Addition theorem of Slater type orbitals: a numerical evaluation of Barnett–Coulson/Löwdin functions

Bouferguène, Ahmed

doi:10.1088/0305-4470/38/13/006

Cited by 22 publications

(12 citation statements)

References 84 publications

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“…More space saving can be achieved by applying symmetry relations to the Gaunt coefficients to avoid redundant storage of identical values. These conditions lead to the first new index function defined in the present work 7–13.…”

Section: Discussionmentioning

confidence: 97%

New index functions for storing Gaunt coefficients

Pinchon

Hoggan

2007

Int J of Quantum Chemistry

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Gaunt coefficients express angular momentum conservation rules. They are therefore required in the combination of atomic orbitals. In this case, the angular factors are spherical harmonics and the Gaunt coefficients appear when their products are linearized. The Gaunt coefficients may be pre-calculated and stored. This work describes new index functions for storing and retrieving the required Gaunt coefficients that are (almost) all nonzero. This strategy is closely related to that of Rasch and Yu, who have compared retrieval to that using recurrence relations and found it to be at least 20 times faster. Some improvements to their work will be found here and the index functions used are different. Only a few arithmetic operations are required to generate the index; therefore, its evaluation and handling takes a negligible time compared to its applications, notably molecular electronic integral evaluation.

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Section: Discussionmentioning

confidence: 97%

New index functions for storing Gaunt coefficients

Pinchon

Hoggan

2007

Int J of Quantum Chemistry

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“…Parenthetically, it is observed that U a l (r ia ) are nearly identical for l > L which justifies the rearrangements in Eqs. (10) and (11).…”

Section: B Pseudopotentials Parametrisationmentioning

confidence: 99%

“…Interestingly enough, there has been a significant progress on this issue in recent years. In fact, looking at only the past 15 years, there are many notable works of Bouferguene et al [10][11][12][13], Rico et al [14][15][16][17][18][19][20][21][22][23][24], Hoggan et al [25][26][27][28][29][30], Pachucki [31][32][33][34][35], and others [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. In particular, for the diatomic systems STOs can be now used routinely [51].…”

Section: Introductionmentioning

confidence: 99%

Combining Slater-type orbitals and effective core potentials

2017

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We present a general methodology to evaluate matrix elements of the effective core potentials (ECPs) within one-electron basis set of Slater-type orbitals (STOs). The scheme is based on translation of individual STO distributions in the framework of Barnett-Coulson method. We discuss different types of integrals which naturally appear and reduce them to few basic quantities which can be calculated recursively or purely numerically. Additionally, we consider evaluation of the STOs matrix elements involving the core polarisation potentials (CPP) and effective spin-orbit potentials. Construction of the STOs basis sets designed specifically for use with ECPs is discussed and differences in comparison with all-electron basis sets are briefly summarised. We verify the validity of the present approach by calculating excitation energies, static dipole polarisabilities and valence orbital energies for the alkaline earth metals (Ca, Sr, Ba). Finally, we evaluate interaction energies, permanent dipole moments and ionisation energies for barium and strontium hydrides, and compare them with the best available experimental and theoretical data.

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“…In previous work,29 preliminary results have shown that a numerical procedure using a tailored Gauss quadrature, known as GB, can be a good candidate for the evaluation of the semi‐infinite integral T l,m (σ, τ). The selection of this method was motivated by two facts.…”

Section: Strategies For the Evaluation Of Tlm(σ τ)mentioning

confidence: 99%

Strategies for an efficient implementation of the Gauss–Bessel quadrature for the evaluation of multicenter integral over STFs

2007

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In a previous work, a new Gauss quadrature was introduced with a view to evaluate multicenter integrals over Slater-type functions efficiently. The complexity analysis of the new approach, carried out using the three-center nuclear integral as a case study, has shown that for low-order polynomials its efficiency is comparable to the SD. The latter was developed in connection with multi-center integrals evaluated by means of the Fourier transform of B functions. In this work we investigate the numerical properties of the Gauss-Bessel quadrature and devise strategies for an efficient implementation of the numerical algorithms for the evaluation of multi-center integrals in the framework of the Gaussian transform/Gauss-Bessel approach. The success of these strategies are essential to elaborate a fast and reliable algorithm for the evaluation of multi-center integrals over STFs.

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Addition theorem of Slater type orbitals: a numerical evaluation of Barnett–Coulson/Löwdin functions

Cited by 22 publications

References 84 publications

New index functions for storing Gaunt coefficients

New index functions for storing Gaunt coefficients

Combining Slater-type orbitals and effective core potentials

Strategies for an efficient implementation of the Gauss–Bessel quadrature for the evaluation of multicenter integral over STFs

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