The Box Model and Electron Densities in Conjugated Systems

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Abstract
Part I describes the pi‐electron density distributions of some conjugated systems, computed by generalizing Schmidt's model, with the electrons free to move in a properly shaped box of constant potential. Only products and sums of sine functions are needed for rectangular boxes (polyacenes, porphine) and Bessel functions for circular (coronene) or circular‐sector boxes (phenanthrene). Plaster models of the pi‐electron density surface are shown for 10 molecules. In aromatics, ring‐shaped regions of high density are found at the same locations as the rings of the carbon skeleton. In Part II it is shown that the density maxima in the boxes usually coincide with the high‐order bonds or high‐density atoms predicted by resonance theory or LCAO theory or the free‐electron‐network theory, with similar correspondence for low‐density bonds or atoms. This suggests that the common success of these three other theories rests not on their various special assumptions, but on primitive general requirements of wave continuity and orthogonality in space. In Part III this point is elaborated into a theorem that the density and transition energy of a closed‐shell system are stable under large changes in the one‐particle potential function if the changes occur below the highest‐filled orbital. Taken together with electron repulsion and antisymmetrization, this helps explain why Coulomb and short‐range forces can be successfully approximated by the smoothed‐potential model of the nucleus and the free‐electron model of metals and molecules. In Part IV it is shown that the box model leads to a ``periodic table'' of stabilities of convex conjugated hydrocarbons. Their possible spectral types are discussed. Some new hydrocarbons are described which may be stable.

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