Experimental and theoretical study of the vibrational spectrum, structure and electron density distribution of neutral 11-vertex dicarbaborane 2,3-C2B9H11

Journal of Molecular Structure 794 (2006) 148–153 www.elsevier.com/locate/molstruc

Experimental and theoretical study of the vibrational spectrum, structure and electron density distribution of neutral 11-vertex dicarbaborane 2,3-C2B9H11 E.G. Kononova, L.A. Leites *, S.S. Bukalov, I.V. Pisareva, I.T. Chizhevsky A.N. Nesmeyanov Institute of Organoelement Compounds, The Russian Academy of Sciences, 28 Vavilova street, 119991 Moscow, Russian Federation Received 13 September 2005; received in revised form 31 January 2006; accepted 31 January 2006 Available online 30 March 2006

Abstract The presence of low-frequency large-amplitude modes in the vibrational spectrum, experimental and computed data on interboron distances and the results of the topological analysis of the electron density distribution in 2,3-C2B9H11, the molecule of a neutral 11-vertex dicarbaborane, lead to the conclusion that this polyhedron is not a deltahedron. This species lacks at least four two-center B–B bonds and thus it is formed not by triangular faces only. Hence, this dicarbaborane, as well as monocarbaborate [2-CB10H11]K, another representative of 11-vertex polyhedra, do not have the closo-structure, traditionally ascribed to both by formal [2nC2]-electron count. q 2006 Elsevier B.V. All rights reserved. Keywords: closo-Carbaborane; Vibrational spectrum; Molecular structure

1. Introduction It is known that not all the polyhedral boron-containing clusters obey the Williams/Wade [1,2] cluster-geometry/electron-counting formalism. The exceptions, the so-called ‘disobedient skeletons’ with fragile structures, were comprehensively reviewed by Kennedy [3]. A prominent role among these exceptions play the 11-vertex polyhedra, which incorporate a cage atom characterized by a unique coordination number 6k [1]. In particular, the [B11H11]2K and [2-CB10H11]K species, though possessing 2nC2 electrons for skeletal bonding and thus deserving the descriptor ‘closo’, differ from the 12- and 10vertex closo-boranes and -carbaboranes in their chemical behaviour and are ‘fluxional’ in solution [4,5]. Recently, we have reported a detailed experimental and theoretical study of the vibrational spectrum, geometrical structure and topology of electron density distribution of the [2-CB10H11]K anion [6]. All the results obtained were mutually consistent and showed that this anion cannot be regarded as a genuine deltahedral closo-carbaborane, because it lacks at least four two-center B–B bonds (those of 6k–5k type [1]). It was of interest to investigate in exactly the same way a neutral 11-vertex dicarbaborane, 2,3-C2B9H11 (1) (Fig. 1), also having * Corresponding author. Tel.: C7 495 135 9262; fax: C7 495 135 5085. E-mail address: [email protected] (L.A. Leites).

0022-2860/$ - see front matter q 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2006.01.051

2nC2 skeletal electrons and thus also referred to as a closo-polyhedron [1,2,7–10]. Compounds with {2-CB10} and {2,3-C2B9} skeletons have some remarkable features in common, e.g. both [2-CB10H11]K (2) and 2,3-Me2K2,3C2B9H9 (3) undergo oxidative insertion of a metal-containing species with formation of icosahedral metallacarbaboranes [11,12]. However, 1 significantly differs from 2 and from the anion [B11H11]2K (4) in that 1 is not ‘fluxional’ in solution, its 11 B NMR spectrum strictly corresponds to the C2v symmetry of the molecule [10]. 2. Experimental A sample of 2,3-C2B9H11 was synthesized by the reported procedure [8]. Raman spectra for the solid samples sealed in capillaries in vacuo were recorded in the region 30–3500 cmK1 using a LabRAM and a U-1000 Jobin–Yvon laser Raman spectrometers. The spectra were excited by 632.8 nm line of a He–Ne laser and 514.5 nm line of an ArC laser Spectra Physics 2020. IR spectra in the region 150–3500 cmK1 were obtained from thin layer samples as well as from nujol mulls on a Carl Zeiss M-82 spectrophotometer and a Nicolet Magna-750 FTIR spectrometer. Geometry optimization and normal coordinate analysis were carried out at the DFT B3LYP/6-311CCG(d,p) level, using the G94W program suite [13]. Topological analysis of the theoretical electron density (ED) distribution (based on the results of the DFT calculation) was accomplished according to Bader’s theory [14], using AIMpac program package [15].

E.G. Kononova et al. / Journal of Molecular Structure 794 (2006) 148–153

Fig. 1. Traditional {2,3-C2B9} closo-polyhedron depiction with atom numbering. Black circles—carbon atoms, all the rest vertices imply boron atoms.

3. Results 3.1. Vibrational spectra The molecule 2,3-C2B9H11 belongs to the C2v symmetry point group; the irreducible representations for its 60 normal modes are as follows: G Z 19A1 C 11A2 C 16B1 C 14B2 The vibrations of A1, B1 and B2 symmetry species are both IR and Raman active, while A2 ones are only Raman active. The Raman and IR spectra of 1, not reported previously,1 are presented in Fig. 2. The spectrum of 1, unlike that of 2 [6], exhibits a broad Rayleigh wing in the Raman region below 100 cmK1 and is characterized by rather broad bands without crystal splittings. Such spectral features indicate that 1, as other neutral globular closo-carbaboranes [16], forms a plastic mesophase at room temperature, in which the molecules, being fixed in the nodes of the crystal lattice by their centers of gravity, undergo isotropic reorientations [17]. The normal mode assignment to the symmetry species and to particular molecular vibrations has been proposed. It was based on the experimental data on Raman and IR activities, on comparison with the spectra of related molecules [6,16,18] and on the results of a DFT B3LYP calculation of the normal mode frequencies and eigenvectors. The results are presented in Table 1. As is seen from Fig. 2 and Table 1, the number of spectral features is much less than the theoretical value 60. This fact can be rationalized in terms of the results of normal coordinate analysis, which show that the frequencies of some normal modes, having close displacement eigenvectors but belonging to different symmetry species, nearly coincide (Table 1). It is notable that the calculation underrates the frequencies of lower-frequency modes (200–500 cmK1), reproduces the frequencies in the middle region of the spectrum more or less correctly, and strongly overvalues the 1 The IR spectrum of 1 as a nujol mull in a limited region 700–3100 cmK1 was published in [10b] as a set of frequencies.

149

nBH and nCH frequencies (2500–3100 cmK1). The same was observed for 2 [6]. There are two low-frequency modes in the vibrational spectrum of 1: 201/225 cmK1 (Raman, IR) and 289 cmK1 (Raman). The first mode of B2 species involves mainly a displacement of the B(1) atom while the second one is of A2 species and involves displacements of B(4,5,6,7) atoms. The presence of the low-frequency modes in the spectrum of 1, as well as in that of anion 2 [6] points to nonrigidity of both polyhedra. None of the unsubstituted closo-boranes and carbaboranes studied previously [16,18] exhibited vibrational modes with frequencies lower than 450 cmK1. The modes in the region 400–500 cm K1 are cage deformations with predominant participation of the abovementioned B(1,4,5,6,7) atoms. The modes in the region 550– 650 cmK1 are also cage deformations, but displacements of also B(8,9,10,11) atoms become noticeable. The modes in the region 650–700 cmK1 are of heavily mixed origin, with participation of cage stretching and deformational coordinates. The higher the frequency, the more is the contribution from stretching coordinates. The most intense Raman line at 735 cmK1 is evidently the cage breathing mode of A1 species. The weak features in the region of 800–1000 cmK1 belong to mixed modes with dBH bending vibration predominance. The bands in the region 1080–1180 cmK1 correspond to mixed bending dCHCdBH modes. Theoretically, there should be nine nBH stretching modes (4A1C2B1C2B2CA2), however, in the observed spectrum they coalesce into two broad Raman and two broad IR entities situated in the region 2550–2620 cmK1. Eigenvector calculations show that in the A1 nBH mode with the highest frequency (intense Raman band at 2613 cmK1) all the B–H bonds participate while the other nBH modes are attributable to various couplings of some of these coordinates. The frequency of nCH stretching mode for 1 is 3079 cmK1, slightly increased compared to that of 2 (3075 cmK1). The Raman intensity of these modes for 1 and 2 is high while the IR intensity is rather low, which reflects the high electron density and low polarity of these C–H bonds and is in good agreement with the ED data (see below). The overall pattern of the vibrational spectrum of icosahedral 1,7-dicarba-closo-dodecaborane [16], whose molecule contains two carbon atoms in the same ‘meta’ position as in 1 and also belongs to C2v point symmetry group, remarkably differs from that of 1. This fact reflects different chemical nature of these two molecules. 3.2. Geometry of the polyhedron {2,3-C2B9} The structure of 1 has not been characterized by X-ray crystallography. As this compound forms the isotropic plastic mesophase at room temperature, the corresponding X-ray data could be obtained only if one manages to grow a single crystal at low temperature, below the temperature of the phase transition to an ordered crystal (still undiscovered). Two X-ray structures are available for substituted 1. The first one characterizes the low-temperature crystalline phase of

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Fig. 2. The Raman and IR spectra of solid 2,3-C2B9H11. (a) thin layer of the sample; (b) nujol mull.

2,3-Me2-2,3-C2B9H9 (3) [19], whose molecule possesses the same symmetry as 1; the second one is that for 10-Br-4,7(OH)2-2,3-Me2K2,3-C2B9H6 (5) [20]. Quite recently the molecular geometry of 1 was determined using gas-phase electron diffraction (GED) [21]. Fully optimized geometries for 1 are reported by von Schleyer and Najafian [7] (calculated by RMP2/6-31G* method) and by Mackie et al. [21] (MP2/6311CG* level of theory). We have also carried out geometry optimization for 1 at the DFT B3LYP/6-311CCG(d,p) level. These results together with the calculated data [7,21] for 1 and the experimental geometry for 1 [21] and 3 [19] are presented in Table 2. The agreement between the calculated data for 1 from [7,21] and this work and the experimental values for 1 and 3 is very good. It is noteworthy that, as in the case of 11-vertex monocarbaborate 2 and its derivatives [6], interatomic distances between 6k B(1) and 5k B(4,5,6,7) atoms in 1 ˚ , that is, anomalously long for a (Fig. 1) and 3 are 2.00–2.08 A two-center B–B bond. Such ‘long connectivities’ have been recognized in some other ‘disobedient’ closo-clusters to be typical for fragile structures [3]. It is pertinent to mention here that after insertion of a metalcontaining fragment into 2 or 3 with formation of an icosahedral closo-metallacarbaborane, all the interboron distances acquire normal values [12]. 3.3. Theoretical topological analysis of electron density distribution Polyhedral boranes and carbaboranes are known to belong to electron-deficient systems which involve not only twocenter but also multicenter bonding. To determine the network of bonds in such systems, one can use Bader’s theory of atoms

in molecules [14]. This theory based on the topological analysis of ED distribution has shown itself as relevant and fruitful (see, e.g. [22,23] and our previous study [6]). Analogous results obtained for 1 are presented in Table 2; the molecular graph of 1 based on ED calculations is given in Fig. 3. According to the calculated data, 10 of the 27 edges of the polyhedron 1 do not correspond to the localized two-center chemical bonds, because there are no bond critical points (CP) of (3,-1) type between the following pairs of boron atoms (Fig. 1) Bð1Þ–Bð4Þ Z Bð1Þ–Bð5Þ Z Bð1Þ–Bð6Þ Z Bð1Þ–Bð7Þ Bð5Þ–Bð6Þ Z Bð4Þ–Bð7Þ Bð5Þ–Bð8Þ Z Bð4Þ–Bð8Þ Z Bð6Þ–Bð9Þ Z Bð7Þ–Bð9Þ: If the above-mentioned 10 connectivities in 1 are broken, then the polyhedron incorporates only two 3-membered rings, four 4-membered rings and two 6-membered rings and thus is far from being a deltahedron. Notably, in the structure of monocarbaborate 2, critical points of the type (3,K1) were absent only for the first eight pairs of atoms indicated above [6]. The values of bond ED rb(r) on exo-polyhedral C–H and B– H bonds are 0.282 and 0.187–0.181 a.u., respectively, slightly higher than those in anion 2. The rb(r) values of the cage C–B bonds in molecule 1 lie in the same interval (0.155–0.126 a.u.) as in 2, while those of B–B bonds (0.119–0.104 a.u.) are lower compared to 2 (0.141–0.107 a.u.). Multicenter bonding in 1 manifests itself by the presence of the ring rr(r) critical points of (3,C1) type. The rr(r) values in

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151

Table 1 Vibrational spectrum of C2B9H11 Calculated

Experimental frequencies (cmK1) IR intensity

IR

Raman

3209 2707 2699 2698 2664 1178 1171 1157 1108 1000 957 934 913 894 885 881 852 848 836 800 782 769 754 733 707 691 667 659 635 619 568 551 524 399

0.0 0.03 0.67 1.0 0.29 0.11 0.05 0.0 0.11 0.01 0.0 0.01 0.01 0.0 0.0 0.0 0.0 0.05 0.04 0.03 0.0 0.05 0 0 0.02 0.02 0 0.01 0 0 0 0 0 0.01

3078m

3079s 2613vs 2597sh

279 145

0 0.06

Frequency (cm

K1

)

2599vvs 2562sh 1187vw 1144s 1089s 986w 936w 918vw 896w

2563sh

1143vw 1087w 989vw 962vw 933w 919w 887s 867w 843ms

829ms 793m 762m 733vw 700mw 690sh 656vw 615vw 575vw 555w 417w 355vw 200m/222sh

828sh 793vw 771m 763sh 757sh 735vs 702mw 690sh 665sh 655w 633w 620vw 569sh 558m 528w 415mw 289vw 201m/225sh 139vvw

Assignment

A1 B1 A1 B1 B2 A1 B2 B1 B2 A2 A1 B1 B2 A2 A1 B2 B2 A2 B1 A1 B2 B1 A2 B2 A1 A1 B1 B1 A1 B2 A1 B2 A1 A2 B1 A2 B1 A1 A2 A1 ? A2 B2 ?

nCH All nBH nBH in various combinations dCHCdBH

dBHCdCH Mainly dBH

dBHCnBCCnBB

Cage breathing nBBCnBC CdBH

Cage deformations

wB(4,5,6,7) wC2B1C3

s, strong; m, medium; w, weak; sh, shoulder.

the 3- and 4-membered ring critical points (0.111–0.104) are only slightly lower than the rb(r) values in the cage bond (3,-1) critical points. This fact, along with high ellipticities of the cage bonds (2.0–3.2), points to a pronounced electron delocalization over the surface of the polyhedron. As in the case of 2 [6], the two 6-membered rings in 1 are characterized by a significant decrease in rr(r) (0.061 a.u.) compared to 3and 4-membered rings. This suggests an uneven ED distribution in both polyhedra. 4. Discussion According to the computed molecular graph of 1, the connectivities are broken between the 6k B(1) and 5k B(4,5,6,7) atoms. This agrees well with the abnormally long ˚ , see corresponding interboron distances (2.000–2.086 A Table 2), which are longer than those predicted by Wade for a 6k–5k B–B bond in terms of formal bond orders [2b].

The absence of these bonds evidently leads to nonrigidity of the polyhedron. The most spectacular is the cage geometry of 5 [20], in which the 6k boron atom B(1) is shifted away from the ˚ , far beyond the conceivable value B(4,7) atoms up to 2.35 A for a B–B bond. The B(4)–B(7) distance in 5 is also too long ˚ ) for a normal 5k–5k B–B bond (1.79 A ˚ [2b]). These (2.04 A elongations are evidently due to a strong influence of substituents. However, it is also obvious that such a dramatic cage distortion can happen only to a nonrigid, floppy, ‘disobedient’ {2,3-C2B9} skeleton. Strikingly, the ED calculations for 1 and 2 show that there are no (3,-1) bond critical points also between the pairs of boron atoms, whose interatomic distances lie within the reasonable limits for B–B bonds. For the B(5)–B(6)aB(4)– B(7) pairs, the interatomic distances are still somewhat ˚ ) compared to those of ‘normal’ 5k–5k B– elongated (1.87 A B bonds, but for the B(4)–B(8)aB(5)–B(8)aB(6)–B(9)aB(7)– ˚ . At this time, an B(9) pairs they have ordinary values w1.80 A

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Table 2 Interatomic distances and bond electron density inside {2,3-C2B9} polyhedron Pairs of cage atoms

B(1)C(2)aB(1)C(3) C(2)B(8)aC(3)B(9) C(2)B(4)aC(2)B(5)a C(3)B(6)aC(3)B(7) B(1)B(4)aB(1)B(5)a B(1)B(6)aB(1)B(7) B(8)B(10)aB(8)B(11)a B(9)B(10)aB(9)B(11) B(4)B(7)aB(5)B(6) B(4)B(10)aB(5)B(11)a B(6)B(11)aB(7)B(10) B(4)B(8)aB(5)B(8)a B(6)B(9)aB(7)B(9) B(10)B(11) a

˚) Interatomic distances (A a

Presence of the bond critical points (3,-1) in 1

rb(r) (a.u.)

0.144 0.126 0.155

GED for 1 [21]

X-ray for 3 [19]

Calcd for 1 [7]

[21]

This work

1.622 1.670 1.579

1.67 1.70 1.595

1.626 1.660 1.573

1.631 1.668 1.579

1.621 1.670 1.576

C C C

2.000

2.055

2.055

2.067

2.086

K

1.808

1.80

1.776

1.783

1.780

C

0.119

1.886 1.807

1.87 1.78

1.862 1.771

1.870 1.779

1.880 1.772

K C

0.119

1.774

1.82

1.792

1.801

1.790

K

1.866

1.85

1.835

1.841

1.855

C

0.104

2,3-Me2-2,3-C2B9H9.

explanation of this contradiction is not at hand, it needs a larger set of similar studies. The absence of 6k–5k B–B two-center bonds readily explains the presence in the vibrational spectrum of the lowfrequency modes. According to normal coordinate analysis, the latter modes involve mainly the displacements of the ‘more free’ B atoms. One of these modes, at w200 cmK1, is a large-amplitude wagging displacement of the B(1) atom in the CB(1)C ‘handle’, the second mode, at w290 cmK1, includes displacements of B(4,5,6,7) atoms. If we accept, in accordance with the ED results (Fig. 3), that there are no two-center bonds also between 5k and 5k boron atoms mentioned above (in spite of their rather normal interboron distances), then the B(4,5,6,7) atoms appear linked only to two other atoms (as well as B(1) atom), which leads to their increased mobility. In this case, the low-frequency mode at w290 cmK1 is a combination of large-amplitude swingings of B(4,5,6,7) atoms in the corresponding CBB ‘handles’. This view is strongly supported by extraordinary large amplitudes of B(1)–B(4) and B(4)–B(7) vibrations, recently reported in [21]. It should be emphasized that none of the previously studied unsubstituted 12-, 10-, 6- and 5-vertex closo-boranes and -carbaboranes [16,18] exhibited lowfrequency vibrations, thus manifesting cage rigidity. The presence in 1 of 6-membered rings with lowered ED is a rationale for the insertion reaction of metal-containing fragments into this part of the polyhedron with formation of icosahedral metallacarbaboranes [12]. Formation by 1 of solid adducts with Lewis bases [10] could be also explained in this way, the more so that the authors [10] supposed the latter reaction requires that the ‘closed polyhedron be opened upon attack by the ligand’. Comparison of the computed ED data for 1 and 2 shows that the introduction of the second carbon atom into the 11-vertex polyhedron causes an increase in the number of ‘nonbonded’ B atoms (10 pairs in 1 versus 8 pairs in 2) and weakening of the

B–B bonds. The latter is in accord with energy and NISC calculations [7] which point to a decrease in stability and aromaticity on going from 2 to 1. In any event, the absence of 6k–5k two-center B–B bonds in both dicarbaborane 2,3-C 2B 9H 11 and monocarbaborate [2-CB10H11]K [6] is evidenced by all the experimental and theoretical approaches used. Hence, these polyhedra, though possesing 2nC2 skeleton electrons (electron count for a closostructure), are, in essence, not deltahedra, because they do not

Fig. 3. Molecular graph of 2,3-C2B9H11 obtained as a result of the theoretical topological analysis of electron density distribution based on DFT B3LYP method. Bond critical points are denoted by small circles.

E.G. Kononova et al. / Journal of Molecular Structure 794 (2006) 148–153

incorporate triangular faces only. That is why we propose to dub them quasi-closo-polyhedra.2 Being both nonrigid and pliable, the two species studied still differ in one important respect, namely, monocarbaborate 2 is ‘fluxional’. As it is common in the relevant literature (see, e.g. [25]), by fluxionality we mean that the 11B NMR spectrum in solution is ‘averaged’. However, dicarbaborane 1 does not exhibit any fluxionality in this sense, its 11B NMR spectrum strictly corresponds to its molecular symmetry. The reason of the fluxionality of [2-CB10H11]K is the absence of the aforementioned 6k–5k two-center B–B bonds along with a low activation barrier [6]. These two factors facilitate the process of degenerate interconversion of identical isomers. This process regenerates the initial geometry and results only in permutation of boron atoms in the skeleton. Although 1 has also a pliable skeleton, its fluxionality is suppressed because in this case any cage rearrangement would lead to formation of other positional isomers, much less stable than the initial 2,3-isomer (see Williams [1] and Gimarc et al. [9]), because two carbon atoms in the latter occupy the most advantageous nonadjacent sites with lowest connectivities. Acknowledgements The authors are indebted to M. Yu. Antipin and K.A. Lyssenko for helpful discussions and acknowledge partial financial support from the Russian Academy of Sciences in the frames of the programs ‘Theoretical and experimental study of chemical bonding’ (grant # 591-07) and ‘Scientific school support’ (grant NSh-1765.2003.3) as well as from the Russian Foundation for Basic Research (project # 06-03-32172). References [1] R.E. Williams, J.W. Bausch, in: Yu.N. Bubnov (Ed.), Boron Chemistry at the Beginning of the 21st Century, Editorial URSS, Moscow, 2003, p. 3; R.E. Williams, Chem. Rev., 92 (1992) 177; R.E. Williams, in Advances in Inorganic Chemistry and Radiochemistry, 18 (1976) 67. [2] M.A. Fox, K. Wade, in: Yu.N. Bubnov (Ed.), Boron Chemistry at the Beginning of the 21st Century, Editorial URSS, Moscow, 2003, p. 17; K. Wade, in Advances in Inorganic Chemistry and Radiochemistry, 18 (1976) 44. [3] J.D. Kennedy, in: J. Casanova (Ed.), The Borane–Carborane–Carbocation Continuum, Wiley, NY, 1998, p. 85.

2

A descriptor ‘pseudocloso’ would be also appropriate but it has been already applied to a quite another case, namely, to 12-vertex metallacarbaboranes with 4-membered cicles of the MCBC type [24]).

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[4] E.I. Tolpin, W.N. Lipscomb, J. Am. Chem. Soc. 95 (1973) 2384. [5] R.J. Wiersema, M.F. Hawthorne, Inorg. Chem. 12 (1973) 785; E.L. Muetterties, E.L. Hoel, C.G. Salentine, M.F. Hawthorne, Inorg. Chem. 14 (1975) 950. [6] E.G. Kononova, L.A. Leites, S.S. Bukalov, A.V. Zabula, I.V. Pisareva, V.E. Konoplev, I.T. Chizhevsky, Chem. Phys. Letters 390 (2004) 279. [7] P. Rague von Schleyer, K. Najafian, Inorg. Chem. 37 (1998) 3454. [8] M.A. Fox, A.K. Hughes, J.M. Malget, J.Chem. Soc. Dalton Trans. (2002) 3505. [9] B.M. Gimarc, B. Dai, D.S. Warren, J.J. Ott, J. Am. Chem. Soc. 112 (1990) 2597. [10] T.E. Berry, F.N. Tebbe, M.F. Hawthorne, Tetrahedron Lett. 12 (1965) 715; F.N. Tebbe, P.M. Garrett, M.F. Hawthorne, J. Am. Chem. Soc. 90 (1968) 869. [11] F.W.E. Carrol, M. Green, F.G.A. Stone, A.J. Welch, J. Chem. Soc. Dalton Trans. (1975) 2263. [12] M.P. Garcia, M. Green, F.G.A. Stone, R.G. Somerville, A.J. Welch, C.E. Briant, D.N. Cox, D.M. Mingos, J. Chem. Soc. Dalton Trans. (1985) 2343. [13] M.J. Frisch et al., GAUSSIAN 94W, Revision E.2, Gaussian, Inc., Pittsburgh PA, 1995. [14] R.F.W. Bader, Atoms in Molecules: a Quantum Theory, Clarendon Press, Oxford, 1990, p. 438. [15] J. Cheeseman, T.A. Keith, R.W.F. Bader, AIMpac Program Package, McMaster University, Hamilton (Ontario), 1992. [16] L.A. Leites, Chem. Rev. 92 (1992) 279. [17] S.S. Bukalov, L.A. Leites, Izv. Acad. Nauk SSSR, Ser. Fis., 53 (1989) 1715; S.S. Bukalov, L.A. Leites, Proceedings of the 12th International Conference on Raman Spectroscopy, Whiley, Chichester, 1990, p. 428. [18] E.G. Kononova, S.S. Bukalov, L.A. Leites, K.A. Lyssenko, V.A. Ol’shevskaya, Russian Chem. Bull. 52 (2003) 85. [19] C.-C. Tsai, W.E. Streib, J. Am. Chem. Soc. 88 (1966) 4513. [20] M.E. Leonowicz, F.R. Scholer, Inorg. Chem. 19 (1980) 122. [21] I.D. Mackie, H.E. Robertson, D.W.H. Rankin, M.A. Fox, J.M. Malget, Inorg. Chem. 43 (2004) 5387. [22] R.F.W. Bader, D.A. Legare, Can. J. Chem. 70 (1992) 657; T.A. Keith, R.F.W. Bader, Y. Aray, Int. J. Quantum Chem. 57 (1996) 183. [23] M.Yu. Antipin, A.V. Polyakov, V.G. Tsirel’son, M. Kappkhan, V.V. Grushin, Yu.T. Struchkov, Organomet. Chem. USSR 3 (1990) 421; M. Antipin, R. Boese, D. Blaser, A. Maulitz, J. Am. Chem. Soc. 119 (1997) 326; K.A. Lyssenko, M.Yu. Antipin, V.N. Lebedev, Inorg.Chem. 37 (1998) 5834. [24] A.J. Welch, in: P. Braunstein, L.A. Oro, P.R. Raithby (Eds.), Metal Clusters in Chemistry, Wiley-VCH, Weinheim, 1999, p. 26. a review; G. Barbera, S. Dunn, M.A. Fox, R.M. Garrioch, B.E. Hodson, K.S. Low, G.M. Rosair, F. Teixidor, C. Vinas, A.J. Welch, A.S. Weller, in: M.G. Davidson, A.K. Hughes, T.B. Marder, K. Wade (Eds.), Contemporary Boron Chemistry, Royal Society of Chemistry, Cambridge, 2000, p. 329. [25] S. Herma˜nek, Chem. Rev. 92 (1992) 325.