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Some Integrals for Molecular Properties and Relativistic Effects over Hermite-Gaussian Functions

Z. B. Maksić ; Theoretical Chemistry Group, »Ruder Boskovic« Institute, 41001 Zagreb, Yugoslavia
A. Graovac ; Theoretical Chemistry Group, »Ruder Boskovic« Institute, 41001 Zagreb, Yugoslavia
M. Primorac ; Metalski skolski centar »Prvomajska«, Drziceva bb, 41000 Zagreb, Yugoslavia

Puni tekst: engleski pdf 7.123 Kb

str. 265-279

preuzimanja: 283



Formulas for some integrals over Hermite-Gaussian functions
occurring in the calculations of the molecular first and second order
properties as well as relativistic corrections arising in the Breit
hamiltonian are discussed. It is shown that all these molecular
properties integrals can be reduced to the integrals already encountered
in the minimum energy calculations. More specifically, the
one-electron and two-electron integrals involving (l/r1 j)" operator,
where j denotes either the coordinates of a nucleus or the coordinates
of the electron 2 and n is an integer, are expressed in terms
of nuclear attraction and Coulomb repulsion integrals, respectively.
Therefore the electric and magnetic properties of molecules can be
computed with little additional effort if the Hermite-Gaussian basis
set is employed. The same conclusion holds for the matrix elements
arising in the pseudo-potential calculations involving the Bonifacic-
Huzinaga model potential which in turn give a fair description
of the heavy atoms inner-shell electrons. Since the Hermite-
Gaussian functions are particularly advantageous for atomic orbitals
with higher angular momentum quantum numbers (f, g, h
etc.) their use is expected to be preferable in molecules involving
heavy atoms. The relativistic effects are of great importance for
the latter and it is gratifying that the corresponding integrals over
Hermite-Gaussians can be expressed in a closed form.

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