General Relation between Potential Energy and Internuclear Distance for Diatomic and Polyatomic Molecules. I

Abstract

A general relation between potential energy and internuclear distance is proposed which is applicable to the ground states of diatomic and polyatomic molecules. The relation has the form V = D_e[1—exp(—nΔr²/2r)]×[1+af(r)], where the parameter n is defined by the equation n = k_er_e/D_e. For large values of r, the f(r) term assumes the form of a Lennard‐Jones (6—12) repulsive potential. With a = 0 the function assumes a simple form which is numerically easier to use and much more accurate than the Morse function. By using the simple function dissociation energies are readily calculated with greater accuracy than hitherto possible through the use of bond lengths, force constants, and anharmonicity constants. Independent empirical methods are given for evaluating the parameter n and with its use anharmonicity constants as well as dissociation energies may be calculated more accurately than was possible previously. The use of the general relation gives improved correlations and predictions of the five spectroscopic constants r_e, k_e, D_e, ω_eχ_e, and α_e. The wide application of these potential functions to a large number of molecules indicates that the potential energy curves for most molecules have a general form to which the proposed relation is a reasonable approximation. The application of the proposed functions to strongly ionic or charged molecules has not been fully investigated.