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-The '''LeRoy radius''', derived by [[Robert J. LeRoy]], defines the internuclear distance between two atoms at which LeRoy-[[Richard Barry Bernstein|Bernstein]] theory (sometimes called near-dissociation theory) becomes valid.
-LeRoy-Bernstein theory is a semi-classical ([[WKB approximation|WKB]]) approach for describing [[Molecular vibration|vibrational energy levels]] near the molecular dissociation limit.<ref>{{cite journal|last=Leroy|first=Robert J.|coauthors=Richard B. Bernstein|year=1970|title=Dissociation energies of diatomic molecules from vibrational spacings of higher levels: application to the halogens|journal=Chemical Physics Letters|volume=5|issue=1|pages=42–44|doi=10.1016/0009-2614(70)80125-7 |bibcode = 1970CPL.....5...42L }}</ref> In this limit, the interaction potential between two atoms can be approximated as <math>V(r) = \mathfrak{D} - C_{n}/r^{n}</math>, which gives rise to a simple analytical approximation for the vibrational energy levels:
-:<math>G(v) = \mathfrak{D}-X_n(C_n)[v_{\mathfrak{D}} - v]^{\frac{2n}{n-2}}.</math>
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-In this expression, <math>X_n(C_n)</math> is a simple function depending only upon ''n'' and ''C''<sub>''n''</sub>, and <math>v_{\mathfrak D}</math> can be identified as an effective vibrational quantum number at dissociation.
-LeRoy later defined an expression for the radius that approximates a boundary between the region where electron exchange ([[Quantum mechanics|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 force|van der Waals interactions]] expressible as a power series in the internuclear separation).
-This radius is defined as<ref>{{cite journal |last=LeRoy |first=Robert J. |year=1974 |title=Long-Range Potential Coefficients From RKR Turning Points: C<sub>6</sub> and C<sub>8</sub> for B(<sup>3</sup>Π<sub>Ou</sub><sup>+</sup>)-State Cl<sub>3</sub>, Br<sub>2</sub>, and I<sub>2</sub> |journal=Canadian Journal of Physics |volume=52 |issue=3 |pages=246–256 <!-- doi appears to be wrong |doi=10.1139/p74-035-->}}</ref>
-:<math>R_{\mathrm{LR}} = 2[\langle r_A^2 \rangle ^{1/2} + \langle r_B^2 \rangle ^{1/2}]</math>,
-where ''r<sub>A</sub>'' and ''r<sub>B</sub>'' denote the [[Atomic radius|atomic radii]] of the two atoms.
-For <math>r>R_{LR}</math>, the internuclear potential can be reasonably approximated by charge independent atomic distributions, and the vibrational levels can be well described by LeRoy-Bernstein theory.
-For <math>r<R_{LR}</math>, there is no generally applicable expression for the internuclear potential. Likewise, there is no analogous expression for the vibrational level energies for this region and more [[Computational chemistry|sophisticated approximations]] must be employed.
-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.<ref>{{cite journal|last=Ji|first=Bing|coauthors=Tsai, Chin-Chun; Stwalley, William C.|year=1995|title=Proposed modification of the criterion for the region of validity of the inverse-power expansion in diatomic long-range potentials|journal=Chemical Physics Letters|volume=236|issue=3|pages=242–246|doi=10.1016/0009-2614(95)00216-Q |bibcode = 1995CPL...236..242J }}</ref>  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).
-==References==
-{{reflist}}
-[[Category:Molecular physics]]
-{{quantum-stub}}

14 (number): Difference between revisions

Revision as of 10:25, 28 February 2014

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