Problems In Physical Chemistry Research Articles

Ozone Decomposition Data for Kinetics Exercises

The goal of this paper is to provide data that can be used in a variety of exercises ranging from kinetics in general chemistry to advanced problems in physical chemistry. The data provided relates to ozone-decay kinetics in various atmospheres (O2, N2, Ar) as measured by ultraviolet/visible absorbance spectroscopy (UV/vis) at 254 nm. The absorbance of ozone is monitored over a 75-min time period, and by using Beer’s law the concentration is calculated. Nine data sets, each repeated three times, of absorbance measurements are provided for student exercises, and prelaboratory and postlaboratory questions are suggested.

Principles and problems in physical chemistry for biochemists (3rd ed.)

Principles and problems in physical chemistry for biochemists (3rd ed.)

Dynamics of biochemical and biophysical reactions: insight from computer simulations.

1. Introduction 5632. Obtaining rate constants from molecular-dynamics simulations 5642.1 General relationships between quantum electronic structures and reaction rates 5642.2 The transition-state theory (TST) 5692.3 The transmission coefficient 5723. Simulating biological electron-transfer reactions 5753.1 Semi-classical surface-hopping and the Marcus equation 5753.2 Treating quantum mechanical nuclear tunneling by the dispersed-polaron/spin-boson method 5803.3 Density-matrix treatments 5833.4 Charge separation in photosynthetic bacterial reaction centers 5844. Light-induced photoisomerizations in rhodopsin and bacteriorhodopsin 5965. Energetics and dynamics of enzyme reactions 6145.1 The empirical-valence-bond treatment and free-energy perturbation methods 6145.2 Activation energies are decreased in enzymes relative to solution, often by electrostatic effects that stabilize the transition state 6205.3 Entropic effects in enzyme catalysis 6275.4 What is meant by dynamical contributions to catalysis? 6345.5 Transmission coefficients are similar for corresponding reactions in enzymes and water 6365.6 Non-equilibrium solvation effects contribute to catalysis mainly through Δg[Dagger], not the transmission coefficient 6415.7 Vibrationally assisted nuclear tunneling in enzyme catalysis 6485.8 Diffusive processes in enzyme reactions and transmembrane channels 6516. Concluding remarks 6587. Acknowledgements 6588. References 658Obtaining a detailed understanding of the dynamics of a biochemical reaction is a formidable challenge. Indeed, it might appear at first sight that reactions in proteins are too complex to analyze microscopically. At room temperature, even a relatively small protein can have as many as 1034 accessible conformational states (Dill, 1985). In many cases, however, we have detailed structural information about the active site of an enzyme, whereas such information is missing for corresponding chemical systems in solution. The atomic coordinates of the chromophore in bacteriorhodopsin, for example, are known to a resolution of 1–2 Å. In addition, experimental studies of biological processes such as photoisomerization and electron transfer have provided a wealth of detailed information that eventually may make some of these processes classical problems in chemical physics as well as biology.

A microscopic basis for the global appearance of energy landscapes.

It is shown that the appearance of a multidimensional potential energy surface, or potential energy landscape, can be related to the form of the interatomic or intermolecular potential. Catastrophe theory enables us to describe how the geometry of the surface changes with parameters in the potential, and provides universal scaling relations that explain, for example, the asymmetric reaction profiles observed for systems bound by long-range forces. The principal result is an unexpected connection between barrier heights, path lengths, and vibrational frequencies, with applications to a wide variety of problems in chemical physics, ranging from Hammond's postulate in organic chemistry, to the relaxation dynamics of complex systems such as glasses and biomolecules.

Inhibition of Chain Reactions By E. T. Denisov and V. V. Azatyan (Institute of Problems of Chemical Physics). Institute of Problems of Chemical Physics University Press and Foundation for International Scientific and Education Cooperation (Realized by Gordon and Breach Publishers): London and Moscow. 2000. xiv + 338 pp. $120.00. ISBN 90-6994-002-7.

Inhibition of Chain Reactions By E. T. Denisov and V. V. Azatyan (Institute of Problems of Chemical Physics). Institute of Problems of Chemical Physics University Press and Foundation for International Scientific and Education Cooperation (Realized by Gordon and Breach Publishers): London and Moscow. 2000. xiv + 338 pp. $120.00. ISBN 90-6994-002-7.

Transient laser frequency modulation spectroscopy.

Explicitly time-dependent implementations of optical frequency modulation spectroscopy have been recently applied to a wide range of problems in chemical physics. We provide a brief description of the methodology, with an emphasis on its intrinsic advantages for interrogating transient species. Several examples highlight the application of the technique to high-resolution absorption spectra of free radicals, rate measurements for gas-phase reactions, and Doppler spectroscopy of the gas-phase products of photoinitiated reactions.

Genesis, selected applications, and future prospects of the mode coupling theory

The decade of 1960–1970 was a very exciting one when the critical phenomena attracted world's best minds. At that time, very little was understood about the mysterious ways in which large-scale critical fluctuations affect both static and dynamic behavior of systems near criticality as were revealed by the wealth of experimental findings accumulated since the end of the last century. The mode coupling theory (MCT) originated in this decade as a promising approach to dynamic critical phenomena. By 1980, however, the mystery of critical phenomena was largely solved thanks to the renormalization group idea among others. Starting the mid-1970s, a new life was imbued to MCT when the theory was successfully applied to liquid dynamics, and then to glass transitions in the 1980s. Further applications are being made to problems in chemical physics like polymer dynamics. These developments are briefly reviewed together with future prospects.

Iterative and direct methods employing distributed approximating functionals for the reconstruction of a potential energy surface from its sampled values

The reconstruction of a function from knowing only its values on a finite set of grid points, that is the construction of an analytical approximation reproducing the function with good accuracy everywhere within the sampled volume, is an important problem in all branches of sciences. One such problem in chemical physics is the determination of an analytical representation of Born–Oppenheimer potential energy surfaces by ab initio calculations which give the value of the potential at a finite set of grid points in configuration space. This article describes the rudiments of iterative and direct methods of potential surface reconstruction. The major new results are the derivation, numerical demonstration, and interpretation of a reconstruction formula. The reconstruction formula derived approximates the unknown function, say V, by linear combination of functions obtained by discretizing the continuous distributed approximating functional (DAF) approximation of V over the grid of sampling. The simplest of contracted and ordinary Hermite-DAFs are shown to be sufficient for reconstruction. The linear combination coefficients can be obtained either iteratively or directly by finding the minimal norm least-squares solution of a linear system of equations. Several numerical examples of reconstructing functions of one and two variables, and very different shape are given. The examples demonstrate the robustness, high accuracy, as well as the caveats of the proposed method. As to the mathematical foundation of the method, it is shown that the reconstruction formula can be interpreted as, and in fact is, frame expansion. By recognizing the relevance of frames in determining analytical approximation to potential energy surfaces, an extremely rich and beautiful toolbox of mathematics has come to our disposal. Thus, the simple reconstruction method derived in this paper can be refined, extended, and improved in numerous ways.

A class of exactly solvable matrix models

Some exactly solvable matrix models are discussed. Possible applications to problems in physical chemistry are pointed out, in particular the Huckel problem, the problem of torsional vibrations of polyatomic molecules, and of vibrations of finite polymer chains.

Intramolecular dynamics due to electron transitions: from photoelectron spectroscopy to Femtochemistry

Abstract Select spectroscopic and chemical physics problems associated with atomic motion triggered by electronic transitions are the topics of this paper. The story starts with the initial stimulation provided by Dick Brundle's photoelectron spectroscopy studies of adsorbed molecules and continues to contemporary examples in photoelectron spectroscopy and Femtochemistry, all of which are theoretically modelled within a unified framework of time-dependent, driven oscillators and decaying states.

Molecular Theory for the Effects of Specific Solute−Solvent Interaction on the Diffusion of a Solute Particle in a Molecular Liquid

An understanding of the effect of specific solute-solvent interactions on the diffusion of a solute probe is a long standing problem of physical chemistry. In this paper a microscopic treatment of this effect is presented. The theory takes into account the modification of the solvent structure around the solute due to this specific interaction between them. It is found that for strong, attractive interaction, there is an enhanced coupling between the solute and the solvent dynamic modes (in particular, the density mode), which leads to a significant increase in the friction on the solute. The diffusion coefficient of the solute is found to depend strongly and nonlinearly on the magnitude of the attractive interaction. An interesting observation is that specific solute-solvent interaction can induce a crossover from a sliplike to a sticklike diffusion. In the limit of strong attractive interaction, we recover a dynamic version of the solvent-berg picture. On the other hand, for repulsive interaction, the diffusion coefficient of the solute increases. These results are in qualitative agreement with recent experimental observations.

Production of Numerical Chemical Problems Using a Spreadsheet

The article describes how a spreadsheet can be used together with a word-processing package (the example being based on Excel 5 and Word 6) to produce individual problems for a class of students. The data for the problems are in the spreadsheet, either input as a data base or generated by the software using its random number function. The example described in detail is the creation of initial rates problems. In addition to the problems, the spreadsheet is able to produce a table of answers. The Mail Merge property of the word-processing package then allows a large number of different problems to be produced - if required with students names and hand-in dates included. The method is ideally suited to numerical problems in physical chemistry but has been extended to nomenclature problems in polymer chemistry and to the preparation of non-identical practical scripts (an example from polymer chemistry being slightly different di-acid, di-ol combinations in a polymerization reaction).

Identifying patterns in multicomponent signals by extended cross correlation

The analysis of current problems in physical chemistry often requires the identification of patterns that encode the composition, structure, and dynamics of a system. Overlapped patterns, unexpected patterns, and patterns whose forms are initially unknown are especially difficult to identify and to extract. We have developed two new techniques for pattern recognition and extraction designed for these situations. These techniques, extended cross correlation (XCC) and extended auto correlation (XAC), identify and extract multiple patterns from experimental data even when the number of derived patterns exceeds the number of experiments. The XCC, which is the focus of this paper, allows the rapid identification and extraction of patterns that are repeated in multiple experimental records. The related XAC technique permits the identification of complex patterns that are parameterized in a multidimensional way, even when the patterns are obscured by the presence of interfering data. The XCC and XAC provide straightforward methods for extracting the features which comprise a pattern, and can be applied in a model-free way. This paper provides a formal description of multidimensional forms of the XCC technique, and illustrates use of the XCC on large data sets with multiple patterns.

Global optimization using ab initio quantum mechanical potentials and simulated annealing of the classical Liouville equation

The routine location of the global minimum energy structures of a molecular system remains a challenging problem in chemical physics. Recently Straub and co-workers [J. Ma et al., J. Chem. Phys. 99, 4024 (1993) and 101, 533 (1994)] have introduced a number of novel dynamic simulated annealing algorithms for global optimization. Instead of using Newton’s equations, they are based on Liouville’s equation and the particles are described with phase space distributions. The methods were shown to have significantly enhanced effectiveness over traditional methods when used to locate the global minima of Lennard-Jones clusters. In this paper the extensions necessary to use these methods with ab initio quantum mechanical potentials are presented and their application is illustrated by the simulated annealing of a small lithium atom cluster.

Matrix spectroscopy: Computation of interior eigenstates of large matrices using layered iteration.

The computation of a small group of interior eigenstates of a large matrix H is an important problem in chemical physics. This general problem is approached in this study through the application of a two-layer iteration scheme. The design of the outer loop is based upon the strategy developed by Ericsson and Ruhe [Math. Comput. 35, 1251 (1980)]. Starting with a variable input energy E, this loop uses the Lanczos algorithm (with no reorthogonalization) to develop a reduced tridiagonal representation of the total Green function G(E). Diagonalization of this small matrix (denoted T) yields, through a simple mapping, excellent approximations to the eigenvalues of H that lie near energy E. The inner iteration loop of the algorithm computes the matrix-vector product G(E)${\mathbf{Q}}_{\mathit{j}}$, where ${\mathbf{Q}}_{\mathit{j}}$ is one of the Lanczos vectors. Both direct and indirect methods may be used for this operation. The direct method uses a perturbative expansion of the Green function, while the indirect method is based upon the iterative solution of a linear algebraic system. The indirect method yields a parametrized polynomial representation of the Green function, with the coefficients chosen variationally. The method is adaptive in the sense that these coefficients change during the course of the Lanczos iteration. Convergence of these iterative methods is improved significantly by developing the Green function in the partial adiabatic representation. Conversion to this representation involves diagonalization of the diagonal block of H involving those states whose zeroth-order energies surround the energy of interest. The two-layer scheme is applied to a model Hamiltonian matrix that has a variable coupling strength within and between a number of dense bands of states. With this scheme it is possible to accurately compute a group of eigenstates near energy E in just a few Lanczos iteration steps (10).

Some current physical chemistry problems in the field of polymer fibres

-- Urgent problems in three fundamental directions of the physical chemistry of polymer fibres have been examined: molecular-weight characteristics, phase equilibria, and fibre structure and morphology. -- The urgency of the following types of studies has been established: interconnection of ultrahigh-molecular weight with fibre properties, character of the effect of the solvent on macromolecule rigidity, complete phase diagrams, criteria for the liquid-crystalline structure, and pore structure and morphology of the shish-kebab type.

Synthesis and uses of ammonia: A unified approach to problem solving in physical chemistry

A collection of 59 physical chemistry problems regarding the synthesis of ammonia are available from the author.

Rapid singular value decomposition for time-domain analysis of magnetic resonance signals by use of the lanczos algorithm

Time-series analysis has become an integral part of signal interpretation in magnetic resonance and other experiments. As an example, linear prediction with singular value decomposition (LPSVD) (I, 2) and the related method, Hankel SVD (HSVD) (3)) have been recently applied to problems in NMR (2)) 2D NMR (4), 2D electron spin-echo spectroscopy (2D ESE) (5,6), Fourier transform ESR correlation spectroscopy ( 7)) time-resolved femtosecond spectroscopy (8)) and nonstationary neurological currents ( 9). The minimal goal of time-series analysis is to separate signal from noise. Spectral transform methods, such as FFT filtering (IO), maximum entropy ( MEM ) ( I I ) , and LPZ ( 12)) replace the original data with a new time series (or its spectrum) that has an enhanced signal-to-noise ratio. In contrast spectral decomposition methods, such as LPSVD or HSVD, which assume a certain functional form for the time series, provide both a recipe for separating signal from noise and a listing of the harmonic components contained in the original data. This harmonic list simplifies spectral analysis and can be used to (1) extend the noise-reduced time series, (2) selectively reconstruct certain regions of the harmonic spectrum, and (3) data-compress the signal. The substantial benefits of spectral decomposition are often offset by the requirements of considerable computational time and memory storage. For a time series of N data points spectral transform techniques usually require computational time of O(N logzN) to O(N’) and storage of O(N) whereas spectral decomposition, such as HSVD, requires computational time of 0( N3) and storage of O(N2). We have investigated a new approach for solving the spectral decomposition problem which is based on the Lanczos algorithm (LA) (13). In the past the LA has provided an effective means for solving slow-motional magnetic resonance spectra ( 14, 15) as well as other complicated problems in chemical physics ( 16, 17). The LA is an extremely fast method for solving large eigenelement problems when either (1)

An automatic grid generation scheme for pseudospectral self-consistent field calculations on polyatomic molecules

In a series of previous papers,'-3 a new algorithm for solution of self-consistent electronic structure equations has been proposed and implemented. The algorithm involves a synthesis of conventional quantum chemical techniques with the pseudospectral meth~d,~ an efficient numerical method originally applied to large-scale hydrodynamic simulations5 and recently employed in various contexts in chemical physics problems.6 The essential feature of the approach is use of both a basis set and a numerical grid representation of the solution, allowing accurate evaluation of derivatives and integrals but also permitting multiplications to be carried out efficiently on the physical space grid. The net results for the Hartree-Fock equations are elimination of twoelectron integrals and an scaling of both integral evaluation and Fock matrix assembly, thus potentially yielding 2-3 orders of magnitude reduction in computation time for large molecules. In ref 3, quantitatively accurate results (as compared to equivalent calculations done via the Roothaan procedure') for the

Erratum: Solution of Kramers–Moyal equations for problems in chemical physics [J. Chem. Phys. 8 1, 1285 (1984)

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