Theory of the Electronic Spectra and Structure of the Polyacenes and of Alternant Hydrocarbons

Abstract

A previously given theory of the electronic spectra and structure of complex unsaturated molecules is further elucidated by listing specific formulas for the charge density, bond order, transition moment, and configuration interaction matrix elements. The theory is then applied to give a number of simple rules for alternant hydrocarbons. These refer to the energies of the singly excited states and the effects of configuration interaction, the degeneracy between certain singlet and triplet states, the prohibition of certain electronic transitions which would be allowed from a group theoretical point of view, and the charge density distribution of the ground and singly excited states. A mechanism is proposed to explain some of the anomalously rapid singlet-triplet radiationless transitions which are observed in connection with studies of the lower triplet states of complex molecules. Quantitative application of the theory is made to the spectra of the polyacenes, benzene through pentacene, and to the bond orders of naphthalene and anthracene, employing a high-speed digital computer. The calculated results are compared with experiment. Some previous assignments of electronic bands are confirmed, and some new assignments are suggested. The location of a number of excited states which have not, as yet, been observed is predicted.

Large-scale correlated study of excited state absorptions in naphthalene and anthracene

“…Upon comparing our ͑n +1͒A g states with the nA g states predicted by Kawashima et al, 17 we obtain a very good agreement with the MRMP calculations. The calculations performed by other authors using SDCI/M, 22 SDCI/P, 22 CASSCF, 17 and SCI, 18 approaches predict the states discussed at relatively larger energies than our results.…”

“…Upon comparing our results with the MRMP and CASSCF calculations of Hashimoto et al, 16 we found that their CASSCF energies are much higher than ours, as well as compared to experimental energies, while MRMP results are comparable. Similarly, SCI results of Pariser 18 predict much higher energy differences as compared to our values.…”

Singlet-Fission Sensitizers for Ultra-High Efficiency Excitonic Solar Cells: 15 August 2005 - 14 October 2008

“…This follows from the alternant pairing theorem long known from simple molecular orbital (MO) theory of π-electron systems, 5,6 according to which the highest occupied MO (HOMO) and the lowest unoccupied MO (LUMO) have large absolute amplitudes on the same set of atoms. As a result, the exchange integral K HOMO,LUMO between these two MOs is large, and so is the S 1 -T 1 splitting, which is approximately equal to 2K HOMO,LUMO .…”

Electronic excitations in long polyenes revisited

“…The covalent excitations are the 2A − g , 1B − u , and 3A − g states as classified by the irreducible representations of the C 2h point groups of the all-trans polyenes and by the "Pariser alternancy symmetry" (PAS), which provides the additional labels "+" and "−." 14,19 The PAS is an artificial symmetry appearing in π -electron models such as Hückel, 20 PPP, or Hubbard, which assume a zero-differential overlap (ZDO) between the atomic p z orbitals. In correlated ZDO models the covalent singlet states of the polyenes are all characterized by the PAS label "−.…”