The adaptive hierarchical expansion of the kinetic energy operator

The hierarchical expansion of the kinetic energy (HEKE) operator in curvilinear coordinates presented recently (Strobusch and Scheurer, J. Chem. Phys. 2011a, 135, 124102; Strobusch and Scheurer, J. Chem. Phys. 2011b, 135, 144101) relies on a many-body expansion of the metric tensor. It is shown how this expansion can be adapted to a specific system. An analytic formula is derived, which yields an estimate of the impact of a certain expansion term on the spectrum. In combination with the hierarchical structure of the many-body expansion and interpolation techniques, the memory consumption and evaluation time of the HEKE operator as well as the computational costs for subsequent vibrational self-consistent field and vibrational configuration interaction calculations are reduced significantly, which is demonstrated by studies on two small test systems H2O2 and formaldehyde (H2CO).