Generalized exponential functions in variational calculations of molecular systems

Abstract

A generalization of exponential and Gaussian trial functions is proposed for variational calculations of few-body Coulomb systems. It is shown that the new functions allow us to express the matrix elements of the Hamiltonian in a closed form. In comparison with other methods they allow us, in the case of two-center Coulomb systems, to reduce the length of variational expansion by an order without loss of accuracy. The efficiency of the method is demonstrated in calculations of three-particle systems $ppe$, $dde$, $tte$, $\ensuremath{\mu}\ensuremath{\mu}e$ and four-particle systems ${\mathrm{H}}_{2}$ and $\text{He}{\mathrm{H}}^{+}$ of different isotopic composition.