Integral-Transform Gaussian Functions for Heliumlike Systems

The one‐dimensional Laplace transform of the Gaussian exp (−r²x), $$\mathrm{g(r)=}\mathfrak{L}\mathrm{\{G(x)\}=}{\displaystyle {\int }_0^{\infty }}{e}^{{\mathrm{-r}}^{2}x}\mathrm{G(x)dx}$$ , was used to generate functions which could be useful as basis sets for atomic and molecular calculations. A particular choice of the weighting function G(x) led to functions of the form g(r) = (qr)^νK_ν(qr), where K_ν(qr) are modified Bessel functions of the second kind. These functions were used as basis functions for the helium isoelectronic series and accounted for 98.98% (H⁻), 99.89% (He), 99.96% (Li⁺), 99.98% (Be⁺⁺), 99.996% (O⁶⁺) of the Hartree‐Fock energy.