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We study the decomposition of the Coulomb integrals of periodic systems intoa tensor contraction of six matrices of which only two are distinct. We findthat the Coulomb integrals can be well approximated in this form already withsmall matrices compared to the number of real space grid points. The cost ofcomputing the matrices scales as O(N^4) using a regularized form of thealternating least squares algorithm. The studied factorization of the Coulombintegrals can be exploited to reduce the scaling of the computational cost ofexpensive tensor contractions appearing in the amplitude equations of coupledcluster methods with respect to system size. We apply the developedmethodologies to calculate the adsorption energy of a single water molecule ona hexagonal boron nitride monolayer in a plane wave basis set and periodicboundary conditions.

Low rank factorization of the Coulomb integrals for periodic coupled cluster theory