Quantum mechanical rate processes in the condensed phase.
Navrotskaya, Irina
2007
Abstract
In this thesis, we develop and apply computational methods for calculating quantum-mechanical rate constants in condensed phase systems. The work is based on a theoretical framework that puts the rate constants in terms of quantum-mechanical time correlation functions (TCF). We focus on two types of rate constants: (1) Reaction rate constants, which can be affected by tunneling and zero point energy effects. (2) Vibrational energy relaxation (VER), where quantum effects originate from the relatively high frequency of molecular vibrations. A numerically exact evaluation of the relevant quantum TCFs is impossible in many-body anharmonic systems such as liquid solutions because of the exponential scaling of computational effort with the number of degrees of freedom (DOF). This difficulty can be bypassed by employing approximate, yet accurate methods. In the first part of this thesis, we describe the use of the centroid molecular dynamics (CMD) method for calculating reaction rate constants in the case of a unimolecular reaction. Our model consists of a double-well potential along the reaction coordinate coupled to a bath of harmonic modes. The fact that the exact quantum mechanical rate constants can be obtained for this model allows us to estimate the accuracy of CMD for calculating reaction rate constants. Our investigation focuses on the effect on quantum reaction rate constants of the asymmetry of the potential along the reaction coordinate, as well as on different types of system-bath coupling. More specifically, we consider a system-bath coupling which is nonlinear in the reaction coordinate and leads to reaction coordinate-dependent friction. Our findings suggest that the dependence of the quantum reaction rate constant on the system-bath coupling strength is <italic>qualitatively</italic> different from that observed in the classical case and coordinate-independent friction case. More specifically, we found that the quantum-mechanical barrier-crossing rate may <italic>monotonically </italic> increase as a function of the system-bath coupling strength, in cases where the classical barrier-crossing rate goes through a turnover, and that the rate of quantum-mechanical barrier-crossing can be <italic>lower </italic> than that of classical barrier-crossing. We also showed that those purely quantum-mechanical effects are of a thermodynamical, rather than dynamical, nature, and that they originate from the difference in friction between the barrier top and the reactant and product wells. The results obtained via the CMD method were found to be in very good agreement with numerically exact calculations and provide a clear interpretation of the observed trends in the reaction rate dependence on coupling strength. The second part of this thesis is concerned with calculating VER rate constants in liquid solutions. We introduce an alternative to the commonly used weak coupling Landau-Teller (LT) approach, which is based on linear response theory (LRT). We also demonstrate the applicability and accuracy of the new approach in the case of iodine in liquid xenon. Finally, we consider the application of the LSC method to calculating the highly quantum VER rates of molecular hydrogen and deuterium in liquid argon. The results are found to be orders of magnitude more accurate than the corresponding classical predictions, and capture the experimentally observed isotopic effect.Subjects
Condensed Phase Quantum Mechanical Rate Quantum-mechanical Rate Rate Processes Semiclassical
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