Iterative diagonalization in the state-averaged multi-configurational time-dependent Hartree approach: excited state tunneling splittings in malonaldehyde.

An iterative block Lanczos-type diagonalization scheme utilizing the state-averaged multi-configurational time-dependent Hartree (MCTDH) approach is introduced. Combining propagation in real and imaginary time and using a set of initial seed wavefunctions corresponding to excitations via the different components of the dipole moment vector, the scheme can favorably be used to selectively compute vibrational states which show high intensities in vibrational absorption spectra. Tunneling splitted vibrational states in double well systems can be described particularly efficient employing an increased set of seed wavefunctions which includes symmetric and anti-symmetric wavefunctions simultaneously. The new approach is used to study the tunneling splittings of the vibrationally excited states of malonaldehyde. Full-dimensional multi-layer MCTDH calculations are performed and results for the tunneling splittings of several excited vibrational states can be obtained. The calculated tunneling splittings agree reasonably well with available experimental data. Order of magnitude differences between tunneling splittings of different vibrationally excited states are found and interpreted.