Activation free energy quantum mechanical solution

A new, more general, way to combine ab initio quantum mechanical calculations with classical mechanical free-energy perturbation approach (QM/FE approach) to calculate the energetics of enzyme-catalysed reactions and the same reaction in solution has been reported." The calculated free energies were in fairly good agreement with the experimental data for the activation energies of the first test case, amide hydrolysis in trypsin and in aqueous solution. 

Classical density functional theory (DFT) [18,19] treats the cluster formation free energy as a functional of the average density distributions of atoms or molecules. The required input information is an intermolecular potential describing the substances at hand. The boundary between the cluster and the surrounding vapor is not anymore considered sharp, and surface active systems can be studied adequately. DFT discussed here is not to be confused with the quantum mechanical density functional theory (discussed below), where the equivalent of the Schrodinger equation is expressed in terms of the electron density. Classical DFT has been used successfully to uncover why and how CNT fails for surface active systems using simple model molecules [20], but it is not practically applicable to real atmospheric clusters if the molecules are not chain-like, the numerical solution of the problem gets too burdensome, unless the whole molecule is treated in terms of an effective potential. 

A theoretical study based on MP2/6-31+G(d,p) and HF/6-31G(d) ab initio quantum mechanical calculations coupled with Langevin dipoles (LD) and polarised continuum (PCM) solvation models have been carried out by Florian and Warshel [387] to achieve a first systematic study of the free energy surfaces for the hydrolysis of methylphosphate in aqueous solution. The important biological implication of this work is the fact that since the energetics of both the associative and the dissociative mechanics are not too different, the active sites of enzymes can select either mechanism depending on the particular electrostatic environment. This conclusion basically means that both mechanisms should be considered, and this fact seems to contradict some previous studies which have focused on phosphoryl transfer reactions. 

A very convincing support for the existence of solvent controlled proton dissociation reactions in aqueous solutions has risen from the theoretical studies of Ando and Hynes [105-108] who have studied the proton dissociation of simple mineral acids HCl and HF in aqueous solutions. The two acids seem to follow a solvent-controlled proton transfer mechanism with a Marcus-like dependence of the activation energy on the acid strength. Recently, a free energy relationship for proton transfer reactions in a polar environment in which the proton is treated quantum mechanically was found by Kiefer and Hynes [109, 110]. Despite the quite different conceptual basis of the treatment the findings bear similarity to those resulting from the Marcus equation Eq. (12.19) which has been used to correlate the proton transfer rates of photoacids with their piG [ 101,102 ]... 

No Barrier Theory (NBT) [1,2] is a new approach to calculating rate constants in solution that uses an experimental equilibrium constant and an assumed mechanism as the only empirical information needed in order to calculate a rate constant. What is directly calculated is the free energy of activation but conversion of this to a rate constant is trivial. The saving thing about these calculations is that relatively low-level quantum chemistry computational methods suffice in many cases semiempirical methods are sufficient. NBT also provides a way to think qualitatively about whether a reaction is likely to be slow or fast thus, it can be used both qualitatively to think about mechanisms and quantitatively to predict rates. 

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