Energy Surfaces and Related Concepts

An analysis of kinetics can arguably be considered the most informative study we can perform to delineate a reaction mechanism. However, the data obtained cannot give a complete picture of a mechanism, because the data do not give us information about which bonds are broken or formed. The greatest value of a kinetic analysis is that it often provides a framework for designing experiments to test a proposed mechanism. 

The study of kinetics is concerned with the details of how one molecule is transformed into another and the time scale for this transformation. This is in stark contrast to thermodynamics. In our analysis of thermodynamics (Chapters 2-5), we were solely concerned with the initial and final states of a system for chemical reactions, this means the reactant and product (often an intermediate), respectively. The mechanism involved in the transformation is not considered in thermodynamics, and therefore, time is not a factor. Yet, the two disciplines, kinetics and thermodynamics, are highly interrelated. In Section 7.1.3, for example, the most widely accepted theory for understanding rate constants (transition state theory) is based upon a thermodynamic analysis. Moreover, at equilibrium, the rate of the overall forward transformation equals the rate of the overall reverse transformation. 

---

The concepts of energy surfaces for molecular motion, equilibrium geometries, transition structures and reaction paths depend on the Bora-Oppenheimer approximation to treat the motion of the nuclei separately from the motion of the electrons. Minima on the potential energy surface for the nuclei can then be identified with the classical picture of equilibrium structures of molecules saddle points can be related to transition states and reaction rates. If the Born-Oppenheimer approximation is not valid, for example in the vicinity of surface crossings, non-adiabatic effects are important and the meaning of classical chemical structures becomes less clear. Non-adiabatic effects are beyond the scope of this chapter and the discussion of energy surfaces and optimization will be restricted to situations where the Bom-Oppenheimer approximation is valid. 

The low-temperature chemistry evolved from the macroscopic description of a variety of chemical conversions in the condensed phase to microscopic models, merging with the general trend of present-day rate theory to include quantum effects and to work out a consistent quantal description of chemical reactions. Even though for unbound reactant and product states, i.e., for a gas-phase situation, the use of scattering theory allows one to introduce a formally exact concept of the rate constant as expressed via the flux-flux or related correlation functions, the applicability of this formulation to bound potential energy surfaces still remains an open question. 

One of the most obvious properties of a disperse system is the vast interfacial area that exists between the dispersed phase and the dispersion medium [48-50]. When considering the surface and interfacial properties of the dispersed particles, two factors must be taken into account the first relates to an increase in the surface free energy as the particle size is reduced and the specific surface increased the second deals with the presence of an electrical charge on the particle surface. This section covers the basic theoretical concepts related to interfacial phenomena and the characteristics of colloids that are fundamental to an understanding of the behavior of any disperse systems having larger dispersed phases. 

The field of chemical kinetics is far reaching and well developed. If the full energy surface for the atoms participating in a chemical reaction is known (or can be calculated), sophisticated rate theories are available to provide accurate rate information in regimes where simple transition state theory is not accurate. A classic text for this field is K. J. Laidler, Chemical Kinetics, 3rd ed., Prentice Hall, New York, 1987. A more recent book related to this topic is I. Chorkendorff and J. W. Niemantsverdriet, Concepts of Modern Catalysis and Kinetics, 2nd ed., Wiley-VCH, Weinheim, 2007. Many other books in this area are also available. 

Ethylene electronic isomerism is introduced as a new concept and examined from the perspective of the generalized electronic diabatic (GED) scheme. In chemistry isomerism is related to distributions in space of atomic nucleus in one and the same adiabatic potential energy surface. Therefore, in this case cis and trans isomers would be indistinguishable when the four hydrogen atoms are identical. Nevertheless, in this paper we show that isomerism is an electronic... 

The concept of potential-energy surface (or just potentials) is of major importance in spectroscopy and the theoretical study of molecular collisions. It is also essential for the understanding of the macroscopic properties of matter (e.g., thermophysical properties and kinetic rate constants) in terms of structural and dynamical parameters (e.g., molecular geometries and collision cross sections). Its role in the interpretation of recent work in plasmas, lasers, and air pollution, directly or otherwise related to the energy crisis, makes it of even greater value. 

Force Fields. The basic assumption underlying molecular mechanics is that classical physical concepts can be used to represent the forces between atoms. In other words, one can approximate the potential energy surface by the summation of a set of equations representing pairwise and multibody interactions. These equations represent forces between atoms related to bonded and nonbonded interactions. Pairwise interactions are often represented by a harmonic potential - 6q) ]... 

---