Formulation of temperature dependent effective Hartree potential incorporating quadratic over linear molecular DOFs-surface modes couplings and its effect on quantum dynamics of D2 (v=0, j=0)/D2 (v=0, j=2) on Cu(111) metal surface

The effect of surface temperature on the scattering and dissociation processes of D2 (v = 0, j = 0)/D2 (v = 0, j = 2) on Cu(111) metal plane is investigated by formulating a time and temperature dependent effective Hamiltonian within mean-field approach, where the molecular degrees of freedom and surface mode vibrations are assumed to be weakly coupled with each other. While constructing such effective Hamiltonian with a Hartree product type wavefunction, we incorporate: (i) an operator algebra method to circumscribe higher orderquadratic (anharmonic) molecular DOFs-surface modes couplings over the linear coupling case implemented previously [Adhikari and coworkers, J. Chem. Phys. 154, 104103 (2021)]; (ii) surface temperature by considering Bose-Einstein or Maxwell-Boltzmann probability factors for the initial state distribution of the surface vibrational modes. Finally, a six-dimensional (6D) quantum dynamical (QD) calculation is performed with such newly formulated effective Hartree potential and calculated transition/dissociation probabilities at various surface temperature situations. The quadratic (anharmonic) molecular DOFs-surface modes couplings modify the reaction and transition probabilities substantially with change of surface temperature, which indicates the crucial role of surface mode vibrations on the molecule-surface scattering phenomena.