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

Abstract

As part of previous studies, we introduced a new type of basis function named Simplified Box Orbitals (SBOs) that belong to a class of spatially restricted functions which allow the zero differential overlap (ZDO) approximation to be applied with complete accuracy. The original SBOs and their Gaussian expansions SBO-3G form a minimal basis set, which was compared to the standard Slater-type orbital basis set (STO-3G). In the present paper, we have developed the SBO basis functions at double-zeta (DZ) level, and we have assessed the option of expanding the SBO-DZ as a combination of Gaussian functions. Finally, we have determined the quality of the new basis set by comparing the molecular properties calculated with SBO-nG with those achieved with some standard basis sets. K E Y W O R D S ab-initio calculations, box orbitals, confined systems, Gaussian expansion, spatially restricted basis functions 1 | INTRODUCTION: SIMPLIFIED BOX ORBITAL AND SIMPLIFIED BOX ORBITAL-nG FUNCTIONS Spatially restricted functions are distinguished as having a value of zero from a certain distance to the center to which they are referred:r > r o ) χ(r,θ,ϕ) = 0. This characteristic makes the integrals S pq , H pq , and (pq|rs) zero when the distance between the centers of the two basis functions χ p and χ q is higher than the sum of the radii associated with those two functions. Therefore, it leads to simplifications analogous to those of the zero differential overlap (ZDO) approximation of the semiempirical methods, but in a completely ab-initio context. This advantage has been proven to be useful for improving the computing calculations as shown by the results obtained, for example, with Ramp functions. [1][2][3] In previous studies based on the pioneering work of Lepetit et al. [4] and Fernández Rico et al., [5][6][7][8] we developed a valid spatially restricted basis set for performing calculations on molecules with atoms from H to Kr, but at "single-zeta level." [9][10][11] 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. [12] An SBO is a spatially restricted function achieved through the linear combination of terms (r − r o ) 3n for the interval 0 < r < r o and with the value of zero outside this interval.with the radial part defined as a piecewise function:

Property‐oriented basis sets for computation of atomization energies

“…The results achieved in this study and in the references 14,17 justify the use of SBO‐3G expansions for calculating molecular properties, although it is not guaranteed that they can completely keep the “ZDO advantage” of the original SBOs. However, assigning an “effective radius” for the Gaussian expansions around 10% bigger than those of the original SBO, the ZDO advantages were found to be applicable again 16 …”

“…We have checked in 17 that using SBO‐3G expansions attains satisfactory results. In addition, we have shown in 14 that obtaining an SBO‐nG development for each SBO individually is unnecessary because SBOs satisfy accurately enough the STO‐nG O‐ohata's ratios 21 : …”

“…The focus of this study was molecular properties such as atomization energy, whose value is obtained from the difference of two very similar values. Thus, in this study, we test the following hypotheses: Obtaining a basis set that directly minimizes the error of that difference is more efficient than standard basis sets (which are generally obtained by independent minimization of every total energy used in the calculation).This is because the use of the variational principle implies an independent error minimization for each of the total energies used, which leads to a different error for each term. Polarization basis functions affect the quality of molecular energy but have very little effect on the quality of HF or DFT atomic energies.Consequently, we have focused the search for parameters that improve atomization energy on the scale factors of the polarization functions, choosing them so that the atomization energies obtained for a set of reference molecules are as close as possible to the results achieved when a very broad basis set is used: the correlation consistent cc‐pV5Z of Dunning et al 13 The basis set used in this study to test the hypothesis proposed was SBO4‐DZ(d,p)‐3G 14 because the improvement obtained in the results of preliminary calculations was much better than those achieved by the 6‐311G(d,p) basis set. In fact, the optimization of the D shell of the 6‐311G(d,p) basis set using the B3LYP method for the molecules set HC n H ( n = 2, 4, 6, 8, and 10) only improves the root mean square error (RMSE) achieved for the atomization energy calculation from 0.389% to 0.255%, when compared regarding the results achieved by the cc‐pV5Z basis set for this set of molecules.…”

“…It seems convenient to remark that an SBO (simplified box orbital) 14–17 is a spatially restricted function achieved through the linear combination of terms (r‐r o ) 3n for the interval 0 < r < r o and with value of zero outside this interval. with the radial part defined as a piecewise function: …”

“…In the same paper, we reported that a minimal basis set formed with 3G expansions of SBO functions (SBO‐3G) used with the Hartree‐Fock method led to considerably better results than the standard HF/STO‐3G procedure . In 14 we developed a SBO4‐DZ(d,p)‐3G basis set by adding a polarization shell to a SBO4‐DZ‐3G basis set, with scale factors for the “D‐3G” shell selected by applying the variational method in homonuclear diatomic molecules.…”