To microscopically model a reaction in solution, one needs to include a very large number of solvent molecules in the system to represent the bulk. The problem stems from the fact that it is computationally impossible with our current capabilities to locate the transition-state structure of the reaction on the complete quantum-mechanical potential energy hypersurface, if all the degrees of freedom are explicitly included. Moreover, the effect of thermal statistical averaging should be incorporated. Then, classical mechanical computer simulation techniques appear to be the most suitable procedures to attack the above problems. [Pg.286]

Whereas the quantum-mechanical molecular Hamiltonian is indeed spherically symmetrical, a simplified virial theorem should apply at the molecular level. However, when applied under the Born-Oppenheimer approximation, which assumes a rigid non-spherical nuclear framework, the virial theorem has no validity at all. No amount of correction factors can overcome this problem. All efforts to analyze the stability of classically structured molecules in terms of cleverly modified virial schemes are a waste of time. This stipulation embraces the bulk of modern bonding theories. [Pg.117]

In the previous chapters, you have learned how to use DFT calculations to optimize the structures of molecules, bulk solids, and surfaces. In many ways these calculations are very satisfying since they can predict the properties of a wide variety of interesting materials. But everything you have seen so far also substantiates a common criticism that is directed toward DFT calculations namely that it is a zero temperature approach. What is meant by this is that the calculations tell us about the properties of a material in which the atoms are localized at equilibrium or minimum energy positions. In classical mechanics, this corresponds to a description of a material at 0 K. The implication of this criticism is that it may be interesting to know about how materials would appear at 0 K, but real life happens at finite temperatures. [Pg.113]

This is of relevance to the mechanism of carbonic anhydrase. This enzyme, which catalyzes the hydration of C02, has at its active site a Zn2+ ion ligated to the imidazole rings of three of its histidines. The classic mechanism for the reaction is that the fourth ligand is a water molecule which ionizes with a pKa of 7.37 The reactive species is considered to be the zinc-bound hydroxyl. Chemical studies show that zinc-bound hydroxyls are no exception to the rule of high reactivity. The H20 in structure 2.31 ionizes with a pKa of 8.7 and catalyzes the hydration of carbon dioxide and acetaldehyde.38 [Pg.49]

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