Molecular orbitals in momentum space

Abstract

The troublesome problem of developing cusps in ordinary molecular wave functions can be avoided by working with momentum-space wavefunctions for these have no cusps. The need for continuum wavefunctions can be eliminated if one works with a hydrogenic basis set in Fock’s projective momentmn space. This basis set is the set of R 4 spherical harmonics and as a consequence one may obtain, solely by the ordinary angular momentum calculus, algebraic expressions for all the integrals required in the solution of the momentum space Schrödinger equation. A number of these integrals and a number of R 4 transformation coefficients are tabulated. The method is then applied to several simple united-atom and l.c.a.o. wavefunctions for H + 2 and ground state energies and corrected wavefunctions are obtained. It is found in this numerical work that the method is most appropriate at internuclear distances somewhat less than the equilibrium distance. In Fock’s representation both l.c.a.o. and unitedatom approximations become exact as the internuclear distance approaches zero. The united-atom expansion can be viewed as an eigenvalue equation for the root-mean-square momentum, p 0 = √( — 2 E ). In the molecule, the matrix operator corresponding to p 0 is related to the operator for the united-atom by a sum of unitary transformations, one for each nucleus in the molecule.