Premium
Fourier transforms of atomic orbitals. I. Reduction to four‐dimensional harmonics and quadratic transformations
Author(s) -
Niukkanen A. W.
Publication year - 1984
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.560250603
Subject(s) - fourier transform , harmonics , quadratic equation , reduction (mathematics) , fourier series , mathematics , spin weighted spherical harmonics , basis function , exponential function , atomic orbital , mathematical analysis , physics , quantum mechanics , electron , geometry , voltage
A general expression for the Fourier transform of the basis functions of exponential class has been derived. Particular cases of Slater functions, hydrogen‐like functions, Shull and Löwdin functions, Shavitt, Filter, and Steinborn functions have been considered. In many particular cases the Fourier transforms have been shown to reveal some important special properties (reduction to four‐dimensional harmonics, quadratic transformations, etc.) which considerably simplify the mathematical treatment of these functions and lead to new possibilities in the development of calculation methods for multicenter integrals.