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
In this expression,
LeRoy later defined an expression for the radius that approximates a boundary between the region where electron exchange (quantum-mechanical) terms are prominent, and the region where atoms and molecules approximately interact through the laws of classical physics and, thus, LeRoy-Bernstein theory (as independent charge distributions and van der Waals interactions expressible as a power series in the internuclear separation).
This radius is defined as
where rA and rB denote the atomic radii of the two atoms.
For
For
A derivation of a more general expression, called the m-dependent LeRoy radius, which depends on the magnetic quantum number (m), was derived in 1995. This expression yields the traditional LeRoy Radius in the special case of a spherical, S-state, atom.
The LeRoy radius is described in high school level chemistry textbooks in Ontario (particularly, in Nelson Chemistry 12, which is the standard required textbook for grade 12 chemistry education in Ontario).