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

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

doi:10.1002/jcc.20131

Cited by 55 publications

(31 citation statements)

References 92 publications

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“…In addition the code accepts both GTO and STO basis sets; for the latter basis the many-center integrals are obtained with the SMILES code. 41 The code features such as computations of HF, HL, HF-HL, MC-HF, MC-HL, and MC-HF-HL wave functions are detailed elsewhere. 42,43 …”

Section: Computational Detailsmentioning

confidence: 99%

Energy and density analyses of the H2 molecule from the united atom to dissociation: The ∑1g+ states

Corongiu

Clementi

2009

The Journal of Chemical Physics

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The first 15 (1)Sigma(g)(+) states of the H(2) molecule are computed with full configuration interaction (CI) both from Hartree-Fock molecular orbitals and Heitler-London atomic orbitals; the computations are correlated with a comprehensive analysis. The basis sets utilized are extended and optimized Slater-type functions [Slater-type orbital (STO)] and spherical Gaussian functions [Gaussian-type orbital (GTO)]. The full CI computations cover the internuclear distances from 0.01 to 10,000 bohr. The available accurate data by Wolniewicz and co-workers for the first five excited states verify the quality of our computations. We focus on the characterization of the orbitals in the wave functions, on the electronic density evolution from the united atom to dissociation, on quantitative decomposition of the total energy into covalent and ionic components, and on detailed analyses of energy contributions to the total state energy from selected STO and GTO subsets. These analyses lead to study (with full CI) the H(-) negative ion with a proton and the H(+)H(-) ion pair systems. The ground and excited states for the He and H atoms and for the H(-) ion are computed to discuss the united atom and the dissociation products H(1s)+H(nl) of the n state manifolds. With the exception of n=1, each manifold has one state, specifically the EF, H, 7, and 11, whose second minimum has strong ionic character; state 11 dissociates as H(+)H(-).

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Section: Computational Detailsmentioning

confidence: 99%

Energy and density analyses of the H2 molecule from the united atom to dissociation: The ∑1g+ states

Corongiu

Clementi

2009

The Journal of Chemical Physics

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“…The Gauss transform methods are more involved and use some integral representations in order to transform STO into a more computationally convenient form. The initial proposition of Shavitt and Karplus [27][28][29] was to use the Laplace transform of the exponential function but now a handful of different schemes is in use, along with suitable discretization techniques [30].…”

Section: Introductionmentioning

confidence: 99%

Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. I. Coulomb and hybrid integrals

Lesiuk

Moszyński

2014

Phys. Rev. E

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In this paper, which constitutes the first part of the series, we consider calculation of two-center Coulomb and hybrid integrals over Slater-type orbitals. General formulas for these integrals are derived with no restrictions on the values of the quantum numbers and nonlinear parameters. Direct integration over the coordinates of one of the electrons leaves us with the set of overlaplike integrals which are evaluated by using two distinct methods. The first one is based on the transformation to the ellipsoidal coordinates system and the second utilizes a recursive scheme for consecutive increase of the angular momenta in the integrand. In both methods simple one-dimensional numerical integrations are used in order to avoid severe digital erosion connected with the straightforward use of the alternative analytical formulas. It is discussed that the numerical integration does not introduce a large computational overhead since the integrands are well-behaved functions, calculated recursively with decent speed. Special attention is paid to the numerical stability of the algorithms. Applicability of the resulting scheme over a large range of the nonlinear parameters is tested on examples of the most difficult integrals appearing in the actual calculations including, at most, 7i-type functions (l=6).

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“…2 Full configuration interaction ͑CI͒ computations within the Born-Oppenheimer ͑BO͒ approximation are performed with extended Slater and Gaussian basis sets. In our computer code for nonorthogonal CI, 3 the integrals with Slater-type function ͑STF͒ functions are calculated by the SMILES code developed by Fernandez Rico et al 4 Discussions on the basis sets and details of the techniques used to analyze the computed wave functions and energies, when common to the work in Refs. 1 and 2, are only summarized.…”

Section: Introductionmentioning

confidence: 99%

“…For example, in the 3 ⌺ g + manifold, note the barriers in states 2 and 5-10 after the internuclear distance of 4 bohrs. For the 3 ⌺ u + manifold, note the bumps for states [3][4][5][6][7][8][9][10][11][12][13][14]. Note in addition the crossings for the 3 ⌺ g + manifold, immediately before the equilibrium distance, between states 2 and 3, 4 and 5, and the very close energies for the three states 11-13.…”

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confidence: 97%

Energy and density analysis of the H2 molecule from the united atom to dissociation: The Σ3g+ and Σ3u+ states

Corongiu

Clementi

2009

The Journal of Chemical Physics

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The first 14 (3)Sigma(g)(+) and the first 15 (3)Sigma(u)(+) states of the H(2) molecule are computed with full configuration interaction both from Hartree-Fock molecular orbitals and Heitler-London atomic orbitals within the Born-Oppenheimer approximation, following recent studies for the (1)Sigma(g)(+) and (1)Sigma(u)(+) manifolds [Corongiu and Clementi, J. Chem. Phys. 131, 034301 (2009) and J. Phys. Chem. (in press)]. The basis sets utilized are extended and optimized Slater-type functions and spherical Gaussian functions. The states considered correspond to the configurations (1s(1)nl(1)) with n from 1 to 5; the internuclear separations sample the distances from 0.01 to 10,000 bohrs. For the first three (3)Sigma(g)(+) and (3)Sigma(u)(+) states and for the fourth and fifth (3)Sigma(g)(+) states, our computed energies at the equilibrium internuclear separation, when compared to the accurate values by Staszewska and Wolniewicz and by Kołos and Rychlewski, show deviations of about 0.006 kcal/mol, a test on the quality of our computations. Motivation for this work comes not only from obtaining potential energy curves for the high excited states of H(2) but also from characterizing the electronic density evolution from the united atom to dissociation to provide a detailed analysis of the energy contributions from selected basis subsets and to quantitatively decompose the state energies into covalent and ionic components. Furthermore, we discuss the origin of the seemingly irregular patterns in potential energy curves in the two manifolds, between 4 and 6-9 bohrs--there are two systems of states: the first, from the united atom to about 4 bohrs, is represented by functions with principal quantum number higher than the one needed at dissociation; this system interacts at around 4 bohrs with the second system, which is represented by functions with principal quantum number corresponding to one of the dissociation products.

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

Cited by 55 publications

References 92 publications

Energy and density analyses of the H2 molecule from the united atom to dissociation: The ∑1g+ states

Energy and density analyses of the H2 molecule from the united atom to dissociation: The ∑1g+ states

Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. I. Coulomb and hybrid integrals

Energy and density analysis of the H2 molecule from the united atom to dissociation: The Σ3g+ and Σ3u+ states

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