Wavelength Formulas and Configuration Interaction in Brooker Dyes and Chain Molecules

Abstract

The zero‐order wavelength of absorption, λ_I, of a conjugated chain of N bonds with all bonds equal is $${\lambda }_I{\mathrm{=N\lambda }}_{\mathrm{c}}{\mathrm{+\lambda }}_L{\mathrm{+\lambda }}_R,$$ where λ_c is a universal constant, about 500 A per bond, and λ_L, λ_R are end‐group corrections. The corresponding energy, E_I, is modified in second order by configurational mixing of the ground state with a certain excited state, to give within experimental error the observed transition energy $${\mathrm{E=[E}}_I^2{\mathrm{+(b}}_L{\mathrm{-b}}_R{)}^2{]}^{\frac{1}{2}}.$$ The derivation is a simplified adaptation of the ideas of Brooker, Herzfeld, and Sklar. The end‐group basicities, b_L and b_R, or stabilizations of alternative resonance structures, locate the electron density maxima in the chain and determine the bond density alternations and bond length alternations that probably produce the mixing. They are additive and consistent for over 50 end groups and can be derived theoretically in many cases. Their dependence on chain length and solvent is shown. Substituent groups have two parameters, λ, b, as in aromatic ultraviolet spectra. The changes in transition band widths, vibrational structure, and intensity in changing solvents are accounted for. The strong convergence of polyene series spectra and the nonharmonic spacing of their higher states is attributed to their large b‐values, about 20 kK. The corresponding mixing of states is related to the probable character of the excited state wave functions and to the probable strong alternation of polyene bond lengths even in long chains.