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 Modeljournal_title
Journal of molecular modelingauthors
Guseinov IIdoi
10.1007/s00894-005-0093-8subject
Has Abstractpub_date
2006-09-01 00:00:00pages
757-61issue
6eissn
1610-2940issn
0948-5023journal_volume
12pub_type
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