The average bond-length of diatomic molecules in thermodynamical equilibrium depends on the volume

Abstract

In the framework of classical statistical mechanics and assuming the electronic ground-state Born-Oppenheimer approximation, we show in this work that a dependence of the equilibrium bond-length on the available volume is to be expected for a dilute gas of diatomic molecules. In a nutshell, this dependence is controlled by the relation between the potential well depth $D$ (through the factor $e^{-\beta D}$) and the quotient $L/R$ of the linear size of the container $L$ and the potential well width $R$. Using simplified analytical estimations, we predict that the equilibrium bond-length $\langle \rho \rangle$ is independent of $L$ for a range of volumes which is exponentially large on $\beta D$. At some point of the $L$ axis, $\langle \rho \rangle$ starts to increase and it eventually diverges, as it is to be expected, when $L \to \infty$, thus describing dissociated atoms. According to our estimations, it is possible that some diatomic molecules, such as halogens, could present volume dependence of their equilibrium bond-lengths for laboratory-size volumes at room temperature.