Carbometallic derivatives of C 1v and C 5v boranes: Enumeration and identification of substitution isomers and the calculation scheme of the properties of C 5v based on pascal’s triangle numbers

Abstract

Combinatorial analysis methods are employed to solve the problem of determining the number and form of X-substituted (X, XY, … are some substituents) of carbometallic derivatives of boranes (C5H5)Co(C2B9H11) C1v and (C5H5)Co(C5B6H11) C5v (over vertices) based on Polya’s theorem. formulas of Z symmetry and generating functions of the number of chiral and achiral substitution stereoisomers are determined. Family distributions of the isomers depending on the form and number of substituents and depending on the number m of possible substitution sites are found. Mono-, di-, and tri-X-substituted (X = CH3, F, …) isomers of (C5H5)Co(C5B6H11) C5v are identified. Based on the partition of simple (n) and triangular numbers (K3) of Pascal’s triangle, additive schemes are obtained which take into account valence and non-valence pair interactions of atoms in the polyhedron framework and contain 2, 6, and 23 parameters for the calculation of properties of X-substituted borane (C5H5)Co(C5B6H11) C5v.