An expression is derived which relates the distribution of vibrational levels near the dissociation limit $D$ of a given diatomic species to the nature of the long‐range interatomic potential, in the region where the latter may be approximated by $D\u2009\u2212\u2009Cn\u2009/\u2009Rn$. Fitting experimental energies directly to this relationship yields values of $D$, $n$, and $Cn$. This procedure requires a knowledge of the relative energies and relative vibrational numbering for at least four rotationless levels lying near the dissociation limit. However, it requires no information on the rotational constants or on the number and energies of the deeply bound levels. $D$ can be evaluated with a much smaller uncertainty than heretofore obtainable from Birge–Sponer extrapolations. The formula predicts the energies of all vibrational levels lying above the highest one measured, with uncertainties no larger than that of the binding energy of the highest level. The validity of the method is tested with model potentials, and its usefulness is demonstrated by application to the precise data of Douglas, Mo/ller, and Stoicheff for the $B 3\Pi 0u+$ state of Cl_{2}.

## REFERENCES

*Dissociation Energies*(Chapman and Hall Ltd., London, 1968), 3rd. ed.

*Molecular Structure and Molecular Spectra: I. Spectra of Diatomic Molecules*(D. Van Nostrand Co., Inc., Toronto, 1950), 2nd ed.

*Table of Integrals, Series and Products*(Academic Press Inc., New York, 1965), Sec. 3.251, p. 295.

*Handbook of Mathematical Functions*(Dover Publications, Inc., New York, 1965).

*E*(υ) at a slightly smaller υ, W. C. Stwalley (private communication, 1969) independently obtained a result for $n\u2009=\u20096$ which, upon generalization for any $n>2,$ may be cast into the useful form of Eq. (6). However, his factor equivalent to the present $Kn$ is slightly less general, and his approach (unlike the present one) cannot be applied to cases with $n\u2a7d2.$

*Methods of Theoretical Physics*(McGraw‐Hill Book Co., New York, 1953), Vol. 2, Sec. 12.3.

*D*. For $n\u2009=\u20092,$ the levels extend down to infinite binding energy, and there are an infinite number of levels in any finite neighborhood of

*D*.

*n*. The purely attractive exponential potential has both a discrete lowest level and a finite number of bound states within any finite neighborhood of

*D*.

*D*, the position of the dissociation limit.

*Molecular Theory of Gases and Liquids*(John Wiley & Sons, Inc., New York, 1964).

*n*may then lie outside the range of the

*m*’s of the contributing terms. If the lowest inverse‐power term is repulsive while the higher power terms are attractive, this gives rise to a potential maximum at large

*R*. This appears to be the case for the $\Pi 0g+3$ state of $I2;$

*D*.

^{27}and in practice this introduces some error. Experience has shown that while trial parameter values from Eqs. (15) and (16) are satisfactory, they are measurably improved by four‐parameter fittings to Eq. (6).

^{26}

^{26,30}

*D*and $Kn$ obtained at different values of υ, to yield a mutually consistent set of parameters. It is interesting that analogous to Eq. (17)

^{30}the experimental uncertainty introduces considerable imprecision into the four‐parameter fits, so that

*n*could not be directly determined within required accuracy of better than $\xb11.$

^{16}). A more exact value of the numerical constant in their Eq. (92) is 1.6826.

*n*, $Cn$, and $\upsilon D$ show similar behavior. Including more levels in each fit dampens these oscillations.

*D*fixed dampens the “noise” due to experimental uncertainty,

^{42}yielding a more reliable segmented potential.

^{41}may be somewhat too large. M. T. Marron (private communication, 1969) points out that Fischer’s

^{41}values of $\u3008r2\u3009$ are based on Hartree‐Fock wavefunctions which do not have correct asymptotic tails and that correcting for this may decrease $\u3008r2\u3009$, and hence the theoretical $C2$.

*Atomic and Electron Physics: Atomic Interactions, Part A*, L. Marton, B. Bederson, and W. L. Fite, Eds. (Academic Press Inc., New York, 1968), Vol. 7, Chap. 3.1, p. 227.

*D*.

^{6,52}for $\theta \u2009=\u20090$ and $\theta \u2009=\u200910\u22124$ shows that this introduces negligible error.

^{12}

*D*.

^{15}Hence the quantities $(\upsilon D\u2212\upsilon )$ and Curve A in Fig. 8 are significant in the semiclassical (WKB) approximation.

^{41}that for the $0g+$ states of $O2$ and $Cu2$, these effects do not dominate the interaction until $R>60\u2009a.u.$

^{20b}point out that only an excited H atom can have a permanent dipole moment.