Free energy calculations background

The book consists of 14 chapters, in which we attempt to summarize the current state of the art in the field. We also offer a look into the future by including descriptions of several methods that hold great promise, but are not yet widely employed. The first six chapters form the core of the book. In Chap. 1, we define the context of the book by recounting briefly the history of free energy calculations and presenting the necessary statistical mechanics background material utilized in the subsequent chapters. 

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... 

In this chapter, we focus on the method of constraints and on ABF. Generalized coordinates are first described and some background material is provided to introduce the different free energy techniques properly. The central formula for practical calculations of the derivative of the free energy is given. Then the method of constraints and ABF are presented. A newly derived formula, which is simpler to implement in a molecular dynamics code, is given. A discussion of some alternative approaches (steered force molecular dynamics [35-37] and metadynamics [30-34]) is provided. Numerical examples illustrate some of the applications of these techniques. We finish with a discussion of parameterized Hamiltonian functions in the context of alchemical transformations. 

With the above background, we start the discussion of the evaluation of AG, which in fact is the most important step. We would also like to emphasize that the ability to calculate AG (and the corresponding free energy profiles) for enzyme reactions and the corresponding reference solution reaction is crucial for any attempt to obtain a quantitative understanding of enzyme reactions. 

A number of reports have described theoretical calculations for superhydrophobic surfaces. Marmur [10] and Quere and co-workers [11,12] show the theoretical background for surface roughness. There are also many reports regarding creation of superhydrophobic surfaces using hthography [13], fractal structure of wax [14], chemical vapor deposition (CVD) of poly(tetrafluoroethylene) (PITH) [15] carbon nanotubes and web-like structures [16-18] and by coating hydrophobic silanes onto aluminum acetylacetonate [19] and so on. These micro-structured surfaces show a decrease in apparent surface free energies. 

Before we can discuss in detail the simulation of adsorption and diffusion in zeolites using atomistic simulation we must ensure that the methods and potentials are appropriate for modelling zeolites. The work of Jackson and Catlow reviewed in the previous section shows the success of this approach. Perhaps the most critical test is to apply lattice dynamics and model the effect of temperature as any instability will cause the calculation to fail. Thus we performed free energy minimization calculations on a range of zeolites to test the methodology and applicability to zeolites. As noted in Section 2.2, the extension of the static lattice simulation technique to include the effects of pressure and temperature leading to the calculations of thermodynamic properties of crystals and the theoretical background to this technique have been outlined by Parker and Price [21], and this forms the basis of the computer code PARAPOCS [92] used for the calculations. 

Cortona embedded a DFT calculation in an orbital-free DFT background for ionic crystals [183], which necessitates evaluation of kinetic energy density fiinctionals (KEDFs). Wesolowski and Warshel [184] had similar ideas to Cortona, except they used a frozen density background to examine a solute in solution and examined the effect of varying the KEDF. Stefanovich and Truong also implemented Cortona s method with a frozen density background and applied it to, for example, water adsorption on NaCl(OOl) [185]. 

A 3.5 ml portion in a 4 ml polyethylene vial was irradiated for 5 min. Another portion, 3.0 ml in a 3.5 ml silica vial, was irradiated for 3 d. After the short irradiation, 3 ml of the irradiated solution were transferred into an activity-free vial and submitted to y-ray spectrometry with a Ge(Ii) detector coupled to a 4000-channel analyser. After the long irradiation, the sample was allowed to cool for 3 d, then the surface of the silica ampoule was cleaned with dilute nitric acid and the sealed ampoule was placed in the counter (the background activity of the ampoule was negligible). Gamma-ray energy and the areas under peaks were calculated by computer. To determine the half-fives of the nuclides produced, the counting was repeated at appropriate intervals. 

---