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


Guseinov I. I.

JOURNAL OF MOLECULAR MODELING, cilt.12, ss.757-761, 2006 (SCI İndekslerine Giren Dergi) identifier identifier identifier

  • Cilt numarası: 12 Konu: 6
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1007/s00894-005-0093-8
  • Dergi Adı: JOURNAL OF MOLECULAR MODELING
  • Sayfa Sayıları: ss.757-761

Özet

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.