Calculation of molecular integrals in momentum space

Epstein, Irving R.

doi:10.1016/0009-2614(71)80167-7

Cited by 24 publications

(1 citation statement)

References 11 publications

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“…Consequently several theoretical contributions to the study of atomic electron momentum distributions have been reported so far, including analytical expressions for electron momentum distributions of small atoms using Slater basis sets [13][14][15][16][17], as well as calculations of CP of elements at Hartree-Fock level (HF) using double-zeta and numerical wave functions [18,19]. Furthermore, total momentum expectation values and other p-space properties [20][21][22] have been computed, and more recently, Ozdogan and Eraslam have published analytical calculations of CP using Clementi Roothan-Hartree-Fock functions for atoms ranging from helium to neon [23].…”

Section: Introductionmentioning

confidence: 99%

Accurate atomic momentum integrals and Compton profiles

Miguel¹,

López²,

Vega³

2020

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

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Analytical expressions for integrals involving momentum density have been developed, and an algorithm for the efficient computation of Compton profiles (CPs) based in those equations is reported. The performance of the algorithm is tested by computing the CPs of atoms from helium to xenon for a wide range of incident photon energies. Calculations have been made at Hartree–Fock level (HF), using three different Slater basis sets, showing a good agreement with the experimental results.

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Section: Introductionmentioning

confidence: 99%

Accurate atomic momentum integrals and Compton profiles

Miguel¹,

López²,

Vega³

2020

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

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Slater‐orbital molecular integrals by numerical Fourier‐transform methods. II. Four‐center integrals over is orbitals

Graovac

Kovačević²,

Maksi

et al. 1980

Int J of Quantum Chemistry

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AbstractsThe four-center nonplanar electron repulsion integrals over 1s Slater-type atomic orbitals are considered by a numerical Fourier-transform method. It is shown that the highly oscillating integrand appearing in the Fourier inversion formula could be successfully treated by using Tchebyscheff quadrature. The resulting formulas are thoroughly discussed with particular emphasis on their numerical features and convergence properties. It follows that the aforementioned integrals may be calculated with a good accuracy with a moderate amount of computing time. Les intkgrales de la repulsion

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Calculation in K space of integrals arising in the theory of Van Der Waals forces

Malinowski

Tanner

Lee

et al. 1982

Int J of Quantum Chemistry

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We derive basic integrals needed for calculation of matrix elements of the Fourier transformed Coulomb operator and the Fourier transformed square of the Coulomb operator between 1s Slater functions. These integrals arise, for example, in the momentum space (k space) susceptibility formulation of van der Waals forces. The advantages of integration i n k space (rather than r space) are that in k space there is a drastic reduction in the number of integration variables, and contour integration can be used. The derivation is completely analytic and the auxiliary integrals are all obtained in closed form.

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Calculation of molecular integrals in momentum space

Cited by 24 publications

References 11 publications

Accurate atomic momentum integrals and Compton profiles

Accurate atomic momentum integrals and Compton profiles

Slater‐orbital molecular integrals by numerical Fourier‐transform methods. II. Four‐center integrals over is orbitals

Calculation in K space of integrals arising in the theory of Van Der Waals forces

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