It has long been suspected that the amount of useful information in the two-electron repulsion integrals was far less than it would appear at first glance. A number of approaches such as the resolution-of-the-identity (also known as density fitting), pseudospectral, and Cholesky factorization methods have been developed as ansatzes to enforce compact and efficient representations of the Coulomb operator. We show that a more flexible formulation exists (tensor hypercontraction), uncovering hidden structure in the fourth-order two-electron repulsion integral tensor. This tensor hypercontraction approach reduces the scaling of many electronic structure methods by one to two powers of the molecular size. We further show that the same ideas can be applied to wavefunction amplitudes, leading to an O(N4) scaling coupled cluster single and double excitation method.  Finally, we show that the tensor hypercontraction scheme is ideally suited to GPUs.

Tensor hypercontraction and graphical processing units for electronic structure and ab initio molecular dynamics

246th National Meeting (2013)

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