Sturmian approach to one-electron many-center systems: integrals and iteration schemes

Aquilanti, Vincenz̊o; Caligiana, Andrea

doi:10.1016/s0009-2614(02)01532-4

Cited by 31 publications

(15 citation statements)

References 23 publications

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“…(26) for N = 150 and v max = 20 using different translations of orbitals. As can be seen from Tables I–III, our results are in good agreement with values obtained in literature 19, 21, 31.…”

Section: Numerical Results and Discussionsupporting

confidence: 92%

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Evaluation of one‐electron molecular integrals over complete orthonormal sets of Ψ^α ‐ETO using auxiliary functions

Guseinov

Şahin

2009

Int J of Quantum Chemistry

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By the use of expansion and one-range addition theorems, the oneelectron molecular integrals over complete orthonormal sets of ⌿ ␣ -exponential type orbitals arising in Hartree-Fock-Roothaan equations for molecules are evaluated. These integrals are expressed through the auxiliary functions in ellipsoidal coordinates. The comparison is made using Slater-, Coulomb-Sturmian-, and Lambda-type basis functions. Computation results are in good agreement with those obtained in the literature. The relationships obtained are valid for the arbitrary quantum numbers, screening constants, and location of orbitals.

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Section: Numerical Results and Discussionsupporting

confidence: 92%

“…The Coulomb–Sturmian ETO basis set has long been used by various authors in atomic and molecular electronic structure calculations (see Refs. 21–24 and references therein).…”

Section: Introductionmentioning

confidence: 99%

Evaluation of one‐electron molecular integrals over complete orthonormal sets of Ψ^α ‐ETO using auxiliary functions

Guseinov

Şahin

2009

Int J of Quantum Chemistry

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“…The efficient application of Coulomb Sturmians in atomic physics makes possible to use this method to molecular calculations. For one-electron many-centre systems the calculations with Coulomb Sturmians have been reported in several papers [3][4][5][6][7][8][9]. In [10,11] Coulomb Sturmians have been used to treat many-centre manyelectron problems and the pilot calculations have been performed for N -electron molecules using the generalised Sturmian method.…”

Section: Introductionmentioning

confidence: 99%

Coulomb Sturmians in spheroidal coordinates and their application for diatomic molecular calculations

2015

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Coulomb Sturmians are obtained in prolate spheroidal coordinates by separation of variables in the Schrödinger equation and direct solution of the appropriate one-dimensional equations. Molecular orbitals are expressed as linear combinations of the introduced Coulomb Sturmians and some low-lying energy terms and corresponding wave functions are calculated for one-electron diatomic molecules. It is shown that similarity of the one-and two-centre orbitals in spheroidal coordinates, combined with completeness and good convergence properties of Coulomb Sturmians, substantially speeds up convergence and makes the calculated results closer to the exact ones. Application of the elaborated calculating scheme for diatomic many-electron molecules is discussed.

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“…The efficient application of Coulomb Sturmians in atomic physics makes possible the use of this method in molecular calculations. For systems of one electron and many centres, calculations with Coulomb Sturmians are reported in several papers [5][6][7][8][9][10][11]. Coulomb Sturmians have been used to treat problems involving many centres and many electrons [12,13]; pilot calculations were performed for N-electron molecules using the generalised Sturmian method.…”

Section: Introductionmentioning

confidence: 99%

Derivation, properties and application of Coulomb Sturmians defined in spheroidal coordinates

et al. 2015

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Coulomb Sturmian amplitude functions are derived in prolate spheroidal coordinates and are presented in a closed algebraic form. Spheroidal Sturnian functions are revealed to be related to the polynomial solutions of Heun's confluent equation. A reduction of symmetry from spherical to axial leads to the coupling of spherical polar orbitals and the formation of hybrid orbitals. The contribution of each spherical orbital into a hybrid orbital depends strongly on distance R from a nucleus to the dummy centre, and substantially alters when R varies. At two limiting cases R = 0 and R → ∞ spheroidal Sturmians are purely atomic orbitals, whereas at intermediate R they contain many features intrinsic to diatomic molecular orbitals. Applications of spheroidal Sturmian basis are discussed; Coulomb spheroidal Sturmians are asserted to be the most appropriate basis functions for diatomic molecular calculations.

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Sturmian approach to one-electron many-center systems: integrals and iteration schemes

Cited by 31 publications

References 23 publications

Evaluation of one‐electron molecular integrals over complete orthonormal sets of Ψ^α ‐ETO using auxiliary functions

Evaluation of one‐electron molecular integrals over complete orthonormal sets of Ψ^α ‐ETO using auxiliary functions

Coulomb Sturmians in spheroidal coordinates and their application for diatomic molecular calculations

Derivation, properties and application of Coulomb Sturmians defined in spheroidal coordinates

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Sturmian approach to one-electron many-center systems: integrals and iteration schemes

Cited by 31 publications

References 23 publications

Evaluation of one‐electron molecular integrals over complete orthonormal sets of Ψα ‐ETO using auxiliary functions

Evaluation of one‐electron molecular integrals over complete orthonormal sets of Ψα ‐ETO using auxiliary functions

Coulomb Sturmians in spheroidal coordinates and their application for diatomic molecular calculations

Derivation, properties and application of Coulomb Sturmians defined in spheroidal coordinates

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Evaluation of one‐electron molecular integrals over complete orthonormal sets of Ψ^α ‐ETO using auxiliary functions

Evaluation of one‐electron molecular integrals over complete orthonormal sets of Ψ^α ‐ETO using auxiliary functions