A FAST FOURIER-TRANSFORM METHOD FOR THE QUASI-CLASSICAL SELECTION OF INITIAL ROVIBRATIONAL STATES OF TRIATOMIC-MOLECULES

This paper describes the use of an exact fast Fourier transform method to prepare specified vibrational-rotational states of triatomic molec ules. The method determines the Fourier coefficients needed to describ e the coordinates and momenta of a vibrating-rotating triatomic molecu le. Once the Fourier coefficients of a particular state are determined , it is possible to easily generate as many random sets of initial Car tesian coordinates and momenta as desired. All the members of each set will correspond to the particular vibrational-rotational state select ed. For example, in the case of the ground vibrational state of a nonr otating water molecule, the calculated actions of 100 sets of initial conditions produced actions within 0.001HBAR of the specified quantiza tion values and energies within 5 cm(-1) of the semiclassical eigenval ue. The numerical procedure is straightforward for states in which all the fundamental frequencies are independent. However, for states for which the fundamental frequencies become commensurate (resonance state s), there are additional complications. In these cases it is necessary to determine a new set of ''fundamental'' frequencies and to modify t he quantization conditions. Once these adjustments are made, good resu lts are obtained for resonance states. The major problems are in label ing the large number of Fourier coefficients and the presence of regio ns of chaotic motion. Results are presented for the vibrational states of H2O and HCN and the rovibrational states of H2O. (C) 1995 American Institute of Physics.