New method of rapid and accurate evaluation for multicenter bielectronic integrals over B functions

Safouhi, Hassan; Hoggan, Philip E.

doi:10.1002/1097-461x(2000)80:2<236::aid-qua18>3.0.co;2-i

Cited by 5 publications

(2 citation statements)

References 34 publications

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“…This computational procedure is entirely carried out in the configuration space, without recourse, for instance, to Fourier‐transform expedients, auxiliary functions as B‐functions, etc. 13, 20. As will be better appreciated in the next sections, the successful outcome of our approach is essentially the result of a valid strategy involving use of pondered numerical quadrature techniques and suitable code organization, through appropriate grouping of the STOs over each center, so as to evaluate simultaneously sets of many integrals, with good precision, taking advantage of the mean characteristics of the integrands involved.…”

Section: Introductionmentioning

confidence: 99%

“…A review of this much work lies outside our intent. An exhaustive bibliography on the subject, however, is available in a number of recent articles, where indication of the current development lines can also be found 13, 16–25. In this article we essentially propose to bring to the attention of the quantum chemist community an approach developed in its essence at Pisa many years ago and insufficiently exposed at that time 26–28, in the firm belief that the procedure elaborated has sufficient merits to deserve to be better known.…”

Section: Introductionmentioning

confidence: 99%

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Computational quantum chemistry in terms of multicenter Slater‐type orbitals: Entirely numerical procedure for the accurate evaluation of the basic integrals

Guidotti

Salvetti

Durante

et al. 2003

Int J of Quantum Chemistry

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Ab initio quantum mechanical calculations in terms of multicenterSlater-type orbitals require accurate evaluation of basic one-and two-electron integrals, a difficult mathematical task that becomes in particular challenging in the two-electron case as four different expansion centers are involved. Here, we propose to illustrate the feasibility of attacking the problem of the multiple integrations needed entirely by numerical quadratures, in conjunction with a strategic program organization that allows evaluating simultaneously sets of thousands of integrals exploiting the mean characteristics of the integrands. This approach, envisaged and implemented many years ago by two of the present authors (C.G., O.S.), perhaps without adequate exposure, is endowed in our experience with good properties. The program package, which allows dealing on the same footing with linear and nonlinear molecular geometries, has been largely revised by introducing suitable adjustments and improvements (in particular extension to orbitals with azimuthal quantum number l ϭ 3). © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 59 -71, 2003 Key words: general computational methods in quantum chemistry; computational quantum chemistry in terms of Slater-type orbitals; two-electron integrals and Slater orbitals; calculation of multicenter two-electron integrals by numerical quadrature; fourand three-center two-electron integrals

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Computational quantum chemistry in terms of multicenter Slater‐type orbitals: Entirely numerical procedure for the accurate evaluation of the basic integrals

Guidotti

Salvetti

Durante

et al. 2003

Int J of Quantum Chemistry

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Polarized basis sets of Slater‐type orbitals: H to Ne atoms

et al. 2003

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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 H(2) or Li(2)) 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.

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Electric field integrals for Slater‐type orbitals

Rico

López

Ramı́rez

et al. 2004

Int J of Quantum Chemistry

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ABSTRACT:General algorithms for electric field integrals with Slater-type orbitals (STO) are reported, and the efficiency of the computational procedure based in these algorithms is analyzed. An accuracy of nine decimal places, at least, is estimated for the molecular electric field computed on any point. Timing was examined for calculations with STO basis sets ranging from 30 to 300 basis functions. Computational cost was moderate, even for the largest basis set.

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New method of rapid and accurate evaluation for multicenter bielectronic integrals over B functions

Cited by 5 publications

References 34 publications

Computational quantum chemistry in terms of multicenter Slater‐type orbitals: Entirely numerical procedure for the accurate evaluation of the basic integrals

Computational quantum chemistry in terms of multicenter Slater‐type orbitals: Entirely numerical procedure for the accurate evaluation of the basic integrals

Polarized basis sets of Slater‐type orbitals: H to Ne atoms

Electric field integrals for Slater‐type orbitals

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