Free energy optimization

This equation is exact, but since the thermal average has to be estimated by a finite sample, statistical errors will grow along the magnitude of the perturbation AU. As shown by Lu et al. perturbation schemes with better performance can be formulated [159,160], The final simulation and calculation of properties are done in the free-energy optimal geometry thus obtained. 

Free energy optimization [179] can give critical nuclei size (number of molecules N in 2D nuclei) under the action of field while nucleation is occurring. 

Free Energy Gradient Method and Its Recent Related Developments Free Energy Optimization and Vibrational Frequency Analysis in Solution... 

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]. 

Larger aggregates seldom have spherical geometry, but tend to form cylindrical micelles. In this case, the diameter of the cylinders can usually be adjusted such that the head groups can cover their optimal head group area Uq, and the interaction free energy per surfactant reduces to the constant The size distribution for cylindrical micelles is then exponential in the limit of large N,... 

Random interface models for ternary systems share the feature with the Widom model and the one-order-parameter Ginzburg-Landau theory (19) that the density of amphiphiles is not allowed to fluctuate independently, but is entirely determined by the distribution of oil and water. However, in contrast to the Ginzburg-Landau approach, they concentrate on the amphiphilic sheets. Self-assembly of amphiphiles into monolayers of given optimal density is premised, and the free energy of the system is reduced to effective free energies of its internal interfaces. In the same spirit, random interface models for binary systems postulate self-assembly into bilayers and intro-... 

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