Generalized quantum mechanical two-centre problems

If χ _i (χ _k ) is an exact generalized diatomic orbital (solution of Eq. (1) of text), a sequence of functions χ _i ^(N) converging to χ _i may be constructed so that matrix elements of frequently occurring operators between χ _i ^(N) and χ _k ^(N) may be computed without any numerical integration. Exact expectation values are given for kinetic and potential energy, dipole moment, θ ²=x ²+y ², and quadrupole moment 3z ²?r ², for various ratios of nuclear charges Z ₁,Z ₂ and for several distances R. Special subjects discussed in terms of computed expectation values are:

1. R-dependence of the contributions to total energy of HeH²⁺ in state 2pσ and of LiH³⁺ in state 3dσ
2. RZ-and λ-dependence of dipole and quadrupole moment functions in state 1sσ
3. Some properties of those generalized diatomic orbitals which approach, for R going to 0, Slater-type atomic functions.