Model Based on Classical Mechanics

Molecular Symmetry David J. Willock 2009 John Wiley Sons, Ltd. ISBN 978-0-470-85347  

The factor of one-half arises from the usual choice of k based on Hooke s law the restoring force due to the extension of a spring is directly proportional to that extension. So, following classical mechanics  

At any nonzero temperature the classical atoms of the molecule will also be moving if the H atom has a velocity v with respect to the F atom, then the kinetic energy T to do with the bond distortion is 

At all times the total energy (sum of potential and kinetic) E will have a constant value, and so we can use the conservation of energy to write 

This is a differential equation for the bond extension jc as a function of time. It teUs us that the squares of the first derivative and the extension itself are linked. For this classical model of masses and a spring we should expect an oscillating solution, and so a good starting guess for the solution is 

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The conceptual simplicity is both the beauty and the strength in the MD simulation methods, but its limitations become obvious as soon as we are dealing with any kind of chemical processes. Since electrons are involved in Chemistry, even the simplest chemical reaction is beyond the simulation models, based on Classical Mechanics. 

The first of the theoretical chapters (Chapter 9) treats approaches to the calculation of thermal rate constants. The material is familiar—activated complex theory, RRKM theory of unimolecular reaction, Debye theory of diffusion-limited reaction—and emphasizes how much information can be correlated on the basis of quite limited models. In the final chapt, the dynamics of single-collision chemistry is analyzed within a highly simplified framework the model, based on classical mechanics, collinear collision geometries, and naive potential-energy surfaces, illuminates many of the features that account for chemical reactivity. 

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