Publications (28)46.29 Total impact
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ABSTRACT: We have shown that interesting physical phenomena can be revealed in high resolution quantum recurrence spectra by application of the harmonic inversion technique, thereby circumventing the restrictions imposed by the uncertainty principle of the conventional Fourier transform. The method allows, e.g., to test the validity of semiclassical theories, to identify hidden ghost or bits in the quantum spectra, and to observe the symmetry breaking in the spectra of the hydrogen atom in crossed magnetic and electric fields. The analysis has been demonstrated here on theoretically calculated quantum spectra but can be applied to experimental spectra as well.  [Show abstract] [Hide abstract]
ABSTRACT: The first order form of the manybody theory for inelastic scattering (called random phase approximation) has been applied in the 29.6 eV<or=E<or=81.63 eV energy region for the electron impact excitation of the 21S, 21P, 23S, 23P states of helium. Differential and integral cross sections are calculated and compared with recent experiments. The results for each state are discussed and compared with other calculations.  [Show abstract] [Hide abstract]
ABSTRACT: Using the MartinSchwinger variational technique (1959), a new theory is obtained for electronatom (molecule) inelastic scattering. This theory constitutes a higher order approximation than the GRPA elastic theory. In analogy with elastic scattering, an equivalent optical potential, named, the transition potential, is introduced for inelastic scattering. In the GRPA this transition potential is of the firstorder staticexchange type. The present theory adds three new effects to the GRPA transition potential. One of them represents the screening of the firstorder exchange term, another one the transition polarization effect and the third the effect of the final state field. In contrast to closecoupled or Kohntype variational theories, the present theory has the advantage of decoupling the scattering channels through the use of the energydependent transition potential.  [Show abstract] [Hide abstract]
ABSTRACT: The second order transition potential introduced in the previous paper (see ibid., vol. 6, no. 10, 2040 of 1973) is generalized and analysed from the energydependency point of view. The adiabatic limit and the first nonadiabatic correction is given. The same potential is analysed also in terms of multipole moments and it is shown how wavefunction methods can be used to calculate it. In the adiabatic, dipole limit the longrange part of the transition polarization potential agrees with the one used in the polarized Born approximation (Truhlar 1970, Rice et al. 1972). The same limit gives a generalization of Temkin's (1957) polarized orbital method for inelastic scattering.  [Show abstract] [Hide abstract]
ABSTRACT: The electron scattering of an atom in a laser is formulated from a manybody Green's function point of view. The advantage of the formalism is, as is usual with manybody theory, that the target responses and projectile motions are formally separated allowing for different physical approximations to be applied to each. The formalism is able to treat freefree scattering with the net absorption (emission) of n photons. 
Article: Manybody Green's function theory of electron impact ionization: coincident ionization of helium
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ABSTRACT: The manybody Green's function theory of Yarlagadda and Taylor (1975) is applied in the lowest order to the coincident ionization of the helium atom. Significant agreement is obtained with the experimental results of Ehrhardt and coworkers (1972). The success of the twotime model of inelastic processes is demonstrated.  [Show abstract] [Hide abstract]
ABSTRACT: Using the methods of manybody Green's function formalism, several different formally exact (and therefore impractical for computation) expressions are derived for the S matrix for electron impact ionization of atoms (molecules). The expressions differ in the lowest order where computation is possible. The physical models implied by the various loworder expressions are discussed. Computationally simple formulae which are physically reasonable result from the analysis. Consideration of the physics suggests that different formulae will apply in different energy regimes. The suggested key to understanding the physics is a 'twotime' model which considers relative passage and excitation (ionization) times. A direction for new work on the general electron scattering and ionization problem based on twotime ideas is discussed.  [Show abstract] [Hide abstract]
ABSTRACT: The stabilisation method is used to compute the resonant states of HCl . Resonant states of HCl that dissociate to H +Cl and Cl+H are found as well as those that dissociate to H+Cl+e. The totality of these states explain all the known qualitative and threshold features of vibrational excitation, dissociative attachment and associative detachment without doing rigorous electronpolarmolecule scattering computations. The computations were carried out using Gaussian orbitals and SCF+CI methods.  [Show abstract] [Hide abstract]
ABSTRACT: A nonlinear parameter estimator with frequencywindowing for signal processing, called Decimated Signal Diagonalization (DSD), is presented. This method is used to analyze exponentially damped time signals of arbitrary length corresponding to spectra that are sums of pure Lorentzians. Such time signals typically arise in many experimental measurements, e.g., ion cyclotron resonance (ICR), nuclear magnetic resonance or Fourier transform infrared spectroscopy, etc. The results are compared with the standard spectral estimator, the Fast Fourier Transform (FFT). It is shown that the needed absorption spectra can be constructed simply, without any supplementary experimental work or concern about the phase problems that are known to plague FFT. Using a synthesized signal with known parameters, as well as experimentally measured ICR time signals, excellent results are obtained by DSD with significantly shorter acquisition time than that which is needed with FFT. Moreover, for the same signal length, DSD is demonstrated to exhibit a better resolving power than FFT.  [Show abstract] [Hide abstract]
ABSTRACT: Three novel nonlinear parameter estimators are devised and implemented for accurate and fast processing of experimentally measured or theoretically generated time signals of arbitrary length. The new techniques can also be used as powerful tools for diagonalization of large matrices that are customarily encountered in quantum chemistry and elsewhere. The key to the success and the common denominator of the proposed methods is a considerably reduced dimensionality of the original data matrix. This is achieved in a preprocessing stage called beamspace windowing or bandlimited decimation. The methods are decimated signal diagonalization (DSD), decimated linear predictor (DLP), and decimated Padé approximant (DPA). Their mutual equivalence is shown for the signals that are modeled by a linear combination of timedependent damped exponentials with stationary amplitudes. The ability to obtain all the peak parameters first and construct the required spectra afterwards enables the present methods to phase correct the absorption mode. Additionally, a new noise reduction technique, based upon the stabilization method from resonance scattering theory, is proposed. The results obtained using both synthesized and experimental time signals show that DSD/DLP/DPA exhibit an enhanced resolution power relative to the standard fast Fourier transform. Of the three methods, DPA is found to be the most efficient computationally.  [Show abstract] [Hide abstract]
ABSTRACT: We present and compare three generically applicable signal processing methods for periodic orbit quantization via harmonic inversion of semiclassical recurrence functions. In a first step of each method, a bandlimited decimated periodic orbit signal is obtained by analytical frequency windowing of the periodic orbit sum. In a second step, the frequencies and amplitudes of the decimated signal are determined by either decimated linear predictor, decimated Padé approximant, or decimated signal diagonalization. These techniques, which would have been numerically unstable without the windowing, provide numerically more accurate semiclassical spectra than does the filter diagonalization method.  [Show abstract] [Hide abstract]
ABSTRACT: Periodic orbit quantization requires an analytic continuation of nonconvergent semiclassical trace formulae. We propose a method for semiclassical quantization based upon the Padé approximant to the periodic orbit sums. The Padé approximant allows the resummation of the typically exponentially divergent periodic orbit terms. The technique does not depend on the existence of a symbolic dynamics and can be applied to both bound and open systems. Numerical results are presented for two different systems with chaotic and regular classical dynamics, viz. the threedisk scattering system and the circle billiard.  [Show abstract] [Hide abstract]
ABSTRACT: We calculated all 3170 A1 and B2 (J = 0) vibronic bound states of the coupled electronic ground ( 2A1) and the first excited ( 2B2) surfaces of NO2, using a modification of the ab initio potentials of Leonardi et al. [J. Chem. Phys. 105, 9051 (1996)]. The calculation was performed by harmonic inversion of the Chebyshev correlation function generated from a DVR Hamiltonian in Radau coordinates. The rms error of the eigenenergies is about 2.5 cm−1, corresponding to a relative error of 10−4 near the dissociation energy. The results are compared with the adiabatic and diabatic levels calculated from the same surfaces, with experimental data, and with some approximations for the number of states function N(E). The experimental levels are reproduced fairly well up to an energy of 12 000 cm−1 above the potential minimum while the total number of bound levels agrees to within 2% with that calculated from the phase space volume. © 1999 American Institute of Physics. 
Article: Resonance partial widths and partial photodetachment rate using the rotatedcoordinate method
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ABSTRACT: A procedure based on the rotatedcoordinate method (RCM) is proposed to obtain widths for the decay of resonance into individual channels and it is demonstrated for a simple model potential.  [Show abstract] [Hide abstract]
ABSTRACT: We calculated all 2967 even and odd bound states of the adiabatic ground state of NO2, using a modification of the ab initio potential energy surface of Leonardi et al. [J. Chem. Phys. 105, 9051 (1996)]. The calculation was performed by harmonic inversion of the Chebyshev correlation function generated by a DVR Hamiltonian in Radau coordinates. The relative error for the computed eigenenergies (measured from the potential minimum), is 10−4 or better, corresponding to an absolute error of less than about 2.5 cm−1. Near the dissociation threshold the average density of states is about 0.2/cm−1 for each symmetry. Statistical analysis of the states shows some interesting structure of the rigidity parameter Δ3 as a function of energy. © 1998 American Institute of Physics. 
Article: All bound states of NO_2 (J=0)
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ABSTRACT: We calculated all 2967 even and odd bound states of the adiabatic ground state of NO_2, using a modification of the ab initio potential energy surface of Leonardi et al. [J. Chem. Phys. 105, 9051 (1996)]. The calculation was performed by harmonic inversion of the Chebyshev correlation function generated by a DVR Hamiltonian in Radau coordinates. The relative error for the computed eigenenergies is $10^{4}$ or better. Near the dissociation threshold the density of states is about 0.3cm$^{1}$. Statistical analysis of the states shows some interesting structure of the rigidity parameter $\Delta_3$ as a function of energy.  [Show abstract] [Hide abstract]
ABSTRACT: New methods of high resolution spectral analysis of short time signals are presented. These methods utilize the filterdiagonalization approach of Wall and Neuhauser [J. Chem. Phys. 102, 8011 (1995)] that extracts the complex frequencies w k and amplitudes d k from a signal C(t) = Σ kd ke itωk in a small frequency interval by recasting the harmonic inversion problem as the one of a small matrix diagonalization. The present methods are rigorously adapted to the conventional case of the signal available on a sparse equidistant time grid and use a more efficient boxlike filter. Various applications are discussed, such as iterative diagonalization of large Hamiltonian matrices for calculating bound and resonance states, scattering calculations in the presence of narrow resonances, etc. For the scattering problem the harmonic inversion is directly applied to the signal c n=(X fT n(Ĥ)X i), generated by the dynamical system governed by a modified Chebyshev recursion, avoiding the usual recasting the problem to the time domain. Some challenging numerical examples are presented. The general filterdiagonalization method is shown to be stable and efficient for the extraction of thousands of complex frequencies ω k and amplitudes d k from a signal. When the model signal is "spoiled" by a moderate amount of an additive Gaussian noise the obtained spectral estimate is still superior to the conventional Fourier spectrum.  [Show abstract] [Hide abstract]
ABSTRACT: Two relatively new methods, the spectral projection method and the stabilization method, of implementing scattering calculations are described, and are here applied to two devices. Both methods use essentially short range spectral projection operators to produce a complete set of solutions of the wave equation that need be valid only inside the interaction region. While the spectral projection method is more generic than the stabilization method which is based on using the more difficult to compute spectral density operator, the latter becomes very efficient when narrow resonances exist. For problems of small size both methods are practical in the sense that they involve only real, symmetric matrices resulting from Hamiltonians represented onL2basis sets. For more challenging larger systems the spectral projection method lends itself to a very efficient time independent iterative procedure that obtains results simultaneously at all energies. This procedure uses modified Chebyshev recursion relations to essentially expand the operator (E−H)−1. It requires minimal storage and the resulting series converges rapidly in a manner that is uniform in energy.  [Show abstract] [Hide abstract]
ABSTRACT: For the reaction of He with H2+, starting with accurate theoretically computed reactive, elastic, and inelastic scattering data that reveals many complex unassignable narrow resonances, the detailed motions governing the dynamics of the tight transition state are extracted. Methods ranging from scattering theory, the stabilization theory of dynamics, nonlinear dynamic periodic orbit theory, and hierarchical smoothing theory which was developed to study complex ‘‘chaotic’’ spectra, are all used in the analysis. Relationships between the doorway model of nuclear physics, aspects of transition state theory, and models of nonlinear chaotic dynamics are pointed out and used to shed light on the fact that the complex resonance structure observed is one quantum manifestation of classical transient chaos in scattering processes. The transition (or doorway) state corresponds to the only populous and robust periodic orbit or set of similar periodic orbits whose motion allows the types of energy transfers necessary to go from reactants to products. Wave packet motion and quantum eigenfunctions are influenced by these periodic orbits. © 1995 American Institute of Physics.  [Show abstract] [Hide abstract]
ABSTRACT: A new method of doing scattering calculations is presented and illustrated. Reactive state‐to‐state transition amplitudes, microcanonical rate, resonance parameters, and related quantities are computed for the collinear H+H2→H2+H exchange reaction. The method only involves diagonalizations of a real symmetric system Hamiltonian placed in a series of enclosing boxes.
Publication Stats
699  Citations  
46.29  Total Impact Points  
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Institutions

19932007

University of Southern California
 Department of Chemistry
Los Angeles, CA, United States


2001

Argonne National Laboratory
Lemont, Illinois, United States
