  We study the decomposition of the Coulomb integrals of periodic systems into
a tensor contraction of six matrices of which only two are distinct. We find
that the Coulomb integrals can be well approximated in this form already with
small matrices compared to the number of real space grid points. The cost of
computing the matrices scales as O(N^4) using a regularized form of the
alternating least squares algorithm. The studied factorization of the Coulomb
integrals can be exploited to reduce the scaling of the computational cost of
expensive tensor contractions appearing in the amplitude equations of coupled
cluster methods with respect to system size. We apply the developed
methodologies to calculate the adsorption energy of a single water molecule on
a hexagonal boron nitride monolayer in a plane wave basis set and periodic
boundary conditions.
