Conceptual Framework Energy Surfaces

Strictly speaking, each molecule is characterized by a specific energy surface, different from those of other molecules. It can be expected, however, that energy surfaces of similar molecules are themselves similar, at least as far as their low-energy regions are concerned. We shall describe two approaches to the structure-energy problem  

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The paradigm of free energy surfaces provides a very convenient and productive conceptual framework to analyze the thermodynamics and dynamics of electronic transitions in condensed phases. It, in fact, replaces the complex dynamics of a quantum subsystem interacting with a many-body... 

In the framework of the assiamptions discussed in the previous section equation (51.Ill) is an accurate collision theory expression for the rate constant which is valid, in principle, for any potential energy surface. It represents a very useful formulation from both conceptual and practical point of view /20/. 

The formalism for the quasiseparation of nuclear coordinates from electronic coordinates was introduced by Born and Oppenheimer in 1927 [12]. However, it was the 1929 paper by London [13] and the 1931 paper by Eyring and Polanyi [14] that introduced the potential-energy surface (PES) for a chemical reaction and thus created the conceptual framework for modern kinetic theory. The following year Pelzer and Wigner [15] identified the saddle point on the PES as the TS. The stage had been set. 

For a reaction with a defined transition state and without recrossing, reaction rate can be well approximated by many methods. For such reaction, we can assume that there is a dynamics bottleneck located at the transition state (conventional transition state theory, TST) or at a generalized transition state obtained by a canonical (CTV) or microcanonical (/zVT) criterion. In the later cases, the dividing surface is optimized variationally to minimize the recrossing. Evans first proposed to place the transition state at the location that maximizes the free energy of activation which provides a key conceptual framework for modern variational transition state theory [33]. However, recrossing always possibly exists and only a full-dimensional reactive scattering dynamics calculations are able to provide us the exact rate constant on a defined PES. Eor a detailed discussion, one may refer to the reviews by Truhlar et al. [38,136]. 

Potential energy surfaces, which were presented in Chapter 6, form the conceptual framework for thinking about and analyzing many problems in chemistry. The surface, of course, is the effective potential for vibrations of the molecule. But continued to large atom-atom separations, the surface encodes the energetic information about reactions and bond breaking. It also provides a picture of the pathways for reactions. 

The most lucid way of conceptually and quantitatively understanding the rich structural variation and structural transitions of microemulsions is to use the framework of the flexible surface model (35). The basic assumption in this model is to describe a surfactant monolayer or bilayer as a mathematical surface dividing space into two or more separate regions. With each configuration of the surface one associates a curvature (free) energy G. obtained as a surface integration of a local curvature free-energy density... 

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