Analytic dynamics of the Morse oscillator derived by semiclassicalclosures

摘要

The quantized Hamilton dynamics methodology [O. V. Prezhdo and Y. V. Pereverzev, J. Chem.Phys. 113, 6557 (2000)] is applied to the dynamics of the Morse potential using the SU(2) ladderoperators. A number of closed analytic approximations are derived in the Heisenberg representationby performing semiclassical closures and using both exact and approximate correspondencebetween the ladder and position-momentum variables. In particular, analytic solutions are given forthe exact classical dynamics of the Morse potential as well as a second-order semiclassicalapproximation to the quantum dynamics. The analytic approximations are illustrated with the O–Hstretch of water and a Xe–Xe dimer. The results are extended further to coupled Morse oscillatorsrepresenting a linear triatomic molecule. The reported analytic expressions can be used to accelerateclassical molecular dynamics simulations of systems containing Morse interactions and to capturequantum-mechanical effects.