On the momentum-space approach to calculation of one-electron energy spectra and wave functions of atomic clusters

Abstract

Momentum-space approach to calculation of one-electron energies and wave functions proposed initially by Fock for a hydrogen atom and considered later by Shibuya, Wulfman, and Koga for diatomic molecules is applied to clusters composed of three and more atoms. The corresponding basis set in the coordinate space is of the Sturmian type since all the hydrogenlike orbitals in this set have a common exponent, i.e., correspond to the same energy (as opposed to one-electron atomic orbitals). By the examples of He$_4^{+7}$ and He$_6^{+11}$ cluster ions it is shown that increase in the number of orbitals in the set results in rapid convergence of eigenenergies and eigenfunctions of highly excited states. The momentum-space approach to the one-electron many-center problem may be used for various solid-state and quantum-chemical applications.