Numerical Studies of the Tunneling Splitting of Malonaldehyde and the Eigenstates of Hydrated Hydroxide Anion Using MCTDH

A detailed and accurate description of vibrations of molecules and chemical reactions in the field of physical chemistry often requires a full quantum mechanical treatment of the system of interest. This usually implies that the time-dependent or the time-independent Schrödinger equation of the nuclear degrees of freedom (DOF) has to be solved explicitly. For small systems (up to six internal DOF) this can be done with standard methods, i.e., by directly sampling the quantum mechanical wavefunction on a (product-) grid and solving the Schrödinger equation on these grid points. Numerically, within the standard method the multi-dimensional quantum mechanical wavefunction is stored as an f-way tensor, where f is the number of DOF. Due to the linearity of the Schrödinger equation the resulting numerical tasks then usually reduce to standard problems such as the calculation of eigenvalues or solving first order differential equations.