The quality of s‐orbitals determined by least‐squares fitting and constrained variational methods

Abstract

Calculations of a wide range of position and momentum space properties of 23 orbital basis sets for atomic helium are performed to supplement our previous work. The combined results on 94 orbital basis sets are used to demonstrate that, as in the case of d-orbitals, the least squares error is not as discriminating as other information theoretic measures of overall quality for s-orbitals. Detailed comparisons suggest that constrained variation can improve the overall quality of the resulting orbital provided that the constraints are selected carefully to complement the bias inherent in the energy expectation value and the functional form of the basis functions.

Hyperbolic cosine functions applied to atomic Roothaan-Hartree-Fock wavefunctions: further improvements

“…In order to reduce the number of required basis functions, however, there is a continuing effort to find alternative functions which are more efficient than STFs and GTFs. In particular, various unconventional functions have been proposed for the simplest case of the helium atom and its isoelectronic analogues, where we have only one occupied s orbital; an extensive bibliography may be found in [5][6][7]. However, few of the proposed basis functions can be applied to many-electron or multi-orbital atoms, because of the increased complexity in the integral evaluation.…”

Reduction of Dimensionality, Order, and Classification in Spaces of Theoretical Descriptions of Molecules: An Approach Based on Metrics, Pattern Recognition Techniques, and Graph Theoretic Considerations

“…It was further tested on OH [5], BH, CH, NH [6], and the triatomic H 2 O [7] molecule. It was also used by other researchers on a variety of problems as the performance of various types of basis sets in studies on helium [8,9] and copper [10]. Later, the method was extended to treat simultaneously a group of molecules and was tested on a collection of properties for the sequence CH 4 , NH 3 , H 2 O, FH, and Ne [11].…”