Tensor Decomposition and Vibrational Coupled Cluster Theory

The use of tensor decomposition in the calculation of anharmonic vibrational wave functions is discussed. The correlation amplitudes of vibrational coupled cluster (VCC) and vibrational configuration interaction (VCI) theories are considered as tensors and decomposed. A pilot code is implemented allowing a numerical study of the performance of the canonical decomposition/parallel factors (CP) for three and higher mode couplings in computations on water, formaldehyde, and 1,2,5-thiadiazole. The results show that there is a significant perspective in applying tensor decomposition in the context of anharmonic vibrational wave functions, with the CP tensor decomposition providing compression of data and a computational convenient representation. The calculations also illustrate how the multiplicative separability of the VCC ansatz with respect to noninteracting degrees of freedom goes well together with a tensor decomposition approach. Tensor decomposition opens for adjusting the computational effort spent on a particular mode-coupling according to the significance of that particular coupling, which is guaranteed to decrease to zero in the case of VCC in the limit of noninteracting subsystems.