Molecular orbital studies on small molecules using H2+-type elliptical basis orbitals. Application to H2+, H2, He2++ and H3+

H₂⁺-type elliptical orbitals are defined in Section 1. These orbitals, which in elliptical coordinates involve a factor (1 + ξ)^σ, are employed in variational calculations on the ground states of H₂⁺ and H₂ (Sections 2 and 3). Various choices of σ are explored for H₂⁺, while two choices are used for H₂ : the “boundary condition” (Equation 6) and the “cusp condition” (Equation 9) values. Variational energies are calculated and compared to the results of similar calculations. Section 3 concludes by employing the H₂⁺-type orbitals in LCETO-MO-SCF calculations on the ground states of H₂ and He₂⁺⁺. For both molecules a four-function basis set with two (nonlinear) variational parameters yields more than 99% of the Hartree-Fock limit. Section 4 deals with LCETO-MO-SCF calculations on triangular H₃⁺. Three four-function basis sets are used, and the best energy is -1.2306 a.u., which is in reasonable agreement with the Hartree-Fock limit, -1.2999 a.u. Our best basis set is a four-term two-center expansion of the wave function with only one nonlinear variational parameter. Section 5 concludes the paper with a summary of the methods used to evaluate the integrals which arise in SCF calculations in the H₂⁺-type elliptical orbital basis.