New program for molecular calculations with Slater-type orbitals

Rico, J. Fernández; López, Rafael; Aguado, Alfredo; Ema, I.; Ramı́rez, G.

doi:10.1002/1097-461x(2001)81:2<148::aid-qua6>3.0.co;2-0

Cited by 60 publications

(13 citation statements)

References 16 publications

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“…This situation has been maintained along the last 40 years, but it is changing at present and might be inverted in the near future 2. It is noteworthy, in particular, that the considerable research on the STO integrals carried out in the 90s has fructified in new programs3–5 and updated versions of old programs6 for the calculations of the electron structure of polyatomics (not necessarily linear), that already perform more efficiently than those using GTO in some applications.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the research in this field has been intensified in the last years,7–9 and it seems reasonable to forecast that still more efficient solutions will be developed in the future; but up to date, the above‐mentioned programs have not been superseded yet. Two of these programs were developed in our own group4, 5 on the basis of the algorithms for STO integrals that we developed in the 90s.…”

Section: Introductionmentioning

confidence: 99%

“…This second program5 was notably more efficient and versatile than the first one 4. It was tested and debugged over the last 3 years and, as a consequence, it has undergone several modifications and refinements.…”

Section: Introductionmentioning

confidence: 99%

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Efficiency of the algorithms for the calculation of Slater molecular integrals in polyatomic molecules

et al. 2004

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The performances of the algorithms employed in a previously reported program for the calculation of integrals with Slater-type orbitals are examined. The integrals are classified in types and the efficiency (in terms of the ratio accuracy/cost) of the algorithm selected for each type is analyzed. These algorithms yield all the one- and two-center integrals (both one- and two-electron) with an accuracy of at least 12 decimal places and an average computational time of very few microseconds per integral. The algorithms for three- and four-center electron repulsion integrals, based on the discrete Gauss transform, have a computational cost that depends on the local symmetry of the molecule and the accuracy of the integrals, standard efficiency being in the range of eight decimal places in hundreds of microseconds.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficiency of the algorithms for the calculation of Slater molecular integrals in polyatomic molecules

et al. 2004

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“…The algorithm described in Eq. (29) has been incorporated into a computer program written in the MATHEMATICA programming language with the included numerical computation packages. The MATHEMATICA program language can handle approximate real numbers with any number of digits and it is suitable only for benchmark evaluation in the view of the calculation times.…”

Section: Resultsmentioning

confidence: 99%

“…Nevertheless, it may not be said they have vital importance in nonrelativistic electronic structure theory. Many calculations [27][28][29][30][31] show that obtaining an adequate level of accuracy is possible by using appropriate basis sets of STOs. In fact, the NSTOs start to play a major role in relativistic electronic structure theory, hence the importance of accurate calculation of molecular integrals over NSTOs.…”

Section: Introductionmentioning

confidence: 99%

Benchmark values for molecular two-electron integrals arising from the Dirac equation

Bağcı

Hoggan

2015

Phys. Rev. E

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The two-center two-electron Coulomb and hybrid integrals arising in relativistic and nonrelativistic ab initio calculations on molecules are evaluated. Compact, arbitrarily accurate expressions are obtained. They are expressed through molecular auxiliary functions and evaluated with the numerical Global-adaptive method for arbitrary values of parameters in the noninteger Slater-type orbitals. Highly accurate benchmark values are presented for these integrals. The convergence properties of new molecular auxiliary functions are investigated. The comparison for two-center two-electron integrals is made with results obtained from single center expansions by translation of the wave function to a single center with integer principal quantum numbers and results obtained from the Cuba numerical integration algorithm, respectively. The procedures discussed in this work are capable of yielding highly accurate two-center two-electron integrals for all ranges of orbital parameters.

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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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New program for molecular calculations with Slater-type orbitals

Cited by 60 publications

References 16 publications

Efficiency of the algorithms for the calculation of Slater molecular integrals in polyatomic molecules

Efficiency of the algorithms for the calculation of Slater molecular integrals in polyatomic molecules

Benchmark values for molecular two-electron integrals arising from the Dirac equation

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

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