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

Abstract

AbstractH2+‐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.