Open-system quantum dynamics for gas-surface scattering: Nonlinear dissipation and mapped Fourier grid methods

Including Memory Friction in Single- and Two-State Quantum Dynamics Simulations

We present a simple computational algorithm that allows for the inclusion of memory friction in a quantum dynamics simulation of a small, quantum, primary system coupled to many atoms in the surroundings. We show how including a memory friction operator, F̂, in the primary quantum system's Hamiltonian operator builds memory friction into the dynamics of the primary quantum system. We show that, in the harmonic, semi-classical limit, this friction operator causes the classical phase-space centers of a wavepacket to evolve exactly as if it were a classical particle experiencing memory friction. We also show that this friction operator can be used to include memory friction in the quantum dynamics of an anharmonic primary system. We then generalize the algorithm so that it can be used to treat a primary quantum system that is evolving, non-adiabatically on two coupled potential energy surfaces, i.e., a model that can be used to model H atom transfer, for example. We demonstrate this approach's computational ease and flexibility by showing numerical results for both harmonic and anharmonic primary quantum systems in the single surface case. Finally, we present numerical results for a model of non-adiabatic H atom transfer between a reactant and product state that includes memory friction on one or both of the non-adiabatic potential energy surfaces and uncover some interesting dynamical effects of non-memory friction on the H atom transfer process.

Quantum dynamical treatment of inelastic scattering of atoms at a surface at finite temperature: the random phase thermal wave function approach

We present quantum dynamical calculations for the inelastic scattering of atoms at a nonrigid surface at finite temperature. The surface degrees of freedom are discretized and treated in a multiconfigurational wave function picture. The thermal averaging is carried out with the random phase thermal wave function approach. We show that it is sufficient to restrict the random phases to the intermediate basis of single particle functions, discuss the convergence of the method with the number of configurations and realizations, and analyze the flow of energy between different parts of the system for a range of temperatures between 4 and 500 K.

Reduced density matrix quantum approach for particle trapping and sticking on corrugated moving surfaces

A short time propagation algorithm for the reduced density matrix is derived to model the interaction of a quantum particle with a moving corrugated surface. The algorithm includes dissipative terms, which can be derived directly from the full Hamiltonian. The scattering of He from a corrugated Cu surface is examined as a function of incident energy and angle and the temperature of the substrate, with a focus on the nature of trapping. It is found that corrugation can make a significant contribution to trapping, even on a metal surface. Energy exchange with the phonons is shown to significantly modify the nature of diffraction mediated selective adsorption.

Mapped grid methods for long-range molecules and cold collisions

The paper discusses ways of improving the accuracy of numerical calculations for vibrational levels of diatomic molecules close to the dissociation limit or for ultracold collisions, in the framework of a grid representation. In order to avoid the implementation of very large grids, Kokoouline et al. [J. Chem. Phys. 110, 9865 (1999)] have proposed a mapping procedure through introduction of an adaptive coordinate x subjected to the variation of the local de Broglie wavelength as a function of the internuclear distance R. Some unphysical levels ("ghosts") then appear in the vibrational series computed via a mapped Fourier grid representation. In the present work the choice of the basis set is reexamined, and two alternative expansions are discussed: Sine functions and Hardy functions. It is shown that use of a basis set with fixed nodes at both grid ends is efficient to eliminate "ghost" solutions. It is further shown that the Hamiltonian matrix in the sine basis can be calculated very accurately by using an auxiliary basis of cosine functions, overcoming the problems arising from numerical calculation of the Jacobian J(x) of the R-->x coordinate transformation.