The use of Gaussian (exponential quadratic) wave functions in molecular problems - I. General formulae for the evaluation of integrals

Abstract
It is shown that for wave functions of the form ψ = ∑ k ⁡ C k exp ⁡ ( − Q k ) , , where Q k is any positive definite quadratic form in the Cartesian co-ordinates of n particles and C k a constant, all integrals required for the calculation of the electronic energy of molecules by the variation method can be readily evaluated. The potential energy integrals are reduced to quadratures and the other integrals are expressed in closed form. In the general case the quadratic forms Q k determine many-electron functions formed from correlated electron orbitals of ellipsoidal symmetry and with variable centres. The results are easily extended to wave functions of the form ψ = ∑ k ⁡ P k exp ⁡ ( − Q k ) , , where P k is a polynomial.

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