Neural networks as tools for predicting materials properties

Materials science is of fundamental significance to science and technology because our industrial base and society depend upon our ability to develop advanced materials. Materials and materials processing cuts across almost every sector of industry. The key in all of these areas is the ability to rapidly screen possible designs which will have significant impact. However up to now materials design and processing have been to a large extent empirical sciences. In addition we are still unable to design new alloys and polymers to meet application specific requirements. Being able to do so quickly and at minimum cost would provide an incredible advantage. Obviously, the ability to predict physical, chemical, or mechanical properties of compounds prior to their synthesis is of great technological value in optimizing their design, processing, or recycling. In addition, in order to realize the ultimate goal of materials by computational design, the reverse problem, prediction of chemical structure based on desired properties, has to be resolved. Research at ORNL has lead to the development of a novel computational paradigm (coupling computational neural networks with graph theory, genetic algorithms, wavelet theory, fuzzy logic, molecular dynamics, and quantum chemistry) capable of performing accurate computational synthesis (both predictions of properties or the design of compounds that have specified performance criteria). The computational paradigm represents a hybrid of a number of emerging technologies and has proven to work very well for test compounds ranging from small organic molecules to polymeric materials. Fundamental to the method is the neural network-based formulation of the correlations between structure and properties. The advantages of this method is in its ease of use, speed, accuracy, and that it can be used to predict both properties from structure, and also structure from properties

Semiclassical calculation of the vibrational echo

The infrared echo measurement probes the time scales of the molecular motions that couple to a vibrational transition. Computation of the echo observable within rigorous quantum mechanics is problematic for systems with many degrees of freedom, motivating the development of semiclassical approximations to the nonlinear optical response. We present a semiclassical approximation to the echo observable, based on the Herman-Kluk propagator. This calculation requires averaging over a quantity generated by two pairs of classical trajectories and associated stability matrices, connected by a pair of phase-space jumps. Quantum, classical, and semiclassical echo calculations are compared for a thermal ensemble of noninteracting anharmonic oscillators. The semiclassical approach uses input from classical mechanics to reproduce the significant features of a complete, quantum mechanical calculation of the nonlinear response

Effects of Large-Scale Convection on p-mode Frequencies

We describe an approach for finding the eigenfrequencies of solar acoustic modes (p modes) in a convective envelope in the WKB limit. This approximation restricts us to examining the effects of fluid motions which are large compared to the mode wavelength, but allows us to treat the three-dimensional mode as a localized ray. The method of adiabatic switching is then used to investigate the frequency shifts resulting from simple perturbations to a polytropic model of the convection zone as well as from two basic models of a convective cell. We find that although solely depth-dependent perturbations can give frequency shifts which are first order in the strength of the perturbation, models of convective cells generate downward frequency shifts which are second order in the perturbation strength. These results may have implications for resolving the differences between eigenfrequencies derived from solar models and those found from helioseismic observations.Comment: 27 pages + 6 figures; accepted for publication in Ap

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.Comment: 37 pages including 3 poscript figures, submitted to Phys. Rev.

Classical approach in quantum physics

The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a semiclassical spectrum of hydrogen atom in crossed electric and magnetic fields, a spontaneous decay of excited states of a hydrogen atom, Gutzwiller's approach to Stark problem, long-lived excited states of a helium atom recently discovered with the help of Poincar$\acute{\mathrm{e}}$ section, inelastic transitions in slow and fast electron-atom and ion-atom collisions - is reviewed. Further, a classical representation in quantum theory is discussed. In this representation the quantum states are treating as an ensemble of classical states. This approach opens the way to an accurate description of the initial and final states in classical trajectory Monte Carlo (CTMC) method and a purely classical explanation of tunneling phenomenon. The general aspects of the structure of the semiclassical series such as renormgroup symmetry, criterion of accuracy and so on are reviewed as well. In conclusion, the relation between quantum theory, classical physics and measurement is discussed.Comment: This review paper was rejected from J.Phys.A with referee's comment "The author has made many worthwhile contributions to semiclassical physics, but this article does not meet the standard for a topical review"

Dynamical Tunneling in Mixed Systems

We study quantum-mechanical tunneling in mixed dynamical systems between symmetry-related phase space tori separated by a chaotic layer. Considering e.g. the annular billiard we decompose tunneling-related energy splittings and shifts into sums over paths in phase space. We show that tunneling transport is dominated by chaos-assisted paths that tunnel into and out of the chaotic layer via the ``beach'' regions sandwiched between the regular islands and the chaotic sea. Level splittings are shown to fluctuate on two scales as functions of energy or an external parameter: they display a dense sequence of peaks due to resonances with states supported by the chaotic sea, overlaid on top of slow modulations arising from resonances with states supported by the ``beaches''. We obtain analytic expressions which enable us to assess the relative importance of tunneling amplitudes into the chaotic sea vs. its internal transport properties. Finally, we average over the statistics of the chaotic region, and derive the asymptotic tail of the splitting distribution function under rather general assumptions concerning the fluctuation properties of chaotic states.Comment: 28 pages, Latex, 16 EPS figure

Classical, non-linear, internal dynamics of large, isolated, vibrationally excited molecules

This work reports numerical experiments intended to clarify the internal equilibration process in large molecules, following vibrational excitation. A model of amorphous and oxygenated hydrocarbon macromolecule (about 500 atoms)--simulating interstellar dust-- is built up by means of a chemical simulation code. Its structure is optimized, and its normal modes determined. About 4.5 eV of potential energy is then deposited locally by perturbing one of the C-H peripheral bonds, thus simulating the capture of a free H atom by a dangling C bond. The ensuing relaxation of the system is followed for up to 300 ps, using a molecular mechanics code. When steady state is reached, spectra and time correlation functions of kinetic energy and bond length fluctuations indicate that most normal modes have been activated, but the motion remains quasi-periodic or regular. By contrast, when the molecule is violently excited or embedded in a thermal bath (modelled by Langevin dynamics), the same markers clearly depict chaotic motions. Thus it appears that even such a large system of oscillators is unable to provide the equivalent of a thermal bath to any one of these, unless there are strong resonances between some of them. In general, therefore, an energy of a few eV's deposited in an isolated molecule will not be immediately thermalized. This conclusion is of consequence for the interpretation of astronomical UIB spectra. Key Words:IS dust--UIBs--Excitation, relaxation processes.Comment: 19 pages, 9 figures, J. of Phys. B 2002, vol 35(17

Monte Carlo Simulations of HIV Capsid Protein Homodimer

Capsid protein (CA) is the building block of virus coats. To help understand how the HIV CA proteins self-organize into large assemblies of various shapes, we aim to computationally evaluate the binding affinity and interfaces in a CA homodimer. We model the N- and C-terminal domains (NTD and CTD) of the CA as rigid bodies and treat the five-residue loop between the two domains as a flexible linker. We adopt a transferrable residue-level coarse-grained energy function to describe the interactions between the protein domains. In seven extensive Monte Carlo simulations with different volumes, a large number of binding/unbinding transitions between the two CA proteins are observed, thus allowing a reliable estimation of the equilibrium probabilities for the dimeric vs monomeric forms. The obtained dissociation constant for the CA homodimer from our simulations, 20–25 μM, is in reasonable agreement with experimental measurement. A wide range of binding interfaces, primarily between the NTDs, are identified in the simulations. Although some observed bound structures here closely resemble the major binding interfaces in the capsid assembly, they are statistically insignificant in our simulation trajectories. Our results suggest that although the general purpose energy functions adopted here could reasonably reproduce the overall binding affinity for the CA homodimer, further adjustment would be needed to accurately represent the relative strength of individual binding interfaces