Water free energy calculations

Eor instance, the contribution of water beyond 12 A from a singly charged ion is 13.7 kcal/mol to the solvation free energy or 27.3 kcal/mol to the solvation energy of that ion. The optimal treatment is to use Ewald sums, and the development of fast methods for biological systems is a valuable addition (see Chapter 4). However, proper account must be made for the finite size of the system in free energy calculations [48]. 

We can expect to see future research directed at QM/MM and ab initio simulation methods to handle these electronic structure effects coupled with path integral or approximate quantum free energy methods to treat nuclear quantum effects. These topics are broadly reviewed in [32], Nuclear quantum effects for the proton in water have already received some attention [30, 76, 77]. Utilizing the various methods briefly described above (and other related approaches), free energy calculations have been performed for a wide range of problems involving proton motion [30, 67-69, 71, 72, 78-80]. 

A solvated MD simulation is performed to determine an ensemble of conformations for the molecule of interest. This ensemble is then used to calculate the terms in this equation. Vm is the standard molecular mechanics energy for each member of the ensemble (calculated after removing the solvent water). G PB is the solvation free energy calculated by numerical integration of the Poisson-Boltzmann equation plus a simple surface energy term to estimate the nonpolar free energy contribution. T is the absolute temperature. S mm is the entropy, which is estimated using... 

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... 

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. 

Crown ethers continue to be one of the most useful parts of supramolecular chemistry/91 From the beginning computations of metal ions complexes with synthetic ionophores/101 which have been aptly reviewed/111 emphasized the importance of including explicitly solvation in free energy calculations, also with ab initio calculations on calixarene complexes/121 Molecular dynamics simulations of 18-crown-6 ether complexes in aqueous solutions predict too low affinities, but at least correctly reproduce the sequence trend K+ > Rb+ > Cs+ > Na+. However, only the selection of K+ over Rb+ and Cs+ is ascribed to the cation size relative to that of the crown cavity, whereas K+ appears in these calculations to be selected over Na+ as consequence of the greater free energy penalty involved in displacing water molecules ftomNa/1131... 

In the case of determining the freezing temperature, a more robust calculation for the solid phase must be completed, as the solid lattice free energy calculation must consider factors, such as the Pauling entropy. For this reason, the latticecoupling-expansion method, which incorporates such factors, is employed for these types of simulations. For the Einstein lattice used in the simulations, a 6 x 4 x 4 unit cell was used, which consists of 768 water molecules. This simulations size was... 

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... 

Extrapolation of the AG = /(C ) curves to the water free energy axis enable us to estimate the maximum magnitude of variations in the free energy of water caused by adsorption (AG, i,x). The AG ux value determined in accordance with this method and the data for the free surface energy calculated using Eq. (2) are listed in Table 8. The values of maximum water layers thickness (t/ " ) perturbed by the surface, calculated on the basis of the Cw " value, are also listed in Table 8. These data permit us to conclude that the free surface energy for the adsorbents studied increases in the following order ... 

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