728:
785:
227:
104:
687:
Ji, Bing; Tsai, Chin-Chun; Stwalley, William C. (1995). "Proposed modification of the criterion for the region of validity of the inverse-power expansion in diatomic long-range potentials".
557:, 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
518:, the internuclear potential can be reasonably approximated by charge independent atomic distributions, and the vibrational levels can be well described by LeRoy-Bernstein theory.
455:
315:
273:
555:
516:
826:
593:
Leroy, Robert J.; Richard B. Bernstein (1970). "Dissociation energies of diatomic molecules from vibrational spacings of higher levels: application to the halogens".
769:
819:
112:
860:
576:), was derived in 1995. This expression yields the traditional LeRoy Radius in the special case of a spherical, S-state, atom.
812:
855:
320:
LeRoy later defined an expression for the radius that approximates a boundary between the region where electron exchange (
39:
near the molecular dissociation limit. In this limit, the interaction potential between two atoms can be approximated as
42:
845:
762:
569:
558:
25:
324:) terms are prominent, and the region where atoms and molecules approximately interact through the laws of
341:
755:
291:
696:
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602:
329:
36:
235:
524:
485:
792:
735:
325:
321:
32:
704:
669:
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106:, which gives rise to a simple analytical approximation for the vibrational energy levels:
21:
700:
665:
606:
850:
796:
739:
628:
LeRoy, Robert J. (1974). "Long-Range
Potential Coefficients From RKR Turning Points: C
839:
708:
614:
476:
317:
can be identified as an effective vibrational quantum number at dissociation.
328:
and, thus, LeRoy-Bernstein theory (as independent charge distributions and
727:
24:, defines the internuclear distance between two atoms at which LeRoy-
673:
222:{\displaystyle G(v)={\mathfrak {D}}-X_{n}(C_{n})^{\frac {2n}{n-2}}.}
784:
28:
theory (sometimes called near-dissociation theory) becomes valid.
332:
expressible as a power series in the internuclear separation).
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A derivation of a more general expression, called the
527:
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45:
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99:{\displaystyle V(r)={\mathfrak {D}}-C_{n}/r^{n}}
568:-dependent LeRoy radius, which depends on the
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31:LeRoy-Bernstein theory is a semi-classical (
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450:{\displaystyle R_{\mathrm {LR} }=2}
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310:{\displaystyle v_{\mathfrak {D}}}
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726:
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1:
799:. You can help Knowledge by
742:. You can help Knowledge by
709:10.1016/0009-2614(95)00216-Q
615:10.1016/0009-2614(70)80125-7
559:sophisticated approximations
268:{\displaystyle X_{n}(C_{n})}
654:Canadian Journal of Physics
550:{\displaystyle r<R_{LR}}
511:{\displaystyle r>R_{LR}}
877:
778:
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335:This radius is defined as
330:van der Waals interactions
35:) approach for describing
37:vibrational energy levels
689:Chemical Physics Letters
595:Chemical Physics Letters
861:Molecular physics stubs
570:magnetic quantum number
795:–related article is a
738:-related article is a
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856:Quantum physics stubs
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232:In this expression,
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701:1995CPL...236..242J
666:1974CaJPh..52..246L
607:1970CPL.....5...42L
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561:must be employed.
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695:(3): 242–246.
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660:(3): 246–256.
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20:, derived by
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801:expanding it
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744:expanding it
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657:
653:
623:
601:(1): 42–44.
598:
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563:
520:
481:
477:atomic radii
469:
462:
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334:
319:
284:
280:
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231:
30:
18:LeRoy radius
17:
15:
475:denote the
840:Categories
640:)-State Cl
580:References
428:⟩
409:⟨
389:⟩
370:⟨
207:−
183:−
139:−
69:−
26:Bernstein
697:Bibcode
662:Bibcode
648:, and I
636:for B(Π
603:Bibcode
461:where
288:, and
851:Radii
791:This
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632:and C
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521:For
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482:For
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630:6
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566:m
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540:L
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