Comparison of the Kingston and Morse‐6 Hybrid Potentials Based on Second Virial Coefficients Available to Purchase

A. E.

Kingston

, , ().

A. E.

Kingston

, , ().

D. A.

Copeland

and

N. R.

Kestner

, , ().

We cannot estimate what these errors might be since Kingston did not specify how he treated the freehand‐drawn portion of his hybrid in his calculations.

L. W.

Bruch

and

I. J.

McGee

, Jr., , ().

D. D.

Konowalow

, , ().

R. L.

Matcha

and

R. K.

Nesbet

, , ().

R. K.

Nesbet

, , ().

In effect we demand that the two potential segments of Eqs. (1) and (2) be equal, and thus make zero‐order contact (see Ref. 6, Footnote 28) at some finite separation $r = q0$ to the right of the potential minimum. Depending on the values of ε, c, σ, and $C6,$ there might be 0, 1, or 2 such intersections. In the case of two intersections, we shall be interested only in the larger finite $q0$ value throughout this paper. (In the limit $q0→∞,$ the M‐6 hybrid reduces to the ordinary three‐parameter Morse potential.) In general, the derivatives of the M‐6 hybrid will be discontinuous at $r = q0.$

D. S. Zakheim, B. A. thesis, Harpur College, State University of New York at Binghamton, 1969, gives algorithms for calculating B(T) in terms of the M‐6 potential.

B. E. F.

Fender

and

G. D.

Halsey

, Jr., , ().

G.

Thomaes

,

R.

van Steenwinkel

, and

W.

Stone

, , ().

E.

Whalley

and

W. G.

Schneider

, , ().

J. P. Chandler, “STEP IT—Minimum of a Function of Several (N) Variables,” Program 66.1, Quantum Chemistry Program Exchange, Indiana University.

Kingston (Ref. 1) suggests that experimental errors in B(T) may be $≈3%$ at low temperatures and $≈1 cm3 mole−1$ at high temperatures when B(T) is small. Here we define B(T) to be “small” when $|B(T)|⩽20 cm3 mole−1.$

D. D.

Konowalow

and

S.

Carrà

, , ().

See

R. B.

Bernstein

and

J. T.

Muckerman

, , (). They suggest that, for potentials such as those considered here, the reduced curvature of the potential, $κ = d2(φ/ε)/d(r/rm)2,$ evaluated at the minimum, $r = rm,$ be the natural “third” parameter. For the Morse and M‐6 hybrid, κ is given by $κ = 2(c+ln2).$² [Note that the furthest right term in their Eq. (19) should read $2a2$ and not 12a.]