VIBRATIONAL MOTION IN ISOTOPOMERS OF THE HEH- AN APPLICATION OF THE ELECTRON-NUCLEAR DYNAMICS METHOD( MOLECULAR ION )

The importance of isotopic substitution as a tool for elucidation of c hemical reaction events originates in the fact that the Coulombic Hami ltonian is isotopically invariant except for the nuclear kinetic energ y term. Thus, in theories of isotope effects based on the Born-Oppenhe imer scheme, the basic presumption is the invariance of the potential energy surface (PES). We use, however, a fully dynamic approach, calle d Electron Nuclear Dynamics (END), which does not require a preconstru cted PES. Since the END formalism is rather different from commonly us ed procedures, we study the anharmonic nuclear vibration in isotopic s pecies of the HeH+ molecular ion as a model problem. A single time-dep endent complex parametrized determinantal wave function is used for th e electrons and the nuclei are treated classically The time evolution of the nuclear and electronic dynamical variables obtained by integrat ion of equations of motion are reported as bond length, nuclear kineti c energy, and Mulliken populations. The molecule vibrates as a classic al object. The product of the reduced mass and the square of the vibra tional frequency is isotopomer invariant for any common total energy. The difference between the total energy and the nuclear kinetic energy as a function of the internuclear distance is interpreted as the aver age dynamic potential. (C) 1997 John Wiley & Sons, Inc.