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-lightheavy 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.

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. 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.

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.

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.

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.