Straightforward theoretical calculation for molecular systems using eigenfunctions built up from atomic orbitals and employing actual and approximate methods for the evaluation of certain integrals have recently been widely applied with considerable success. Most of these calculations have evaluated the difficult multicentered electron repulsion integrals by use of an approximate formula suggested by Mulliken, in terms of Coulombic and overlap integrals. Previous work has indicated the general utility of this relationship. Here, direct numerical comparison is made of actual and approximate values of the multicenter 1sorbital integrals. The comparisons indicate that this approximation of integrals is moderately accurate over a wide range of internuclear configurations. Direct calculations of the energy of the linear triatomic hydrogen complex molecule with this approximate integral formula disclose that the total binding energy obtained by the two procedures is different by several kcal/mole. However the energy variation with internuclear separations obtained from the approximate calculations has its minimum very near that obtained using actual integrals. This indicates that energy minimization by variation of the parameters included in the trial eigenfunction may be accomplished using these approximate integrals. Single calculations may then be made using these ``best'' parametric values.
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