The energy levels of the one-dimensional and the linear two-dimensional Morse oscillators have been calculated by the method of Harris, Engerholm, and Gwinn in the harmonic-oscillator representation. The method compares favorably with diagonalization of the exactly calculated Hamiltonian matrix. In the one-dimensional case the calculations can be improved by using displaced basis functions.

Quantum calculations of the dynamics of a Morse oscillator with a Gaussian initial wave packet have been performed. As previously observed in other simple oscillators the classical and quantum expectation values for the coordinate exhibit significantly different behaviors, especially after the first few cycles. Some theories of chemical kinetics require the classical-mechanical calculation of lifetimes which may be quite long compared to vibrational periods. These theories deserve re-examination in view of the dynamical behavior observed in the present work.Corresponding eigenvalues: (A) 0.3389X1Q-11 erg, (B) 0.3348X 10-11 erg, and (C) 0.3673XlQ-11 erg.

The method of Shuler and Zwanzig is extended to permit the calculation of collisional transition probabilities for triatomic molecules having harmonic intramolecular potentials and interacting impulsively with the bombarding atoms. Only colinear systems are considered. The results are qualitatively similar to those obtained for atom-diatomic systems. Excitation of the symmetric mode of oscillation is favored over the antisymmetric mode in the systems considered.

The method of Shuler and Zwanzig has been used to calculate the vibrational transition probabilities for a Morse oscillator suffering an impulsive, colinear collision with an atom. Results are presented for the system H2 colliding with D.

The method of Shuler and Zwanzig is used to calculate quantum transition probabilities between vibration levels of colliding diatomic molecules. The molecules are assumed to have harmonic bond potentials, the intermolecular interaction is taken to be impulsive, and only collinear configurations are investigated. Vibration–vibration transfer is found to be a quite significant mode of energy transfer, and it is apparently not sensitive to the degree of close matching of the vibration frequencies of the colliding molecules. It is suspected that this insensitivity may be due to the impulsive collision model used.