Adiabatic approximation and nonadiabatic corrections in the discrete variable representation: Highly excited vibrational states of triatomic molecules
Abstract
An adiabatic approximation for the calculation of excited vibrational (J=0) levels of triatomic molecules is developed using the discrete variable representation (DVR). The DVR is in the large amplitude bending motion coordinate which is taken to be the adiabatic degree of freedom. We show that the adiabatic treatment in the DVR has some major advantages over the usual formulation in the finite basis representation (FBR), namely improved accuracy and broader range of applicability. An adiabatic rearrangement of the full Hamiltonian matrix in the DVRray eigenvector (REV) basis is defined, such that the diagonal blocks provide the rigorous matrix representation of the adiabatic bend Hamiltonian; their diagonalization yields bending level progressions corresponding to various stretching states. The offdiagonal blocks contain all nonadiabatic coupling matrix elements. The nonadiabatic corrections to the adiabatic vibrational levels are readily taken into account via secondorder perturbation theory. One unique feature of our approach is that, in contrast to the FBR formulation, evaluation of the adiabatic and nonadiabatic matrix elements does not require evaluation of derivatives of the stretching wave functions with respect to the adiabatic variable. This approach is tested on the twomode LiCN/LiNC (fixed CN distance) and the threemode HCN/HNC. The adiabatic vibrational levels are in good agreement with accurate variational results. When corrected by secondorder perturbative treatment, many levels are given very accurately (to within 0.1%) even for energies above the isomerization barriers. More localized states are better represented in the adiabatic approximation then delocalized vibrational states.
 Publication:

Journal of Chemical Physics
 Pub Date:
 October 1987
 DOI:
 10.1063/1.452904
 Bibcode:
 1987JChPh..87.4008L
 Keywords:

 Degrees Of Freedom;
 Energy Dissipation;
 Ion Beams;
 Perturbation Theory;
 Triatomic Molecules;
 Vibrational Spectra;
 Computational Chemistry;
 Energy Levels;
 High Frequencies;
 Low Frequencies;
 Optimization;
 Potential Energy;
 Wave Functions;
 Atomic and Molecular Physics