Efficient Singular-Value Decomposition of the Coupled-Cluster Triple Excitation Amplitudes

We demonstrate a novel technique to obtain singular‐value decomposition (SVD) of the coupled‐cluster triple excitations amplitudes, urn:x-wiley:01928651:media:jcc25788:jcc25788-math-0001. The presented method is based on the Golub‐Kahan bidiagonalization strategy and does not require urn:x-wiley:01928651:media:jcc25788:jcc25788-math-0002 to be stored. The computational cost of the method is comparable to several coupled cluster singles and doubles (CCSD) iterations. Moreover, the number of singular vectors to be found can be predetermined by the user and only those singular vectors which correspond to the largest singular values are obtained at convergence. We show how the subspace of the most important singular vectors obtained from an approximate triple amplitudes tensor can be used to solve equations of the CC3 method. The new method is tested for a set of small and medium‐sized molecular systems in basis sets ranging in quality from double‐ to quintuple‐zeta. It is found that to reach the chemical accuracy (≈1 kJ/mol) in the total CC3 energies as little as 5 − 15% of SVD vectors are required. This corresponds to the compression of the urn:x-wiley:01928651:media:jcc25788:jcc25788-math-0003 amplitudes by a factor of about 0.0001 − 0.005. Significant savings are obtained also in calculation of interaction energies or rotational barriers, as well as in bond‐breaking processes.