Tensor Hypercontraction for Electronic Structure Theory

Todd Martinez, Stanford
December 10th, 2014 at 3:30PM–4:30PM in 939 Evans Hall [Map]

The solution of the electronic Schrodinger equation, often known as quantum chemistry, can be computationally challenging. It has often been thought that the problem was of exponential complexity (with respect to the size of the molecule). A number of methods have been developed to solve the problem approximately in polynomial time but the simplest wavefunction-based methods including electron correlation already require computational effort scaling with the fifth power of the molecular size. We discuss the origin of this scaling behavior and give an overview of the types of manipulations which are required by the standard methods. Then we will introduce the tensor hypercontraction method as applied to the electron repulsion integrals. Tensor hypercontraction is a tensor decomposition technique and leads to scaling reductions of up to two powers of the molecular size for widely used methods. We show that the numerical accuracy of tensor hypercontraction is well within chemical accuracy (and indeed is more accurate than many other commonly used approximations). Relationships between tensor hypercontraction and numerical quadrature are explored. We further explain how the tensor hypercontraction idea can be applied not only to the Coulomb operator but also to the molecular wavefunction.