Semiclassical and Quantum Instanton approximations for thermal rate constants of chemical reactions

The calculation of thermal rate constants k ( T) for chemical reactions has been an important challenge for generations of theoretical chemists and it represents a fundamental issue for the entire chemistry community. In this thesis, several theoretical methods have been reported as a result of the efforts to discover an approximation of the "exact & direct" flux correlation functions for the rate constant. The main goal was to develop methods which can include quantum effects and are amenable to practical implementation for complex systems at the same time. Two main avenues have been pursued in this sense: one by using classical trajectories in the Semiclassical Initial Value Representation formalism, the other by looking for a quantum analog of Transition State Theory in the context of Instanton approximations.;Several variants of the above mentioned methods have been proposed and tested on gas phase kinetic reactions (mainly barrier transmission problems and collinear reactions) ranging from high to low temperatures in deep tunneling regime and trade-off between advantages and disadvantages, that each theory necessarily embodies, has been constantly taken into account during the writing of this thesis.;The state-of-the-art of semiclassical theories is presented and it is shown how a Path Integral expression for the flux operator can be incorporated into semiclassical Monte Carlo integrations. Then tunneling from asymptotic conditions, i.e. by placing the flux operator away from the interactive scattering region, is calculated and it is discussed in which sense we can consider these conditions asymptotic. To complete the semiclassical part of the thesis, a recently developed time averaging formulation of the flux autocorrelation function and its tests on barrier transmission problems are reported.;By choosing a different approach to the calculation of rate constants, mainly inspired by the imaginary time dynamics that in classical mechanics is the equivalent of tunnelling, we have studied the theory of semiclassical instanton dynamics and thanks to the physical picture that this approximation offers, we have developed and tested a novel method which goes under the name of Quantum Instanton approximation. This latest theory has been proven to be precise within 2--5% percent in its most recent version and to be a practical tool for the calculation of thermal rate constants in complex systems. Its accuracy is intact in the lowest temperatures and in the free particle regime as well, except for situations where dynamical corrections to transition state theory (i.e. re-crossing dynamics) are evident. Since re-crossing effects are substantially reduced in higher dimensionality, this is not a cause for serious concern. Besides; the method is formulated in terms of quantities that are amenable to be evaluated using the METROPOLIS algorithm in the Monte Carlo path integral implementation. It is this last property that make the Quantum Instanton approximation suitable for calculations of thermal rate constants in complex systems.