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arXiv1996

Theory for the Ultrafast Structural Response of optically excited small clusters: Time-dependence of the Ionization Potential

Combining an electronic theory with molecular dynamics simulations we present results for the ultrafast structural changes in small clusters. We determine the time scale for the change from the linear to a triangular structure after the photodetachment process Ag$_3^- \rightarrow {\rm Ag}_3$. We show that the time-dependent change of the ionization potential reflects in detail the internal degrees of freedom, in particular coherent and incoherent motion, and that it is sensitive to the initial temperature. We compare with experiment and point out the general significance of our results.

chem-ph↗

arXiv1996

Stability and Teller's Theorem: A Thomas-Fermi Theory of Fullerenes

We study {{\rm C}$_{60}$} with the use of Thomas-Fermi theory. A spherical shell model is invoked to treat the nuclear potential, where the nuclear and core charges are smeared out into a shell of constant surface charge density. The valence electron distribution and the electrostatic potential are efficiently computed by integration of the Thomas-Fermi equation, subject to the shell boundary conditions. Total energy is numerically calculated over a range of shell radii, and the mechanical stability of the model is explored, with attention to the constraints of Teller's theorem. The calculated equilibrium radius of the shell is in good agreement with experiment.

chem-ph↗

arXiv1994

Low-temperature dynamical simulation of spin-boson systems

The dynamics of spin-boson systems at very low temperatures has been studied using a real-time path-integral simulation technique which combines a stochastic Monte Carlo sampling over the quantum fluctuations with an exact treatment of the quasiclassical degrees of freedoms. To a large degree, this special technique circumvents the dynamical sign problem and allows the dynamics to be studied directly up to long real times in a numerically exact manner. This method has been applied to two important problems: (1) crossover from nonadiabatic to adiabatic behavior in electron transfer reactions, (2) the zero-temperature dynamics in the antiferromagnetic Kondo region 1/2<K<1 where K is Kondo's parameter.

chem-ph↗

arXiv1994

Magic Numbers of Silicon Clusters

A structural model for intermediate sized silicon clusters is proposed that is able to generate unique structures without any dangling bonds. This structural model consists of bulk-like core of five atoms surrounded by fullerene-like surface. Reconstruction of the ideal fullerene geometry results in the formation of crown atoms surrounded by $π$-bonded dimer pairs. This model yields unique structures for \Si{33}, \Si{39}, and \Si{45} clusters without any dangling bonds and hence explains why these clusters are least reactive towards chemisorption of ammonia, methanol, ethylene, and water. This model is also consistent with the experimental finding that silicon clusters undergo a transition from prolate to spherical shapes at \Si{27}. Finally, reagent specific chemisorption reactivities observed experimentally is explained based on the electronic structures of the reagents.

chem-ph↗

arXiv1994

Optical absorption spectra of A6C60 and A6C70: Reduction of effective Coulomb interactions in Frenkel excitons

We theoretically investigate optical absorption spectra of $\soc^{6-}$ and $\rug^{6-}$, and discuss relations with the optical properties of alkali metal doped fullerides $A_6\soc$ and $A_6\rug$. This is a valid approach for systems where Frenkel exciton effects are dominant. We use a tight binding model with long ranged Coulomb interactions and bond disorder. Optical spectra are obtained by the Hartree-Fock approximation and the configuration interaction method. We find that the Coulomb interaction parameters, which are relevant to the optical spectra of $A_6\soc$ ($A_6\rug$) in order to explain the excitation energies and relative oscillator strengths of absorption peaks, are almost the half of those of the neutral $\soc$ ($\rug$). The reduction of the effective Coulomb interactions is concluded for the heavily doped case of $\soc$ and $\rug$. This finding is closely related with the experimental fact that dielectric constants of fullerides which are maximumly doped with alkali metals become about twice as large as those of the neutral systems.

cond-mat↗

arXiv1995

Structure of Si12 Cluster

Tight-binding molecular dynamic simulations have revealed that Si$_{12}$ is an icosahedron with all atoms on the surface of an approximately 5 Å~ diameter sphere. This is the most spherical cage structure for silicon clusters in the 2-13 atom size range.

chem-ph↗

arXiv1994

Periodic Orbits and Shell Structure in Octupole Deformed Potentials

The effect of an octupole term in a quadrupole deformed single particle potential is studied from the classical and quantum mechanical view point. Whereas the problem is nonintegrable, the quantum mechanical spectrum nevertheless shows some shell structure in the superdeformed prolate case for particular, yet fairly large octupole strengths; for spherical or oblate deformation the shell structure disappears. This result is associated with classical periodic orbits which are found by employing the removal of resonances method; this approximation method allows determination of the shape of the orbit and of the approximate octupole coupling strength for which it occurs. The validity of the method is confirmed by solving numerically the classical equations of motion. The quantum mechanical shell structure is analysed using the particle number dependence of the fluctuating part of the total energy. In accordance with the classical result this dependence turns out to be very similar for a superdeformed prolate potential plus octupole term and a hyperdeformed prolate potential without octupole term. In this way the shell structure is explained at least for some few hundred levels. The Fourier transform of the level density further corroborates these findings.

nucl-th↗

arXiv1994

Infrared and Raman Evidence for Dimers and Polymers in Rb1C60

The infrared- and Raman-active vibrational modes of C60 were measured in the various structural states of Rb1C60. According to earlier studies, Rb1C60 has an $fcc$ structure at temperatures above ~100C, a linear chain polymer orthorhombic structure when slowly cooled, and an as yet undetermined structure when very rapidly cooled ("quenched"). We show that the spectra obtained in the polymer state are consistent with each C60 molecule having bonds to two diametrically opposite neighbors. In the quenched state, we find evidence for further symmetry breaking, implying a lower symmetry structure than the polymer state. The spectroscopic data of the quenched phase are shown to be consistent with Rb2(C60)2, a dimerization of C60.

cond-mat↗

arXiv1995

Occupation numbers in density-functional calculations

It is the intention of this paper to rigorously clarify the role of the occupation numbers in the current practical applications of the density functional formalism. In these calculations one has to decide how to distribute a given, fixed number of electrons over a set of single-particle orbitals. The conventional choice is to have orbitals below the Fermi level completely occupied and the orbitals above the Fermi level empty. Although there is a certain confusion in literature why this choice is superior to any others, the general belief is that it can justified by treating the occupation numbers as variational parameters and then applying Janak's theorem or similar reasoning. We demonstrate that there is a serious flaw in those arguments,mainly the kinetic energy and therefore the exchange-correlation potential are not differentiable with respect to density for arbitrary occupation numbers. It is rigorously shown that in the present context of the density functional calculations there is no freedom to vary the occupation numbers. The occupation numbers cannot be considered as variational parameters.

cond-mat↗

arXiv1995

Two-Photon Spectroscopy Between States of Opposite Parities

Magnetic- and electric-dipole two-photon absorption (MED-TPA), recently introduced as a new spectroscopic technique for studying transitions between states of opposite parities, is investigated from a theoretical point of view. A new approximation, referred to as {\it weak quasi-closure approximation}, is used together with symmetry adaptation techniques to calculate the transition amplitude between states having well-defined symmetry properties. Selection rules for MED-TPA are derived and compared to selection rules for parity-forbidden electric-dipole two-photon absorption (ED-TPA).

atom-ph↗

arXiv1995

A generalized local approximation to the exchange potential

A new method to obtain a local parameterization for the exchange term in the many--body electronic problem is presented. The approach amounts to the introduction of a coordinate dependent electron effective mass. Numerical results for metallic clusters in the jellium model are compared with other standard methods.

chem-ph↗

arXiv1995

A Monte Carlo study of temperature-programmed desorption spectra with attractive lateral interactions

We present results of a Monte Carlo study of temperature-programmed desorption in a model system with attractive lateral interactions. It is shown that even for weak interactions there are large shifts of the peak maximum temperatures with initial coverage. The system has a transition temperature below which the desorption has a negative order. An analytical expression for this temperature is derived. The relation between the model and real systems is discussed.

chem-ph↗

arXiv1995

Metal-Insulator Transition in C60-Polymers

Variations in the band structures of C60-polymers are studied, when pi-conjugation conditions are changed. We look at band structures in order to discuss a metal-insulator transition, using a semi-empirical model with the Su-Schrieffer-Heeger type electron-phonon interactions. We find that electronic structures change among direct-gap insulators and the metal, depending on the degree of pi-conjugations. High pressure experiments could observe such pressure-induced metal-insulator transitions.

chem-ph↗

arXiv1995

Nonlinearity and trapping in excitation transfer: Dimers and Trimers.

We study the interplay between nonlinearity in exciton transport and trapping due to a sink site for the dimer and the trimer with chain configuration by a numerical integration of the discrete nonlinear Schroedinger equation. Our results for the dimer show, that the formation of a self trapped state due to the nonlinear coupling increases the life time of the exciton substantially. Self trapping can be enhanced by the sink for short times, but for long times it disappears. In the trimer consisting of a subdimer extended by a sink site exists a transition between states localized on the two sites of the subdimer before for larger nonlinear coupling self trapping on one site of the subdimer is observed. For large trapping rates the fear of death effect leads to an increasing life time of the excitation on both, the dimer and the trimer. The sink site is then effectively decoupled. We explain this effect using an asymptotic theory for strong trapping and demonstrate it by direct numerical computation.

chem-ph↗

arXiv1995

Memory Loss and Auger Processes in a Many Body Theory of Charge Transfer

Charge transfer between hyperthermal alkali atoms and metallic scattering surfaces is an experimental and theoretical arena for many-body interactions. To model new facets, we use a generalized time-dependent Newns-Anderson Hamiltonian which includes electron spin, multiple atomic orbitals with image shifted levels, intra-atomic Coulomb repulsion, and resonant exchange. A variational electronic many-body wave function solves the dynamical problem. The wave function consists of sectors with either zero or one particle-hole pair and goes beyond earlier work through the inclusion of amplitudes for a neutral atom plus an electron-hole pair. Higher order sectors with more than one particle-hole pair are suppressed by powers of $1/N$; hence the wave function ansatz is equivalent to a $1/N$ expansion. The equations of motion are integrated numerically without further approximation. The solution shows improved loss-of-memory -- the final charge state is independent of the initial one -- in agreement with theoretical and experimental expectations. Understanding of this phenomenon is deepened through an analysis of entropy production. By studying the independent-particle approximation, and by examining the role played by different sectors of the Hilbert space in entropy production, we arrive at necessary and sufficient conditions for loss-of-memory to occur in the many-body solution. As further tests of the theory, we reproduce the experimentally observed peak in the excited neutral Li(2p) occupancy at intermediate work functions starting from different initial conditions. Next, we include Auger processes by adding two-body interaction terms to the many-body Hamiltonian. Several types of Auger processes are considered, and these are shown to affect the final state occupancies at low

cond-mat↗

arXiv1995

Corrections to scaling in 2--dimensional polymer statistics

Writing $ = AN^{2ν}(1+BN^{-Δ_1}+CN^{-1}+ ...)$ for the mean square end--to--end length $ $ of a self--avoiding polymer chain of $N$ links, we have calculated $Δ_1$ for the two--dimensional {\em continuum} case from a new {\em finite} perturbation method based on the ground state of Edwards self consistent solution which predicts the (exact) $ν=3/4$ exponent. This calculation yields $Δ_1=1/2$. A finite size scaling analysis of data generated for the continuum using a biased sampling Monte Carlo algorithm supports this value, as does a re--analysis of exact data for two--dimensional lattices.

cond-mat↗

arXiv1995

Towards a Linear-Scaling DFT Technique: The Density Matrix Approach

A recently proposed linear-scaling scheme for density-functional pseudopotential calculations is described in detail. The method is based on a formulation of density functional theory in which the ground state energy is determined by minimization with respect to the density matrix, subject to the condition that the eigenvalues of the latter lie in the range [0,1]. Linear-scaling behavior is achieved by requiring that the density matrix should vanish when the separation of its arguments exceeds a chosen cutoff. The limitation on the eigenvalue range is imposed by the method of Li, Nunes and Vanderbilt. The scheme is implemented by calculating all terms in the energy on a uniform real-space grid, and minimization is performed using the conjugate-gradient method. Tests on a 512-atom Si system show that the total energy converges rapidly as the range of the density matrix is increased. A discussion of the relation between the present method and other linear-scaling methods is given, and some problems that still require solution are indicated.

mtrl-th↗

arXiv1996

Vibrational Spectra of Defects in Silicon: An Orbital Radii Approach

A phenomenological approach to the stretching mode vibrational frequencies of defects in semiconductors is proposed. A novel quantum scale is defined in terms of the first principles pseudopotential based orbital radius and the principal quantum number of the element concerned. A universal linear relationship between the Sanderson electronegativity and this quantum scale is established. Next, we show that the stretching mode vibrational frequencies of hydrogen and chlorine in the silicon network scale linearly with this quantum scale. Predictions and identifications of defect environments around the Si-H and Si-Cl are possible. The assignments of vibrational modes in porous silicon are critically examined. We discuss our proposed scale in the context of Mendeleveyan scales in general, and suggest justifications for it. We believe that our approach can be gainfully extended to the vibrational spectra of other semiconductors.

mtrl-th↗