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arXiv1998

Two-Color Coherent Photodissociation of Nitrogen Oxide in Intense Laser Fields

A simple one-dimensional semi-classical model with a Morse potential is used to investigate the possibility of two-color infrared multi-photon dissociation of vibrationally excited nitrogen oxide. The amplitude ratio effects and adiabatic effects are investigated. Some initial states are found to have thresholds smaller than expected from single-mode considerations and multiple thresholds exist for initial states up to 32. PACS: 42.50.Hz

chem-ph↗

arXiv1995

Classical and quantum Malus' law

The classical and the quantum Malus' Laws for light and spin are discussed. It is shown that for spin-1/2, the quantum Malus' Law is equivalent in form to the classical Malus' Law provided that the statistical average involves a quasi-distribution function that can become negative. A generalization of Malus' Law for arbitrary spin-s is obtained in the form of a Feynman path-integral representation for the Malus amplitude. The classical limit of the Malus amplitude for large s is discussed.

quant-ph↗

arXiv1996

Boson-realization model for the vibrational spectra of tetrahedral molecules

An algebraic model of Boson-realization is proposed to study the vibrational spectra of a tetrahedral molecule, where ten sets of boson creation and annihilation operators are used to construct the Hamiltonian with $T_{d}$ symmetry. There are two schemes in our model. The first scheme provides an eight-parameter fit to the published experimental vibrational eigenvalues of methane with a root-mean-square deviation 11.61 $cm^{-1}$. The second scheme, where the bending oscillators are assumed to be harmonic and the interactions between the bending vibrations are neglected, provided a five-parameter fit with a root-mean-square deviation 12.42 $cm^{-1}$

chem-ph↗

arXiv1996

From Heisenberg matrix mechanics to EBK quantization: theory and first applications

Despite the seminal connection between classical multiply-periodic motion and Heisenberg matrix mechanics and the massive amount of work done on the associated problem of semiclassical (EBK) quantization of bound states, we show that there are, nevertheless, a number of previously unexploited aspects of this relationship that bear on the quantum-classical correspondence. In particular, we emphasize a quantum variational principle that implies the classical variational principle for invariant tori. We also expose the more indirect connection between commutation relations and quantization of action variables. With the help of several standard models with one or two degrees of freedom, we then illustrate how the methods of Heisenberg matrix mechanics described in this paper may be used to obtain quantum solutions with a modest increase in effort compared to semiclassical calculations. We also describe and apply a method for obtaining leading quantum corrections to EBK results. Finally, we suggest several new or modified applications of EBK quantization.

chem-ph↗

arXiv1996

Variational calculations of dispersion coefficients for interactions between H, He, and Li atoms

The dispersion coefficients $C_6$, $C_8$, and $C_{10}$ for the interactions between H, He, and Li are calculated using variational wave functions in Hylleraas basis sets with multiple exponential scale factors. With these highly correlated wave functions, significant improvements are made upon previous calculations and our results provide definitive values for these coefficients.

atom-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

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↗

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

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

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↗

arXiv1996

Charge transfer excitons in optical absorption spectra of C60-dimers and polymers

Charge-transfer (CT) exciton effects are investigated for the optical absorption spectra of crosslinked C60 systems by using the intermediate exciton theory. We consider the C60-dimers, and the two (and three) molecule systems of the C60-polymers. We use a tight-binding model with long-range Coulomb interactions among electrons, and the model is treated by the Hartree-Fock approximation followed by the single-excitation configuration interaction method. We discuss the variations in the optical spectra by changing the conjugation parameter between molecules. We find that the total CT-component increases in smaller conjugations, and saturates at the intermediate conjugations. It decreases in the large conjugations. We also find that the CT-components of the doped systems are smaller than those of the neutral systems, indicating that the electron-hole distance becomes shorter in the doped C60-polymers.

cond-mat↗

arXiv1996

Variational quantum Monte Carlo ground state of GaAs

Variational quantum Monte Carlo calculations are reported for the bulk GaAs semiconductor in order to present values for the ground-state energy, the lattice constant, the bulk modulus, and some derived properties. The statistical accuracy is significantly higher than the remaining differences to the experimental values, especially for the total-energy upper bound. The agreement with experiment is satisfactory. The results are also compared with those of density functional calculations. The accuracy of our results is comparable to the best of those calculations.

mtrl-th↗

arXiv1996

Basis Functions for Linear-Scaling First-Principles Calculations

In the framework of a recently reported linear-scaling method for density-functional-pseudopotential calculations, we investigate the use of localized basis functions for such work. We propose a basis set in which each local orbital is represented in terms of an array of `blip functions'' on the points of a grid. We analyze the relation between blip-function basis sets and the plane-wave basis used in standard pseudopotential methods, derive criteria for the approximate equivalence of the two, and describe practical tests of these criteria. Techniques are presented for using blip-function basis sets in linear-scaling calculations, and numerical tests of these techniques are reported for Si crystal using both local and non-local pseudopotentials. We find rapid convergence of the total energy to the values given by standard plane-wave calculations as the radius of the linear-scaling localized orbitals is increased.

mtrl-th↗