ABSTRACT
Free energy is arguably the most important thermodynamic quantity, especially for chemists who often describe chemical reactions in terms of free energy change and free energy barrier (related to the reaction rate). Thermodynamics tells us that any spontaneous physical/chemical process performed at a given temperature (either constant [N,V,T] or constant [N,P,T]) will always lead to a decrease in the free energy of the system. Thus free energy gives us an important predictive tool to discern the spontaneous direction of any process. In addition, free energy differences can be related to the equilibrium constant of a chemical reaction, partition coefficient of a solute between two immiscible solvents, rate constant of a chemical reaction and so on. In general, free energy can be related to the population distribution of any species or even a property of interest. In this chapter, we shall discuss various modern computational techniques based on computer simulations and statistical mechanical theories to compute relevant free energy profiles. In other words, we show that the free energy difference between any two states can be obtained directly from computer simulation(s) without the need to compute the whole partition function. These techniques are indispensable for studying complex systems, where obtaining a completely analytical solution to the underlying free energy landscape becomes practically impossible. We shall also discuss the concept of rare events, various biased sampling techniques that allow us to cross large barriers.
