A new collocation-based multi-configuration time-dependent Hartree (MCTDH) approach for solving the Schrödinger equation with a general potential energy surface.

Abstract

We present a new collocation-based multi-configuration time-dependent Hartree (MCTDH) approach for solving the Schrödinger equation required to compute (ro-)vibrational spectra, photodissociation cross sections, reaction rate constants, etc., that can be used with general potential energy surfaces. Collocation obviates the need for quadrature and facilitates using complicated kinetic energy operators. When the basis is good, the accuracy of collocation solutions to the Schrödinger equation is not sensitive to the choice of the collocation points. We test the collocation MCTDH equations we derive by showing that they can be used to compute accurate vibrational energy levels of CH3. It is possible to choose (imaginary) time-independent collocation points with which collocation-based MCTDH energies are accurate. It is therefore not necessary to calculate potential values many times during the propagation.