Kenneth Haug

Exact classical simulation of hydrogen migration on Ni(100) : the role of fluctuations, recrossing, and multiple jumps

We examine the migration of a classical hydrogen atom adsorbed on a Ni(100) surface, in a temperature range when the motion consists of jumps between lattice sites. We view these jumps as isomerization reactions and calculate exactly their rate constants by using the correlation function theory. We examine in detail the effect of lattice motion, lattice fluctuations and lattice distortion on the jumping rates and test the accuracy of the transition state theory. We propose a new approximation to the rate constant which includes all the effects incorporated in the transition state theory and calculates approximately the dynamic correction due to recrossing. We find that the magnitude of the diffusion coefficient is affected by multiple jumps.

A test of the possibility of calculating absorption spectra by mixed quantum‐classical methods

Some of the most efficient methods for studying systems having a large number of degrees of freedom treat a few degrees of freedom quantum mechanically and the remainder classically. Here we examine how these methods fare when used to calculate the cross section for photon absorption by a quantum system imbedded in a medium. To test the method, we study a model which has two degrees of freedom and mimicks the properties of a one‐dimensional alkali atom–He dimer. We treat the electron motion quantum mechanically and the distance between the He atom and the alkali ion classically. Light absorption occurs because the electron is coupled to radiation. The calculation of the absorption cross section by quantum‐classical methods fails rather dramatically−at certain frequencies, the absorption coefficient is negative. By comparing with exact quantum calculations, we show that this failure takes place because the time evolution of the classical variables influences the dynamics of the quantum degree of freedom through the Hamiltonian only; important information, which a fully quantum treatment would put in the wave function, is missing. To repair this flaw, we experiment with a method which uses a swarm of classical trajectories to generate a ‘‘classical wave function.’’ The results are encouraging, but require substantial computer time when the number of classical variables is large. We argue that in the limit of many classical degrees of freedom, accurate calculations can be performed by using the time‐dependent Hartree method and treating some degrees of freedom by exact numerical methods (e.g., a fast Fourier transform procedure) and the others by Gaussian wave packets or any other propagation method that is accurate for a very short time. This procedure leads to a simple time domain picture of dephasing and line broadening in the case of a localized quantum system imbedded in a medium with heavy atoms.

Absorption spectrum calculations using mixed quantum-Gaussian wave packet dynamics

We calculate the absorption spectrum of a cluster using a computational method in which classical‐like degrees of freedom for the nuclei are described by Gaussian wave packets while the valence electrons are treated quantum mechanically. We examine the spectral features in comparison to an even simpler mixed quantum‐classical model in which the nuclear motion is treated by purely classical mechanics. Anomalous features (such as negative absorption) in the absorption spectrum which can arise from mixed quantum‐classical methods are examined and the Gaussian wave packet nuclear dynamics is found to substantially reduce these anomalous features. This method is applied to a two‐coordinate model problem in which exact numerical results can be obtained and we find that the method works fairly well. We also apply the method to the valence electronic absorption spectrum for a KXe6 cluster. The method does not suffer from the dramatic failure seen when Xe motion is treated classically. The method is used to calcul...

Hydrogen motion on a rigid Cu surface: the calculation of the site to site hopping rate by using flux-flux correlation functions

We use the quantum flux–flux correlation function theory to calculate the rate coefficient for site‐to‐site hopping by a single hydrogen atom absorbed on a rigid Cu(100) surface. We investigate hydrogen dynamics during barrier crossing and determine the time scales on which the hydrogen atom crosses or recrosses the barrier, as well as the time scale on which double jumps occur. We define two kinds of transition state theory rate coefficients: one (Miller and Tromp) which assumes that only the short time dynamics contributes to the rate coefficient and another which includes the effect of the earliest recrossing. We examine numerically the accuracy of these approximations and compare them to other transition state theory calculations and to our ‘‘exact’’ calculations. The simulations are also used to study the contribution of multiple jumps to the diffusion coefficient, to calculate the isotope effect on the rate coefficient and to determine the role of dimensionality in modeling surface diffusion. We fin...

Quantum simulation of hydrogen migration on Ni(100) : the role of fluctuations, recrossing, and multiple jumps

We examine the mobility of a hydrogen atom adsorbed on a Ni(100) in a temperature range (200–400 K) where the motion consists of jumps between lattice sites. We view these jumps as isomerization reactions and calculate their rate constants by using the flux–flux correlation function theory. We examine in detail the effect of lattice fluctuations and lattice distortion on the jumping rates and test the accuracy of several short time approximations which provide an extension of the transition state theory to quantum systems. We find that the magnitude of the diffusion coefficient is affected by multiple jumps and that recrossing effects are significant. By comparing the present quantum results to those obtained previously by classical simulations, we find that in this temperature range the quantum effects are small (i.e., at most a factor of 6) and originate mostly from the differences in the magnitudes of the thermodynamic quantities appearing in the rate coefficient expression. Numerical experiments show ...

Hydrogen motion on a Cu surface: A model study of the rate of single and double site‐to‐site jumps and the role of the motion perpendicular to the surface

We use the Miller, Schwartz, and Tromp flux–flux correlation function formula to calculate the rate coefficient for site‐to‐site hopping by an adsorbed hydrogen atom on Cu(100). We examine several one‐ and two‐dimensional models with a rigid surface. We reach several qualitative conclusions which are relevant to real systems: the motion perpendicular to the surface plays a very important role in determining the site‐to‐site hopping rate; there is substantial barrier recrossing which makes transition state theory inaccurate; at moderate temperatures multiple jumps become important.

The absorption spectrum of an electron solvated in sodalite

We use a simple model to study the color change taking place when sodium atoms are absorbed in the zeolite sodalite. The Hamiltonian is that of an electron moving in the electrostatic field created by the ions in the zeolite framework and by the alkali ion core. We examine the sensitivity of the absorption spectrum on the magnitude of framework charges, the orientation of the Na4 cluster in the sodalite cells, the localization of the electron, the nature of the alkali impurity (Li, Na, K), and the laser polarization. Comparisons with the experiment help decide which framework charge models are consistent with the absorption spectrum.

The absorption spectrum of a potassium atom in a Xe cluster

We calculate the absorption spectrum for a simple model that mimics a potassium atom in a Xe cluster. The time evolution of the electron wave function is calculated by a fast Fourier transform method while the nuclear motion is treated classically. The initial nuclear configurations are generated by a Monte Carlo method. We examine which features in the spectrum are caused by electron, potassium ion or Xe motion and the frequency resolution at which these features appear.

A new method for calculating time-dependent quantum correlation functions for systems with many degrees of freedom

Abstract We present a method for the computation of time-dependent quantum correlation functions. We calculate the temperature dependence of the correlation function at zero time and analytically continue to obtain the time dependence at finite temperature.

A model study of quantum dot polarizability calculations using time-dependent density functional methods

We compare two time-dependent methods (time-dependent Hartree and time-dependent density functional methods) with a time-independent density functional method for the calculation of the frequency dependent polarizability and resulting absorption spectrum of two interacting quantum confined particles (quantum dots). The system is examined within the dipole approximation and the methods are evaluated in terms of the optical absorption spectrum. The spectral noise generated by time-dependent methods is a sensitive measure of the degree of broken correlation between the quantum degrees of freedom and the time-dependent density functional method may help to quantify the efficacy of correlation-exchange potentials that are used in density functional models. With respect to the quantum confinement issue, we find that increasing the interaction energy between nearest neighbor quantum dot sites represented in our model tends to shift absorption intensity to higher energy transitions.