Nature of the lowest excited states of neutral polyenyl radicals and polyene radical cations.

Due to the close relation of the polyenyl radicals C(2n+1)H(2n+3) () and polyene radical cations C(2n)H(2n+2) (+) to the neutral linear polyenes, one may suspect their excited states to possess substantial double excitation character, similar to the famous S(1) state of neutral polyenes and thus to be equally problematic for simple excited state theories. Using the recently developed unrestricted algebraic-diagrammatic construction scheme of second order perturbation theory and the equation-of-motion coupled-cluster method, the vertical excitation energies, their corresponding oscillator strengths, and the nature of the wave functions of the lowest excited electronic states of the radicals are calculated and analyzed in detail. For the polyenyl radicals two one-photon allowed states are found as D(1) and D(4) states, with two symmetry-forbidden D(2) and D(3) states in between, while in the polyene radical cations D(1) and D(2) are allowed and D(3) is forbidden. The order of the states is conserved with increasing chain length. It is found that all low-lying excited states exhibit a significant but similar amount of doubly excited configuration in their wave functions of 15%-20%. Using extrapolation, predictions for the excitation energies of the five lowest excited states of the polyene radical cations are made for longer chain lengths.