Exponential basis functions with quadratic dependence on interelectron distance for variational calculations of two-electron atoms

A new class of correlated basis functions is proposed for variational calculations of three-particle Coulomb systems. Apart from the usual linear term, the functions contain the square of the interelectron distance within the exponent. It is shown that all appearing integrals are analytically tractable. An algorithm is devised for exact calculation of such auxiliary functions as the complementary error integral and its derivatives of up to 20th order. The efficiency of the proposed expansion is tested on the helium isoelectronic sequence. It is found that a ten-function basis set is sufficient to calculate the ground state energy and the first excited triplet state energy with an accuracy of 10-6 Hartree.