Abstract
We have analyzed the electronic populations of chemical bonds and atoms in the highly symmetric closo-carboranes 1,5-C2B3H5 (I) and 1,6-C2B4H6 (II). The overlap populations σXY are compared with the corresponding Mulliken indices. We note substantial nonadditivity of the populations σXY for “closed” three-center bonds BCB' and the closeness of the total overlap population σt to its maximum value. We have established the localization of the natural MOs on the bonds CH, BH, and BCB', and for molecule I also on the CBC' bonds. The effects of conjugation of bonds in the closo-carborane polyhedron are apparent in the linear dependence of these MOs. The corresponding nonorthogonal hybrid AOs of carbon and boron are also linearly dependent. We have formulated the concept of unshared population of an atom.
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Literature cited
L. V. Vilkov, V. S. Mastryukov, and N. I. Sadova, Determination of the Geometrical Structure of Free Molecules, Mir, Moscow (1983).
A. D. Walsh, “The structures of ethylene oxide, cyclopropane, and related molecules,” Trans. Farad. Soc., 45, No. 314, 179–190 (1949).
S. G. Semenov, “Quantum chemical study of the electronic structure of 1,6-dicarbacloso-hexaborane in the CNDO approximation,” Zh. Strukt. Khim., 22, No. 5, 164–166 (1981).
J. A. Pople and G. A. Segal, “Approximate self-consistent molecular orbital theory. 2. Calculations with complete neglect of differential overlap,” J. Chem. Phys., 43, No. 10, S136-S149 (1965).
J. A. Pople and G. A. Segal, “Approximate self-consistent molecular orbital theory. 3. CNDO results for AB2 and AB3 systems,” J. Chem. Phys., 44, No. 9, 3289–3296 (1966).
E. A. McNeill, K. L. Gallaher, F. R. Scholar, and S. H. Bauer, “Molecular structure of 1,5-dicarba-closo-pentaborane(5) and 1,6-dicarba-closo-hexaborane(6) by gas-phase electron diffraction,” Inorg. Chem., 12, No. 9, 2108–2111 (1973).
R. Polák, “Optimum hybrid orbitals in localized orbitals,” Int. J. Quant. Chem., 4, No. 3, 271–287 (1970).
E. R. Davidson, “Electronic population analysis of molecular wave functions,” J. Chem. Phys., 46, No. 9, 3320–3324 (1967).
K. R. Roby, “Quantum theory of chemical valence concepts. 1. Definition of the charge on an atom in molecule and of occupation numbers for electron density shared between atoms,” Mol. Phys., 27, No. 1, 81–104 (1974).
M. F. Guest and I. H. Hillier, “Multi-center bonding in the carboranes. An ab initio and semiempirical molecular orbital study,” Mol. Phys., 26, No. 2, 435–452 (1973).
R. S. Mulliken, “Electronic population analysis on LCAO-MO molecular wave functions,” J. Chem. Phys., 23, No. 10, 1833–1840 (1955).
S. G. Semenov, “Population analysis and the problem of nonorthogonality of a multicenter basis of atomic orbitals,” Vestn. Leningr. Univ., No. 22, 125–131 (1977).
P. G. Lykos and H. N. Schmeising, “Maximum overlap atomic and molecular orbitals,” J. Chem. Phys., 35, No. 1, 288–293 (1961).
R. J. Bartlett and Y. Öhrn, “How quantitative is the concept of maximum overlap?” Theor. Chim. Acta, 21, No. 3, 215–234 (1971).
F. R. Gantmakher, Matrix Theory [in Russian], Nauka, Moscow (1967).
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Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 23, No. 4, pp. 451–456, July–August 1987.
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Semenov, S.G. Localization of mos and electronic populations in closo-carboranes 1,5-C2B3H5 and 1,6-C2B4H6 . Theor Exp Chem 23, 422–427 (1988). https://doi.org/10.1007/BF00536360
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DOI: https://doi.org/10.1007/BF00536360