Integral-Transformation Trial Functions of the Fractional-Integral Class

Abstract

We propose fractional integrals (Euler transforms) of conventional quantum-mechanical functions as special integral-transform trial functions. Calculations on the first four members of the He isoelectronic sequence with three different-order Euler transforms of both Slater and Gaussian $1s$ orbitals are reported. A pilot calculation for ${\mathrm{H}}_2$ with an Euler transform of an LCGTO (linear combination of Gaussian-type orbitals) molecular orbital gives a total energy $E=-1.10903\mathrm{}$ a.u. at $R=1.4\mathrm{}$ a.u. (exact value is -1.17444 a.u.). A generalization of the shape function used in this work is given and the general applicability of Euler transforms discussed.