Simplified Box Orbitals (SBO) for H To Ar atoms: Exact expressions, SBO-3G approximations, and relations with the ZDO approximation

Abstract

Jes us S anchez-M arquez, and Manuel Fern andez-N uñez Simplified Box Orbitals (SBO) are a kind of spatially restricted basis functions. SBOs have a similar use and value to Slater functions but, because they fulfill a version of the zerodifferential overlap approximation, they allow for a drastic reduction in the number of two-electron integrals to be calculated when dealing with huge systems, and they seem to be specially adapted to study confined systems such as molecules in solution. In a previous study, the mathematical shape of SBOs was discussed and the necessary parameters were obtained by means of the variational method. In the present study, the parameters of each SBO were obtained by applying the condition that it is as similar as possible to the STO that would be used in a basis set without spatial restrictions. We have developed a method to achieve this likeness and deduced simple formulas to describe all the SBOs of any atom. We also present the SBO-3G expansions of the SBOs obtained, making it possible to use these SBOs with standard quantum chemistry calculation software. Simple formulas were also deduced to directly write the SBOs and SBO-3G corresponding to the atoms with a Z value of between 1 and 18. Finally, as a first example of the usefulness of this kind of functions, an optimized SBO-3G basis set is proposed for atoms from H to Cl in molecules.

Spatially restricted Double Z‐Simplified Box Orbital basis sets: Optimization and comparison with some standard basis sets

“…Figures and , and Tables and show that the results of this basis set in molecular calculations are very similar to those obtained with a molecularly optimized minimal basis set . However, better results can be obtained in a simple way, as can be seen below.…”

“…This advantage has been proven to be useful for improving the computing calculations as shown by the results obtained, for example, with Ramp functions . In previous studies based on the pioneering work of Lepetit et al and Fernández Rico et al, we developed a valid spatially restricted basis set for performing calculations on molecules with atoms from H to Kr, but at “single‐zeta level.” In this paper we have developed an Simplified Box Orbital (SBO) basis set at “double‐zeta level,” which allows calculations to be performed with similar or higher precision than the well‐known standard basis set 6‐311G(d) of Pople et al…”

“…First, we developed a preliminary SBO‐DZ basis set, which led to much better atomic calculations than the SBO‐SZ developed in Reference . This basis set was then modified to improve its results in the calculation of molecular properties, as indicated below.…”

“…The results shown in Table justify the use of the SBO‐3G expansions for the calculation of molecular properties, although they cannot be guaranteed to keep the “ZDO advantage” of the original SBOs. However, assigning a slightly bigger “effective radius” for the Gaussian expansions than that of the original SBOs showed that the ZDO advantages can be applicable again …”

“…It is important to point out that “ZDO advantage” is what we call the possibility of avoiding the calculation of any integral which includes the product of SBOs with centers farther than the sum of their radii. This advantage is irrelevant in small molecules, where most of the SBOs involved have nonzero overlaps but its importance increases enormously as the treated system becomes larger …”