LeRoy Radius

The LeRoy radius, derived by Robert J. LeRoy, defines the internuclear distance between two atoms at which LeRoy-Bernstein theory (sometimes called near-dissociation theory) becomes valid.

LeRoy-Bernstein theory is a semi-classical (WKB) approach for describing vibrational energy levels near the molecular dissociation limit. In this limit, the interaction potential between two atoms can be approximated as ${\displaystyle V(r)={\mathfrak {D}}-C_{n}/r^{n}}$, which gives rise to a simple analytical approximation for the vibrational energy levels:

In this expression, ${\displaystyle X_{n}(C_{n})}$ is a simple function depending only upon n and C_n, and ${\displaystyle v_{\mathfrak {D}}}$ can be identified as an effective vibrational quantum number at dissociation.

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