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The electrical properties of oligoresorcinols with various concentrations of paramagnetic centres (Ns) in constant and variable electric fields have been investigated. It has been established that the electrical conductivity and the tangent of the dielectric loss angle are increased with the growth of Ns in the composition of the oligoresorcinol. With increase of frequency the electrical conductivity of oligoresorcinol increases according to the usual law. It has been shown that the electrical conductivity and concentration of paramagnetic centres of oligoresorcinol are interrelated and charge transfer in a variable field predominates at the expense of jumps of charge bearers between localized states with energy near the Fermi level. The densities of the states near the Fermi level for resorcinol examples have been calculated. The results show that, in this case, paramagnetic centres of the aroxyl type determine the density of the localized states near the Fermi level. © 1997 SCI.

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The series expansion formulae are derived for the overlap integrals with arbitrary integer n and noninteger n* Slater-type orbitals (ISTOs and NISTOs) in terms of a product of well-known auxiliary functions A(sigma) and B (k). The series becomes an ordinary closed expression when both principal quantum numbers n* and n'* of orbitals are integer n*= n and n'*= n'. These formulae are especially useful for the calculation of overlap integrals for large quantum numbers. Accuracy of the results is satisfactory for values of integer and noninteger quantum numbers up to n= n'=60, n*= n'*<33 and for arbitrary values of screening constants of orbitals and internuclear distances.

Using binomial coefficients, new, simple, and efficient algorithms are presented for the accurate and fast calculation of the heat capacity of solids depending on the Debye temperature. As will be seen, the present formulation yields compact, closed-form expressions which enable the straightforward calculation of the heat capacity of solids for arbitrary temperature values. Finally, the algorithm is used to simulate the variation of the specific heat capacity with temperature of MgO and ZnO crystals. The results were compared with those reported in the literature and found to be in close agreement with those of other studies.

Recursion and analytical relations for the evaluation of integer and noninteger n-dimensional Debye functions have been derived. Using the binomial expansion theorem, these functions are expressed through the binomial coefficients and familiar incomplete gamma functions. This simplification and the use of the memory of the computer for calculation of binomial coefficients may extend the limits to large arguments for users and result in speedier calculation, should such limits be required in practice. Comparison of numerical results shows that analytical solutions are accurate almost from the beginning of the calculation time. The series expansion relations obtained is sufficiently accurate over the entire range of parameters. The convergence rate of the series is estimated and discussed.

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