Detection of Weak Intramolecular Interactions in Ru3 (CO) 12 by

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J. Phys. Chem. A 2010, 114, 9368–9373

Detection of Weak Intramolecular Interactions in Ru3(CO)12 by Topological Analysis of Charge Density Distributions Giuliana Gervasio,† Domenica Marabello,*,† Riccardo Bianchi,‡ and Alessandra Forni*,‡ Dipartimento di Chimica I.F.M. and Centro Interdipartimentale di Ricerca per lo SViluppo della Crystallografia Diffrattometrica (CrisDi), UniVersity of Torino, Torino, Italy, and CNR-ISTM, Istituto CNR di Scienze e Tecnologie Molecolari and UniVersita` degli Studi di Milano, Via Golgi 19, 20133 Milano, Italy ReceiVed: June 4, 2010; ReVised Manuscript ReceiVed: July 26, 2010

The presence of weak intramolecular interactions among the axial carbon atoms in Ru3(CO)12, previously detected by topological analysis of the 120 K X-ray derived charge density, has been here confirmed by theoretical calculations on the isolated, “gas-phase” molecule, using the all-electron B97D/3-21G approach, as well as by further experimental determinations of higher accuracy on data collected at 100 K. The importance of using density functional theory (DFT) approaches where dispersion terms are explicitly added to the usual Kohn-Sham energy to reproduce such weak intramolecular interactions has been evidenced. This result confirms the multipole approach as an efficient and sensitive tool to extract fine details of electron density distributions. 1. Introduction Dodecacarbonyltriruthenium, Ru3(CO)12, is the parent of a great number of derivatives and is considered a model of trinuclear clusters. Its molecular and crystal structure has been known for a long time.1,2 The molecule has approximate D3h configuration, corresponding to the most hindered structure. In fact the D3 and C2V configurations appear the most reliable arrangements on the basis of sterical and energetical approaches.3 A thermal motion analysis and the generation of alternative crystal structures from a variable temperature study have appeared in literature;4 new theoretical insights have been obtained on M3(CO)12 clusters,5 and the ultrafast photoinduced rearrangement of Ru3(CO)12 has been studied.6 Recently, a high pressure study of Ru3(CO)12 by X-ray diffraction and Raman and infrared spectroscopy has been published.7 All of the spectroscopic, structural, and theoretical studies, however, have never justified either the significant deviation of the RuCax-Oax bond angles (where ax stands for axial), 173°, from linearity, or the fact that the internuclear distances between vicinal axial carbons Cax are significantly shorter (by 0.04 Å on average) than those between the ruthenium atoms to which they are bonded. In fact, while steric nonbonded repulsions can explain the tendency of the axial oxygen atoms to go apart from each other, the reason for the opposite tendency shown by the Cax atoms is not evident. It is to be noted that analogous structural features are observed in Os3(CO)12,8 where the Os-Cax-Oax bond angles measure 175(1)°. Furthermore, both structures show longer metal-Cax bonds with respect to the metal-Ceq bonds (eq standing for equatorial), as a consequence of the severe competition of back-donation for the mutually trans (CO)ax ligands, which is instead minimal for the (CO)eq ligands. A topological study of the experimental charge density of Ru3(CO)12 has been recently published.9 The electron density * To whom correspondence should be addressed. [email protected]; [email protected]. † University of Torino. ‡ CNR-ISTM.

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distribution, obtained from a multipolar analysis of X-ray data collected at 120 K and analyzed using the Quantum Theory of Atoms In Molecules (QTAIM),10 unexpectedly revealed the presence of Cax · · · Cax stabilizing interactions between pairs of vicinal (CO)ax groups. The presence of such interactions could be associated with the significant nonlinearity of the RuCax-Oax bond angles and could justify the pseudo D3h symmetry instead of the apparently more stable D3 symmetry. Closed shell intramolecular interactions between pairs of identical (in both species and charge) atoms approaching to within or just outside the sum of their van der Waals radii have been evidenced and discussed in both theoretical and experimental charge density studies. For example, Matta et al.11 found theoretically bond paths linking adjacent H atoms in planar aromatic systems such as phenanthrene, chrysene, and planar biphenyl. They demonstrated that such “hydrogen-hydrogen bonding”, as distinguished from the “dihydrogen bonding” between H atoms of opposite charge, contributes to stabilize locally the system, even in cases where, in previous studies, it had been described as “steric nonbonded repulsion”.12,13 The presence of bond paths between identical atoms has been recently explained14 as the result of pairwise stabilizing contributions (essentially, the exchange-correlation term) prevailing over the destabilizing ones (that is, the atomic self-energies), both of which being always present between a pair of atoms. On the other hand, the theoretical description of interactions between parts of a molecule which are relatively far apart represents in general a nontrivial task, because long-range contributions, such as dispersion forces, may assume a nonnegligible role. Ignoring such contributions can cause a failure of the theoretical description of such weak interactions. On the experimental side, there are only few charge density studies reporting on such weak intramolecular interactions. A C · · · C intramolecular interaction has been found by a T ) 19 K charge density study of syn-1,6:8,13-biscarbonyl[14]annulene between the two carbon atoms of the carbonyl bridges.15 A weak O · · · O intramolecular interaction has been detected as well in a T ) 123 K charge density study of 2,2′-ethynylenedibenzoic acid.16

10.1021/jp105130z  2010 American Chemical Society Published on Web 08/12/2010

Weak Intramolecular Interactions in Ru3(CO)12 The question arises as to whether such weak intramolecular interactions, as observed in experimental determinations of electron density, may be considered real constructive interactions rather than an artifact resulting from the multipolar refinement of X-ray data. In particular, the presence of heavy atoms in the structure, such as in the presently investigated system, may make it even more difficult to obtain accurate information on the distortion of the electron distribution. The effect of chemical bonding is in fact concentrated in the valence shell, while the scattering by the core electrons does not carry relevant information. The above considerations prompted us to re-examine the title compound by both theoretical and experimental approaches. An extensive set of calculations has been carried out at several levels of theory on the isolated, “gas-phase” complex. Moreover, further experimental charge density studies have been undertaken, where a new data set of greater accuracy, measured at a lower temperature (100 K) than the previous one, has been collected. The results will be reported and discussed in the present paper. 2. Methods X-ray Data Collection. X-ray diffraction data have been collected at 100 K on an Oxford Gemini Ultra diffractometer equipped with a low temperature device (N2 stream). Crystal data: orange, prismatic, 0.08 × 0.08 × 0.14 mm, monoclinic space group P21/n, a ) 7.9959(2) Å, b ) 14.6373(8) Å, c ) 14.3746(8) Å, β ) 100.58(1)°, Z ) 4, V ) 1653.8(1) Å3, Fcalcd ) 2.552 g/cm3, graphite-monochromatized λ(Mo-KR) ) 0.71073 Å, ω-scan technique (∆ω ) 1.0°), 15 and 60 s exposure time for low and high angle data collection, 149 997 measured reflections (2.94 < θ < 50.44°), and 17 574 independent reflections (Rint ) 0.0290); absorption correction applied with faces accurately determined, µ ) 2.75 mm-1, min/max transmission ) 0.85. The programs used were CrysAlisPro (collection and integration) and SHELXTL (molecular graphics). A total of 12 159 reflections with I > 2σ(I) was used for the multipole refinement. Multipole Refinement. X-ray diffraction data have been subjected to multipole refinement, according to the formalism developed by Stewart17 as implemented in VALTOPO software.18 The density at each rigid pseudoatom was approximated using the following multipole model (POP): Fatomic(r) ) lmax l Rl(r) ∑m)-l Plm Ylm(θ,φ), PcoreFcore(r) + PvalenceFvalence(r) + ∑l)1 where Fcore and Fvalence are the spherical core and valence densities, respectively, and the summation in the third term accounts for the valence deformations. For all atoms the core and valence densities were calculated from Hartree-Fock atomic wave functions.19 Rl(r) is a radial function of the Slater type or a fixed linear combination of exponentials, and Ylm(θ,φ) is a real spherical harmonic. Pcore, Pvalence, and Plm are the population parameters to optimize. The adopted multipole model was identical to that used for the previously reported refinement of the 120 K X-ray data.9 A κ expansion/contraction parameter was refined separately for O and C valence monopoles. On the Ru position, functional expansions up to the hexadecapole level were introduced (lmax ) 4), whereas the expansions were broken at the octupole level at the C and O positions. For the higher multipoles (l g 1) a single Slater-type R exponent was refined for Ru, while for C and O a fixed value was assigned, based on theory. Third- and fourth-order Gram-Charlier (International Tables) coefficients for Ru atoms were included.

J. Phys. Chem. A, Vol. 114, No. 34, 2010 9369 The quantity minimized in the least-squares procedures was ∑w(|Fo|2 - K2|Fc|2)2 based on all independent reflections, where w ) 1/σ2(Fo2). Details of refinement: 12159 reflections used for multipole refinement, 784 refined parameters, R(F2) ) 0.0208, wR(F2) ) 0.0199, goodness of fit ) 1.0206, and shift/ esd < 0.01. The residual map based on Fobserved - Fmultipole and computed on all reflections in the Ru3 plane does not show any significant feature, and the largest peak is 0.49 e Å-3; the average standard deviation (σ) of the total density, representative of the error in the difference density, is 0.20 e Å-3 at positions away from the nuclei. All of the features in the residual maps are below 3σ, indicating that the POP model used in the refinement was adequate. Hirshfeld’s rigid bond test20 was applied to the final thermal parameters. The root-mean-square (rms) of the mean-square displacement amplitude for bonded atoms along the bond vector was below 0.001 Å; therefore, the final model is consistent with the rigid-bond hypothesis. Computational Details. All calculations have been performed on the isolated, gas-phase molecule within the density functional theory (DFT) approach. MP2 or coupled cluster calculations, which are more suitable for the study of weak interactions, resulted in being prohibitive due to the size of the problem. Several exchange-correlation functionals have been used, that is, (i) the popular Becke three-parameter hybrid functional21 with the nonlocal correlation given by the Lee-Yang-Parr22 expression (B3LYP); (ii) the same functional with the nonlocal correlation provided by Perdew-Wang in 1991 (B3PW91);23 (iii) the B9724 and (iv) B97-125 functionals, the latter having been recently demonstrated to be the most accurate one for the prediction of gas-phase enthalpies of formation for 3d transition metal containing systems;26 and (v), the recently developed B97D27 functional, which is explicitly parametrized by including damped atom-pairwise empirical dispersion corrections. The latter functional has been proved to be an accurate method for large systems, including transition metal complexes, where dispersion forces are of general importance.27 Several basis sets have been tested, either including all of the electrons in calculations or freezing the core electrons of ruthenium by the use of effective core potentials (ECP). Allelectron calculations have been performed with the 3-21G basis set on all atoms, owing to the lack of more extended all-electron basis sets for ruthenium. Frozen core calculations have been performed with the Dunning/Huzinaga double-ζ basis set28 together with the Los Alamos (LanL2DZ)29 ECP on Ru. More accurate frozen core calculations have been carried out using basis sets30 of split valence (SV) and triple-ζ valence (TZV) quality plus polarization functions (P) together with the Stuttgart/ Dresden ECP31 on Ru (Def2-SVP and Def2-TZVP basis sets, respectively). Independent of the basis set used, the free (i.e., without imposing any symmetry constraint) geometry optimization led to a loss of the pseudo D3h symmetry of the experimental geometry, a result recently obtained also by Peng et al. using other DFT approaches.32 Optimized geometries have in fact D3 symmetry which deviates from the D3h one by a rotation of the four carbonyl groups on each ruthenium. To get a meaningful comparison with the topological properties of the experimental electron density, a constrained optimization of a fully D3hsymmetrized geometry has been therefore performed. Symmetrization of the experimental geometry was obtained with SYMMOL.33 DFT calculations have been performed with Gaussian 09.34 The AIMPAC program35 has been used for the topological analysis of the electron density.

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TABLE 1: Bond Lengths and BCP Properties from VALTOPO Refinement at 100 K (First Line) and from B97D/3-21G Calculations on the D3h Optimized Geometry (Second Line Italics)a bond

R (Å)

FBCP (e Å-3)

32FBCP (e Å-5)

Ru1-Ru2

2.8459(4) 2.826 2.8468(4) 2.8558(4) 1.9415(8) 1.967 1.9516(8) 1.9173(7) 1.942 1.9299(7) 1.9402(8) 1.9501(8) 1.9146(8) 1.9359(8) 1.9403(9) 1.9556(9) 1.9326(8) 1.9139(8) 1.141(1) 1.154 1.139(1) 1.156

0.184(2) 0.268 0.184(2) 0.183(2) 0.93(2) 0.84 0.91(1) 0.96(9) 0.89 0.94(1) 0.93(28) 0.90(1) 0.93(1) 0.93(2) 0.90(20) 0.89(17) 0.90(18) 0.98(12) 3.6(1) 2.70 3.8(1) 2.70

1.97(4) 1.20 1.95(4) 1.91(4) 12.0(3) 11.7 12.1(2) 12.3(6) 12.2 12.5(1) 12.4(41) 12.5(2) 12.7(2) 12.4(2) 11.9(31) 12.5(24) 12.2(29) 13.1(21) -42(10) 6.3 -53(10) 6.7

Ru1-Ru3 Ru2-Ru3 Ru1-C11 Ru1-C12 Ru1-C13 Ru1-C14 Ru2-C21 Ru2-C22 Ru2-C23 Ru2-C24 Ru3-C31 Ru3-C32 Ru3-C33 Ru3-C34 C-Oax(av.) C-Oeq(av.)

a For DFT results, only the values referring to bonds unique for symmetry are reported.

3. Results and Discussion The QTAIM10 correlates the bonding properties with the topology of the charge density, F(r), and of its Laplacian, 32F(r), obtainable by a sum of the eigenvalues λi (i ) 1 to 3, with λ1 e λ2 e λ3) of the density Hessian matrix (the 3 × 3 array of the second derivatives). The topological features of F(r) and 32F(r) are determined by their critical points (CPs), where the respective first derivatives vanish. A critical point is characterized by two numbers, (ω,σ): ω (rank) is equal to the nonzero eigenvalues of the Hessian of F(r) or 32F(r), and σ (signature) is the algebraic sum of their signs. At nuclear positions, F(r) exhibits a local maximum, that is, all curvatures are negative (ω ) 3, σ ) -3 or (3,-3) CP). Two atoms are to be considered bonded when a bond path (a line of maximum density) connects the two interacting nuclei, or equivalently, along it there is a (3,-1) CP, a saddle point which is called bond critical point (BCP). In this point, (i) the positive eigenvalue λ3 is associated to the eigenvector directed along the bond path (“parallel curvature”), denoting that charge is locally depleted at the BCP relative to points along the bond path; (ii) the negative eigenvalues λ1 and λ2 are associated to eigenvectors perpendicular to the bond path (“perpendicular curvatures”), indicating that charge on the surface perpendicular to the bond path is here concentrated. The character of a bonding interaction may be classified on the basis of the properties of the Laplacian of F(r) at the BCP, denoted by 32FBCP, in terms of its sign and magnitude.36 Closedshell interactions are characterized by 32FBCP > 0, that is, by local depletion of charge density at the BCP, while shared-shell interactions have 32FBCP < 0, that is, local charge concentration at the BCP. Table 1 collects the bond lengths and the values of charge density and of its Laplacian at the BCPs (FBCP and 32FBCP, respectively) for Ru3(CO)12, as obtained from the VALTOPO refinement at 100 K and from DFT calculations (see Figure 1 for atom labeling). Interatomic distances and topological proper-

Figure 1. ORTEP plot of Ru3(CO)12 at 100 K (VALTOPO refinement) with atom-numbering scheme. Displacement ellipsoids are drawn at the 50% probability.

TABLE 2: Cax · · · Cax Distances and BCP Properties from VALTOPO Refinement at 100 K (First Line) and from B97D/3-21G Calculations on the D3h Optimized Geometry (Second Line)a bond

R (Å)

bond path length (Å)

FBCP (e Å-3)

32FBCP (e Å-5)

C11 · · · C21

2.8327(9) 2.790 2.7852(9) 2.7978(10) 2.8294(9) 2.8074(9) 2.8243(9)

2.976 2.940 2.845 2.900 3.029 2.980 3.009

0.10(8) 0.116 0.11(2) 0.11(8) 0.10(1) 0.10(2) 0.11(1)

0.92(45) 0.95 1.03(8) 0.97(41) 0.91(1) 0.94(13) 0.93(9)

C11 · · · C31 C21 · · · C31 C12 · · · C22 C12 · · · C32 C22 · · · C32

a For DFT results, only the values referring to bonds unique for symmetry are reported.

ties for the Cax · · · Cax intramolecular interactions from 100 K data collection, as well as from DFT calculations, are reported in Table 2. The details about the topology of the charge density of this complex have been already discussed in our previous work,9 based on a VALTOPO refinement of data collected at 120 K. A comparison between the 120 and 100 K results indicates that the new data set is of better quality, thanks to the reduction of atomic thermal motion leading to higher resolution data. The new data set essentially reproduces the FBCP values obtained at 120 K for the Ru-C, C-O, and Cax · · · Cax bonds, while it gives slightly lower FBCP values for the Ru-Ru bonds (on average, 0.184 vs 0.215 e Å-3 from the 100 and 120 K data collection, respectively). About the Cax · · · Cax BCPs, their presence and topological features have been confirmed by the new, most accurate data set. It is to be noted that the Cax · · · Cax bond paths (see Figure 2 and Table 2) resemble the H · · · H ones found by Matta et al.11 in their theoretical investigation on planar polybenzenoids. Similar to such kind of interactions, the Cax · · · Cax interactions have in fact bond paths significantly curved, with bond path lengths computed with PAMoC37 exceeding the bond distances by 0.14 Å (at T ) 100 K) on average. Moreover, they show low densities at the BCP (0.11 eÅ-3 on average), small and positive values of the corresponding Laplacian (0.95 e Å-5 on average). It is also important to observe that our values of FBCP and 32FBCP are very close to those obtained by Destro and Merati15 for the C · · · C intramolecular interaction between the bridging CO’s in biscarbonyl[14]annulene (0.116(3) e Å-3 and 1.53(1) e Å-5, respectively), though in that structure the

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Figure 2. Experimental (100 K, VALTOPO refinement) bond paths plotted on the map of 32F(r) in the Ru1, Ru2, C12, C22 plane. The absolute value of the contour (a.u.) increases from the outermost inward in steps of 2 × 10n, 4 × 10n, 8 × 10n, n beginning at -3 and increasing in steps of one. Positive values are denoted by dashed contours; negative values are denoted by solid contours.

Figure 3. Bond paths in the C11, O11, C11′, O11′ plane (apex ) 1 x, -y, 1 - z) and relative bond critical points.

internuclear distance (2.593 Å) was significantly shorter than those of our complex (2.813 Å on average at T ) 100 K). To investigate the weak Cax · · · Cax interactions by theoretical methods, DFT calculations have been performed using different approaches and several functionals and basis sets. Geometry optimizations of Ru3(CO)12 led in all cases to a loss of the pseudo-D3h symmetry of the experimental geometry, a result already reported by Peng et al. in their theoretical investigation on a series of unsaturated trinuclear ruthenium carbonyls using other DFT approaches.32 The optimized structures assume in fact a D3 symmetry, where the coordination octahedra around each ruthenium are slightly rotated one with respect to the other, allowing to slightly increase the interatomic distance between vicinal axial carbons. These D3 optimized structures, however, are only a little more stable (by 1.7 up to 3.1 kcal/mol according to the method) than the corresponding D3h-constrained optimized geometries. The reason of the preferred pseudo-D3h symmetry as observed in the solid state can be probably traced back to crystal packing

effects. Analysis of the crystal structure of Ru3(CO)12 reveals in fact that each (CO)ax group is involved in one or two intermolecular contacts with other (CO)ax groups arranged with antiparallel orientation.38 The observed C · · · O intermolecular distances range from 3.154(1) to 3.602(1) Å at T ) 100 K. This structural motif is very similar to that of most carbonylcarbonyl dipolar interactions in ketonic organic compounds as found by crystallographic data survey39 on the Cambridge Structural Database.40 For this arrangement, shown by 650 instances, a median C · · · O separation of 3.33 Å was reported.39 In spite of the different chemical nature of the involved groups (nearly triply bonded CO in Ru3(CO)12 versus doubly bonded CO as from the CSD survey39), such noncovalent intermolecular interactions are expected to give nonnegligible stabilization for the Ru3(CO)12 crystal structure. We have demonstrated experimentally their existence by locating the corresponding BCPs and relative bond paths connecting the interacting (CO)ax groups. A representative example is reported in Figure 3. The low FBCP values (ranging from 0.022(3) to 0.045(1) e Å-3) associated to such intermolecular (CO)ax · · · (CO)ax contacts are indicative of very weak interactions. It is to be noted that the pattern of such antiparallel-oriented intermolecular interactions can be realized only with a D3h or pseudo-D3h symmetry for the Ru3(CO)12 molecule. Since calculations on the isolated molecule, as said before, do not preserve the experimental pseudo-D3h symmetry of the molecule, geometry optimizations were performed by imposing a D3h constrain to get a meaningful comparison with the experimental findings, in particular as far as the Cax · · · Cax interactions are concerned. Selected geometrical parameters obtained from such calculations are reported in Table 3. Allelectron calculations were shown on the whole to be more reliable to model the present system. In particular, the B3LYP and B97D functionals reproduced accurately the difference between Ru-Ru and Cax · · · Cax distances. On the other hand, optimizations using ECPs on ruthenium, while giving a slightly better description of the Ru-C distances, largely overestimated the Ru-Ru and Cax · · · Cax interatomic distances. These results suggest particular caution in using ECPs to model molecular complexes where metal-metal bonds are present. From a topological analysis of the computed electron densities, it resulted that all methods, while reproducing the topological features for the Ru-Ru, Ru-C, and C-O bonds as derived from experiment, failed to detect the intramolecular Cax · · · Cax interactions, with the only important exception of the B97D/ 3-21G approach. These results therefore clearly indicate the dispersive origin of such noncovalent interactions, and the consequent necessity to include the dispersion contribution in

TABLE 3: Relevant Geometrical Parameters Observed at 100 K and Computed by Different Theoretical Approaches method

rRu-Ru(R1), Å

experiment B3LYP/3-21G B3PW91/3-21G B97/3-21G B97-1/3-21G B97D/3-21G B3LYP/def2-SVP B3PW91/def2-SVP B97/def2-SVP B97-1/def2-SVP B97D/def2-SVP B3LYP/def2-TZVP B3LYP/LanL2DZ

a

a

2.8495 2.837 (-0.012) 2.797 (-0.052) 2.814 (-0.035) 2.817 (-0.032) 2.825 (-0.024) 2.929 (0.079) 2.888 (0.038) 2.903 (0.053) 2.905 (0.055) 2.935 (0.085) 2.948 (0.098) 2.924 (0.074)

rCax · · · Cax(R2), Å a

2.813 2.801 (-0.012) 2.774 (-0.039) 2.790 (-0.023) 2.787 (-0.026) 2.788 (-0.025) 2.859 (0.046) 2.833 (0.020) 2.846 (0.033) 2.842 (0.029) 2.855 (0.042) 2.894 (0.081) 2.869 (0.056)

Average value observed at 100 K with multipolar refinement.

∆(R1-R2), Å 0.036 0.036 (0.000) 0.023 (-0.013) 0.024 (-0.012) 0.030 (-0.006) 0.037 (0.001) 0.070 (0.034) 0.055 (0.019) 0.057 (0.019) 0.063 (0.027) 0.080 (0.044) 0.054 (0.018) 0.055 (0.019)

rRu-Cax, Å a

1.947 1.972 (0.025) 1.956 (0.009) 1.964 (0.017) 1.965 (0.018) 1.967 (0.020) 1.954 (0.007) 1.940 (-0.007) 1.947 (0.000) 1.948 (0.001) 1.950 (0.003) 1.953 (0.006) 1.959 (0.012)

rRu-Ceq, Å 1.924a 1.954 (0.030) 1.932 (0.008) 1.945 (0.021) 1.945 (0.021) 1.943 (0.019) 1.920 (-0.004) 1.902 (-0.022) 1.912 (-0.012) 1.912 (-0.012) 1.914 (-0.010) 1.919 (-0.005) 1.933 (0.009)

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the DFT energy, to get a correct theoretical description of these weak interactions. Such an energy contribution is in fact ignored in all of the other functionals used in the present study. It is to be noted that the B97D functional was demonstrated to be particularly successful in cases where the interatomic distances are below those of typical van der Waals contacts but are far away from the values of covalent bonds,27 such as in the present case. Because the relative arrangement of the Cax atoms in Ru3(CO)12 is strictly dependent on the Ru-Ru distance, the results concerning their reciprocal interaction can be biased by an incorrect description of the intermetallic separation. It appears then evident the inadequacy of the basis sets including ECPs (see Table 3) to treat the weak intramolecular interactions in the present system. The topological properties of all of the covalent and noncovalent interactions as obtained within the B97D/3-21G approach are reported in Tables 1 and 2, respectively. Theoretical results confirm the specificity of the different bonds present in the structure, that is, low FBCP and small and positive 32FBCP values for the metal-metal bonds, large and positive curvatures for the Ru-C bonds, and very small and positive 32FBCP values for the weak Cax · · · Cax interactions. The agreement with the experimental results is good, considering the presence of heavy atoms in the structure. For Ru-Ru, Ru-C, and Cax · · · Cax bonds, theoretical calculations reproduce the experimental FBCP and 32FBCP values within 0.1 e Å-3 and 1 e Å-5, respectively. The only significant discrepancy concerns the Laplacian values of the CO bonds, owing to the well-known fact that, for polar bonds, the BCP is usually placed in a region where the parallel curvature (λ3) changes considerably, making plausible even large differences between experimental and theoretical 32FBCP values.41 4. Conclusions The present analysis, based on the use of a more accurate data set to test the reliability of previously reported results on Ru3(CO)12,9 has confirmed, together with theoretical calculations, the existence of Cax · · · Cax stabilizing interactions in the structure. These interactions cannot therefore be considered an artifact of the multipolar analysis. Calculations on the isolated molecule have shown that such noncovalent interactions, owing to their long-range character, could not be detected using the traditional DFT exchangecorrelation functionals. Such functionals, in fact, ignore the dispersion contribution to the total interaction energy, which can be important in cases where the interacting atoms are midway between the typical van der Waals contacts and the bond distances. In the present study, where an extensive set of DFT approaches has been tested, only the B97D functional was found to reproduce the Cax · · · Cax interactions. This functional is the only one of the examined series where empirical dispersion corrections are explicitly included in the energy expression.27 These results therefore indicate the importance to include the dispersion forces not only for the study of van der Waals complexes, where the traditional DFT functionals notoriously fail, but also to detect weak interactions between molecular groups which are relatively far apart. Moreover, they indicate that the all-electron 3-21G basis set, though relatively small, can be more reliable in reproducing the experimental geometry than more extended basis sets including necessarily ECPs on ruthenium, in systems where intermetallic bonds are present. At the same time, this work indicates that multipole analysis of X-ray derived charge density distributions is sensitive enough to detect weak interactions also in the presence of heavy atoms in the structure.

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