Alternative basis functions for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>calculations on the molecular continuum. I. The basic prototype integrals

Fortunelli, Alessandro; Carravetta, Vincenzo

doi:10.1103/physreva.45.4426

Cited by 2 publications

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References 16 publications

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“…These are generally obtained by a matching with the corresponding regular and irregular Coulomb wave in a region far from the molecule where the potential is purely Coulombic. The several types of L 2 bases employed to represent the molecular electronic continuum have been described and compared by Fortunelli and Carravetta [16].…”

Section: Introductionmentioning

confidence: 99%

Performance of polynomial Gaussian functions in describing the molecular electronic continuum

Cacelli

1997

J. Phys. B: At. Mol. Opt. Phys.

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The continuum molecular orbitals arising from L 2 calculations using special polynomial Gaussian functions are accurately tested to probe their capability in producing accurate photoemission cross sections. The molecular potential is represented by the local Xα approximation, which permits a comparison with numerically integrated (exact) orbitals. Several strong anisotropic molecules are taken into account to check the flexibility of the L 2 bases in the presence of strong attractive potentials. This work shows that for adequate choices of Gaussian functions, phase shifts may be estimated with reasonable accuracy while the errors in the continuum transition probabilities are within 2-3% in the more unfavourable cases. Therefore, the proposed basis sets appear to be suitable for the description of the electronic continuum in molecular photoionization calculations.

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Section: Introductionmentioning

confidence: 99%

Performance of polynomial Gaussian functions in describing the molecular electronic continuum

Cacelli

1997

J. Phys. B: At. Mol. Opt. Phys.

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Alternative basis functions forL2calculations on the molecular continuum. II. Integrals with higher-order functions

Fortunelli¹,

Carravetta²

1992

Phys. Rev. A

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By differentiation of the expressions for the basic s-type integrals previously presented, analytic expressions are here derived for integrals, relevant for quantum-chemistry calculations, involving oscillating Hermite Gaussian functions (OHGF's) and many-center Hermite Gaussian functions (HGF's) of any order. The OHGF is the product of a HGF and a radial trigonometric factor cos(kr), and has been proposed for describing the continuum orbitals in L calculations on molecules. The resulting expressions are compact and particularly suitable for numerical implementation on a computer, while the increase in the computational effort of the integral evaluation with respect to the s-type functions is estimated to be of the same order as that found in the standard case of simple Gaussian functions. Applications of the OHGF basis to the calculation of continuum states are presented and compared to the exact results for test cases: the hydrogen atom and the H, + molecule, in order to discuss advantages and limitations of the proposed approach.PACS number(s): 31.15. +q, 02.60.+y

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Alternative basis functions forL2calculations on the molecular continuum. I. The basic prototype integrals

Cited by 2 publications

References 16 publications

Performance of polynomial Gaussian functions in describing the molecular electronic continuum

Performance of polynomial Gaussian functions in describing the molecular electronic continuum

Alternative basis functions forL2calculations on the molecular continuum. II. Integrals with higher-order functions

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