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Computation of Fourier transform quantities in Hartree–Fock calculations for simple crystals
Author(s) -
Graovac Ante,
Monkhorst Hendrik J.,
Glasser M. L.
Publication year - 1975
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560090206
Subject(s) - fourier transform , computation , atomic orbital , simple (philosophy) , orbital overlap , lattice (music) , hartree–fock method , fractional fourier transform , discrete fourier transform (general) , physics , mathematical analysis , mathematics , fourier analysis , chemistry , quantum mechanics , algorithm , philosophy , epistemology , acoustics , electron
An efficient method is presented to compute the Fourier transforms of lattice sums over Slater‐type orbital products that arise in crystal Hartree–Fock calculations. Introduction of one‐dimensional integral representations for the Fourier transforms of the STO 'S enables a separation of the three infinite sums under the (two‐dimensional) integral sign. This, in turn, makes it possible to calculate and store quantities associated with the three Fourier transform vector components separately. The orbital transform integrations are then performed numerically. The method is very advantageous when lattice sum transforms are needed for a large number of transform vectors. Formulas and results are presented for simple‐cubic crystals when 1 s , 2 s , and 2 p Slater orbitals are involved.