Distributed basis sets of s‐type Gaussian functions for simple diatomics: Anharmonic‐model distribution

Abstract

An and H 2 diatomic systems. The total ground state energies for the one-electron systems and the ground state Hartree-Fock energy for the H 2 molecule supported by distributed basis sets constructed by means of the anharmonic model are compared with the corresponding energies obtained by invoking the variation principle to determine optimal exponents and positions. The use of a series of anharmonic distributions of s-type Gaussian functions centred on regularly spaced points is also investigated. Calculated energy expectation values supported by our largest distributed basis sets differ from the corresponding exact values by 0.70 µHartree for the H + 2 ion and by 0.89 µHartree for the HeH 2+ ion. For the ground state Hartree-Fock energy of the H 2 molecule, our distributed basis set yields a value which differs from the finite difference Hartree-Fock value by 0.67 µHartree.

The Coulson–Fischer wave functions for the ground and excited states of H2and HeH+: parametrisation using distributed Gaussian basis sets

“…can be very useful [96,97] in terms of economy and accuracy of computation. Different parameters α k and β k can be used for the ground (k = 0) and excited (k = 1) states.…”

“…α k and β k can be taken to be functions of m. In 1979, it was established [42] that for atoms well-defined schemes can be constructed such that even-tempered basis sets approach a complete set in the limit of large m and, therefore, the Hartree-Fock limit is approached. It has been shown [96,97] that an anharmonic model can be profitably used to distribute the basis functions along the internuclear axis in diatomic molecules. In the present study, we used a series of anharmonic distributions with shifted origins to generate subsets of functions centred on regularly spaced points lying on the straight line passing through the two nuclei.…”

“…The parameter k is determined by invoking the variation theorem. The functions in the second subset are distributed according to the relation where m 2 (< m 1 ) is the number of functions in the second subset and x 0 is related to k through the equation [96,97],…”

Efficient generation of distributed spherical Gaussian basis sets for molecules

“…Practical results based on this idea were reported during the late 1960s [45,46], but these earlier works were concerned with the development of small basis sets providing qualitative results. The emphasis of recent investigations for the H 2 ϩ [47,48], H 2 , LiH, BH [49], and HeH and BeH molecules [50] was to design fully optimized spherical FGO basis sets capable of supporting sub-hartree accuracy at the HF level. Certainly such variational calculations involve a time-consuming nonlinear optimization procedure.…”

“…Certainly such variational calculations involve a time-consuming nonlinear optimization procedure. The positions and orbital exponents obtained by minimizing the HF energy of molecules were investigated with a view to develop empirical schemes for constructing distributed Gaussian basis sets [47][48][49][50].…”