Robert Q. Topper

Cylindrical manifolds in phase space as mediators of chemical reaction dynamics and kinetics. I. Theory

A microcanonical kinetic theory of reactions based upon the structure within phase space is developed. It is shown that the dynamics of reaction across an energetic barrier is mediated by invariant manifolds embedded in phase space that have the geometry of simple cylinders. The ideas are developed by considering molecular systems modeled by two vibrational degrees of freedom, a reaction coordinate and a ‘‘bath’’ coordinate. The kinetic theory is constructed by focusing on the dynamics between n mapping planes (‘‘n‐map’’) and the ‘‘reactive island’’ (RI) structure within them. We discuss how the structure of the conformer population decay in isomerization reactions can be obtained from the RI kinetic model. Formal solutions of the kinetic equations are discussed with specific attention given towards the calculation of the isomerization reaction rate. The formal theory is developed in Paper I of this series. Numerical considerations and applications to the reaction dynamics of model molecular systems with ...

COMPUTATIONAL STUDY OF THE STRUCTURES AND THERMODYNAMIC PROPERTIES OF AMMONIUM CHLORIDE CLUSTERS USING A PARALLEL JUMP-WALKING APPROACH

The thermodynamic and structural properties of (NH4Cl)n clusters, n=3–10 are studied. Using the method of simulated annealing, the geometries of several isomers for each cluster size are examined. Jump‐walking Monte Carlo simulations are then used to compute the constant‐volume heat capacity for each cluster size over a wide temperature range. To carry out these simulations a new parallel algorithm is developed using the parallel virtual machine (PVM) software package. Features of the cluster potential energy surfaces, such as energy differences among isomers and rotational barriers of the ammonium ions, are found to play important roles in determining the shape of the heat capacity curves.

Quantum free-energy calculations : optimized Fourier path-integral Monte Carlo computation of coupled vibrational partition functions

The Fourier coefficient path‐integral representation of the quantum density matrix is used to carry out direct, accurate calculations of coupled vibrational partition functions. The present implementation of the Fourier path‐integral method incorporates two noteworthy features. First, we use a Gaussian in Fourier space as a probability density function, which is sampled using the Box–Muller algorithm. Second, we introduce an adaptively optimized stratified sampling scheme in Cartesian coordinates to sample the nuclear configurations. We illustrate these strategies by applying them to a coupled stretch–bend model which resembles two of the vibrational modes of H2O. We also apply a simple, yet accurate method for estimating the statistical error of a Metropolis integration, and we compare the Box–Muller and Metropolis sampling algorithms in detail. The numerical tests of the new method are very encouraging, and the approach is promising for accurate calculations of quantum free energies for polyatomic molecules.

Cylindrical manifolds in phase space as mediators of chemical reaction dynamics and kinetics. II. Numerical considerations and applications to models with two degrees of freedom

In Paper I we discussed the existence of cylindrical manifolds embedded in phase space which mediate the dynamics of chemical reactions. A kinetic theory of population decays and decay rate constants was developed which we called ‘‘reactive island’’ (RI) theory. In this paper we discuss the details of the numerical implementation of the theory and then apply it to several molecular models (with two coupled degrees of freedom) representing isomerization between two and three states. Numerical simulations of population decays and asymptotic decay rate constants are compared to the RI theoretical predictions as well as the predictions from the Purely Random Theory (PRT) and Transition State Theory (TST) of reactions. Of the ten systems studied we find that RI theory is generally in good to excellent agreement with the numerical simulations. Only one system exhibits significant deviation between the RI and numerical results. This deviation is seen to be a result of a strong intraconformer dynamical bottleneck...

Quantum steam tables. Free energy calculations for H2O, D2O, H2S, and H2Se by adaptively optimized Monte Carlo Fourier path integrals

Converged quantum mechanical vibrational–rotational partition functions and free energies are calculated using realistic potential energy surfaces for several chalcogen dihydrides (H2O, D2O, H2S, H2Se) over a wide range of temperatures (600–4000 K). We employ an adaptively optimized Monte Carlo integration scheme for computing vibrational–rotational partition functions by the Fourier path‐integral method. The partition functions and free energies calculated in this way are compared to approximate calculations that assume the separation of vibrational motions from rotational motions. In the approximate calculations, rotations are treated as those of a classical rigid rotator, and vibrations are treated by perturbation theory methods or by the harmonic oscillator model. We find that the perturbation theory treatments yield molecular partition functions which agree closely overall (within ∼7%) with the fully coupled accurate calculations, and these treatments reduce the errors by about a factor of 2 compared...

Quantum free‐energy calculations: A three‐dimensional test case

An optimized integration scheme for calculating vibrational–rotational partition functions by the Fourier path‐integral method, as presented in the previous paper [R. Q. Topper and D. G. Truhlar, J. Chem. Phys. XX, ▪▪▪▪ (19▪▪)] is applied to a three‐dimensional test case involving the coupled vibrational and rotational motions of a diatomic HCl molecule in Cartesian coordinates. Converged partition functions are calculated by the new Fourier path‐integral Monte Carlo scheme and by standard variational methods, and the two sets of results are compared. We obtain good agreement (∼2%) between the two methods over a range of a factor of 20 in temperature.

A note on the application of the “Boltzmann simplex”-simulated annealing algorithm to global optimizations of argon and water clusters

Abstract We report our application of a recently published simulated annealing algorithm which we call “Boltzmann simplex”-simulated annealing (BSSA) to global optimizations of argon and water clusters. The Lennard–Jones model of argon clusters serves as a challenging benchmark for global optimization methods, and we use it as a test case. We find that the BSSA method is most useful when followed by a local optimization via the Powell method. This is because the Powell method quenches to the equilibrium geometry more effectively than a downhill simplex, which is the zero-temperature limit of the BSSA algorithm. We also find that very slow annealing rates are required to achieve acceptable results. A study of small water clusters [(H 2 O) m , m =2–6] using a recently published flexible-monomer interaction potential yields ring-like structures which are in good agreement with other theoretical and experimental studies for m =3–5. A highly puckered ring structure is obtained for m =6.

Stochastic Neural Network Approach for Learning High-Dimensional Free Energy Surfaces

The generation of free energy landscapes corresponding to conformational equilibria in complex molecular systems remains a significant computational challenge. Adding to this challenge is the need to represent, store, and manipulate the often high-dimensional surfaces that result from rare-event sampling approaches employed to compute them. In this Letter, we propose the use of artificial neural networks as a solution to these issues. Using specific examples, we discuss network training using enhanced-sampling methods and the use of the networks in the calculation of ensemble averages.

Erratum: “Quantum free-energy calculations: A three-dimensional test case” [J. Chem. Phys. 97, 3668 (1992)]

iniEquation~6! for the Dunham coefficient A0 should read A05ve /4Be . In Table I, the following changes are to be made: Va of D0 in atomic units is 1.629 3169 310 ; value of Be in atomic units is 4.826 752 286 310; value of ae is 0.307 181; and value of r e in atomic units is 2.408 555. Foot note b has an error: 1 cm 54.556 37310 hartree. Line 5 in column 1 on page 3673 should read ‘‘dime sional triatomic. ’’