Dissipative dynamics of an adsorbate near a metal surface is formulated consistently by replacing the infinite system-bath Hamiltonian by a finite surrogate Hamiltonian. This finite representation is designed to generate the true short time dynamics of a primary system coupled to a bath. A detailed wave packet description is employed for the primary system while the bath is represented by an array of two-level systems. The number of bath modes determines the period the surrogate Hamiltonian reproduces the dynamics of the primary system. The convergence of this construction is studied for the dissipating Harmonic oscillator and the double-well tunneling problem. Converged results are obtained for a finite duration by a bath consisting of 4–11 modes. The formalism is extended to dissipation caused by electron-hole-pair excitations. The stopping power for a slow moving proton is studied showing deviations from the frictional limit at low velocities. Vibrational line shapes of hydrogen and deuterium on nickel were studied. In the bulk the line shape is mostly influenced by nonadiabatic effects. The interplay between two baths is studied for low temperature tunneling between two surface sites of hydrogen on nickel. A distinction between lattice modes that enhance the tunneling and ones that suppress it was found.
The representation of a quantum system by an evenly spaced Fourier grid is examined. This grid faithfully represents wave functions whose projection is contained in a rectangular phase space. This is mathematically equivalent to a band limited function with finite support. In general, have packets decay exponentially in classically forbidden regions of phase space. This idea is then used first to optimize the rectangular shape of the Fourier grid, leading to exponential convergence. Nevertheless, in most cases the representation is suboptimal. The representation efficiency can then be extremely enhanced by mapping the coordinates. The mapping procedure reshapes the wave function to fit into the rectangular Fourier shape such that the wasted phase space area is minimal. It is shown that canonical transformations, which rescale the coordinates, improve the representation dramatically. A specific scaling transformation enables the representation of the notoriously difficult Coulomb potentials. The scaling transformation enables one to extract almost as many converged eigenstate energies as there are grid points. The method is extendible to more than one dimension, which is demonstrated by the study of the H + 2 problem. This scaling transformation can bridge the gap between quantum chemistry and quantum molecular dynamics by enabling the treatment of electronic problems in the vicinity of Coulomb potentials by grid methods developed for molecular dynamics.
The dissociation dynamics of oxygen on silver surfaces is studied theoretically. The method is based on a quantum-mechanical time-dependent non-adiabatic picture. A universal functional form for the potential energy surfaces is employed. The diabatic potentials describing the sequence of events leading to dissociation begin from the physisorption potential crossing over to a charged molecular chemisorption potential and crossing over again to the dissociated atomic-surface potential. Within such a potential surface topology, two different surfaces leading to dissociation are studied: the empirical potential of Spruit and the ab-initio potential of Nakatsuji. It is found that the system is captured by the molecular chemisorption well for a considerable length of time, long enough for thermalization. Thus the calculation is split into two parts: the calculation of “direct” dissociation probability and the calculation of nonadiabatic dissociative tunneling rate from the thermalized chemisorbed molecular state. For the direct probabilities, the Fourier method with the Chebychev polynomial expansion of the evolution operator is used to solve the time-dependent Schrödinger equation. For the tunneling rate calculation, a similar expansion of Green's operator is used. The output of the direct-reaction calculation is the dissociation probability as a function of the initial energy content, while the tunneling calculation yields the dissociation rate. The dependence of the direct dissociation probability on the initial kinetic energy is found to be non-monotonic. A strong isotope effect has been found, favoring the dissociation of the light species.
The flux of an evolving wavepacket is the definite time integral of its probability current density. A new method for calculating the flux, based on a Chebychev polynomial expansion of the quantum evolution operator is presented. The central point of the development is that the time integration of the current density is performed analytically, resulting in a scheme which eliminates additional numerical errors. Using this method, one benefits from both the time-dependent and time-independent frameworks of the dynamics. Furthermore, the method requires only a small modification to the existing Chebychev polynomial evolution code. Examples of performance and accuracy and an application to the calculation of recombinative desorption probabilities of N2 on Re are shown and discussed.
Spectroscopic observables are governed by the dynamics on the ground and excited potential energy surfaces. An inversion scheme is presented to iteratively construct the potential surface which reproduces experimental data. Special attention is drawn to the nonlinear character of the inversion problem and, in particular, to the role of ultrafast pump-probe spectroscopy for dealing with it. The regions of inversion, Le., the nuclear configurations for which the potential is to be determined, are identified by calculating the observablepotential sensitivity function. A method is introduced for calculating these sensitivity functions in a numerically converged time-dependent quantum mechanical fashion. These functions are the basic building blocks of the inverted potential. Two demonstrations of the procedure are presented, both use simulated pump-probe spectroscopic data. The first, applied to the ICN molecule, reconstructs the medium- and long-range parts of the dissociative excited surface. The second attempts to reconstruct the bound excited potential surface of NCO.
Kosloff, R. ; Baer, R.Impulsive Iterative Inversion. In Mode Selective Chemistry Jerusalem Symposia on Quantum Chemistry and Biochemistry; Jortner, J. ; LEVINE, R. D. ; Pullman, B., Ed.; Kluwer: Dordecht, 1991; Vol. 24, pp. 345.