Overview
As originally formulated by Benjamin Widom in 1963, the approach can be summarized by the equation:
where is called the 'insertion parameter', is the number density of species, is the activity of species, is the Boltzmann constant, and is temperature, and is the interaction energy of an inserted particle with all other particles in the system. The average is over all possible insertions. This can be understood conceptually as fixing the location of all molecules in the system and then inserting a particle of species at all locations through the system, averaging over a Boltzmann factor in its interaction energy over all of those locations.
Read more about this topic: Widom Insertion Method