The general Gaussian product theorem

The Gaussian Product Theorem between two 1s Gaussian Type Orbitals (GTOs) is extended to an arbitrary number of s-type functions, giving a compact formula which permits to express the condensed GTO result. Then, this new formulation is combined with the product of arbitrary GTO Cartesian angular parts, obtaining a finite expansion expressing this product as a multilinear combination of such functions sharing a common center. The combination of both results constitutes the General Gaussian Product Theorem (GGPT), a final compact expression for the product of an arbitrary number of Cartesian GTOs. The notation provides an easy way to express algebraically any general multicenter GTO product expression. It is also shown how by means of Nested Summation Symbols the computational implementation can be easily and elegantly achieved. Computational parallelizable schemes of the GGPT are provided.