Calculating vibrational excitation energies using tensor-decomposed vibrational coupled-cluster response theory

The first implementation of tensor-decomposed vibrational coupled cluster (CP-VCC) response theory for calculating vibrational excitation energies is presented. The CP-VCC algorithm, which has previously been applied to solving the vibrational coupled cluster (VCC) ground-state equations without explicitly constructing any tensors of order three or higher, has been generalized to allow transformations with the Jacobian matrix necessary for computation of response excitation energies by iterative algorithms. A new eigenvalue solver for computing CP-VCC excitation energies is introduced, and the different numerical thresholds used for controlling the accuracy of the obtained eigenvalues are discussed. Numerical results are presented for calculations of the 20 lowest eigenvalues on a set of 10 four-atomic molecules, as well as for a number of polycyclic aromatic hydrocarbons (PAHs) of increasing size, up to PAH8 with 120 modes. It is shown that the errors introduced by the tensor decomposition can be controlled by the choice of numerical thresholds. Furthermore, all thresholds can be defined relative to the requested convergence threshold of the equation solver, which allows black-box calculations with minimal user input to be performed. Eigenstates of PAHs were efficiently computed without any explicitly constructed tensors, showing improvements in both memory and central processing unit time compared to the existing full-tensor versions.