The fourth order electron repulsion integral (ERI) tensor is a ubiquitous source of complexity in electronic structure theory. Tensor hyper-contraction (THC) approximates the ERI tensor as a product of second-order tensors: (pq|rs) = ΣPQ [XpPXqQZPQXrQXsQ]. In this talk, we discuss recent progress towards developing accurate and efficient electron correlation methods for excited state simulations via THC. We begin with the physical intuition behind THC and the efficient computation of THC tensors through exploitation of atomic orbital sparsity and implementation on graphics processing units (GPUs). We then focus on how the THC factorization of ERI tensors leads to low-scaling formulations of electron correlation methods, in particular second order perturbation theory. In the simplest case of single-reference MP2, the THC factorization of the ERI tensor naturally leads to factorizations of both the wave function amplitudes and the perturbation operator. This allows both the MP2 correlation energy and gradients to be formulated as tensor operations that scale as O(N4) with respect to the system size, providing an efficient way to incorporate dynamic correlation in ab initio molecular dynamics (AIMD) simulations. To describe strong electron correlation, multi-reference wavefunctions are needed, e.g. multi-state second order perturbation theory (MSPT2). We show how the concepts and tensor operations developed in single reference MP2 can be generalized and extended to the multi-reference case.

Reduced-order formulation of multi-reference perturbation theory via tensor hyper-contraction

253rd National Meeting (2017)

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