Semiclassical instanton approach to calculation of reaction rate constants in multidimensional chemical systems

The semiclassical instanton approximation is revisited in the context of its application to the calculation of chemical reaction rate constants. An analytical expression for the quantum canonical reaction rate constants of multidimensional systems is derived for all temperatures from the deep tunneling to high-temperature regimes. The connection of the derived semiclassical instanton theory with several previously developed reaction rate theories is shown and the numerical procedure for the search of instanton trajectories is provided. The theory is tested on seven different collinear symmetric and asymmetric atom transfer reactions including heavy-light-heavy, light-heavy-light and light-light-heavy systems. The obtained thermal rate constants agree within a factor of 1.5–2 with the exact quantum results in the wide range of temperatures from 200 to 1500 K

Quantum-classical correspondence in response theory

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2008.Includes bibliographical references (p. 113-118).In this thesis, theoretical analysis of correspondence between classical and quantum dynamics is studied in the context of response theory. Thesis discusses the mathematical origin of time-divergence of classical response functions and explains the failure of classical dynamic perturbation theory. The method of phase space quantization and the method of semiclassical corrections are introduced to converge semiclassical expansion of quantum response function. The analysis of classical limit of quantum response functions in the Weyl-Wigner representation reveals the source of time-divergence of classical response functions and shows the non-commutativity of the limits of long time and small Planck constant. The classical response function is obtained as the leading term of the h-expansion of the Weyl-Wigner phase space representation and increases without bound at long times as a result of ignoring divergent higher order contributions. Systematical inclusion of higher order contributions improves the accuracy of the h expansion at finite times. The time interval for the quantum-classical correspondence is estimated for quasiperiodic dynamics and is shown to be inversely proportional to anharmonicity. The effects of dissipation on the correspondence between classical and quantum response functions are studied. The quantum-classical correspondence is shown to improve if coupling to the environment is introduced. In the last part of thesis the effect of quantum chaos on photon echo-signal of two-electronic state molecular systems is studied. The temporal photon echo signal is shown to reveal key information about the nuclear dynamics in the excited electronic state surface.(cont.) The suppression of echo signals is demonstrated as a signature of level statistics that corresponds to the classically chaotic nuclear motion in the excited electronic state.by Maksym Kryvohuz.Ph.D

Multidimensional characterization of stochastic dynamical systems based on multiple perturbations and measurements

Generalized nonlinear response theory is presented for stochastic dynamical systems. Experiments in which multiple measurements of dynamical quantities are used along with multiple perturbations of parameters of dynamical systems are described by generalized response functions (GRFs). These constitute a new type of multidimensional measures of stochastic dynamics either in the time or the frequency domains. Closed expressions for GRFs in stochastic dynamical systems are derived and compared with numerical non-equilibrium simulations. Several types of perturbations are considered: impulsive and periodic perturbations of temperature and impulsive perturbations of coordinates. The present approach can be used to study various types of stochastic processes ranging from single-molecule conformational dynamics to chemical kinetics of finite-size reactors such as biocells

Multidimensional measures of response and fluctuations in stochastic dynamical systems

A class of experiments is proposed which involve multiple measurements combined with multiple perturbations of a nonlinear classical complex system. A family of multipoint n + m − 1 dimensional measures R^((n,m)) that provide complementary information on complex systems is obtained by combining m nonlinear stimuli and n measurements. They represent the combined effect of causal response and noncausal spontaneous fluctuations. The proposed signals can be measured either in the frequency domain or in the time domain. Generalized fluctuation-dissipation relations which hold in the nonlinear regime restrict the number of independent techniques. Two-dimensional correlation plots derived from such measurements can reveal various types of couplings among collective modes

Calculation of Kinetic Isotope Effects for Intramolecular Hydrogen Shift Reactions Using Semiclassical Instanton Approach

Primary H/D kinetic isotope effects for the [1,5] hydrogen shift reaction in 13-atomic 1,3-pentadiene and [1,7] hydrogen shift reaction in 23-atomic 7-methylocta-1,3,5-triene are calculated using the semiclassical instanton approach. All 33 and 63 internal degrees of freedom, respectively, are treated quantum mechanically with multidimensional tunneling automatically accounted for by the instanton approach. Reactive potential energy surfaces are calculated on-the-fly using mPW1K/6-31+G­(d,p) and mPWB1K/6-31+G­(d,p) electronic structure methods. The calculated kinetic isotope effects agree well with the previously reported experimental measurements. The analytical expressions of the semiclassical instanton approach allow one to determine quantitative contributions of various physical mechanisms to the calculated kinetic isotope effects. Multidimensional tunneling is found to play important role in both studied hydrogen shift reactions

Nonlinear response theory in chemical kinetics.

A theory of nonlinear response of chemical kinetics, in which multiple perturbations are used to probe the time evolution of nonlinear chemical systems, is developed. Expressions for nonlinear chemical response functions and susceptibilities, which can serve as multidimensional measures of the kinetic pathways and rates, are derived. A new class of multidimensional measures that combine multiple perturbations and measurements is also introduced. Nonlinear fluctuation-dissipation relations for steady-state chemical systems, which replace operations of concentration measurement and perturbations, are proposed. Several applications to the analysis of complex reaction mechanisms are provided

The influence of dissipation on the quantum-classical correspondence: Stability of stochastic trajectories

The quantum-classical correspondence in the presence of dissipation is studied. The semiclassical expression for the linear response function of an anharmonic system is expressed in a series containing classical stability matrix elements, which can diverge due to the chaotic behavior of stochastic trajectories. The presence of dissipation in most cases removes the divergence of higher-order correction terms, thus suppressing quantum effects and making the system more classical. The regime of system-bath coupling, which makes quantum dynamics completely classical, is obtained in terms of friction, temperature, and anharmonicity. Special cases when bath coupling may lead to enhancement of quantum effects are discussed.National Science Foundation (U.S.) (Grant no. 0806266