Free energy, calculated for

Procedures to compute acidities are essentially similar to those for the basicities discussed in the previous section. The acidities in the gas phase and in solution can be calculated as the free energy changes AG and AG" upon proton release of the isolated and solvated molecules, respectively. To discuss the relative strengths of acidity in the gas and aqueous solution phases, we only need the magnitude of —AG and — AG" for haloacetic acids relative to those for acetic acids. Thus the free energy calculations for acetic acid, haloacetic acids, and each conjugate base are carried out in the gas phase and in aqueous solution. 

In the following, we will briefly illustrate the application of nonequilibrium free energy calculations for a simple ID model system. Shown in Fig. 5.1 are the potential energy surfaces... 

In practice it is helpful to know the order of magnitude of the sample size N needed to reach a reasonably accurate free energy. The inaccuracy model described above presents an effective way to relate the sample size N and the finite sampling error through perturbation distribution functions. Alternatively, one can develop a heuristic that does not involve distribution functions and is determined by exploring the common behavior of free energy calculations for different systems [25]. Although only FEP calculations are considered in this section, the analysis extends to NEW calculations. 

Simonson, T., Electrostatic free energy calculations for macromolecules a hybrid molecular dynamics/continuum electrostatics approach, J. Phys. Chem. B 2000, 104, 6509-6513. 

Gouda, H. Kuntz, I.D. Case, D.A. Kollman, P.A., Free energy calculations for theophylline binding to an RNA aptamer Comparison of MM-PBSA and thermodynamic integration methods, Biopolymers 2003, 68,16-34. 

In other words, the relative free energy difference in binding between the two inhibitors is equal to the difference in the free energies calculated for the non-physical mutations. 

M. D. Paulsen and R. L. Omstein, Binding free energy calculations for P450cam-... 

Thymidylate Synthase Free Energy Calculations for Estimating Inhibitor Binding Affinities... 

Dihydrofolate Reductase Free Energy Calculations for the Design of Mechanism-Based Inhibitors... 

The background theory that underlies the FEP method as well as the molecular mechanics force fields that relate molecular structure to energy are reviewed in section one of the book. Section two describes the use of free energy calculations for determining molecular properties of ligands, including solvation, as calculated using both implicit and explicit water... 

Studies using free energy calculations for the design and analysis of potential drug candidates are reviewed in section five. The chapters in this section cover drug discovery programs targeting fructose 1,6-bisphosphatase (diabetes), COX-2 (inflammation), SRC SH2 domain (osteoporosis and cancer), HIV reverse transcriptase (AIDS), HIV-1 protease (AIDS), thymidylate synthase (cancer), dihydrofolate reductase (cancer) and adenosine deaminase (immunosuppression, myocardial ischemia). 

The results of the free energy calculations for electron transfer in bulk water show that the full free energy curves are well approximated by paraboli. The calculations for electron transfer at the solution/metal interface are also, in general, in agreement with the linear response assumption. 

Westacott, R.E., Rodger, P.M., Direct Free Energy Calculations for Gas Hydrates, in Proc. 213th ACS National Meeting, San Francisco, CA, April 13-17, 42(2) 539 (1997). 

This replica-trick method was used in the Refs. [60,61] for the polymer network free energy calculation. For averaging of Z"-value over the ensemble of realizations the probability distribution should be chosen. The authors of Refs. [60,61] have used the condition of the thermodynamical equilibrium for the Gibbs probability distribution corresponding to the conditions of network preparation. To our mind, it is a beautiful idea but it should be considered more deeply because not all the types of networks can be described in such a way - many networks cannot be prepared under any equilibrium conditions. Using some additional tube-like approximations, the authors have obtained rather simple results for network elastic constants and for some other parameters. 

Figure 9. Free energy calculation for a perturbed (mutant) enzyme-catalyzed reaction.

A QUANTUM CHEMICAL APPROACH TO FREE ENERGY CALCULATION FOR CHEMICAL REACTIONS IN CONDENSED SYSTEM COMBINATION OF A QUANTUM CHEMICAL METHOD WITH A THEORY OF STATISTICAL MECHANICS... 

A second aspect of electronic structure issues was the estimation of electron correlation effects. As discussed further within, the 0 K HF reaction free energy calculations for several of the cases examined, when augmented by zero point energy and thermal effects, give reaction free energies of the acid ionization that are small... 

A convention has been adopted to simplify free-energy calculations for biochemical reactions. The standard state is defined as having a pH of 7. Consequently, when H+ is a reactant, its activity has the value 1 (corresponding to a pH of 7) in equations 1 and 4 (below). The activity of water also is taken to be 1 in these equations. The standardfree-energy... 

---