Free energy calculations future developments

Finally, the material presented in this chapter paves the way for further improvements in free energy calculations. Two promising directions for future studies are improving the methods for sampling phase space so that is satisfies the most effective overlap and/or subset relationships and developing better techniques for averaging samples and extrapolating from finite-sampled sets. 

In natural waters organisms and their abiotic environment are interrelated and interact upon each other. Such ecological systems are never in equilibrium because of the continuous input of solar energy (photosynthesis) necessary to maintain life. Free energy concepts can only describe the thermodynamically stable state and characterize the direction and extent of processes that are approaching equilibrium. Discrepancies between predicted equilibrium calculations and the available data of the real systems give valuable insight into those cases where chemical reactions are not understood sufficiently, where nonequilibrium conditions prevail, or where the analytical data are not sufficiently accurate or specific. Such discrepancies thus provide an incentive for future research and the development of more refined models. 

As a final note, we would like to mention that the development of SIESTA is certainly an ongoing task, and new capabilities are being implemented or will be in the future. Developments which are already available in a prehmi-nary stage, and which will be included shortly in the public distribution of SIESTA, include accelerated relaxations and dynamics techniques [316, 317], hybrid quantum mechanics-molecular mechanics schemes [309-311], implementations of time dependent DFT [266, 318], electronic transport properties at the nanoscale [289], and the determination of transition states [319]. In the longer term, there are plans to implement methods based on exact and Hartree-Fock exchange (including hybrid XC functionals), GW approaches for the accurate determination of electronic excitations, and the calculations of free energies from molecular dynamics simulations. 

As E is decreased one observes a change from the unimodal distribution for subcritical clusters to a bimodal form indicating growth of supercritical clusters. Because the system is adiabatic, the biomodal distributions also represent stationary states in which there are maximum supercritical cluster sizes, which, if exceeded, result in destruction of that supercritical cluster size new bonds formed in the system increase the cluster kinetic energy and decrease the pressure of the monomer gas. In the future it would be desirable to extract from the molecular-dynamics calculation accurate values for the free energy of formation of clusters. Such calculations would resolve the differences between the B - D theory and the Lothe-Pound theory. In the future, molecular-dynamics calculations should make possible development of correct mesoscopic and microscopic theories of homogeneous and even heterogeneous nucleation. 

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