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Study applies the nonequilibrium collision theory of reaction rates to the estimation of rate constants for simple reactions. The complications in the quantum mechanical description of chemical reactions and the care needed in approximating the exact wave function for the collision are shown.
Quantum mechanical inverse problem of elastic scattering theory, discussing Hylleraas solution for determining potential energy function from phase shift
In this paper a completely classical model for laser action is discussed. An active medium consisting of classical anharmonic oscillators interacts with a classical electromagnetic field in a resonant cavity. Comparison with the case of a medium consisting of harmonic oscillators shows the significance of nonlinearities for producing self-sustained oscillations in the radiation field. The results for the classical model are found to be similar to those for a semiclassical model of the ammonia-beam maser. The conclusion is that laser action is not intrinsically a quantum-mechanical effect. The classical-laser theory as given in this paper can also be applied to the case of the electron-cyclotron maser.
The study of cosmological models by means of equations of motion in Hamiltonian form is considered. Hamiltonian methods applied to gravity seem to go back to Rosenfeld (1930), who constructed a quantum-mechanical Hamiltonian for linearized general relativity theory. The first to notice that cosmologies provided a simple model in which to demonstrate features of Hamiltonian formulation was DeWitt (1967). Applications of the ADM formalism to homogeneous cosmologies are discussed together with applications of the Hamiltonian formulation, giving attention also to Bianchi-type universes. Problems involving the concept of superspace and techniques of quantization are investigated.
The concept of tunnelling in the theory of electron and proton transfer reactions has recently been questioned on the ground that the situation is a nonstationary one. It has been suggested that time-dependent perturbation theory should be applied to obtain the quantum mechanical transition probability. We have done this for a square barrier. The result for most reactions is the same as obtained by the WKB approximation.
Ab initio quantum mechanical methods, including coupled-cluster theory, are used to determine the equilibrium geometries, dipole moments, and harmonic vibrational frequencies of ClONO2, NO2(+), and four isomers of protonated ClONO2. It was found that, for the equilibrium structures and harmonic frequencies of ClONO2, HOCl, and NO2(+), the highest-level theoretical predictions are consistent with the available experimental information concerning the reactions of ClONO2 and HOCl with HCl on the surface of polar stratospheric clouds (PSCs). The study supports a recent hypothesis that the reaction of ClONO2 on the surface of PSCs is proton catalyzed, although the mechanism is different.
Many body effects on conduction and diffusion of electrons and holes in a semiconductor quantum well are studied using a microscopic theory. The roles played by the screened Hartree-Fock (SHE) terms and the scattering terms are examined. It is found that the electron and hole conductivities depend only on the scattering terms, while the two-component electron-hole diffusion coefficients depend on both the SHE part and the scattering part. We show that, in the limit of the ambipolax diffusion approximation, however, the diffusion coefficients for carrier density and temperature are independent of electron-hole scattering. In particular, we found that the SHE terms lead to a reduction of density-diffusion coefficients and an increase in temperature-diffusion coefficients. Such a reduction or increase is explained in terms of a density-and temperature dependent energy landscape created by the bandgap renormalization.
This report summarizes the accomplishments during a three year research project to investigate the use of surfaces, particularly in microelectromechanical systems (MEMS), to exploit quantum vacuum forces. During this project, we developed AFM instrumentation to repeatably measure Casimir forces in the nanoNewton range at 10 6 torr, designed an experiment to measure attractive and repulsive quantum vacuum forces, developed a QED based theory of Casimir forces that includes non-ideal material properties for rectangular cavities and for multilayer slabs, developed theoretical models for a variety of microdevices utilizing vacuum forces, applied vacuum physics to a gedanken spacecraft, and investigated a new material with a negative index of refraction.
A feasible initiation step for particle growth in the interstellar medium (ISM) is simulated by means of ab quantum chemistry methods. The systems studied are dimer ions formed by pairing nitrogen containing small molecules known to exist in the ISM with ions of unsaturated hydrocarbons or vice versa. Complexation energies, structures of ensuing complexes and electronic excitation spectra of the encounter complexes are estimated using various quantum chemistry methods. Moller-Plesset perturbation theory (MP2, Z-averaged perturbation theory (ZAP2), coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)), and density functional theory (DFT) methods (B3LYP) were employed along with the correlation consistent cc-pVTZ and aug-cc-pVTZ basis sets. Two types of complexes are predicted. One type of complex has electrostatic binding with moderate (7-20 kcal per mol) binding energies, that are nonetheless significantly stronger than typical van der Waals interactions between molecules of this size. The other type of complex develops strong covalent bonds between the fragments. Cyclic isomers of the nitrogen containing complexes are produced very easily by ion-molecule reactions. Some of these complexes show intense ultraviolet visible spectra for electronic transitions with large oscillator strengths at the B3LYP, omegaB97, and equations of motion coupled cluster (EOM-CCSD) levels. The open shell nitrogen containing carbonaceous complexes especially exhibit a large oscillator strength electronic transition in the visible region of the electromagnetic spectrum.
The design of new high-energy density molecules as candidates for jet and rocket fuels is an important goal of modern chemical thermodynamics. The NASA Glenn Research Center is home to a database of thermodynamic data for over 2000 compounds related to this goal, in the form of least-squares fits of heat capacities, enthalpies, and entropies as functions of temperature over the range of 300 - 6000 K. The chemical equilibrium with applications (CEA) program written and maintained by researchers at NASA Glenn over the last fifty years, makes use of this database for modeling the performance of potential rocket propellants. During its long history, the NASA Glenn database has been developed based on experimental results and data published in the scientific literature such as the standard JANAF tables. The recent development of efficient computational techniques based on quantum chemical methods provides an alternative source of information for expansion of such databases. For example, it is now possible to model dissociation or combustion reactions of small molecules to high accuracy using techniques such as coupled cluster theory or density functional theory. Unfortunately, the current applicability of reliable computational models is limited to relatively small molecules containing only around a dozen (non-hydrogen) atoms. We propose to extend the applicability of coupled cluster theory- often referred to as the 'gold standard' of quantum chemical methods- to molecules containing 30-50 non-hydrogen atoms. The centerpiece of this work is the concept of local correlation, in which the description of the electron interactions- known as electron correlation effects- are reduced to only their most important localized components. Such an advance has the potential to greatly expand the current reach of computational thermochemistry and thus to have a significant impact on the theoretical study of jet and rocket propellants.
An introductory account of the semiclassical theory of the S-matrix for molecular collision processes is presented, with special emphasis on electronically nonadiabatic transitions. This theory is based on the incorporation of classical mechanics with quantum superposition, and in practice makes use of the analytic continuation of classical mechanics into the complex space of time domain. The relevant concepts of molecular scattering theory and related dynamical models are described and the formalism is developed and illustrated with simple examples - collinear collision of the A+BC type. The theory is then extended to include the effects of laser-induced nonadiabatic transitions. Two bound continuum processes collisional ionization and collision-induced emission also amenable to the same general semiclassical treatment are discussed.
Prof. Nussenzveig has dedicated part of his career to a surprising and unusual pursuit harking back to the heyday of classical physics: Mie theory, or the scattering of electromagnetic radiation by a homogeneous sphere. M e theory was not put forward until around 1908 (nearly simultaneously by Debye in a different form) and was quickly forgotten in the rush to the then-new quantum mechanics. It remained somewhat of a backwater until Prof. Nussenzveig brought it back by adapting complex angular momentum ideas from Regge pole theory, which had originally been invented for quantum mechanics. Since 1960, he has made fundamental contributions to actually understanding (as opposed to merely calculating) Mie theory. I became involved with this work in 1978 by inviting Prof. Nussenzveig to visit me at the National Center for Atmospheric Research. Since then we have written several papers together on approximate methods for Mie cross-sections, bubble scattering, and other subjects. This lecture will review that work, ending with his recent work on Mie resonances. The emphasis will be on the applications in atmospheric sciences.
Dependence of energy gap on quantum number and external magnetic field and its influence on other properties of a hollow superconducting cylinder, considered via ginzburg-landau theory
Papers are presented which deal with electrochemical research activities. Emphasis is placed on electrochemical energy storage devices. Topics discussed include: adsorption of dendrite inhibitors on zinc; proton discharge process; electron and protron transfer; quantum mechanical formulation of electron transfer rates; and theory of electrochemical kinetics in terms of two models of activation; thermal and electrostatic.
A statistical approach to sound propagation is considered in situations where, due to the presence of large gradients of properties of the medium, the classical (deterministic) treatment of wave motion is inadequate. Mathematical methods for wave motions not restricted to small wavelengths (analogous to known methods of quantum mechanics) are used to formulate a wave theory of sound in nonuniform flows. Nonlinear transport equations for field probabilities are derived for the limiting case of noninteracting sound waves and it is postulated that such transport equations, appropriately generalized, may be used to predict the statistical behavior of sound in arbitrary flows.
Although the Landau-Teller vibrational model accurately predicts vibrational excitation process in post-shock and compressing flows, it under-predicts the rate of de-excitation in cooling and expanding flows. In the present paper, detailed calculations of the vibrational relaxation process of N2 and CO in cooling flows are conducted. A coupled set of vibrational transition rate equations and quasi-one-dimensional fluid dynamic equations is solved. Multiple quantum level transition rates are computed using SSH theory. The SSH transition rate results are compared with available experimental data and other theoretical models. Vibration-vibration exchange collisions are responsible for some vibrational relaxation acceleration in situations of high vibrational temperature and low translational temperature. The present results support the relaxation mechanisms proposed by Bray and by Treanor Rich and Rehm.
It is well known that the quantum Yang-Baxter equations (QYBE) play an important role in various theoretical and mathematical physics, such as completely integrable system in (1 + 1)-dimensions, exactly solvable models in statistical mechanics, the quantum inverse scattering method and the conformal field theories in 2-dimensions. Recently, much remarkable progress has been made in constructing the solutions of the QYBE associated with the representations of lie algebras. It is shown that for some cases except the standard solutions, there also exist new solutions, but the others have not non-standard solutions. In this paper by employing the weight conservation and the diagrammatic techniques we show that the solution associated with the 10-D representations of SU (4) are standard alone.
Scalability of a low-cost, Intel Xeon-based, multi-Teraflop Linux cluster is tested for two high-end scientific applications: Classical atomistic simulation based on the molecular dynamics method and quantum mechanical calculation based on the density functional theory. These scalable parallel applications use space-time multiresolution algorithms and feature computational-space decomposition, wavelet-based adaptive load balancing, and spacefilling-curve-based data compression for scalable I/O. Comparative performance tests are performed on a 1,024-processor Linux cluster and a conventional higher-end parallel supercomputer, 1,184-processor IBM SP4. The results show that the performance of the Linux cluster is comparable to that of the SP4. We also study various effects, such as the sharing of memory and L2 cache among processors, on the performance.