Horia Metiu

An efficient procedure for calculating the evolution of the wave function by fast Fourier transform methods for systems with spatially extended wave function and localized potential

Various methods using fast Fourier transform algorithms or other ‘‘grid’’ methods for solving the time‐dependent Schrodinger equation are very efficient if the wave function remains spatially localized throughout its evolution. Here we present and test an extension of these methods which is efficient even if the wave function spreads out, provided that the potential remains localized. The idea is to split the wave function at various times during the propagation into two parts, one localized in the interaction region and the other in the force free region; the first is propagated by a fast Fourier transform method on a grid whose size barely exceeds the interaction region, and the latter by a single application of a free particle propagator. This splitting is performed whenever the interaction region wave function comes close to the end of the grid. The total asymptotic wave function at a given time t is reconstructed by adding coherently all the asymptotic wave function pieces which were split at earlier...

The effects of the interaction between resonances in the electromagnetic response of a sphere-plane structure; applications to surface enhanced spectroscopy

Abstract We compute the enhancement of light by a structure consisting of a sphere and a half-space. We study the dependence of the enhancement factor on the nature of the material, the geometric parameters, the light frequency and polarization, and on the spatial position. Possible applications to enhanced spectroscopy and photochemistry are discussed.

Surface enhanced spectroscopy

Abstract We review the physical processes occuring when solid surfaces are used to modify, in a substantial way, the spectroscopic properties of molecules located nearby. This is achieved by enhancement of the local laser field, increase in molecular emission, and decrease in excited state lifetime. We survey the use of flat surfaces, gratings, attenuated total reflection prisms, surfaces with small and large random roughness, isolated spheres and ellipsoids, and interacting solid surfaces. The spectroscopic techniques surveyed are surface enhanced Raman, fluorescence, resonant Raman, and absorption. The possibility of enhancing photochemical processes is also discussed. We have made an effort to present all these topics from an unifying point of view and to survey the experiments relevant to the concepts presented. The level of presentation is aimed at a nonexpert or an experimentalist without extensive theoretical skills.

Oxygen adsorption on Au clusters and a rough Au(111) surface: The role of surface flatness, electron confinement, excess electrons, and band gap

It has been shown recently that while bulk gold is chemically inert, small Au clusters are catalytically active. The reasons for this activity and its dramatic dependence on cluster size are not understood. We use density functional theory to study O2 binding to Au clusters and to a Au(111) surface modified by adsorption of Au clusters on it. We find that O2 does not bind to a flat face of a planar Au cluster, even though it binds well to its edge. Moreover, O2 binds to Au clusters deposited on a Au(111) surface, even though it does not bind to Au(111). This indicates that a band gap is not an essential factor in binding O2, but surface roughness is. Adding electrons to the surface of a Au(111) slab, on which one has deposited a Au cluster, increases the binding energy of O2. However, adding electrons to a flat Au surface has no effect on O2 binding energy. These observations have a simple explanation: in clusters and in the rough surface, the highest occupied molecular orbital (HOMO) is localized and its...

The adsorption of molecular oxygen on neutral and negative Aun clusters (n = 2-5)

Abstract We use density functional theory to examine the binding of O 2 to Au n and Au n − clusters. O 2 binds more strongly to clusters having an odd number of electrons than to those with an even number. A second O 2 molecule binds more weakly than the first.

A strategy for time dependent quantum mechanical calculations using a Gaussian wave packet representation of the wave function

We develop methodology for performing time dependent quantum mechanical calculations by representing the wave function as a sum of Gaussian wave packets (GWP) each characterized by a set of parameters such as width, position, momentum, and phase. The problem of computing the time evolution of the wave function is thus reduced to that of finding the time evolution of the parameters in the Gaussians. This parameter motion is determined by minimizing the error made by replacing the exact wave function in the time dependent Schrodinger equation with its Gaussian representation approximant. This leads to first order differential equations for the time dependence of the parameters, and those describing the packet position and the momentum of each packet have some resemblance with the classical equations of motion. The paper studies numerically the strategy needed to achieve the best GWP representation of time dependent processes. The issues discussed are the representation of the initial wave function, the numerical stability and the solution of the differential equations giving the evolution of the parameters, and the analysis of the final wave function. Extensive comparisons are made with an approximate method which assumes that the Gaussians are independent and their width is smaller than the length scale over which the potential changes. This approximation greatly simplifies the calculations and has the advantage of a greater resemblance to classical mechanics, thus being more intuitive. We find, however, that its range of applications is limited to problems involving localized degrees of freedom that participate in the dynamic process for a very short time. Finally we give particular attention to the notion that the GWP representation of the wave function reduces the dynamics of one quantum degree of freedom to that of a set of pseudoparticles (each represented by one packet) moving according to a pseudoclassical (i.e., classical‐like) mechanics whose ‘‘phase space’’ is described by a position and momentum as well as a complex phase and width.

Time dependent calculations of the absorption spectrum of a photodissociating system with two interacting excited electronic states

We use a time dependent method for solving the Schrodinger equation to calculate the photon absorption cross section for the photodissociation of a model H+3 system. The coupling V between the excited states is found to alter the absorption cross section if the time scale ℏ/V is less than the dissociation time. The influence of the relative orientation of the transition dipoles, on the absorption spectrum, is also investigated.

Adsorption of gold on stoichiometric and reduced rutile TiO2 (110) surfaces

We present a density functional study of reduced and stoichiometric rutile TiO2 (110) surfaces, and of binding of gold monomers and dimers to them. On the stoichiometric TiO2 surface, a Au atom binds to either a five-coordinated Ti atom on the basal plane, or atop a bridging oxygen atom. The two sites have nearly the same binding energy, suggesting diffusion of Au across unreduced regions of TiO2 (110) will be fast. The reduction of the rutile surface, by removal of bridging oxygen atoms, causes a charge redistribution in the system, which extends far from the vacancy site. A Au atom binds strongly to the reduced surfaces: the greater the degree of reduction the stronger the binding. On all reduced surfaces, the preferred binding sites are the vacant bridging oxygen sites. Less stable is the binding to a nearby five-coordinated Ti atom. The binding of Au2 on the reduced surfaces follows a similar pattern. Specifically, if two adjacent vacant sites are available, the optimal structure involves the dimer “d...

How the folding rate constant of simple, single-domain proteins depends on the number of native contacts

Experiments have shown that the folding rate constants of two dozen structurally unrelated, small, single-domain proteins can be expressed in terms of one quantity (the contact order) that depends exclusively on the topology of the folded state. Such dependence is unique in chemical kinetics. Here we investigate its physical origin and derive the approximate formula ln(k) = ln(N) + a + bN, were N is the number of contacts in the folded state, and a and b are constants whose physical meaning is understood. This formula fits well the experimentally determined folding rate constants of the 24 proteins, with single values for a and b.

A quantum mechanical study of predissociation dynamics of NaI excited by a femtosecond laser pulse

This work was stimulated by the experiments of Rosker, Rose, and Zewail (RRZ) who used a pump–probe sequence of femtosecond pulses to study the predissociation of NaI. We calculate quantum mechanically the nuclear wave function created by the pump pulse and its subsequent evolution. To make contact with the experiments we assume that, depending on its wavelength, the probe pulse is absorbed by either the free sodium atoms or by the bound molecule in the neutral state, and that the measured fluorescence induced by the probe pulse is proportional to the populations of these two ‘‘species.’’ The similarity between computed populations and the observed signal confirms this conjecture. We study how various factors, such as the pulse length and shape, the initial vibrational state, the temperature, and the diabatic coupling strength affect the populations (and thus the LIF signal). We also show that the RRZ analysis based on classical trajectories and the Landau–Zener formula agrees semiquantitatively with the ...