VIBRATIONAL SELF-CONSISTENT-FIELD METHOD FOR MANY-MODE SYSTEMS - A NEW APPROACH AND APPLICATION TO THE VIBRATIONS OF CO ADSORBED ON CU(100)

We report calculations of the vibrational energies of CO-Cu(100) using a new code to perform vibrational self-consistent field (VSCF) and st ate-mixing calculations for many-mode systems. The major new feature o f the code is the representation of the potential. Unlike recent imple mentations of the VSCF method, the potential is not expanded in terms of normal coordinates as a multinomial series about a minimum. The ful l potential, in normal coordinates, is used in the Watson Hamiltonian. This approach, while rigorous, can lead to prohibitively large numeri cal quadratures, and so we suggest a novel representation of the poten tial as an expansion in all two-mode, or all three-mode, or all four-m ode coupling terms. The new code is tested against previous exact calc ulations of vibrational states of HCO, and also against previous VSCF calculations that used a fourth-order, normal coordinate force field r epresentation of the global HCO potential. The new code is applied to calculations of the vibrations of CO adsorbed to Cu(100). We explicitl y treat nine modes corresponding to the motion of the C and O atoms an d the Cu atom that is bonded to C. The potential used is a semi-empiri cal one developed by Tully and co-workers [J. C. Tully, M. Gomez, and M. Head-Gordon, J. Vac. Sci. Technol. A 11, 1914 (1993)], and is used fully, i.e., without recourse to multinomial expansion in displacement coordinates. We test the convergence of the results with respect to t he number of modes coupled and find that the errors in the two-mode co upling representation vary from 0.6 to 6 cm(-1) for the fundamentals b ut grow to 30 cm(-1) for overtone and combination states. The errors i n the three-mode representation of the potential are less than 0.2 cm( -1) for the fundamentals and no larger than 2.5 cm(-1) for high overto ne/combination states with as much as 9 quanta of excitation. We calcu late the thermally broadened spectra of the GO-stretch fundamental, th e CO-Cu frustrated rotation and the CO-Cu frustrated translation over the temperature range 50-350 K. We compare the temperature dependence of the average frequency and standard deviation of these modes with ex periment, and find semiquantitative agreement. (C) 1997 American Insti tute of Physics.