Papers by Omar A Sharafeddin
If time carries energy, then where and how can it be extracted? I propose that energy carried in ... more If time carries energy, then where and how can it be extracted? I propose that energy carried in time can be extracted when matter transitions in time. The energy of time becomes evident due to the appearance or disappearance of matter and thus a change in mass when matter transitions time. Einstein's Energy/mass equivalence can then be used to give the magnitude of the energy transfer from past to future or from future to past such that overall energy is conserved.
The intersection points between 1-dim wave packet probability densities representing free quantum... more The intersection points between 1-dim wave packet probability densities representing free quantum particles at different times were analyzed. We propose that at an intersection point, there is the potential that a particle can transition to the probability density of a different time. This time transition can happen without the need to assume superluminal motion. The method was also applied to the 3dim free particle and to a particle in a harmonic potential.
Analytic banded approximation for the discretized free propagator
The Journal of Physical Chemistry, 1991
Page 1. J. Phys. Chem. 1991, 95, 8299-8305 8299 disagreement between the vibrational levels of it... more Page 1. J. Phys. Chem. 1991, 95, 8299-8305 8299 disagreement between the vibrational levels of it and those of the Bowman potential and for remaining uncertainties in the as-signment of the observed levels. We have suggested ...
When "Grain Size" Doesn't Matter
The Sixth Distributed Memory Computing Conference, 1991. Proceedings
We describe insights gained from putting a quantum scattering problem on two very different paral... more We describe insights gained from putting a quantum scattering problem on two very different parallel architectures: MasPar MP-I (massively parallel) and nCUBE 2 (moderately parallel). Our nearly trivial port from the SIMD MasPar to the MIMD nCUBE demonstrates that it is not categorically difficult to move software from one parallel architecture class to another. These machines show widely different processor
On the role of parallel architecture supercomputers in time-dependent approaches to quantum scattering
Theoretica Chimica Acta, 1991
Summary Results of our initial study of the use of parallel architecture super-computers in solvi... more Summary Results of our initial study of the use of parallel architecture super-computers in solving time-dependent quantum scattering equations are reported. The specific equations solved are obtained from the time-dependent Lippmann-Schwinger integral equation by means of a quadrature approximation to the time integral. This leads to a modified Cayley transform algorithm in which the primary computational step is a matrix-vector
Numerical evaluation of spherical bessel transforms via fast Fourier transforms
Journal of Computational Physics, 1992
The purpose of this article is to describe a new fast Fourier transform (FFT) method for calculat... more The purpose of this article is to describe a new fast Fourier transform (FFT) method for calculating spherical Bessel transforms. The method is based on an expansion representation of the spherical Bessel functions in terms of sine and cosine trigonometric functions, multiplied by polynomials in inverse powers of the argument of the Bessel function [ 11. The method should be of value in algorithms in which frequent calculations of spherical Bessel transforms are required at many values of the transform variables, which is frequently the situation in time-dependent scattering calculations. The method makes use of FFTs for which the computing time for each transform scales as Nlog,(N), where N is the number of quadrature points, rather than the N2 scaling of ordinary numerical quadratures. Also, the explicit evaluation of the spherical Bessel functions is not required in the method. The method differs from that given in the work of J. D. Talman [2, 33 and A. E. Siegmon [4]. In the work of Talman [2, 33 and Siegman [4], a change to logarithmic variables is required to recast the integral transform as a convolution integral, which is then evaluated by FFT procedures. However, as pointed out by Talman, this makes the step size Ar increase proportionally with r and renders the method unsuitable for functions of an oscillatory nature. In particular, the oscillatory nature of the function is lost in the increasing mesh intervals. In essence, the Talman-Siegman method is excellent for bound state wave functions, but it is not
Journal of Computational Chemistry, 1997
We present results of mixed quantum-classical molecular dynamics simulations of the intramolecula... more We present results of mixed quantum-classical molecular dynamics simulations of the intramolecular proton transfer in acetylacetone. Simulations are performed starting from the reactant and transition state configurations with initial velocities at each configuration chosen from an ensemble at 300 K. The proton motion is treated quantum mechanically and the remaining degrees of freedom are treated classically. Two mixed quantumclassical molecular dynamics methods are implemented. In the first, a Ž. quantum-classical time-dependent self-consistent field method QCrTDSCF , the time-dependent Schrodinger equation for the proton is solved using the spliẗ operator approach and a plane-wave basis. In the second, a mixed quantum-Ž. classical adiabatic method QCrA , the instantaneous ground state wave function is calculated by solving the time-independent Schrodinger equation for the configurations of the classical particles by propagating in imaginary time using the split operator approach and the same plane-wave basis. A comparison of the two approaches with classical trajectories is presented. The QCrTDSCF and QCrA results are very similar for trajectories started from the reactant configuration. The two methods, however, yield somewhat different results when the trajectories are started from the transition state configuration. The proton wave function of the QCrA method adjusts instantaneously to the position of the classical particles, whereas the motion of the QCrTDSCF wavepacket more faithfully represents the true proton dynamics.
Time‐dependent treatment of scattering: Integral equation approaches using the time‐dependent amplitude density
The Journal of Chemical Physics, 1990
The time-dependent form of the Lippmann-Schwinger integral equation is used as the basis of sever... more The time-dependent form of the Lippmann-Schwinger integral equation is used as the basis of several new wave packet propagation schemes. These can be formulated in terms of either the time-dependent wave function or a time-dependent amplitude density. The latter is nonzero only in the region of configuratiaon space for which the potential is nonzero, thereby in principle obviating the necessity of large grids or the use of complex absorbing potentials when resonances cause long collision times (leading, consequently, to long propagation times). Transition amplitudes are obtained in terms of Fourier transforms of the amplitude density from the time to the energy domain. The approach is illustrated by an application to a standard potential scattering model problem where, as in previous studies, the action of the kinetic energy operator is evaluated by fast Fourier transform (FFT) techniques.
Time‐dependent treatment of scattering. II. Novel integral equation approach to quantum wave packets
The Journal of Chemical Physics, 1990
The novel wave-packet propagation scheme presented is based on the time-dependent form of the Lip... more The novel wave-packet propagation scheme presented is based on the time-dependent form of the Lippman-Schwinger integral equation and does not require extensive matrix inversions, thereby facilitating application to systems in which some degrees of freedom express the potential in a basis expansion. The matrix to be inverted is a function of the kinetic energy operator, and is accordingly diagonal in
Spectroscopic analysis of transition state energy levels: Bending–rotational spectrum and lifetime analysis of H3 quasibound states
The Journal of Chemical Physics, 1989
Converged quantum mechanical calculations of scattering matrices and transition probabilities are... more Converged quantum mechanical calculations of scattering matrices and transition probabilities are reported for the reaction of H with H2 with total angular momentum 0, 1, and 4 as functions of total energy in the range 0.85-1.15 eV on an accurate potential energy surface. The resonance structure is illustrated with Argand diagrams. State-to-state reactive collision delay times and lifetimes are presented.
The Journal of Chemical Physics, 1995
We compare pointwise representations and nondirect product basis representations for treating qua... more We compare pointwise representations and nondirect product basis representations for treating quantum dynamics in 2D (,) spherical polar coordinates. As pointwise representations we have considered a modified discrete variable representation ͑DVR͒ and the collocation representation ͑CR͒. As basis representations we used spherical harmonics with 2D Gaussian numerical quadratures ͑FBR͒ and the spectral collocation representation ͑SCR͒. These representations were tested on a simple model potential V(,) and on a realistic ArH 2 O potential ͑at fixed R͒ and the results were compared. The energies obtained from the pointwise representations considered were substantially less accurate than those obtained from the basis representations for given matrix sizes. The basis representations, especially the FBR, appear to require the least computational effort and to be the most simple and accurate for quantum problems in spherical polar coordinates. This illustrates the difficulties in using pointwise representations for angular problems which do not have good direct product bases.
Finite‐difference approach to solving Heisenberg’s operator equations of motion: Application to one‐dimensional time dependent Hamiltonians
The Journal of Chemical Physics, 1995
ABSTRACT
Finite‐difference Heisenberg approach: The treatment of unbound states and the elimination of artificial boundary reflections
The Journal of Chemical Physics, 1996
We apply our recently proposed finite-difference Heisenberg (FDH) approach to the treatment of un... more We apply our recently proposed finite-difference Heisenberg (FDH) approach to the treatment of unbound states and show that, by using this approach, the problem of artificial reflections of the scattered wave packet from the boundaries is totally eliminated. This is because the basis and coordinate frame are dynamic and thus adjust themselves, as dictated by the potential function, to the evolving wave function. The disadvantage of this approach is that it may scale as M3 for M basis and thus become expensive if M is large. However, accurate results can be obtained efficiently for a limited range of energies in the scattered wave packet using a small basis. These results are demonstrated by one-dimensional (1D) scattering from an Eckart barrier.
The Journal of Chemical Physics, 1991
Quadrature‐based, coarse‐grained treatment of the coordinate representation free particle real‐time evolution operator
The Journal of Chemical Physics, 1991
In this paper we report a quadrature evaluation of the coordinate representation, short-time free... more In this paper we report a quadrature evaluation of the coordinate representation, short-time free particle propagator, {l angle}{ital R}{vert bar}exp(-{ital iH}âÏ){vert bar}{ital R}â²{r angle}. The result is the elimination of most of the highly oscillatory behavior in this quantity yielding in its stead a much smoother function, strongly peaked at {ital R}={ital R}â². We view this as a numerical coarse
A comparison of three time‐dependent wave packet methods for calculating electron–atom elastic scattering cross sections
The Journal of Chemical Physics, 1991
Three time-dependent wave packet methods for performing elastic scattering calculations from scre... more Three time-dependent wave packet methods for performing elastic scattering calculations from screened Coulomb potentials are compared. The three methods are the time-dependent amplitude density method (TDADM), a Cayley-transform method (CTM), and the Chebyshev propagation method of Tal-Ezer and Kosloff. Both the TDADM and the CTM are based on a time-dependent integral equation for the wave function. In the first, the time-dependent amplitude density is propagated, while in the other two, the wave function is propagated. As a numerical example, phase shifts and cross sections are calculated using a screened Coulomb, Yukawa type potential over the range 200-1000 eV. It is found that, in most cases, all three methods yield comparable accuracy and are about equally efficient computationally. However for l = 0, where the Coulomb well is not screened by the centrifugal potential, the TDADM requires smaller grid spacings to maintain accuracy.
A DVR based time-dependent wave packet treatment for reactive scattering
Chemical Physics Letters, 1993
... Volume 204, number 1,2 CHEMICAL PHYSICS LETTERS 12 March 1993 for reactive scattering Omar Sh... more ... Volume 204, number 1,2 CHEMICAL PHYSICS LETTERS 12 March 1993 for reactive scattering Omar Sharafeddin and John 1H. ... 12 March 1993 1 d2 1 ~=<k1I-~-~~IEi,)= L <&I-i;~ d2 - IK~ In><nIR~> 1 (j~2 2 N (inn i)- 51~kj~i (jnir I ( 1y Jir2 L2 ~ X sin2[n(i+j)/2(N+1)]) fori#j and T ...
Finite-difference Heisenberg approach: an approximate treatment of many-particle systems, energy level separations and the time-dependent Schrödinger wavefunction
Chemical Physics Letters, 1995
ABSTRACT
Chemical Physics, 1992
We present a simple and efficient approach for extracting the final state-specific information in... more We present a simple and efficient approach for extracting the final state-specific information in trme-dependent quantum wave packet calculattons for scattering or half-scattenng problems without the artificial boundary reflection. The method, whtch is based on the compactness of the interaction picture wavefunctron, employs an optical potential to absorb the flux of the Schriidinger picture wavefunction near the edge of the boundary. However, the absorption does not disturb the mteraction picture wavefunction which is used to compute the stable product state distributions. Two numerical examples using this approach are gtven. One is for a model collinear photodissociation of CH>I involvmg nonadiabatic coupling. and the other is for a rigid rotor scattered off a flat surface.
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Papers by Omar A Sharafeddin