Mayer f-function

The Mayer f-function is an auxiliary function that often appears in the series expansion of thermodynamic quantities related to classical many-particle systems. It is named after chemist and physicist Joseph Edward Mayer.

Definition
Consider a system of classical particles interacting through a pair-wise potential
 * $$V(\mathbf{i},\mathbf{j})$$

where the bold labels $$\mathbf{i}$$ and $$\mathbf{j}$$ denote the continuous degrees of freedom associated with the particles, e.g.,
 * $$\mathbf{i}=\mathbf{r}_i$$

for spherically symmetric particles and
 * $$\mathbf{i}=(\mathbf{r}_i,\Omega_i)$$

for rigid non-spherical particles where $$\mathbf{r}$$ denotes position and $$\Omega$$ the orientation parametrized e.g. by Euler angles. The Mayer f-function is then defined as
 * $$f(\mathbf{i},\mathbf{j})=e^{-\beta V(\mathbf{i},\mathbf{j})}-1$$

where $$\beta=(k_{B}T)^{-1}$$ the inverse absolute temperature in units of energy−1.