SIMPLE BOND-CHARGE MODEL FOR POTENTIAL-ENERGY CURVES OF HOMONUCLEAR DIATOMIC MOLECULES

For a homonuclear diatomic molecule near its equilibrium internuclear distance R,, in some bound electronic state, a potential-energy function W(R) of the form W=W1,+Wi/R-2-W0/R+ has previously been shown to be a good approximation to the true potential. From this equation and the molecular virial theorem, there follow expressions for the total electronic potential energy V(R) and the total electronic kinetic energy T(R), V=2W0+W1/R1 T=-W0+W 1/R2. The Ä-dependent, Coulombic part of V is modeled by locating a positive charge Ze at each nucleus and a negative charge -qe at the bond center, with q=2Z. The .R-dependent, free-electron-like part of T is modeled by assuming that the charge q moves freely in a one-dimensional box of length vR. Thus Wi/R=£(Z*-4Zq)/R, Wi/R-4Wq/SmW, and For 17 molecules in 63 different electronic states, parameters q and v are given that reproduce exactly the experimental equilibrium distance R, and harmonic force constant k,. The v values obtained vary little from state to state in a given molecule, or through a given row of the periodic table. The average v values are y=1.0, 0.80, 0.75, 0.65 for first-, second-, third-, and fourth-row homonuclear diatomics, respectively. A relation between R, and q is derived, A,(A) = 2.98/qv1, and this, together with the observed trends in the q values, shows that q is a reasonable measure of the charge accumulated in the bond region of these molecules. It is suggested that the formula q = (4Re(./7e2) 1/2 may be a useful definition of the bond order for a given state of a homonuclear diatomic molecule. For fixed v, this simple point-charge model, and certain generalizations of it, predict R, to be proportional to (l/q), and the quantity Rfk, to be constant. The one-dimensional-box interpretation is given a justification based on separate virial theorems for the parallel and perpendicular components of the kinetic energy.