Free energy derivatives

The free energy derivatives are also related to the coefficients in a Taylor expansion of the free energy with respect to X. In the case of linear coupling, we let Eba = XdJ-a — Up,)lkT in Eq. (9) we obtain... 

The free energy difference between two stable conformations can be obtained by a thermodynamic integration approach [38,39]. Let q and represent the centers of the two corresponding energy wells. The free energy derivative is seen to be... 

This would of course have drastic consequences as far as the validity of interfacial free energies derived from LH analysis of growth rate data is concerned. 

ATP acts as the energy currency of the cell, transferring free energy derived from substances of higher energy potential to those of lower energy potential. 

C14-0026. Nitrogen-fixing bacteria react N2 with H2 O to produce NH3 and O2 using ATP as their energy source. About 24 molecules of ATP are consumed per molecule of N2 fixed. What percentage of the free energy derived from ATP is stored in NH3 ... 

His residues at configurations sampled using the popular link-host-atom exclusion scheme changes the free energy derivatives by 8-9 kcal/mol despite that the QM/MM frontiers are far from the zinc-bound water. With this effect taken into account, the calculated pKa value for the zinc-bound water in the WT CAII is in encouraging agreement with experiment the value is 7.1 (5.4) for the 20 (25) A-inner-region simulations, as compared to the experimental value of around 7 [86],... 

When biasing the system, an external force AV is applied to improve the sampling along . Since this force is added, the calculation of the derivative of — to must be modified. Consider (4.35). The first term does not require any correction since x and x are sampled according to the correct distribution. However x includes the ABF force whose contribution needs to be removed to compute the free energy derivative. The correction is equal to... 

Without explicit analytical expressions for the free energy derivative (as could be obtained for the case of a Bom ion in a dielectric medium), the integral has to be evaluated numerically by simulation. 

Fig. 12.2. Free energy data for electron transfer between the protein cytochrome c and the small acceptor microperoxidase-8 (MP8), from recent simulations [47]. Top Gibbs free energy derivative versus the coupling parameter A. The data correspond to solvated cytochrome c the MP8 contribution is not shown (adapted from [47]) Bottom the Marcus diabatic free energy curves. The simulation data correspond to cyt c and MP8, infinitely separated in aqueous solution. The curves intersect at 77 = 0, as they should. The reaction free energy is decomposed into a static and relaxation component, using the two steps shown by arrows a static, vertical step, then relaxation into the product state. All free energies in kcalmol-1. Adapted with permission from reference [88]...

D. A. Pearlman, A. free energy derivatives A new method for probing the convergence... 

In analytic work it is more convenient to use a model which takes on continuum values of the variable hj. Moreover, it can be shown that for an isolated step, the free energy derived from the energy (1) is often well approximated(at small slopes) by. 

The first term in Eq. 19.5 consists of the free energies to form the clusters (where the free energy to form a particle is given by Eq. 19.1), and the second term is the free energy derived from the entropy of mixing of the (N — a atoms... 

The coexistence of four phases in a one-component system has never been observed and is ruled out by a famous result from thermodynamics. The same Gibbs who introduced the concept of free energy derived this result by considering a system consisting of c components (individual... 

Also, because such derivatives are to be evaluated at the equilibrium geometry, a key point is the determination of that geometry on the solvated PES, which leads to the so-called indirect solvent effects , which still requires a viable method to calculate free energy gradients (and possibly hessians). The problem of the formulation of free energy derivatives within continuum solvation models is treated elsewhere in this book and for this reason it will not considered here. Instead, it is worth remarking in this context another implication of such a formulation, i.e. that a choice between a complete equilibrium scheme or the account for vibrational and/or electronic nonequilibrium solvent effects [42, 43] should be done (see below). 

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