This thesis describes advances in methods to measure free energy changes in simulations
of molecular systems. In each case the free energy is decomposed into local environments
which reveal insights about the complex systems being studied. Free energy is a fundamental
quantity that can be used to predict whether changes in state are physically favourable.
This can be used to predict the solubility of molecules and whether molecules are likely
to bind to proteins. There are a handful of methods which measure free energy from
molecular simulations. In chapter 3 we show results for an improved endpoint free energy
method using inhomogeneous fluid solvation theory (IFST) which takes second order
fluid-fluid entropy corrections into account. This is applied to a system of Lennard-Jones
particles which show no measurable second order entropy contribution which fits with
theoretical predictions. In chapter 4 an adaptation to the Zwanzig equation for path based
exponential averaging methods is made. The equation is expanded to give contributions
associated with every atom in the system. This method is called atomwise free energy perturbation
and is applied to small molecules and ligand-protein binding. In chapter 5, IFST
is applied to decompose hydration free energy at the surface of a protein into hydration
sites. From these sites, information is inferred about the binding conformation of two
proteins GABARAP and the GABA-A receptor. In chapter 6 statistics from hydration sites
around hundreds of proteins are analysed. The distributions of free energy are shown and
discussed for hydration sites in a range of local chemical environments. Also in chapter 6,
the hydration sites decomposition method is augmented with local energy information
associated with replacing a water molecule at a hydration site with a probe. The probe
represents a ligand, and this is compared to the binding site prediction from the previous
method. Further suggestions for improvements are made
