Chapter 4

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Notes of Applied Chemical Kinetics course Carlo Cavallotti Chapter 1. Introductory aspects and classification of chemical reactions Chapter 2. Kinetic schemes and reaction mechanisms Chapter 3. Kinetic theory of Gases Chapter 4. Fundamentals of Statistical Thermodynamics and Molecular Quantum Mechanics Chapter 5. Transition State Theory and further developments Chapter 4. Fundamentals of Statistical Thermodynamics and Molecular Quantum Mechanics 4.1 Introduction and molecular kinematics Although kinetic theory of gases allows understanding many fundamental aspects of the gas phase reactivity, the attempt to apply it systematically to estimate the kinetic constant of complex reactions pointed out its fundamental limitations. In particular it has been demonstrated that, to describe adequately a chemical reaction characterized by a significant rearrangement of the molecular structure of reactants in the transition to the configuration of the reaction products, it is necessary to describe explicitly the internal motion of the atoms. Such aspect is not considered in the kinetic theory of gases, which considers molecules as spheres. The explicit treatment of internal molecular motions is a complex problem, as it requires describing the evolution in time of the spatial configuration of each atom involved in the reactive process. Defining N the total number of atoms involved in the reaction, the total number of coordinates of which we have to describe the evolution in time is 3N, i.e. three coordinates (xi, yi, zi) for each atom. From this point of view, the kinetics of a molecular system can be equated to that of an integral system made by N spheres of mass mi. The study of the kinematics of such systems is a problem that is well known in analytical mechanics, and it is…