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A theory that describes the non-RRKM (non-Rice-Ramsperger-Kassel-Marcus) effects in the lifetime statistics of activated ozone molecules is derived. The non-RRKM effects are shown to originate due to the diffusive energy exchange between vibrational and rotational degrees of freedom in ozone molecule. The lifetime statistics is found to be intramolecular diffusion controlled at long times. The theoretical results are in good agreement with the direct MD simulations of lifetime statistics. [ABSTRACT FROM AUTHOR]

A classical theory is proposed to describe the non-RRKM effects in activated asymmetric top triatomic molecules observed numerically in classical molecular dynamics simulations of ozone. The Coriolis coupling is shown to result in an effective diffusive energy exchange between the rotational and vibrational degrees of freedom. A stochastic differential equation is obtained for the K-component of the rotational angular momentum that governs the diffusion. [ABSTRACT FROM AUTHOR]

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.

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.

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.

Expressions for reaction rate constants in multidimensional chemical systems are derived by applying semiclassical approximation to the quantum path integrals of the ImF formulation of reaction rate theory. First, the transverse degrees of freedom orthogonal to the reaction coordinate are treated within the steepest descent approximation, after which the semiclassical approximation is applied to the remaining reaction coordinate. Thus derived, the semiclassical expressions account for the multidimensional nature of quantum effects and accurately incorporate nuclear quantum effects such as multidimensional tunneling and zero point energies. The obtained expressions are applicable in the broad temperature range from the deep tunneling to high-temperature regimes. The present paper provides derivation of the semiclassical instanton expressions proposed by Kryvohuz [J. Chem. Phys. 134, 114103 (2011)].

The semiclassical instanton approach to the calculation of reaction rate constants at arbitrary temperatures in multiatomic systems is combined with high-level ab initio calculations of reactive potential energy surface (PES). The number of required ab initio calculations weakly depends on system size and allows on-the-fly evaluations of PES with high accuracy. The approach can be efficiently parallelized and provides a practical way of calculating quantum reaction rate constants with account of nuclear quantum effects such as multidimensional tunneling and zero point energies, which are rigorously incorporated in the theory. An algorithm for the search of instanton trajectories is explained. Application of the approach is illustrated for H + H(2) → H(2) + H and D + D(2) → D(2) + D bimolecular reactions in the wide temperature range with on-the-fly evaluation of PES at the ab initio full configuration interaction (FCI), coupled-cluster single double (CCSD), and single and double excitation configuration interaction (CISD) levels.

A new 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 complimentary information on complex systems is obtained by combining m non linear 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.

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.

The dissipative vibrational dynamics of a symmetric triatomic ABA molecule is extensively studied in a series of three papers. The momentum-dependent rotor model is used to describe the dynamical behavior of an ABA molecule with a single 1:1 nonlinear resonant coupling. Four characteristic modes, including symmetric normal modes, asymmetric normal modes, local modes, and quasi-local modes, are identified at different energy regimes. Under the influence of thermal noise, an ABA molecule switches between the four distinct modes intermittently along its dynamic trajectory, resulting in blinking of vibrational bond energy. The statistics of these dynamic transitions (i.e., "vibrational blinking") is obtained from numerical integration of stochastic equations in this paper and will be analyzed within the theoretical framework of noise-induced symmetry breaking and activated barrier crossing in the next two papers. This study demonstrates the rich dynamic behavior of a highly nonlinear system in a dissipative environment and is instructive for understanding the stability and stochasticity of energy localization in complex systems ranging from polyatomic molecules to nanostructures and micromechanical oscillators.

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.

The paper discusses the effect of quantum chaos on photon-echo signals of two-electronic-state molecular systems. The temporal profile of photon-echo signals is shown to reveal key information about nuclear dynamics on the excited electronic state surface. Specifically, the suppression of echo signals at a particular value of the delay time tau1 between the first and second excitation pulses is demonstrated as a signature of quantum level statistics that corresponds to the classically chaotic nuclear motion in the excited electronic state surface.

The time divergence of classical nonlinear response functions reveals the fundamental difficulty of dynamic perturbation based on classical mechanics. The nature of the divergence is established for systems in regular motions using asymptotic decomposition of Fourier integrals. The asymptotic analysis shows that the divergence cannot be removed by phase-space averaging such as the Boltzmann distribution function. The implications of this study are discussed in the context of the conceptual development of quantum-classical correspondence in dynamic response.

The correspondence principle between the quantum commutator [A, B] and the classical Poisson brackets iota h{A, B} is examined in the context of response theory. The classical response function is obtained as the leading term of the expansion of the phase space representation of the response function in terms of Weyl-Wigner transformations and is shown to increase 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. Resummation of all the higher-order terms establishes the classical-quantum correspondence <--> alpha n e iota n omega t|Jv + nh/2. The time interval of the validity of the simple classical limit [A(t), B(0)] --> iota h{A(t), B(0)} is estimated for quasiperiodic dynamics and is shown to be inversely proportional to anharmonicity.

Time-divergence in linear and nonlinear classical response functions can be removed by taking a phase-space average within the quantized uncertainty volume O(hn) around the microcanonical energy surface. For a quasiperiodic system, the replacement of the microcanonical distribution density in the classical response function with the quantized uniform distribution density results in agreement of quantum and classical expressions through Heisenberg's correspondence principle: each matrix element (u/alpha(t)/v) corresponds to the (u-v)th Fourier component of alpha(t) evaluated along the classical trajectory with mean action (Ju+Jv)/2. Numerical calculations for one- and two-dimensional systems show good agreement between quantum and classical results. The generalization to the case of N degrees of freedom is made. Thus, phase-space averaging within the quantized uncertainty volume provides a useful way to establish the classical-quantum correspondence for the linear and nonlinear response functions of a quasiperiodic system., (2005 American Institute of Physics.)