Universal basis sets of elliptical functions: potential energy curves for some one-electron diatomic molecules

Abstract

The use of universal basis sets of elliptical functions in molecular electronic structure calculations for diatomic systems is investigated. By considering both the united-atom and the separated-atom limits, an empirical relation between screening constants is introduced which leads to sub- mu Hartree accuracy over a wide range of nuclear separations. Calculated energies for the homonuclear one-electron systems X2n (X=XH, He, Li, Be, B, C, N, O and F) obtained by using the same set of integrals over a universal set of elliptical functions are compared with the exact energies. Heteronuclear one-electron systems are also studied.

Determination of electronic energy levels for the heteromolecular ions HeH2+, LiH3+, and BeH4+ from the Hamilton–Jacobi equation

“…Heteronuclear‐type diatomic systems such as HeH 2+ , LiH 3+ , and BeH 4+ have been studied by several methods. Among others, we have the seminumerical two‐dimensional (2D) approach 1, boundaries set in 2 Z given by algebraic topological structures 2, the linear combination of atomic orbitals (LCAO) method 3, the separable Hartree–Fock‐like solution 4, analytical approaches based on the internuclear separation 5, universal basis sets of elliptical functions 6, and treatment of the continuum radial wave functions for the Coulomb two‐center problem 7.…”

Internet-based teleangiography: An indispensable tool for the interventional cardiologist

“…Universal basis sets are often taken to be even‐tempered basis sets; that is, the exponents are taken to form a geometric series 23–26. Universal basis sets of this type have been employed in a wide variety of calculations 27–40 at both the matrix Hartree–Fock level and including correlation effects; in both nonrelativistic and relativistic studies. In 1979, Schmidt and Ruedenberg 41 proposed a practical scheme for systematically extending basis sets of even‐tempered Gaussian functions to approach the complete basis set limit.…”

Distributed Gaussian basis sets: a comparison with finite difference Hartree–Fock calculations for potential energy curves of H2, LiH and BH

“…The introduction of even-tempered basis sets [28][29][30][31][32][33][34], universal basis sets [35][36][37][38][39][40][41][42][43][44], geometric basis sets [45][46][47], systematic sequences of even-tempered basis sets [48][49][50] and universal systematic sequences of even-tempered basis sets [51][52][53][54][55][56][57][58] has led to atomic basis sets which can support high accuracy at the Hartree-Fock level and beyond. The exponents for these basis sets are generated using empirical formulae, almost completely avoiding the need for nonlinear optimization.…”