LAUSR

We report a complete implementation of the coupled-cluster method with single, double, and triple excitations (CCSDT) where tensor decompositions are used to reduce its scaling and overall computational costs. For the decomposition of the electron repulsion integrals the standard density fitting (or Cholesky decomposition) format is used. The coupled-cluster single and double amplitudes are treated conventionally, and for the triple amplitudes tensor we employ the Tucker-3 compression formula, $t_{ijk}^{abc} \approx t_{XYZ} \,U^X_{ai}\,U^Y_{bj} \,U^Z_{ck}$. The auxiliary quantities $U^X_{ai}$ come from singular value decomposition (SVD) of an approximate triple amplitudes tensor based on perturbation theory. The efficiency of the proposed method relies on an observation that the dimension of the ``compressed'' tensor $t_{XYZ}$ sufficient to deliver a constant relative accuracy of the correlation energy grows only linearly with the size of the system, $N$. This fact, combined with proper factorization of t...