MCTDH study on vibrational states of the CO/Cu(100) system

Full (6D) and reduced (4D and 2D) dimensional multiconfiguration time-dependent Hartree (MCTDH) calculations for the vibrational fundamentals and overtones of the CO/Cu(100) system are carried out using the recently reported [R. Marquardt, F. Cuvelier, R. A. Olsen, E. J. Baerends, J. C. Tremblay, and P. Saalfrank, J. Chem. Phys. 132, 074108 (2010)] SAP potential energy surface (PES). To efficiently perform MCTDH calculations with the Heidelberg package (http://mctdh.uni-hd.de), the SAP-PES is first refitted in a sum-of-products form. Then extensive MCTDH calculations are carefully performed including thorough convergence checks to ensure the accuracy of our results. Full dimensional improved-relaxations and/or block-improved-relaxations are then performed to obtain vibrational ground and excited states of CO/Cu(100). In addition, we investigate the frustrated rotation (R mode) and vertical CO-Cu stretch (S mode), as well as C-O stretch, using a 4D Hamiltonian, which includes the distance between CO and the surface, z, bond length of CO, r, and orientation angles of CO, θ, and φ. The complement of this 4D Hamiltonian, a 2D Hamiltonian including only x and y coordinates, is used to alternatively calculate the states of frustrated translation (T mode). The comparison of reduced- with full-dimensional results show that the couplings between the R or S mode and the T mode do not influence the fundamentals and overtones of the R and S modes, however, do considerably influence those of the T mode. For the fundamental of the T mode, the 6D calculation yields an energy of 25.09 cm(-1), a value closer to the experimental result of 31.8 cm(-1) [A. P. Graham, F. Hofmann, J. P. Toennies, G. P. Williams, C. J. Hirschmugl, and J. Ellis, J. Chem. Phys. 108, 7825-7834 (1998)] than previously reported 19.6 cm(-1) [R. Marquardt, F. Cuvelier, R. A. Olsen, E. J. Baerends, J. C. Tremblay, and P. Saalfrank, J. Chem. Phys. 132, 074108 (2010)] although both investigations are based on the SAP-PES. On the other hand, the present calculations give similar results for the fundamentals of the S mode and C-O stretch to previous ones [R. Marquardt, F. Cuvelier, R. A. Olsen, E. J. Baerends, J. C. Tremblay, and P. Saalfrank, J. Chem. Phys. 132, 074108 (2010)]. Furthermore, for the lateral T and R modes, the present calculations give the same excitation pattern. Our calculations also show that the couplings between the R mode and surface are weaker than those between the T mode and surface.