, A. V.; Serezhkina, L. B.; Smirnova, E. S.; Grachova, E. V.; Ostrova, P. V.; Antipin, M. Y. Crystallochemical Formula as a Tool for Describing Metal−Ligand Complexesa Pyridine-2,6-dicarboxylate Example. Acta Crystallogr., Sect. B 2009, 65, 45−53. (32) Meinrath, G. Aquatic Chemistry of Uranium. A Review Focusing on Aspects of Environmental Chemistry. Freiberg On-line Geosci. 1998, 1, 1−100, http://tu-freiberg.de/fakult3/geo/fog/FOG_ Vol_1.pdf. (33) Tsushima, S.; Rossberg, A.; Ikeda, A.; Müller, K.; Scheinost, A. C. Stoichiometry and Structure of Uranyl(VI) Hydroxo Dimer and Trimer Complexes in Aqueous Solution. Inorg. Chem. 2007, 46, 10819−10826. (34) Burns, P. C.; Ewing, R. C.; Hawthorne, F. C. The Crystal Chemistry of Hexavalent Uranium: Polyhedron Geometries, BondValence Parameters, and Polymerization of Polyhedra. Can. Mineral. 1997, 35, 1551−1570. (35) Alcock, N. W.; Roberts, M. M.; Chakravorti, M. C. Structure of Potassium Catena-di-μ-fluoro-difluorotetraoxo-di-μ-sulphatodiuranate(VI) Hydrate. Acta Crystallogr., Sect. B 1980, 36, 687−690. (36) Doran, M. B.; Cockbain, B. E.; O’Hare, D. Structural Variation in Organically Templated Uranium Sulfate Fluorides. Dalton Trans. 2005, 1774−1780. (37) Shishkina, O. V.; Mikhailov, Y. N.; Gorbunova, Y. E.; Serezhkina, L. B.; Serezhkin, V. N. Crystal Structure of Rb[UO2SeO4(OH)·H2O]. Dokl. Chem. 2001, 376, 29−33. (38) le Roux, S. D.; van Tets, A.; Adrian, H. W. W. Structure of Dioxouranium(VI) Formate Hydroxide Monohydrate at 120 K. Acta Crystallogr., Sect. B 1979, 35, 3056−3057. (39) Burkov, V. I.; Mistryukov, V. E.; Mikhailov, Y. N.; Chuklanova, E. B. Chiroptical Properties and Structures of Gyrotropic Crystals of Uranyl Propionates. Russ. J. Inorg. Chem. 1997, 42, 327−331.

of the government mandate of the Ministry of Education and Science of the Russian Federation.

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ABBREVIATIONS CN, coordination number; ELF, electron localization function; PXRD, powder X-ray diffraction; QTAIM, quantum theory “atoms-in-molecules”; VP, Voronoi polyhedron

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REFERENCES

(1) Bader, R. F. W. Atoms in Molecules. A Quantum Theory; Clarendon Press: Oxford, U.K., 1990. (2) Puntus, L. N.; Lyssenko, K. A.; Antipin, M. Y.; Bünzli, J.-C. G. Role of Inner- and Outer-Sphere Bonding in the Sensitization of EuIIILuminescence Deciphered by Combined Analysis of Experimental Electron Density Distribution Function and Photophysical Data. Inorg. Chem. 2008, 47, 11095−11107. (3) Claiser, N.; Souhassou, M.; Lecomte, C. Problems in Experimental Charge Density Modelling of Rare Earth Atom Complexes: the Case of Gadolinium. J. Phys. Chem. Solids 2004, 65, 1927−1933. (4) Zhurov, V. V.; Zhurova, E. A.; Stash, A. I.; Pinkerton, A. A. Characterization of Bonding in Cesium Uranyl Chloride: Topological Analysis of the Experimental Charge Density. J. Phys. Chem. A 2011, 115, 13016−13023. (5) Nelyubina, Y. V.; Puntus, L. N.; Lyssenko, K. A. The Dark Side of Hydrogen Bonds in the Design of Optical Materials: A Charge-Density Perspective. Chem.Eur. J. 2014, 20, 2860−2865. (6) Blatov, V. A.; Shevchenko, A. P.; Serenzhkin, V. N. Crystal Space Analysis by Means of Voronoi−Dirichlet Polyhedra. Acta Crystallogr., Sect. A 1995, 51, 909−916. (7) Serezhkin, V. N.; Andreev, I. V.; Blatov, V. A. Voronoi-Dirichlet Polyhedrons of Neptunium (IV-VII) Atoms in the Structures of Oxygen-Containing Compounds. Russ. J. Coord. Chem. 1997, 23, 733− 736. (8) Blatova, O. A.; Blatov, V. A.; Serezhkin, V. N. Study of Rare-Earth π-Complexes by Means of Voronoi−Dirichlet Polyhedra. Acta Crystallogr., Sect. B 2001, 57, 261−270. (9) Vologzhanina, A. V.; Pushkin, D. V.; Serezhkin, V. N. LnOn Coordination Polyhedra (Ln = La−Lu) in Crystal Structures. Acta Crystallogr., Sect. B 2006, 62, 754−760. (10) Sikora, B. J.; Winnegar, R.; Proserpio, D. M.; Snurr, R. Q. Textural Properties of a Large Collection of Computationally Constructed MOFs and Zeolites. Microporous Mesoporous Mater. 2014, 186, 207−213. (11) Voronin, V. I.; Sherstobitova, E. A.; Blatov, V. A.; Shekhtman, G. S. Lithium-Cation Conductivity and Crystal Structure of Lithium Diphosphate. J. Solid State Chem. 2014, 211, 170−175. (12) Blatov, V. A.; Shevchenko, A. P.; Proserpio, D. M. Applied Topological Analysis of Crystal Structures with the Program Package ToposPro. Cryst. Growth Des. 2014, 14, 3576−3586. (13) Pendás, A. M.; Costales, A.; Luaña, V. Ions in Crystals: The Topology of the Electron Density in Ionic Materials. III. Geometry and Ionic Radii. J. Phys. Chem. B 1998, 102, 6937−6948. (14) Luaña, V.; Costales, A.; Pendás, A. M.; Pueyo, L. Ionic Properties of Perovskites Derived from Topological Analysis of Their Wave Function. J. Phys.: Condens. Matter 1999, 11, 6329−6336. (15) Blatov, V. A. Miltipurpose Crystallochemical Analysis with the Program Package TOPOS. Cryst. Comp. Newsl. 2006, 7, 4−38. (16) Korlyukov, A. A.; Khrustalev, V. N.; Vologzhanina, A. V.; Lyssenko, K. A.; Nechaev, M. S.; Antipin, M. Y. Bis(μ2-2(dimethylamino)ethoxo-N,O,O)-di(phenolato-O)ditin(II): a HighResolution Single-Crystal X-Ray Diffraction and Quantum Chemical Study. Acta Crystallogr., Sect. B 2011, 67, 315−323. (17) Vologzhanina, A. V.; Lyssenko, K. A. Interatomic Interactions in the Crystal of (C4H11N2)2(C4H12N2)[Mo(CN)8]: Comparison of Two Approaches. Russ. Chem. Bull. 2013, 62, 1786−1792. (18) Lyssenko, K. A.; Vologzhanina, A. V.; Torubaev, Y. V.; Nelyubina, Y. V. A Comparative Study of a Mixed-Ligand Copper(II) G



Article

(40) Serezhkina, L. B.; Vologzhanina, A. V.; Klepov, V. V.; Serezhkin, V. N. Crystal structure of R[UO2(CH3COO)3] (R = NH4+, K+, or Cs+). Crystallogr. Rep. 2010, 55, 773−779. (41) Serezhkina, L. B.; Vologzhanina, A. V.; Klepov, V. V.; Serezhkin, V. N. Synthesis and X-Ray Diffraction Study of (Cs0.5Ba0.25)[UO2(CH3COO)3] and Ba0.5[UO2(CH3COO)3]. Crystallogr. Rep. 2011, 56, 265−269. (42) Ramos Moita, M. F.; Duarte, M. L. T. S.; Fausto, R. An Infrared Spectroscopic Study of Crystalline Copper (II) Propionate and Butyrate. Spectrosc. Lett. 1994, 27, 1421−1430. (43) Espinosa, E.; Alkorta, I.; Elguero, J.; Molins, E. From Weak to Strong Interactions: A Comprehensive Analysis of the Topological and Energetic Properties of the Electron Density Distribution Involving X−H···F−Y Systems. J. Chem. Phys. 2002, 117, 5529−5542. (44) Gatti, C. Chemical Bonding in Crystals: New Directions. Z. Kristallog.: Cryst. Mater. 2009, 220, 399−457. (45) del C. Michelini, M.; Russo, N.; Sicilia, E. Gas-Phase Chemistry of Actinides Ions: New Insights into the Reaction of UO+ and UO2+ with Water. J. Am. Chem. Soc. 2007, 129, 4229−4239. (46) Serezhkin, V. N.; Mikhailov, Y. N.; Buslaev, Y. A. The Method of Intersecting Spheres for Determination of Coordination Numbers of Atoms in Crystal Structures. Russ. J. Inorg. Chem. 1997, 42, 2036− 2077. (47) Blatova, O. A.; Blatov, V. A.; Serezhkin, V. N. Analysis of Lanthanide π Complexes in Terms of Voronoi-Dirichlet Polyhedra. Russ. J. Coord. Chem. 2000, 26, 847−856. (48) Blatov, V. A.; Shevchenko, A. P.; Serezhkin, V. N. TOPOS3.2: a New Version of the Program Package for Multipurpose CrystalChemical Analysis. J. Appl. Crystallogr. 2000, 33, 1193−1193. (49) Blatova, O. A.; Blatov, V. A.; Serezhkin, V. N. A New Set of Molecular Descriptors. Acta Crystallogr., Sect. B 2002, 58, 219−226. (50) Espinosa, E.; Molins, E.; Lecomte, C. Hydrogen Bond Strengths Revealed by Topological Analyses of Experimentally Observed Electron Densities. Chem. Phys. Lett. 1998, 285, 170−173. (51) Serezhkin, V. N.; Verevkin, A. G.; Smirnov, O. P.; Plakhtii, V. P. Neutron Diffraction Study of Rb2UO2(SeO4)2 · 2D2O. Russ. J. Inorg. Chem. 2010, 55, 1600−1606. (52) Serezhkin, V. N.; Karasev, M. O.; Serezhkina, L. B. Causes of Uranyl Ion Nonlinearity in Crystal Structures. Radiochemistry 2013, 55, 137−146. (53) Blatov, V. A.; Pogildyakova, L. V.; Serezhkin, V. N. Analysis of Environment of Alkali Atoms in Oxygen-Containing Compounds with Voronoi-Dirichlet Polyhedra. Z. Kristallogr: Cryst. Mater. 1998, 213, 202−209. (54) Serezhkin, V. N.; Serezhkina, L. B.; Pushkin, D. V.; Vologzhanina, A. V. Manganese Stereochemistry in the Structures of Oxygen-Containing Compounds. Russ. J. Coord. Chem. 2005, 31, 737− 746. (55) Serezhkin, V. N.; Serezhkina, L. B.; Pushkin, D. V. Iron Stereochemistry in Oxygen-Containing Compounds. Russ. J. Coord. Chem. 2006, 32, 180−191. (56) Serezhkin, V. N.; Kryuchkova, G. V.; Kazakevich, V. S. Coordination Polyhedra ScXn (X = O, S, Se, Te) in Crystal Structures. Russ. J. Inorg. Chem. 2003, 48, 1199−1206. (57) International Tables for Crystallography; Springer: Berlin, 2004; Vol. C

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Electronic Structure of Cesium Butyratouranylate(VI) as Derived from

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