Calculation of highly excited vibrational levels: a prediagonalized Davidson scheme

We present a new approach based on the Davidson algorithm which provides eigenvalues and eigenvectors of selected highly excited (ro)vibrational states of polyatomic molecules. The key ingredient is a prediagonalization–perturbation scheme applied to a subspace of a curvilinear normal modes basis set (including diagonal anharmonicities). The efficiency of this method is illustrated by computing all vibrational states of the H2CO molecule, up to 9500 cm−1 of internal excitation. Convergence of the levels can be assessed during the iteration process by looking at the residual ||(Ĥ−Eα)|Ψα〉||.