Appraisal of hermite-gaussian expansion of hydrogen orbitals by calculation of some one-electron properties

Abstract

Hydrogen orbitals (HOs) are expanded in terms of Hermite-Gaussian (HG) functions thus making polycentric molecular integrals tractable. The quality of the basis sets is examined by calculating various one-electron properties and similarity measures (SM) between approximate HG expansions and exact HOs. It is shown that σ d,< r 2>, < r> and SM may serve as a riddle in eliminating unsatisfactory basis sets. The average distance < r> appears to be rather insensitive in the H atom in contrast to the molecular case. Hermite-Gaussian functions of the fourth degree (HG4-N ) proved very useful in describing HOs. The highest accuracy is obtained for HOs obeying the n- l = 1 condition. It is concluded that HG4 functions are advantageous for HOs of higher quantum numbers n and l, being superior to 1 s GTO functions possessing the equivalent number of nonlinear parameters. It follows that mixed sets employing STOs for inner-shells and HOs for outer valence shell and polarization functions might be useful in molecules involving heavy atoms provided that they are expanded in HG functions. The nuclear cusp condition is briefly discussed and it is shown that implementation of the off-center HG function ( s ) might improve behavior of AOs near the nucleus without considerable increase in computational effort. It should be pointed out that the corresponding hydrogen-like functions are simply obtained by a rescaling procedure.