A numerically exact correlation discrete variable representation for multi-configurational time-dependent Hartree calculations.

The correlation discrete variable representation (CDVR) enables (multilayer) multi-configurational time-dependent Hartree (MCTDH) calculations with general potentials. The CDVR employs a set of grids corresponding to single-particle functions to efficiently evaluate all potential matrix elements appearing in the MCTDH equations of motion. In standard CDVR approaches, the number of grid points employed is tied to the number of corresponding single-particle functions. This limits the accuracy of the quadrature, which can be achieved for a given single-particle function basis. In this work, an extended CDVR approach that facilitates a numerically exact quadrature of all potential matrix elements is introduced. The number of grid points employed can be increased independent of the number of corresponding single-particle function to achieve any desired quadrature accuracy. The properties of the new scheme are illustrated by numerical calculations studying the photodissociation of NOCl and the vibrational states of CH3. Fast convergence with respect to the number of additional quadrature points is observed: Employing a single additional point in each physical or logical coordinate already ensures negligible quadrature errors.