Dissociation energies of diatoms related to molecular electron density gradients

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Abstract
In earlier work, we have demonstrated that the difference between the total energy E for molecules at equilibrium and (3/2)Es, where Es is the sum of orbital energies, involves (a) the chemical potential μ and (b) the lowest-order density gradient correction to the kinetic energy, proportional to ℱ(∇ρ)2/ρ dr, ρ(r) being the electron density in the molecule. It is stressed here that a consequence of Teller’s theorem is that good molecular binding energies can only be obtained by inclusion of density gradients. This has prompted a plot of the measured dissociation energy per electron D/N for diatoms against E−(3/2)Es+(3/2)Nμ, the latter quantity being estimated from self-consistent field calculations already available in the literature. A striking correlation between these two quantities is revealed. That this plot is indeed closely related to one of D/N vs ℱ(∇ρ)2/ρ dr is apparent not only from Teller’s theorem but also from: (i) the approximate equation E−(3/2)Es+(3/2)Nμ=− (ℏ2/72m)ℱ[(∇ρ)2/ρ]dr, which is the result of the lowest-order gradient expansion theory; (ii) a study of the electron density contours for several diatomic molecules.

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