New complete orthonormal sets of hyperspherical harmonics and their one-range addition and expansion theorems.

Abstract:

:In this study, the complete orthonormal sets of phi(alpha)-momentum space orbitals (where alpha = 1, 0, -1, -2, ...) obtained from the psi(alpha)-ETO in coordinate representation (I.I. Guseinov, J. Mol. Model., 9 (2003) 135) are reduced to the complete orthonormal sets of hyperspherical harmonics (HSH) by means of a Fock transformation of the radial momentum to an angular variable. It is shown that the group of transformations is the four-dimensional rotation group O(4) and, therefore, the HSH presented in this work are the complete orthonormal sets of functions. For these functions, the one-range addition and expansion theorems are obtained. The formulae for HSH and their addition and expansion theorems derived in this work can be used to evaluate the multicenter integrals that arise when exponential-type basis functions are used in atomic and molecular calculations.

journal_name

J Mol Model

authors

Guseinov II

doi

10.1007/s00894-005-0093-8

subject

Has Abstract

pub_date

2006-09-01 00:00:00

pages

757-61

issue

6

eissn

1610-2940

issn

0948-5023

journal_volume

12

pub_type

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