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.^[1] It is named after chemist and physicist Joseph Edward Mayer.

Consider a system of classical particles interacting through a pair-wise potential

${\displaystyle V(\mathbf {i} ,\mathbf {j} )}${\displaystyle V(\mathbf {i} ,\mathbf {j} )}

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

${\displaystyle \mathbf {i} =\mathbf {r} _{i}}${\displaystyle \mathbf {i} =\mathbf {r} _{i}}

for spherically symmetric particles and

${\displaystyle \mathbf {i} =(\mathbf {r} _{i},\Omega _{i})}${\displaystyle \mathbf {i} =(\mathbf {r} _{i},\Omega _{i})}

for rigid non-spherical particles where ${\displaystyle \mathbf {r} }${\displaystyle \mathbf {r} } denotes position and ${\displaystyle \Omega }${\displaystyle \Omega } the orientation parametrized e.g. by Euler angles. The Mayer f-function is then defined as

${\displaystyle f(\mathbf {i} ,\mathbf {j} )=e^{-\beta V(\mathbf {i} ,\mathbf {j} )}-1}${\displaystyle f(\mathbf {i} ,\mathbf {j} )=e^{-\beta V(\mathbf {i} ,\mathbf {j} )}-1}

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

• Virial coefficient
• Cluster expansion
• Excluded volume

• Special functions