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This paper applies stochastic tensor contraction (STC) to the exchange contribution of Laplace-transformed second-order Moller–Plesset perturbation theory (MP2), significantly reducing the computational cost from $O(N^5)$ to $O(N^2)$ for stochastic evaluations. By implementing a hybrid deterministic-stochastic evaluation strategy with grouped index sampling, the authors achieve a remarkable reduction in computation time, with evaluations taking as little as $1/270$ of traditional methods for benchmark molecules with up to 7000 basis functions. The unbiased estimator allows for precise control over stochastic error, enhancing the practicality of MP2 for larger systems in quantum chemistry.
Stochastic tensor contraction slashes MP2 exchange evaluation time to a fraction of traditional methods, making large-scale quantum chemistry calculations feasible.
Second-order Moller--Plesset perturbation theory (MP2) is one of the simplest correlated wave-function methods, but its conventional $O(N^5)$ cost limits its application to large systems. Stochastic tensor contraction (STC) has recently appeared as a general technique to evaluate high-order tensor contractions in quantum chemistry. Here, we apply STC to the exchange contribution of Laplace-transformed MP2, which is the source of $O(N^5)$ scaling in the formulation. The resulting STC exchange algorithm has an $O(N^3)$ deterministic setup cost and an $O(N^2)$ stochastic cost at fixed absolute error. The estimator is unbiased and provides a way to specify the target stochastic error by estimating the number of required samples before the full calculation. We implement the algorithm using a hybrid deterministic--stochastic evaluation strategy, with grouped index sampling, to reduce the computational prefactor. Over a range of benchmark molecules containing up to $\sim 7000$ basis functions, the stochastic exchange evaluation takes as little as $1/270$ of the time of a complete DF-MP2 calculation on the same system. Within the Laplace-transformed formulation, the $O(N^4)$ scaling direct contribution is thus the only significant cost. Our results further substantiate the power of STC to serve as a general tensor-contraction engine for quantum chemistry.