Carbometallic derivatives of hydroborons C2h and D5d: A list of substitution isomers

The problem of determining the number and type of X-substituted (where X represents certain substituents) carbometallic derivatives of hydroborons Co(C₂B₉H₁₁)₂]⁻ C _2h and Co(C₅B₆H₁₁)₂]⁻ D _5d (from apexes) was solved on the basis of G. Pólya’s theorem by means of combinatory analysis. The formulae of symmetry Z and generating functions of the number of achiral substitution isomers were determined. The family distributions of isomers (depending on the type and number of substituents) and the sites of possible substitution depending on the number m were determined. Mono and di-X-substituted isomers of Co(C₅B₆H₁₁)₂]⁻ C _2h , as well as mono and di-X-substituted isomers of Co(C₅B₆H₁₁)₂]⁻ D _5d , were identified. The procedure for plotting an additive model of calculating the properties of isomers of apical substitution of Co(C₅B₆H₁₁)₂]⁻ D _5d was described on the basis of splitting of polygonal numbers (K ₃, K _TE, K ₅, and so on) of Pascal triangle, upon use of which there is no randomization in the choice of parameters of calculation model. The additive schemes containing 7 and 25 parameters for the calculation of properties of X-substituted carbometallic derivative of hydroboron Co(C₅B₆H₁₁)₂]⁻ D _5d to various approximations were obtained.