Molecular Representation of the Environment

In the molecular representation of the environment, the solvent/protein coordinates are treated explicitly. In this case, the probability flux correlation function is  

The above quantities can be evaluated with molecular dynamics simulations of the full solute-solvent system on the reactant vibronic surface Specifi- 

The rate expression in Eq. (16.31) can be simplified under the following well-defined conditions the coupling between the R coordinate and the solvent coordinates is neglected, the surfaces are approximated to be harmonic along the R coordinate, and the R mode frequency is assumed to be the same for both the reactant and product surfaces. In this case, (SR ) = (SR) = 0 and the energy gap derivative defined in Eq. (16.31) becomes 

We have used this theoretical formulation to analyze the dynamical aspects of model PCET reactions in solution with molecular dynamics simulations [56, 57]. For these model systems, the time dependence of the probability flux correlation function is dominated by the solvent damping term, and only the short-time equilibrium fluctuations of the solvent impact the rate. The proton donor-acceptor motion does not impact the dynamical behavior of the reaction but does influence the magnitude of the rate. 

We have applied this theoretical formulation [26-28] to a series of PCET reactions. The systems were chosen based on the availability of experimental data that had not yet been fully explained. The systems that will be discussed in this section are iron bi-imidazoline complexes, ruthenium polypyridyl complexes, amidinium-car-boxylate interfaces, DNA-acrylamide complexes, tyrosine oxidation, and the enzyme lipoxygenase. In all cases, the solvent was treated as a dielectric continuum [58, 59]. 

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We have used this formulation to derive rate expressions for both a dielectric continuum and a molecular representation of the environment. 

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