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Implementation of the Coupled-Cluster Method with Single, Double, and Triple Excitations using Tensor Decompositions
journal contribution
posted on 2019-12-11, 13:08 authored by Michał LesiukWe report a complete implementation of the coupled-cluster
method
with single, double, and triple excitations (CCSDT) in which tensor
decompositions are used to reduce 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, tijkabc ≈ tXYZ UaiX UbjY UckZ. The auxiliary
quantities UaiX 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 tXYZ 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 the coupled-cluster
equations, leads to practically N6 scaling
of the computational costs of the proposed method, as illustrated
numerically for linear alkanes with increasing chain length. This
constitutes a considerable improvement over the N8 scaling of the conventional (uncompressed) CCSDT theory.
The accuracy of the proposed method is verified by benchmark calculations
of total and relative energies for several small molecular systems
and comparison with the exact CCSDT method. The accuracy levels of
1 kJ/mol are easily achievable with reasonable SVD subspace size,
and even more demanding levels of accuracy can be reached with a considerable
reduction of the computational costs. Extensions of the proposed method
to include higher excitations are briefly discussed, along with possible
strategies of reducing other residual errors.