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Experimental and theoretical study of the vibrational spectrum, structure and electron density distribution of the [2-CB10H11]− anion
Chemical Physics Letters 390 (2004) 279–284 www.elsevier.com/locate/cplett
Experimental and theoretical study of the vibrational spectrum, structure and electron density distribution of the [2-CB10H11] anion E.G. Kononova, L.A. Leites *, S.S. Bukalov, A.V. Zabula, I.V. Pisareva, V.E. Konoplev, I.T. Chizhevsky A.N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, 28 Vavilov str., Moscow 119991, Russian Federation Received 12 March 2004; in final form 9 April 2004 Available online 30 April 2004
Abstract The presence of two low-frequency large-amplitude modes in the vibrational spectrum, experimental and computed data on B–B interatomic distances and the results of a topological analysis of the electron density distribution in the molecule of an 11-vertex monocarbaborate [2-CB10 H11 ] lead to the conclusion that this polyhedron is not rigid, missing at least four double-center B–B bonds and thus being formed not only by triangular faces. Hence, this carbaborane does not have the closo-structure traditionally ascribed to it on formal [2n+2]-electron count grounds. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction Vibrational spectra of polyhedral closo-boranes Bn X2 n (n ¼ 12; 10) and dicarba-closo-boranes C2 Bn2 Hn (n ¼ 12; 10; 6; 5) were studied previously in detail (see review [1] and references therein). Recently, analogous data for a monocarba-closo-borate [CB11 H12 ] have been reported [2]. It is important that none of the numerous unsubstituted closo-boranes and closo-carbaboranes studied exhibited normal modes with frequencies lower than 450 cm1 , thus pointing to the rigidity of the polyhedra. Cage rigidity allowed treatment of the closo-carbaboranyl moiety as a pseudoatom, ‘Cb’, and this model worked well for interpretation of the vibrational spectra of bis(carboranyl) Cb–Cb and mono-substituted Cb–X molecules [1]. It was of interest to conduct similar studies for the 11vertex anion [2-CB10 H11 ] 1 (Fig. 1), described in [3].
*
Corresponding author. Fax: +95-135-5085. E-mail address: [email protected] (L.A. Leites).
0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.04.025
The 24-electron 11-vertex borane and carbaborane polyhedra are also regarded as true closo-deltahedra, i.e., as exclusively triangular-faced structures [4–6]; however, they differ from the others in some respects. Kennedy assigned them to ‘disobedient skeletons’ [7], which ‘are recognized to be fragile’ [8]. They incorporate cage atoms characterized by three different coordination numbers (k ¼ 4, 5, 6). Williams [4,5] who paid much attention to the properties of various isomers of the 11-vertex carbaboranes proposed that this polyhedron be viewed as a decaborane-shaped fragment, resembling a boat or canoe, ‘capped’ by a 6k vertex. Since carbon atoms prefer to occupy the lowest connectivity sites [4], the only carbon atom in 1 occupies the 4k position 2. Anion 1 stands out against other large carbaboranes because of its ‘averaged’ 11 B NMR spectrum [9,10], which exhibits only three doublets in the ratio 4:5:1, and because of its unusual chemical properties [11]. All these peculiarities should be reflected also in the vibrational spectrum. That is why we have studied the previously unreported Raman and IR spectra of the cesium and tetramethylammonium salts of 1. Quantumchemical calculations (using the density functional
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3. Results 3.1. Vibrational spectra The undistorted anion 1 belongs to the Cs point symmetry group; its 60 normal modes are distributed among the symmetry species as follows: C ¼ 33A0 þ 27A00 :
Fig. 1. Traditional {2-CB10 } closo-cluster depiction with atom numbering.
approach) of the geometry of an undistorted anion 1 and its vibrational mode frequencies and eigenvectors were also performed. On this basis, the electron density distribution (EDD) in 1 was reconstructed using Bader’s theory of atoms in molecules [12].
2. Experimental Samples of Csþ [CB10 H11 ] and NMeþ 4 [CB10 H11 ] were synthesized by a slightly modified procedure [3]. Raman spectra were recorded for the solid salts and for a saturated aqueous solution of the cesium salt using a T64000 and a U-1000 Jobin-Yvon laser Raman spectrometers with 514.5 nm excitation (an Arþ laser Spectra Physics 2020). Depolarization ratios of the Raman lines in the spectrum of the aqueous solution were qualitatively estimated. IR spectra were obtained for KBr pellets, as well as hexachlorobutadiene and nujol mulls on a Carl Zeiss M-82 spectrophotometer and a Nicolet Magna-750 FTIR spectrometer. Geometry optimization and calculations of vibrational mode frequencies and eigenvectors were carried out at the DFT B3LYP/6-311++G(d,p) level, using the G94W program suite [13]. Topological analysis of the theoretical (based on the results of the DFT calculation) EDD was accomplished using the AI M P A C program package [14].
All the vibrations are to be active both in the Raman and IR spectra. The spectra of the solid cesium salt of anion 1 are presented in Fig. 2. The normal mode assignment to the symmetry species and to particular molecular vibrations was based on the experimental data on the vibrational mode activities, depolarization ratios of the Raman lines, and on the results of the DFT calculation of the normal mode frequencies and eigenvectors. The most striking feature in the spectra of both salts of [2-CB10 H11 ] is the presence of two low-frequency modes (245 and 283 cm1 for the tetramethylammonium salt and 262 and 307 cm1 for the cesium salt). The results of normal coordinate analysis for the ‘free’ anion reproduce these low-frequency modes but with somewhat lower frequencies (227 and 261 cm1 ) as if ‘disencumbered’ of cation influence. According to this calculation, the first mode is a vibration antisymmetric with respect to the mirror plane with the participation of four boron atoms B(4, 5, 6, 7) while the B(1) atom is fixed. By contrast, the second mode involves mainly a B(1) atom displacement. The presence of the low-frequency modes in the spectra of both these salts as well as in the spectrum of a neutral dicarbaborane 2,3-C2 B9 H11 [15] clearly distinguishes these 11-vertex carbaboranes from other closo clusters [1] and points to non-rigidity of some elements in their structure. The well-localized mCH vibration of 1 exhibits a 3075 cm1 frequency which is slightly higher compared to that of the 12-vertex monocarbaborane [2]. The Raman intensity of this mode is very high while its IR intensity is extremely weak, which reflects the high electron density and low polarity of this bond and is in a good agreement with the EDD data (see below). In the broad spectral feature corresponding to the mBH stretching vibrations, the peaks with higher frequencies (2560–2585 cm1 ) characteristic for closocarbaboranes and with lower ones (2475 cm1 ) comparable with the mBH frequencies of nido-structures [1,2,16] are present. 3.2. Geometry of anion 1 The results of the geometry optimization for the isolated anion 1 are given in Table 1. For several variously substituted salts and zwitter-ions of anion 1, the X-ray data are available [10,17,18]. Some experimental
E.G. Kononova et al. / Chemical Physics Letters 390 (2004) 279–284
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Fig. 2. The Raman and IR spectra of the solid salt Csþ [2-CB10 H11 ] . (a) IR spectrum of a KBr pellet. (b) IR spectrum of a nujol mull.
Table 1 Characteristics of interatomic distances inside the polyhedron {2-CB10 } Pairs of cage atoms
C(2)–B(1) C(2)–B(4) ¼ C(2)–B(5) C(2)–B(8) B(1)–B(4) ¼ B(1)–B(5) B(4)–B(8) ¼ B(5)–B(8) B(1)–B(3) B(1)–B(6) ¼ B(1)–B(7) B(4)–B(7) ¼ B(5)–B(6) B(4)–B(10) ¼ B(5)–B(11) B(8)–B(10) ¼ B(8)–B(11) B(3)–B(6) ¼ B(3)–B(7) B(6)–B(11) ¼ B(7)–B(10) B(10)–B(11) B(3)–B(9) B(6)–B(9) ¼ B(7)–B(9) B(9)–B(10) ¼ B(9)–B(11) a b
Interatomic distances, A a
a
Calculated for 1
Exp. for 2 [17]
Exp. for 3 [10]
1.637 1.575 1.671 2.048 1.793 1.735 2.032 1.858 1.769 1.778 1.669 1.786 1.839 1.752 1.784 1.784
1.641 1.609, 1.682 1.938, 1.791 1.704 2.110, 1.833, 1.781, 1.780, 1.611, 1.743, 1.795 1.731 1.755, 1.740,
1.643 1.584, 1.593b 1.676 2.057, 2.043b
1.575b 2.070b
1.950b 1.825b 1.762b 1.763b 1.679b 1.782b
1.808b 1.738b
1.711 2.023, 1.849, 1.789, 1.781, 1.638, 1.792, 1.817 1.748
2.015b 1.826b 1.775b 1.783b 1.667b 1.816b
1.776, 1.789b
Presence of the (3, )1) bond critical point
qb (r)
+ + + ) ) + ) ) + + + + + + + +
0.137 0.156 0.127
0.116
0.120 0.120 0.141 0.116 0.107 0.120 0.117 0.117
2 – [Cp2 Co]þ [2-(Me3 Si)2 CH-closo-2-CB10 H10 ] , 3 – [Et4 N]þ [2-Ph-closo-2-CB10 H10 ] . Two interatomic distances, equivalent for [2-CB10 H11 ] , become non-equivalent in 2 and 3 due to substitution.
interatomic distances for the simplest 2-substituted compounds, namely, [Cp2 Co]þ [2-(Me3 Si)2 CH-closo-2CB10 H10 ] (2) and [Et4 N]þ [2-Ph-closo-2-CB10 H10 ] (3) are also presented in Table 1 for comparison. The agreement between the experimental and calculated values is very good. It is noteworthy that the rB–B distances between 6k B(1) and 5k B(4, 5, 6, 7) atoms are anomalously long for a B–B (Fig. 1), 2.03–2.05 A,
bond. However, the authors [10,17,18] did not comment on this fact. 3.3. Theoretical topological analysis of electron density distribution As has been well-known since the 1960s [19], closopolyhedral boranes and carbaboranes are representatives
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of electron-deficient systems which involve multicenter bonding. Topological analysis of the q(r), electron density, was first applied to this class of compounds by Bader [12, p. 405] with further studies by Bader et al. [20,21] and Antipin et al. [22–24]. Such analyses have lead to the conclusion that ED is essentially delocalized over the whole surface of the polyhedron. Together with conventional localized two-center bonds to which critical points qb (r) of the type the (3, )1) correspond, multicenter bonding in the triangle faces also takes place which manifests itself by ring critical points qr (r) of (3, +1) type. It is important that the obtained ED values at the (3, )1) bond and (3, +1) ring critical points appeared mostly of comparable magnitude. Rather high values of bond ellipticity and significant bond bending were also found as topological characteristics of the cage structures studied. The results of the EDD determination for the anion 1 in the ground state (based on the theoretical DFT calculations) confirm strong delocalization over the polyhedral surface and the essential role of multicenter bonding in the stabilization of 1, noted earlier for other carbaboranes [20–24]. The values of qb (r) on exo-polyhedral C–H and B–H bonds are 0.279 and 0.176–0.172, respectively. The qb (r) values of the cage C–B bonds lie in the interval 0.156–0.127 and those of B–B bonds in the interval 0.141–0.107, only slightly above the values for (3, +1) critical points for the 3-membered rings (0.111– 0.105). Ellipticities of the cage bonds are also rather high. The deviations of the critical points (3, )1) from the bond straight lines are not significant, except for the B(6)–B(9) and B(7)–B(9) bonds for which the bond path is 0.173 ? longer than the interatomic distances. However, some EDD features of 1 strongly differentiate this polyhedron from other closo-structures. The most important are the absence of the bond critical points (3, )1) between the following pairs of boron atoms (Table 1):
rings are characterized by a notable decrease in qr (r) (0.068). The molecular graph based on EDD calculations is presented in Fig. 3. Topological analysis of the EDD of the transition state (one imaginary frequency) showed that connectivity is broken between the following pairs of atoms: Bð5Þ–Bð8Þ ¼ Bð4Þ–Bð8Þ; Bð1Þ–Bð5Þ ¼ Bð1Þ–Bð4Þ; Bð4Þ–Bð7Þ; Bð1Þ–Bð6Þ and as a result the 4-membered [C(2)B(8)B(11)B(5)], [C(2)B(8)B(10)B(4)], [C(2)B(5)B(1)B(6)] and 7-membered [C(2)B(4)B(10)B(7)B(3)B(6)B(1)] faces are formed. The calculated activation barrier (including a ZPE correction) is only 3 kcal mol1 . These rather unexpected results obtained for the EDD in anion 1 prompted us to make a similar computation for the 12-vertex closo-monocarbaborate [CB11 H12 ] which exhibits anomalies neither in the vibrational nor in the NMR spectra, nor in the interatomic distances [2]. The EDD results obtained show that all the edges of this polyhedron correspond to two-center bonds; the qb (r) values for the exo C–H and B–H bonds lie in the range 0.282–0.174 and for the cage C–B and B–B bonds in the range 0.122–0.117, respectively. The qr (r) values in the ring (3, +1) critical points are slightly lower than those of qb (r) in the (3, )1) critical points, and are almost equal
Bð1Þ–Bð4Þ ¼ Bð1Þ–Bð5Þ; Bð1Þ–Bð6Þ ¼ Bð1Þ–Bð7Þ; Bð4Þ–Bð7Þ ¼ Bð5Þ–Bð6Þ; Bð4Þ–Bð8Þ ¼ Bð5Þ–Bð8Þ and an uneven distribution of electron density over the polyhedron surface. According to this calculation, 8 of the 27 edges of the {2-CB10 } polyhedron do not correspond to doublecenter bonds. If the atoms indicated above are not linked by two-center bonds, then 1 incorporates not only 3-membered rings but also 4-membered [C(2)B(4)B(10)B(8)], [C(2)B(5)B(11)B(8)] and 6-membered ones [C(2)B(1)B(3)B(7)B(10)B(4)], [C(2)B(1)B(3)B(6)B(11)B(5)]. The qr (r) values in the (3, +1) critical points of the 4-membered rings do not differ significantly from those for the 3-membered rings; however, the 6-membered
Fig. 3. Molecular graph of the [2-CB10 H11 ] polyhedron, according to the topological analysis of electron density distribution. Small circles correspond to the bond critical points.
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for all its triangular faces (0.114–0.110), Thus, unlike 1, the polyhedron {CB11 } shows rather even distribution of the electron density over its surface, as is expected for a genuine closo-species.
4. Discussion While discussing interatomic distances, it is pertinent to remember Wade’s empirical relation between a B–B interatomic distance in an n-vertex polyhedron and the coordination numbers of the corresponding boron atoms [25]. Using this relation that takes into consideration the formal bond order, Wade predicted in 1976 the following differences in the interatomic rB–B distances for the anion [B11 H11 ]2 : rB4 –B5 ¼ 1:70 A; rB4 –B6 ¼ 1:78 A; rB5 –B5 ¼ 1:79 A; rB5 –B6 ¼ 1:95 A (the upper index refers to the coordination number of a B atom). The data in Table 1 demonstrate that introduction of a carbon atom into the 11-vertex polyhedron does not change the tendency successfully predicted by Wade; his values are in rather good agreement with the experimental and calculated data obtained for 1 for all but the rB5 –B6 distances. According to [25], this distance However, the experimenis to be elongated to 1.95 A. tally observed and DFT-calculated interatomic distances between 6k B(1) and 5k B(4, 5, 6, 7) atoms in 1 values notably exceed this value and reach 2.02–2.07 A, anomalously large for a B–B bond, indicating their extremely low (if any) bond order. The absence of these four bonds agrees well with the EDD results that point to the absence of (3, )1) critical points on the lines connecting these pairs of B atoms. It is noticeable that in 1982 Jemmis [26] noted the absence among carbaboranes of molecules based on six-membered rings. In the frame of his ‘caps and rings’ concept, the orbitals of a BH cap are not diffuse enough to overlap favourably with the orbitals of a sixmembered ring. Our results for anion 1 support this idea. It should be mentioned that the EDD data point to the absence of the (3, )1) critical points not only for the four B–B bonds mentioned above but also for B(4)– B(7) ¼ B(5)–B(6) and B(4)–B(8) ¼ B(5)–B(8) bonds involving 5k atoms. If so, then two six-membered faces would arise which are characterized by a notable decrease in qr (r) (0.068). However, the corresponding experimental and computed interatomic distances for the latter bonds have normal values (Table 1). The reason of this contradiction needs close scrutiny.
283
Anyway, the absence of the four double-center 5k– 6k B-B bonds is supported by both experimental and theoretical data. In this case the two five-membered ‘open faces’ [B(1)C(2)B(5)B(6)B(3)] and [B(1)C(2)B(4) B(7)B(3)] are formed in 1 with significantly weakened multicenter bonding in the rings. This readily explains the non-rigidity of the polyhedron manifested by the presence of the two low-frequency vibrational modes, unusual for closo-clusters. Computer animation shows that the 290 cm1 bending mode is a large-amplitude vibration of the B(1) atom in the CB(1)B(3) ‘handle’ with respect to the mirror plane, eased by the absence of the aforementioned 5k–6k B–B bonds. The same is true of the 250 cm1 mode, which also includes displacements of more ‘free’ atoms, this time B(4, 5, 6, 7). These structural peculiarities can explain the unique oxidative insertion of the zerovalent Ni, Pd and Pt species into polyhedron 1, resulting in the formation of a 12-vertex metallamonocarbaborane, found by Carrol et al. [11]. It is of interest that the authors [11] described this reaction in terms of attack of a metal atom just ‘on one of the B(1)C(2)B(3)BB ‘open faces’ of the closo-2-R2-CB10 H10 octadecahedron’. The non-rigidity of 1 along with its low activation barrier (3 kcal/mol) are obviously the reasons for the fluxionality of 1 as manifested by its ‘averaged’ 11 B NMR spectrum [9,10]. Quite similar vibrational and EDD results obtained for another representative of the 11-vertex polyhedra – a neutral molecule 2,3-C2 B9 H11 – will be published soon [15].
5. Conclusions All the experimental and theoretical results presented in this work as well as those to be published are in good agreement and unambiguously indicate that the electron density in the 11-vertex anion [2-CB10 H11 ] and molecule 2,3-C2 B9 H11 is distributed over the polyhedral surface unevenly; these polyhedra are not rigid and are formed not only by triangular faces typical for deltahedra, hence they cannot be regarded as genuine closo-carbaboranes, although they have (n + 1) valence electron pairs for the skeleton bonding. We propose to name such cages quasicloso-polyhedra.
Acknowledgements The authors are indebted to M.Yu. Antipin and K.A. Lyssenko for helpful discussions and acknowledge 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
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‘Scientific school support’ (Grant NSh-1765.2003.3) as well as from the Russian Foundation for Basic Research (Project # 03-03-32651). References [1] L.A. Leites, Chem. Rev. 92 (1992) 279. [2] G. Kononova, S.S. Bukalov, L.A. Leites, K.A. Lyssenko, V.A. Ol’shevskaya, Russian Chem. Bull. 52 (2003) 85. [3] W. Quintana, L.G. Sneddon, Inorg. Chem. 29 (1990) 3242. [4] 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. [5] R.E. Williams, Chem. Rev. 92 (1992) 177. [6] 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. [7] J.D. Kennedy, in: J. Casanova (Ed.), The Borane–Carborane– Carbocation Continuum, Wiley, New York, 1988, p. 85. [8] M. Bown, B. Gr€ uner, B. Stibr, X.L.R. Fontaine, M. Thornton-Pett, J.D. Kennedy, J. Organomet. Chem. 614–615 (2000) 269. [9] R.J. Wiersema, M.F. Hawthorne, Inorg. Chem. 12 (1973) 785. [10] A. Franken, C.A. Kilner, M. Thornton-Pett, J.D. Kennedy, J. Organomet. Chem. 657 (2002) 180. [11] W.E. Carrol, M. Green, F.G.A. Stone, A.J. Welch, J. Chem. Soc. Dalton (1975) 2263.
[12] R.F.W. Bader, Atoms in Molecules: A Quantum Theory, Clarendon Press, Oxford, UK, 1990, 438 pp. [13] GA U S S I A N 94W, Revision E.2, M.J. Frisch et al., Gaussian, Inc., Pittsburgh PA, 1995. [14] J. Cheeseman, T.A. Keith, R.W.F. Bader, AI M P A C Program Package, McMaster University, Hamiltin (Ontario), 1992. [15] E.G. Kononova, S.S. Bukalov, L.A. Leites, I.V. Pisareva, I.T. Chizhevsky (to be published). [16] L.A. Leites, S.S. Bukalov, L.E. Vinogradova, S.P. Knyazev, Yu.A. Strelenko, Bull. Acad. Sci. USSR, Div. Chem. Sci. 35 (1986) 1633. [17] R.L. Ernest, W. Quintana, R. Rosen, P.J. Caroll, L.G. Sneddon, Organometallics 6 (1987) 80. [18] B. Stibr, Chem. Rev. 92 (1992) 225. [19] See R.N. Grimes, Carboranes, Academic Press, NY, London, 1970, 260 pp and references therein. [20] R.F.W. Bader, D.A. Legare, Can. J. Chem. 70 (1992) 657. [21] T.A. Keith, R.F.W. Bader, Y. Aray, Int. J. Quantum Chem. 57 (1996) 183. [22] M.Yu. Antipin, A.V. Polyakov, V.G. Tsirel’son, M. Kappkhan, V.V. Grushin, Yu.T. Struchkov, Organomet. Chem. USSR 3 (1990) 421. [23] M. Antipin, R. Boese, D. Blaser, A. Maulitz, J. Am. Chem. Soc. 119 (1997) 326. [24] K.A. Lyssenko, M.Yu. Antipin, V.N. Lebedev, Inorg. Chem. 37 (1998) 5834. [25] K. Wade, Structural and Bonding Patterns in Cluster Chemistry, in Advances in: Inorganic Chemistry and Radiochemistry 18 (1976) p. 44. [26] E.D. Jemmis, J. Am. Chem. Soc. 104 (1982) 7017.
Experimental and theoretical study of the vibrational spectrum, structure and electron density distribution of the [2-CB10H11] anion E.G. Kononova, L.A. Leites *, S.S. Bukalov, A.V. Zabula, I.V. Pisareva, V.E. Konoplev, I.T. Chizhevsky A.N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, 28 Vavilov str., Moscow 119991, Russian Federation Received 12 March 2004; in final form 9 April 2004 Available online 30 April 2004
Abstract The presence of two low-frequency large-amplitude modes in the vibrational spectrum, experimental and computed data on B–B interatomic distances and the results of a topological analysis of the electron density distribution in the molecule of an 11-vertex monocarbaborate [2-CB10 H11 ] lead to the conclusion that this polyhedron is not rigid, missing at least four double-center B–B bonds and thus being formed not only by triangular faces. Hence, this carbaborane does not have the closo-structure traditionally ascribed to it on formal [2n+2]-electron count grounds. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction Vibrational spectra of polyhedral closo-boranes Bn X2 n (n ¼ 12; 10) and dicarba-closo-boranes C2 Bn2 Hn (n ¼ 12; 10; 6; 5) were studied previously in detail (see review [1] and references therein). Recently, analogous data for a monocarba-closo-borate [CB11 H12 ] have been reported [2]. It is important that none of the numerous unsubstituted closo-boranes and closo-carbaboranes studied exhibited normal modes with frequencies lower than 450 cm1 , thus pointing to the rigidity of the polyhedra. Cage rigidity allowed treatment of the closo-carbaboranyl moiety as a pseudoatom, ‘Cb’, and this model worked well for interpretation of the vibrational spectra of bis(carboranyl) Cb–Cb and mono-substituted Cb–X molecules [1]. It was of interest to conduct similar studies for the 11vertex anion [2-CB10 H11 ] 1 (Fig. 1), described in [3].
*
Corresponding author. Fax: +95-135-5085. E-mail address: [email protected] (L.A. Leites).
0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.04.025
The 24-electron 11-vertex borane and carbaborane polyhedra are also regarded as true closo-deltahedra, i.e., as exclusively triangular-faced structures [4–6]; however, they differ from the others in some respects. Kennedy assigned them to ‘disobedient skeletons’ [7], which ‘are recognized to be fragile’ [8]. They incorporate cage atoms characterized by three different coordination numbers (k ¼ 4, 5, 6). Williams [4,5] who paid much attention to the properties of various isomers of the 11-vertex carbaboranes proposed that this polyhedron be viewed as a decaborane-shaped fragment, resembling a boat or canoe, ‘capped’ by a 6k vertex. Since carbon atoms prefer to occupy the lowest connectivity sites [4], the only carbon atom in 1 occupies the 4k position 2. Anion 1 stands out against other large carbaboranes because of its ‘averaged’ 11 B NMR spectrum [9,10], which exhibits only three doublets in the ratio 4:5:1, and because of its unusual chemical properties [11]. All these peculiarities should be reflected also in the vibrational spectrum. That is why we have studied the previously unreported Raman and IR spectra of the cesium and tetramethylammonium salts of 1. Quantumchemical calculations (using the density functional
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3. Results 3.1. Vibrational spectra The undistorted anion 1 belongs to the Cs point symmetry group; its 60 normal modes are distributed among the symmetry species as follows: C ¼ 33A0 þ 27A00 :
Fig. 1. Traditional {2-CB10 } closo-cluster depiction with atom numbering.
approach) of the geometry of an undistorted anion 1 and its vibrational mode frequencies and eigenvectors were also performed. On this basis, the electron density distribution (EDD) in 1 was reconstructed using Bader’s theory of atoms in molecules [12].
2. Experimental Samples of Csþ [CB10 H11 ] and NMeþ 4 [CB10 H11 ] were synthesized by a slightly modified procedure [3]. Raman spectra were recorded for the solid salts and for a saturated aqueous solution of the cesium salt using a T64000 and a U-1000 Jobin-Yvon laser Raman spectrometers with 514.5 nm excitation (an Arþ laser Spectra Physics 2020). Depolarization ratios of the Raman lines in the spectrum of the aqueous solution were qualitatively estimated. IR spectra were obtained for KBr pellets, as well as hexachlorobutadiene and nujol mulls on a Carl Zeiss M-82 spectrophotometer and a Nicolet Magna-750 FTIR spectrometer. Geometry optimization and calculations of vibrational mode frequencies and eigenvectors were carried out at the DFT B3LYP/6-311++G(d,p) level, using the G94W program suite [13]. Topological analysis of the theoretical (based on the results of the DFT calculation) EDD was accomplished using the AI M P A C program package [14].
All the vibrations are to be active both in the Raman and IR spectra. The spectra of the solid cesium salt of anion 1 are presented in Fig. 2. The normal mode assignment to the symmetry species and to particular molecular vibrations was based on the experimental data on the vibrational mode activities, depolarization ratios of the Raman lines, and on the results of the DFT calculation of the normal mode frequencies and eigenvectors. The most striking feature in the spectra of both salts of [2-CB10 H11 ] is the presence of two low-frequency modes (245 and 283 cm1 for the tetramethylammonium salt and 262 and 307 cm1 for the cesium salt). The results of normal coordinate analysis for the ‘free’ anion reproduce these low-frequency modes but with somewhat lower frequencies (227 and 261 cm1 ) as if ‘disencumbered’ of cation influence. According to this calculation, the first mode is a vibration antisymmetric with respect to the mirror plane with the participation of four boron atoms B(4, 5, 6, 7) while the B(1) atom is fixed. By contrast, the second mode involves mainly a B(1) atom displacement. The presence of the low-frequency modes in the spectra of both these salts as well as in the spectrum of a neutral dicarbaborane 2,3-C2 B9 H11 [15] clearly distinguishes these 11-vertex carbaboranes from other closo clusters [1] and points to non-rigidity of some elements in their structure. The well-localized mCH vibration of 1 exhibits a 3075 cm1 frequency which is slightly higher compared to that of the 12-vertex monocarbaborane [2]. The Raman intensity of this mode is very high while its IR intensity is extremely weak, which reflects the high electron density and low polarity of this bond and is in a good agreement with the EDD data (see below). In the broad spectral feature corresponding to the mBH stretching vibrations, the peaks with higher frequencies (2560–2585 cm1 ) characteristic for closocarbaboranes and with lower ones (2475 cm1 ) comparable with the mBH frequencies of nido-structures [1,2,16] are present. 3.2. Geometry of anion 1 The results of the geometry optimization for the isolated anion 1 are given in Table 1. For several variously substituted salts and zwitter-ions of anion 1, the X-ray data are available [10,17,18]. Some experimental
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Fig. 2. The Raman and IR spectra of the solid salt Csþ [2-CB10 H11 ] . (a) IR spectrum of a KBr pellet. (b) IR spectrum of a nujol mull.
Table 1 Characteristics of interatomic distances inside the polyhedron {2-CB10 } Pairs of cage atoms
C(2)–B(1) C(2)–B(4) ¼ C(2)–B(5) C(2)–B(8) B(1)–B(4) ¼ B(1)–B(5) B(4)–B(8) ¼ B(5)–B(8) B(1)–B(3) B(1)–B(6) ¼ B(1)–B(7) B(4)–B(7) ¼ B(5)–B(6) B(4)–B(10) ¼ B(5)–B(11) B(8)–B(10) ¼ B(8)–B(11) B(3)–B(6) ¼ B(3)–B(7) B(6)–B(11) ¼ B(7)–B(10) B(10)–B(11) B(3)–B(9) B(6)–B(9) ¼ B(7)–B(9) B(9)–B(10) ¼ B(9)–B(11) a b
Interatomic distances, A a
a
Calculated for 1
Exp. for 2 [17]
Exp. for 3 [10]
1.637 1.575 1.671 2.048 1.793 1.735 2.032 1.858 1.769 1.778 1.669 1.786 1.839 1.752 1.784 1.784
1.641 1.609, 1.682 1.938, 1.791 1.704 2.110, 1.833, 1.781, 1.780, 1.611, 1.743, 1.795 1.731 1.755, 1.740,
1.643 1.584, 1.593b 1.676 2.057, 2.043b
1.575b 2.070b
1.950b 1.825b 1.762b 1.763b 1.679b 1.782b
1.808b 1.738b
1.711 2.023, 1.849, 1.789, 1.781, 1.638, 1.792, 1.817 1.748
2.015b 1.826b 1.775b 1.783b 1.667b 1.816b
1.776, 1.789b
Presence of the (3, )1) bond critical point
qb (r)
+ + + ) ) + ) ) + + + + + + + +
0.137 0.156 0.127
0.116
0.120 0.120 0.141 0.116 0.107 0.120 0.117 0.117
2 – [Cp2 Co]þ [2-(Me3 Si)2 CH-closo-2-CB10 H10 ] , 3 – [Et4 N]þ [2-Ph-closo-2-CB10 H10 ] . Two interatomic distances, equivalent for [2-CB10 H11 ] , become non-equivalent in 2 and 3 due to substitution.
interatomic distances for the simplest 2-substituted compounds, namely, [Cp2 Co]þ [2-(Me3 Si)2 CH-closo-2CB10 H10 ] (2) and [Et4 N]þ [2-Ph-closo-2-CB10 H10 ] (3) are also presented in Table 1 for comparison. The agreement between the experimental and calculated values is very good. It is noteworthy that the rB–B distances between 6k B(1) and 5k B(4, 5, 6, 7) atoms are anomalously long for a B–B (Fig. 1), 2.03–2.05 A,
bond. However, the authors [10,17,18] did not comment on this fact. 3.3. Theoretical topological analysis of electron density distribution As has been well-known since the 1960s [19], closopolyhedral boranes and carbaboranes are representatives
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of electron-deficient systems which involve multicenter bonding. Topological analysis of the q(r), electron density, was first applied to this class of compounds by Bader [12, p. 405] with further studies by Bader et al. [20,21] and Antipin et al. [22–24]. Such analyses have lead to the conclusion that ED is essentially delocalized over the whole surface of the polyhedron. Together with conventional localized two-center bonds to which critical points qb (r) of the type the (3, )1) correspond, multicenter bonding in the triangle faces also takes place which manifests itself by ring critical points qr (r) of (3, +1) type. It is important that the obtained ED values at the (3, )1) bond and (3, +1) ring critical points appeared mostly of comparable magnitude. Rather high values of bond ellipticity and significant bond bending were also found as topological characteristics of the cage structures studied. The results of the EDD determination for the anion 1 in the ground state (based on the theoretical DFT calculations) confirm strong delocalization over the polyhedral surface and the essential role of multicenter bonding in the stabilization of 1, noted earlier for other carbaboranes [20–24]. The values of qb (r) on exo-polyhedral C–H and B–H bonds are 0.279 and 0.176–0.172, respectively. The qb (r) values of the cage C–B bonds lie in the interval 0.156–0.127 and those of B–B bonds in the interval 0.141–0.107, only slightly above the values for (3, +1) critical points for the 3-membered rings (0.111– 0.105). Ellipticities of the cage bonds are also rather high. The deviations of the critical points (3, )1) from the bond straight lines are not significant, except for the B(6)–B(9) and B(7)–B(9) bonds for which the bond path is 0.173 ? longer than the interatomic distances. However, some EDD features of 1 strongly differentiate this polyhedron from other closo-structures. The most important are the absence of the bond critical points (3, )1) between the following pairs of boron atoms (Table 1):
rings are characterized by a notable decrease in qr (r) (0.068). The molecular graph based on EDD calculations is presented in Fig. 3. Topological analysis of the EDD of the transition state (one imaginary frequency) showed that connectivity is broken between the following pairs of atoms: Bð5Þ–Bð8Þ ¼ Bð4Þ–Bð8Þ; Bð1Þ–Bð5Þ ¼ Bð1Þ–Bð4Þ; Bð4Þ–Bð7Þ; Bð1Þ–Bð6Þ and as a result the 4-membered [C(2)B(8)B(11)B(5)], [C(2)B(8)B(10)B(4)], [C(2)B(5)B(1)B(6)] and 7-membered [C(2)B(4)B(10)B(7)B(3)B(6)B(1)] faces are formed. The calculated activation barrier (including a ZPE correction) is only 3 kcal mol1 . These rather unexpected results obtained for the EDD in anion 1 prompted us to make a similar computation for the 12-vertex closo-monocarbaborate [CB11 H12 ] which exhibits anomalies neither in the vibrational nor in the NMR spectra, nor in the interatomic distances [2]. The EDD results obtained show that all the edges of this polyhedron correspond to two-center bonds; the qb (r) values for the exo C–H and B–H bonds lie in the range 0.282–0.174 and for the cage C–B and B–B bonds in the range 0.122–0.117, respectively. The qr (r) values in the ring (3, +1) critical points are slightly lower than those of qb (r) in the (3, )1) critical points, and are almost equal
Bð1Þ–Bð4Þ ¼ Bð1Þ–Bð5Þ; Bð1Þ–Bð6Þ ¼ Bð1Þ–Bð7Þ; Bð4Þ–Bð7Þ ¼ Bð5Þ–Bð6Þ; Bð4Þ–Bð8Þ ¼ Bð5Þ–Bð8Þ and an uneven distribution of electron density over the polyhedron surface. According to this calculation, 8 of the 27 edges of the {2-CB10 } polyhedron do not correspond to doublecenter bonds. If the atoms indicated above are not linked by two-center bonds, then 1 incorporates not only 3-membered rings but also 4-membered [C(2)B(4)B(10)B(8)], [C(2)B(5)B(11)B(8)] and 6-membered ones [C(2)B(1)B(3)B(7)B(10)B(4)], [C(2)B(1)B(3)B(6)B(11)B(5)]. The qr (r) values in the (3, +1) critical points of the 4-membered rings do not differ significantly from those for the 3-membered rings; however, the 6-membered
Fig. 3. Molecular graph of the [2-CB10 H11 ] polyhedron, according to the topological analysis of electron density distribution. Small circles correspond to the bond critical points.
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for all its triangular faces (0.114–0.110), Thus, unlike 1, the polyhedron {CB11 } shows rather even distribution of the electron density over its surface, as is expected for a genuine closo-species.
4. Discussion While discussing interatomic distances, it is pertinent to remember Wade’s empirical relation between a B–B interatomic distance in an n-vertex polyhedron and the coordination numbers of the corresponding boron atoms [25]. Using this relation that takes into consideration the formal bond order, Wade predicted in 1976 the following differences in the interatomic rB–B distances for the anion [B11 H11 ]2 : rB4 –B5 ¼ 1:70 A; rB4 –B6 ¼ 1:78 A; rB5 –B5 ¼ 1:79 A; rB5 –B6 ¼ 1:95 A (the upper index refers to the coordination number of a B atom). The data in Table 1 demonstrate that introduction of a carbon atom into the 11-vertex polyhedron does not change the tendency successfully predicted by Wade; his values are in rather good agreement with the experimental and calculated data obtained for 1 for all but the rB5 –B6 distances. According to [25], this distance However, the experimenis to be elongated to 1.95 A. tally observed and DFT-calculated interatomic distances between 6k B(1) and 5k B(4, 5, 6, 7) atoms in 1 values notably exceed this value and reach 2.02–2.07 A, anomalously large for a B–B bond, indicating their extremely low (if any) bond order. The absence of these four bonds agrees well with the EDD results that point to the absence of (3, )1) critical points on the lines connecting these pairs of B atoms. It is noticeable that in 1982 Jemmis [26] noted the absence among carbaboranes of molecules based on six-membered rings. In the frame of his ‘caps and rings’ concept, the orbitals of a BH cap are not diffuse enough to overlap favourably with the orbitals of a sixmembered ring. Our results for anion 1 support this idea. It should be mentioned that the EDD data point to the absence of the (3, )1) critical points not only for the four B–B bonds mentioned above but also for B(4)– B(7) ¼ B(5)–B(6) and B(4)–B(8) ¼ B(5)–B(8) bonds involving 5k atoms. If so, then two six-membered faces would arise which are characterized by a notable decrease in qr (r) (0.068). However, the corresponding experimental and computed interatomic distances for the latter bonds have normal values (Table 1). The reason of this contradiction needs close scrutiny.
283
Anyway, the absence of the four double-center 5k– 6k B-B bonds is supported by both experimental and theoretical data. In this case the two five-membered ‘open faces’ [B(1)C(2)B(5)B(6)B(3)] and [B(1)C(2)B(4) B(7)B(3)] are formed in 1 with significantly weakened multicenter bonding in the rings. This readily explains the non-rigidity of the polyhedron manifested by the presence of the two low-frequency vibrational modes, unusual for closo-clusters. Computer animation shows that the 290 cm1 bending mode is a large-amplitude vibration of the B(1) atom in the CB(1)B(3) ‘handle’ with respect to the mirror plane, eased by the absence of the aforementioned 5k–6k B–B bonds. The same is true of the 250 cm1 mode, which also includes displacements of more ‘free’ atoms, this time B(4, 5, 6, 7). These structural peculiarities can explain the unique oxidative insertion of the zerovalent Ni, Pd and Pt species into polyhedron 1, resulting in the formation of a 12-vertex metallamonocarbaborane, found by Carrol et al. [11]. It is of interest that the authors [11] described this reaction in terms of attack of a metal atom just ‘on one of the B(1)C(2)B(3)BB ‘open faces’ of the closo-2-R2-CB10 H10 octadecahedron’. The non-rigidity of 1 along with its low activation barrier (3 kcal/mol) are obviously the reasons for the fluxionality of 1 as manifested by its ‘averaged’ 11 B NMR spectrum [9,10]. Quite similar vibrational and EDD results obtained for another representative of the 11-vertex polyhedra – a neutral molecule 2,3-C2 B9 H11 – will be published soon [15].
5. Conclusions All the experimental and theoretical results presented in this work as well as those to be published are in good agreement and unambiguously indicate that the electron density in the 11-vertex anion [2-CB10 H11 ] and molecule 2,3-C2 B9 H11 is distributed over the polyhedral surface unevenly; these polyhedra are not rigid and are formed not only by triangular faces typical for deltahedra, hence they cannot be regarded as genuine closo-carbaboranes, although they have (n + 1) valence electron pairs for the skeleton bonding. We propose to name such cages quasicloso-polyhedra.
Acknowledgements The authors are indebted to M.Yu. Antipin and K.A. Lyssenko for helpful discussions and acknowledge 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
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‘Scientific school support’ (Grant NSh-1765.2003.3) as well as from the Russian Foundation for Basic Research (Project # 03-03-32651). References [1] L.A. Leites, Chem. Rev. 92 (1992) 279. [2] G. Kononova, S.S. Bukalov, L.A. Leites, K.A. Lyssenko, V.A. Ol’shevskaya, Russian Chem. Bull. 52 (2003) 85. [3] W. Quintana, L.G. Sneddon, Inorg. Chem. 29 (1990) 3242. [4] 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. [5] R.E. Williams, Chem. Rev. 92 (1992) 177. [6] 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. [7] J.D. Kennedy, in: J. Casanova (Ed.), The Borane–Carborane– Carbocation Continuum, Wiley, New York, 1988, p. 85. [8] M. Bown, B. Gr€ uner, B. Stibr, X.L.R. Fontaine, M. Thornton-Pett, J.D. Kennedy, J. Organomet. Chem. 614–615 (2000) 269. [9] R.J. Wiersema, M.F. Hawthorne, Inorg. Chem. 12 (1973) 785. [10] A. Franken, C.A. Kilner, M. Thornton-Pett, J.D. Kennedy, J. Organomet. Chem. 657 (2002) 180. [11] W.E. Carrol, M. Green, F.G.A. Stone, A.J. Welch, J. Chem. Soc. Dalton (1975) 2263.
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