On the effectiveness of exponential type orbitals with hyperbolic cosine functions in atomic calculations (original) (raw)
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Bulletin of the Chemical Society of Japan, 2012
An improvement on the total energy results reported in Ref. 9 in atomic calculations based on a modified type hyperbolic cosine function cosh(¢r ® + £) is presented. It is shown that the noninteger n-generalized exponential type orbitals r n à À1 e À¦r ® with modified type hyperbolic cosine as radial basis functions are a much better approximation to the HartreeFock orbitals than a double-zeta basis set of Slater type functions. The efficiency of the new basis function is tested by application to some closed and open shell neutral atoms and their ions. A substantial improvement in both the total and orbital energies is obtained within the minimal basis sets framework. The total energy values obtained in this work are significantly close to the numerical HartreeFock results. These results supersede all previous minimal basis function total energies achieved in the literature.
Atomic orbitals revisited: generalized hydrogen-like basis sets for 2nd-row elements
Theoretical Chemistry Accounts, 2018
In the present work, we revisit the problem of atomic orbitals from the positions mostly dictated by semiempirical approaches in quantum chemistry. To construct basis set, having proper nodal structure and simple functional form of orbitals and representing atomic properties with reasonable accuracy, authors propose an Ansatz based on gradual improvement of hydrogen atomic orbitals. According to it, several basis sets with different numbers of variable parameters are considered and forms of orbitals are obtained for the 2nd-row elements either by minimization of their ground state energy (direct problem) or by extracting from atomic spectra (inverse problem). It is shown that so-derived three-and four-parametric basis sets provide accurate description of atomic properties, being, however, substantially provident for computational requirements and, what is more important, simple to handle in analytic models of quantum chemistry. Since the discussed Ansatz allows a generalization for heavier atoms, our results may be considered not only as a solution for light elements, but also as a proof of concept with possible further extension to a wider range of elements.
Systematic approach to extended even-tempered orbital bases for atomic and molecular calculations
Theoretica Chimica Acta, 1979
Explicit formulas are established for simply generating arbitrarily large basis sets of optimal even-tempered Gaussian primitives which systematically approach complete bases for the entire function space. These bases, moreover, reproduce the corresponding optimal atomic SCF wavefunctions extremely closely and permit an extrapolation of the SCF energies to the Hartree-Fock limit. On the basis of the detailed quantitative information available from these calculations a simple general procedure is formulated for generating optimal even-tempered basis sets for molecular calculations.
Wiley Interdisciplinary Reviews: Computational Molecular Science, 2012
Electronic structure methods for molecular systems rely heavily on using basis sets composed of Gaussian functions for representing the molecular orbitals. A number of hierarchical basis sets have been proposed over the last two decades, and they have enabled systematic approaches to assessing and controlling the errors due to incomplete basis sets. We outline some of the principles for constructing basis sets, and compare the compositions of eight families of basis sets that are available in several different qualities and for a reasonable number of elements in the periodic table.
Polarized basis sets of Slater-type orbitals: H to Ne atoms
Journal of Computational Chemistry, 2003
We present three Slater-type atomic orbital (STO) valence basis (VB) sets for the first and second row atoms, referred to as the VB1, VB2, and VB3 bases. The smallest VB1 basis has the following structure: [3, 1] for the H and He atoms, [5, 1] for Li and Be, and [5, 3, 1] for the B to Ne series. For the VB2 and VB3 bases, both the number of shells and the number of functions per shell are successively increased by one with respect to VB1. With the exception of the H and Li atoms, the exponents for the VB1 bases were obtained by minimizing the sum of the Hartree–Fock (HF) and frozen-core singles and doubles configuration interaction (CISD FC) energies of the respective atoms in their ground state. For H and Li, we minimized the sum of the HF and CISD FC energies of the corresponding diatoms (i.e., of H2 or Li2) plus the ground-state energy of the atom. In the case of the VB2 basis sets, the sum that was minimized also included the energies of the positive and negative ions, and for the VB3 bases, the energies of a few lowest lying excited states of the atom. To account for the core correlations, the VBx (x = 1, 2, and 3) basis sets for the Li to Ne series were enlarged by one function per shell. The exponents of these extended (core-valence, CV) basis sets, referred to, respectively, as the CVBx (x = 1, 2, and 3) bases, were optimized by relying on the same criteria as in the case of the VBx (x = 1, 2, and 3) bases, except that the full CISD rather than CISD FC energies were employed. We show that these polarized STO basis sets provide good HF and CI energies for the ground and excited states of the atoms considered, as well as for the corresponding ions. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 859–868, 2003
International Journal of Quantum Chemistry, 2019
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. [1-3] In previous studies based on the pioneering work of Lepetit et al. [4] and Fdez Rico et al., [5-8] we developed a valid spatially restricted basis set for performing calculations on molecules with atoms from H to Kr, but at "single-zeta level." [9-11] 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. SBO r, θ, ϕ ð Þ= R SBO r ð ÞÁΥ m ℓ θ,ϕ ð Þ ð1Þ with the radial part defined as a piecewise function:
Considering a mixed atomic basis set composed of only 1s STO and 1s GTO in molecular calculations
2019
An atomic basis set composed of only 1s orbitals is introduced, for molecular calculations in the HartreeFock-LCAO approximation. The 1s Slater Type Orbitals are located at the nuclei and the 1s Gaussian Type Orbitals can be used both in fixed locations and as Floating Orbitals. Surprisingly, despite the simplicity of the orbitals, this basis set provides an accurate description of molecular systems containing atoms with two shells such as oxygen and carbon, used as case studies in this work. From a numerical perspective, the basis set is first optimized for the free atoms and then they are introduced into the molecular environment. The molecular calculations for OH_2 and CH_2 show validating results for the energy and the molecular geometry. From the description of the inner atomic and the valence shells achieved with this particular basis set, we can assign a charge to the bonds and the lone pairs by using the Löwdin population analysis, with excellent result from the molecular po...