Charge distributions and chemical effects. XXXIV. Concepts involved in an approximate, but accurate, description of bond energies

Abstract

The concepts underlying the definition of bond energies in terms of potentials at the nuclei are outlined. The theory is rooted, first, in a definition of the energy, E,, of "atom" i in the molecule in terms of the potential energy, V ( i , mol), of nucleus Z, in the field of all the electrons and nuclei of the molecule: E, = K:"'V(I, mol). The K Y ' parameter, which is not required to be a constant in the derivation of the energy expression describing the contribution of an i j bond, turns out to be virtually constant for each atomic species-a situation which is exploited in numerical applications. Second, the Hellmann-Feynman theorem is applied in the calculation of the derivative, dAE$/aZ,, of the atomization energy, AEZ, using (i) the exact quantum-chemical definition of AEZ and (ii) the view that AEZ is the sum of bond energy contributions, E,,, plus a small interaction between nonbonded atoms. The individual bond energies derived in this manner necessarily depend on local charges at the bond-forming atoms. Numerical applications illustrate how this new bond-energy formula provides a simple link between typical saturated, olefinic, acetylenic, and aromatic hydrocarbons.

Charge distributions and chemical effects. XL. Chemical bonds in benzenoid hydrocarbons

“…The expression indicates how their energies depend on the charges of the bond-forming atoms (1)(2)(3): eg is for a reference bond with net charges qp and qy at atoms i and j, respectively, whereas eij corresponds to modified charges, q, = qy+ Aq, and qj = qy+ Aqj. The av and aji parameters, "measuring" the changes in bond energy accompanying unit charge variations at atoms i and j, respectively, are discussed further below, as well as the E~' s .…”

“…1). Equation [3] indicates the steps involved in these energy calculations. We begin with a description of the appropriate av and E; parameters, which will be conveniently tabulated.…”

“…In contrast, when the e8.s are properly chosen, results derived from eq. [3] show that F = 0 is a valid approximation3 (cf. Fig.…”

“…With the set of reference bond energies indicated in Table 2, F is -0 again, and energy calculations can be made in a straightforward manner using eq. [3].…”

Charge distributions and chemical effects. XXXIX. Atomization energies and insitu atomic orbitals in ethylenic hydrocarbons

“…Attention is focussed on which contains information regarding orbital shapes and internuclear distances. In [ 5 ] , qJ = Zf" -NJ is the net atomic charge of atom j bonded to i.…”