Mayer f-function

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The Mayer f-function, or f-bond is defined as (Ref. 1 Chapter 13 Eq. 13.2):

f_{12}=f({\mathbf r}_{12})= \exp\left(-\frac{\Phi_{12}(r)}{k_BT}\right) -1


In other words, the Mayer function is the Boltzmann factor of the interaction potential, minus one.

Diagrammatically the Mayer f-function is written as

Mayer f function.png

Hard sphere model

For the hard sphere model the Mayer f-function becomes:

f_{12}= \left\{ \begin{array}{lll}
-1 & ; & r_{12} \leq  \sigma ~~({\rm  overlap})\\
0      & ; & r_{12} > \sigma ~~({\rm  no~overlap})\end{array} \right.

where \sigma is the hard sphere diameter.


  1. Joseph Edward Mayer and Maria Goeppert Mayer "Statistical Mechanics" John Wiley and Sons (1940)
  2. Joseph E. Mayer "Contribution to Statistical Mechanics", Journal of Chemical Physics 10 pp. 629-643 (1942)