The validity of the semiclassical method for the coupled channel atomic scattering problem
Stationary phase approximation for two-channel atomic scattering system amplitude
TWO-PHASE SYSTEM↗
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Validity of the semiclassical method for the coupled-channel atomic scattering problem.
Stationary phase approximation for evaluation of scattering amplitudes of coupled channel atoms
Greenman, J. V.↗
Molecular hydrogen inelastic electron impact cross sections - A semiclassical method.
Electron impact cross sections for diatomic molecule ionization and excitation from modified Gryzinski theory, discussing results from molecular models
Hettel, H. J.↗
2D Quantum Simulation of MOSFET Using the Non Equilibrium Green's Function Method
The objectives this viewgraph presentation summarizes include: (1) the development of a quantum mechanical simulator for ultra short channel MOSFET simulation, including theory, physical approximations, and computer code; (2) explore physics that is not accessible by semiclassical methods; (3) benchmarking of semiclassical and classical methods; and (4) study other two-dimensional devices and molecular structure, from discretized Hamiltonian to tight-binding Hamiltonian.
Svizhenko, Alexel↗
On the estimation and detection for optical turbulent channels.
Consideration of the problem of filtering and detecting signals received through a turbulent channel at optical frequencies. Adopting the semiclassical method of quantum mechanics, application is made to the direct detection of a single-path optical communication channel where the received field is assumed to be the coherent signal field degraded by the atmospheric turbulence with a signal-independent, additive, zero-mean Gaussian background radiation.
Harger, R. O.↗
Inelastic scattering in atom-diatomic molecule collisions. II - Effect of rotation on vibrational transition
Rotational and vibrational transitions in a diatomic molecule caused by collisions with an atom are analyzed by a semiclassical method for conditions where the rotational transitions can be handled well by the sudden approximation and the vibrational transitions belong to the adiabatic regime. The contribution to the vibrational transition probability from the correction, which takes the finite value of the spacing between rotational energy levels into account, is examined.-
Stallcop, J. R.↗
Electronic excitation and quenching of atoms at insulator surfaces
A trajectory-based semiclassical method is used to study electronically inelastic collisions of gas atoms with insulator surfaces. The method provides for quantum-mechanical treatment of the internal electronic dynamics of a localized region involving the gas/surface collision, and a classical treatment of all the nuclear degrees of freedom (self-consistently and in terms of stochastic trajectories), and includes accurate simulation of the bath-temperature effects. The method is easy to implement and has a generality that holds promise for many practical applications. The problem of electronically inelastic dynamics is solved by computing a set of stochastic trajectories that on thermal averaging directly provide electronic transition probabilities at a given temperature. The theory is illustrated by a simple model of a two-state gas/surface interaction.
Swaminathan, P. K.↗
The optically thick C III spectrum. I - Term populations and multiplet intensities at lower optical depths
The C III spectrum is studied quantitatively under both optically thin and optically thick conditions, yielding term populations and line/multiplet intensities for column lengths from zero to 10 exp 18/sq cm. The roles of escape probabilities and line profiles in the calculation are discussed in some detail. It is shown that use of the fully integrated escape factor, rather than the more appropriate monodirectional escape probability, can lead to appreciable errors in calculated intensities. The results for populations and intensities make it possible to identify two unassigned features in the solar EUV spectrum of Vernazza and Reeves (1978) as C III multiplets, and to establish that an unidentified infrared solar feature at 8500.32 A, seen in both absorption (Fraunhofer) and emission (chromospheric) spectra, is the C III transition 2s3s(1S)-2s3p(1P). Voigt parameters for the C III lines and multiplets, obtained by a modified semiclassical method are tabulated. A new, unambiguous notation for the numerous line ratios present in a typical spectrum, which is argued to be an improvement over present arbitrary notations, is proposed and used.
Bhatia, A. K.↗
The exact eigenfunctions and eigenvalues of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics
Exact eigenfunctions for a two-dimensional rigid rotor are obtained using Gaussian wave packet dynamics. The wave functions are obtained by propagating, without approximation, an infinite set of Gaussian wave packets that collectively have the correct periodicity, being coherent states appropriate to this rotational problem. This result leads to a numerical method for the semiclassical calculation of rovibrational, molecular eigenstates. Also, a simple, almost classical, approximation to full wave packet dynamics is shown to give exact results: this leads to an a posteriori justification of the De Leon-Heller spectral quantization method.
Reimers, J. R.↗
Elastic scattering and rotational excitation of a polyatomic molecule by electron impact - Acetylene
Differential, integral, momentum transfer, and partial cross sections have been calculated for elastic scattering and rotational excitation of C2H2 by 10-eV electrons. The effective potential includes static, exchange, and polarization interactions calculated by the INDOX/1s method and the semiclassical exchange approximation with adiabatic polarization at large electron-molecule distances. The scattering is treated by well converged rotational close coupling using the centrifugal dominant scheme to select the channels included and including up to 32 coupled channels for a given total angular momentum. The calculated integral cross sections for pure elastic scattering and rotation excitation are 54.5 and 41.4 a(0)squared, respectively. These are much larger than the values (34.4 and 18.6 a(0)squared) previously (Onda and Truhlar, 1979) calculated for the isoelectronic molecule N2, at this energy. This illustrates how the greater spatial extent of C2H2 greatly increases the cross sections for pure elastic and rotationally inelastic scattering.
Thirumalai, D.↗
Vibration-translation energy transfer in anharmonic diatomic molecules. 1: A critical evaluation of the semiclassical approximation
The semiclassical approximation is applied to anharmonic diatomic oscillators in excited initial states. Multistate numerical solutions giving the vibrational transition probabilities for collinear collisions with an inert atom are compared with equivalent, exact quantum-mechanical calculations. Several symmetrization methods are shown to correlate accurately the predictions of both theories for all initial states, transitions, and molecular types tested, but only if coupling of the oscillator motion and the classical trajectory of the incident particle is considered. In anharmonic heteronuclear molecules, the customary semiclassical method of computing the classical trajectory independently leads to transition probabilities with anomalous low-energy resonances. Proper accounting of the effects of oscillator compression and recoil on the incident particle trajectory removes the anomalies and restores the applicability of the semiclassical approximation.
Mckenzie, R. L.↗
Vibration-translation energy transfer in anharmonic diatomic molecules. I - A comparative evaluation of the semiclassical approximation
The semiclassical approximation (quantum oscillator, classical path) is applied to anharmonic diatomic oscillators in excited initial states. Multistate numerical solutions giving the vibrational transition probabilities for collinear collisions with an inert atom are compared with equivalent, exact quantum-mechanical calculations. Several symmetrization methods are shown to correlate accurately the predictions of both theories for all initial states, transitions, and molecular types tested, but only if coupling of the oscillator motion and the classical trajectory of the incident particle is considered. In anharmonic heteronuclear molecules, the customary semiclassical method of computing the classical trajectory independently leads to transition probabilities with anomalous low-energy resonances. Proper accounting of the effects of oscillator compression and recoil on the incident particle trajectory removes the anomalies and restores the applicability of the semiclassical approximation.
Mckenzie, R. L.↗
Semiclassical theory of unimolecular dissociation induced by a laser field
A semiclassical nonperturbative theory of direct photodissociation in a laser field is developed in which photon absorption and dissociation are treated in a unified fashion. This is achieved by visualizing nuclear dynamics as a representative particle moving on electronic-field surfaces. Methods are described for calculating dissociation rates and probabilities by Monte Carlo selection of initial conditions and integration of classical trajectories on these surfaces. This unified theory reduces to the golden rule expression in the weak-field and short-time limits, and predicts nonlinear behavior, i.e., breakdown of the golden rule expression in intense fields. Field strengths above which lowest-order perturbation theory fails to work have been estimated for some systems. Useful physical insights provided by the electronic-field representation have been illustrated. Intense field effects are discussed which are amenable to experimental observation. The semiclassical methods used here are also applicable to multiple-surface dynamics in fieldfree unimolecular and bimolecular reactions.
Yuan, J.-M.↗
High Performance Parallel Computational Nanotechnology
At a recent press conference, NASA Administrator Dan Goldin encouraged NASA Ames Research Center to take a lead role in promoting research and development of advanced, high-performance computer technology, including nanotechnology. Manufacturers of leading-edge microprocessors currently perform large-scale simulations in the design and verification of semiconductor devices and microprocessors. Recently, the need for this intensive simulation and modeling analysis has greatly increased, due in part to the ever-increasing complexity of these devices, as well as the lessons of experiences such as the Pentium fiasco. Simulation, modeling, testing, and validation will be even more important for designing molecular computers because of the complex specification of millions of atoms, thousands of assembly steps, as well as the simulation and modeling needed to ensure reliable, robust and efficient fabrication of the molecular devices. The software for this capacity does not exist today, but it can be extrapolated from the software currently used in molecular modeling for other applications: semi-empirical methods, ab initio methods, self-consistent field methods, Hartree-Fock methods, molecular mechanics; and simulation methods for diamondoid structures. In as much as it seems clear that the application of such methods in nanotechnology will require powerful, highly powerful systems, this talk will discuss techniques and issues for performing these types of computations on parallel systems. We will describe system design issues (memory, I/O, mass storage, operating system requirements, special user interface issues, interconnects, bandwidths, and programming languages) involved in parallel methods for scalable classical, semiclassical, quantum, molecular mechanics, and continuum models; molecular nanotechnology computer-aided designs (NanoCAD) techniques; visualization using virtual reality techniques of structural models and assembly sequences; software required to control mini robotic manipulators for positional control; scalable numerical algorithms for reliability, verifications and testability. There appears no fundamental obstacle to simulating molecular compilers and molecular computers on high performance parallel computers, just as the Boeing 777 was simulated on a computer before manufacturing it.
Saini, Subhash↗
Wentzel-Kramers-Brillouin method in the Bargmann representation
It is demonstrated that the Bargmann representation of quantum mechanics is ideally suited for semiclassical analysis, using as an example the WKB method applied to the bound-state problem in a single well of one degree of freedom. For the harmonic oscillator, this WKB method trivially gives the exact eigenfunctions in addition to the exact eigenvalues. For an anharmonic well, a self-consistent variational choice of the representation greatly improves the accuracy of the semiclassical ground state. Also, a simple change of scale illuminates the relationship of semiclassical versus linear perturbative expansions, allowing a variety of multidimensional extensions.
Voros, A.↗
Comparison of Quantum Mechanical and Empirical Potential Energy Surfaces and Computed Rate Coefficients for N2 Dissociation
Physics-based modeling of hypersonic flows is predicated on the availability of chemical reaction rate coefficients and cross sections for the collisional processes. This approach has been built around the use of quantum mechanical calculations to describe the interaction between the colliding particles. In this approach a potential energy surface (PES) is computed by solving the electronic Schrödinger equation and collision cross sections are determined for that PES using classical, semiclassical or quantum mechanical scattering methods. The rate coefficients are computed by integrating the thermally weighted cross sections. State-to-state rate coefficients are determined by only integrating over a thermal distribution of collisional energies. Finally, thermal rate coefficients are determined by summation of the state-to-state rate coefficients for reactions of molecules in all relevant ro-vibrational energy levels. If the flow is in thermal non-equilibrium, the translational, vibrational and rotational energy modes can be represented in different ways: three unique temperatures can be used to describe the distributions, the populations of individual ro-vibrational energy levels can be determined by solving the Master Equation, or through the use of direct simulation in particle-based Monte Carlo sampling. The PES-to-rate coefficient approach had been proposed and attempted in the early days of digital computing, but it is only in the last 15 years that computer hardware and software have been up to the task of calculating accurate interatomic and intermolecular potentials.
Jaffe, Richard L.↗
SCF treatment of charge polarization effects in intermediate-energy electron scattering calculations with applications to N2
Converged rotational close coupling calculations of differential, integral, and momentum-transfer cross sections are obtained for seven model potentials for electron-N2 scattering at an impact energy of 30 eV. The model potentials involve a static potential calculated by the INDO/1s or INDOXI/1s method, and exchange potential calculated by the semiclassical exchange approximation from the INDO/1s or INDOXI/1s unperturbed electron density and a polarization potential. The polarization potentials used include the Buckley-Burke semiempirical one and various modifications of the INDOXI and INDO SCF (self-consistent-field) adiabatic polarization potentials. Without adjustment of parameters, good agreement is obtained with the angle dependence of the experimentally measured sum of the elastic and rotational excitation differential cross sections; however, the absolute value of the calculated cross sections is about 20-30% larger than the measured values in the best case, perhaps indicating that the model potentials are too strong or should have a nonzero imaginary part.
Onda, K.↗
Calculation of rotational transition probabilities in molecular collisions - Application to N2 + N2
A computational method is proposed to obtain rotational transition probabilities in collisions between two diatomic molecules. The potential method of Rabitz and an exponential approximation are used to solve the semiclassical coupled equations without invoking any perturbational technique. The collision trajectory is determined in the classical modified-wave-number approximation. The method can treat systems involving strong interactions and provide probabilities for transitions even with a multiquantum jump. A simultaneous transition in the rotational states of both molecules, i.e., the rotational-rotational energy transfer, is taken into account. An application to the system N2 + N2 is presented.
Itikawa, Y.↗