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The energy of a molecule is expressed as a summation involving the expectations values of a two-electron Hamiltonian. An approximation which has been used for atomic systems, involving the weight factors in this summation, was made to evaluate the energies for the lithium molecule and of an isolated lithium atom. It was found that at 4.0 a.u. the bonding energy was of the correct order of magnitude, but the correlation energy of the system was overestimated giving an error in the total energy of the molecule of 1.3%. An alternative approximation for the evaluation of the summation was proposed, and it was found to give rise to an error of 0.3% in the total energy and a bonding energy of the correct order of magnitude. Attention is given to the application of geminal methods to larger systems.

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