# Chemical potential

## Contents

## Classical thermodynamics[edit]

Definition:

where is the Gibbs energy function, leading to

where is the Helmholtz energy function, is the Boltzmann constant, is the pressure, is the temperature and is the volume.

## Statistical mechanics[edit]

The chemical potential is the derivative of the Helmholtz energy function with respect to the number of particles

where is the partition function for a fluid of identical particles

and is the configurational integral

## Kirkwood charging formula[edit]

The Kirkwood charging formula is given by ^{[1]}

where is the intermolecular pair potential and is the pair correlation function.

## See also[edit]

- Constant chemical potential molecular dynamics (CμMD)
- Ideal gas: Chemical potential
- Overlapping distribution method
- Widom test-particle method

## References[edit]

**Related reading**

- G. Cook and R. H. Dickerson "Understanding the chemical potential", American Journal of Physics
**63**pp. 737-742 (1995) - T. A. Kaplan "The Chemical Potential", Journal of Statistical Physics
**122**pp. 1237-1260 (2006) - Federico G. Pazzona, Pierfranco Demontis, and Giuseppe B. Suffritti "Chemical potential evaluation in NVT lattice-gas simulations", Journal of Chemical Physics
**137**154106 (2012) - E. A. Ustinov "Efficient chemical potential evaluation with kinetic Monte Carlo method and non-uniform external potential: Lennard-Jones fluid, liquid, and solid", Journal of Chemical Physics
**147**014105 (2017) - Claudio Perego, Omar Valsson, and Michele Parrinello "Chemical potential calculations in non-homogeneous liquids", Journal of Chemical Physics 149, 072305 (2018)