Acc. Chem. Res. 1999, 32, 267-276 conducting transparent plastics3 to exploiting the non- Excited-State Electronic linear (both second-order and third-order) optical re- sponse4 and the semiconducting properties, for instance Structure of Conjugated in thin-film field-effect transistors,5 light-emitting diodes,6 Oligomers and Polymers: A solid-state lasers,7 and photovoltaic devices.8 Since, in this specific class of polymers, small variations Quantum-Chemical Approach to in chemical structure play an essential role and the properties of interest directly depend on the electronic Optical Phenomena structure, quantum-chemical approaches,9 which take the Ä Ä ˆ chemical nature fully into account, have provided a JEAN-LUC BREDAS,* JEROME CORNIL, tremendous input to the field. This has helped in forging DAVID BELJONNE, a fundamental understanding of the electronic and optical DONIZETTI A. DOS SANTOS, AND characteristics of the conjugated materials and in guiding ZHIGANG SHUAI the experimental efforts toward novel compounds with Service de Chimie des MateÂriaux Nouveaux, Centre de enhanced characteristics. Recherche en Electronique et Photonique MoleÂculaires, It is the main purpose of our contribution to illustrate Universite de Mons-Hainaut, Place du Parc 20, B-7000 Mons, Belgium the usefulness of quantum-chemical methods (as we have exploited them in the Mons group over the past 10 years) Received April 10, 1998 in the field of conjugated oligomers and polymers, with a focus on luminescence phenomena. We do not wish to dwell on the theoretical methodologies that have been designed (these are detailed elsewhere9,10) but rather on Introduction the concepts. In the first section, we recall the basic Twenty years after the discovery by Heeger, MacDiarmid, electronic-structure ingredients of conjugated systems, Shirakawa, and co-workers1 that an organic conjugated which make their chemistry and physics so rich and polymer can be ªdopedº (i.e., in chemical terminology, fascinating. We then discuss the nature of the lowest oxidized or reduced) to metallic-like electrical conductiv- excited states that play a key role in absorption, emission, 2 ity, the field of conjugated oligomers and polymers has transport, or nonlinear optical processes. As quantum- enjoyed a tremendous development, amply illustrated in chemical calculations had long been restricted to single the present issue of Accounts of Chemical Research. What chains, interchain interactions had often been neglected; once was a mere exotic curiosity has now turned into the their influence, which by now is realized to be significant, market place. The interest goes all the way from making is described in the last section. Jean-Luc Bre´das was born in Fraire, Belgium, in 1954 and has been head of the A Primer on the Electronic Structure of Laboratory for Chemistry of Novel Materials at the University of Mons-Hainaut since 1988. He also acts as codirector of the Interuniversity Center for Research π-Conjugated Oligomers and Polymers in Molecular Electronics and Photonics that he founded in 1992 with Andre´ By π-conjugated system, it is meant a (macro)molecule Persoons from KULeuven. He is the 1997 recipient of the Francqui Prize, which along the backbone of which there occurs a continuous is considered as the highest scientific award in Belgium. path of carbon atoms or heteroatoms, each carrying a π Je´roˆme Cornil was born in Charleroi, Belgium, in 1970. He received his Ph.D. in atomic orbital. When the backbone is fully planar, there chemistry from the University of Mons-Hainaut in 1996 and then went for a exists a strict distinction between orbitals (antisymmet- postdoctoral stay at UCSB (with Alan Heeger) and MIT (with Bob Silbey). He is π currently Charge´ de Recherches of the Belgian National Fund for Scientific ric with respect to the backbone plane) and σ orbitals Research (FNRS). His main interest is devoted to the theoretical characterization (symmetric). The smallest conjugated molecule is ethyl- of the electronic and optical properties of organic conjugated molecules. ene, CH2dCH2. Among its occupied valence molecular David Beljonne was born in Ath, Belgium, in 1969. He received his Ph.D. in orbitals (MOs), there are one σ ªC-Cº MO, four σ ªC-Hº chemistry from the University of Mons-Hainaut, Belgium, in 1994. After a MOs, and one π MO; the latter is formed by the bonding postdoctoral stay at the University of Cambridge (with Richard Friend) and the combination of the two π atomic orbitals and constitutes University of Rochester (with Shaul Mukamel), he is presently Chercheur Qualifie´ FNRS. He works on the theoretical characterization of electronic excitations in the highest occupied MO (HOMO). The antibonding conjugated systems, in relation to their optical and nonlinear optical response. combination of the π atomic orbitals leads to the lowest unoccupied MO (LUMO). Donizetti A. dos Santos was born in SaÄo Bernardo do Campo, Brazil, in 1962. He received his Ph.D. in physics from the State University of Campinas, Brazil, in The determination of the electronic structure of con- 1992. He spent a postdoctoral stay at the University of Mons-Hainaut, where he jugated systems might, at first glance, be considered as is now Charge´ de Recherches and works in the framework of a European Union project dedicated to polymer light-emitting diodes. an easy task. Indeed, every chemist remembers that the first and most simple quantum-chemical method he/she Zhigang Shuai was born in Jiangxi, China, in 1962. He received his Ph.D. in physics has been introduced to, the one-electron HuÈckel tech- from Fudan University, Shanghai, China, in 1989. In 1990, he moved to the University of Mons-Hainaut. His recent work focuses on the electron correlation nique, is mainly designed for conjugated molecules. effects on the optoelectronic properties of conjugated polymers. However, the properties that are nowadays eagerly sought 10.1021/ar9800338 CCC: $18.00 1999 American Chemical Society VOL. 32, NO. 3, 1999 / ACCOUNTS OF CHEMICAL RESEARCH 267 Published on Web 01/20/1999 Electronic Structure of Oligomers and Polymers BreÂdas et al. whose individual wave function can be cast in the form of one Slater determinant. The lowest energetic configu- ration corresponds to the situation where the π electrons occupy two by two the four lowest π MOs and defines the singlet ground-state S0 (of Ag symmetry). At the one- electron level, the lowest (one-photon allowed) excited state (of Bu symmetry) is described by promotion of a single electron from the HOMO to the LUMO; any (one- photon forbidden) Ag excited state lies higher in energy because it requires promotion of a single electron from the HOMO to the LUMO + 1 or the HOMO - 1tothe LUMO or promotion of two electrons from the HOMO to the LUMO, and these processes nominally cost a larger energy (see Figure 1a). However, an entirely different picture emerges when electron correlation is switched on. Various methods have been developed to take account of electron correlation effects;13 for instance, in the often-exploited configuration interaction (CI) approach, each state is cast into a linear combination of electronic configurations (the wave func- tion is then described by a linear combination of the corresponding Slater determinants). In polyenes, it so happens that the singly excited HOMO to LUMO + 1 and HOMO - 1 to LUMO configurations and the doubly excited HOMO to LUMO configuration (illustrated in Figure 1a) strongly mix and result in the 2Ag state being located below the 1Bu state; in other words, in polyenes (at least those longer than butadiene), the lowest excited singlet state, S1, is one-photon forbidden vs the ground state.11 The consequence is that polyenes and polyacet- ylene do not luminesce. Indeed, according to Kasha's rule, luminescence takes place from the lowest excited state;14 in order to observe strong fluorescence, a large one- d 15 FIGURE 1. Schematic illustration, in the case of octatetraene CH2 photon coupling between S0 and S1 is thus required. s d s d s d CH CH CH CH CH CH CH2, of (a) the main electronic con- A major feature that is specific of conjugated com- figurations contributing to the ground state S and the lowest singlet 0 pounds is the interconnection between electronic struc- excited states S1 and S2, (b) the ªdimerizationº of the geometric structure due to the uneven distribution of the π electrons over the ture and geometric structure. This connection has been bonds, and (c) the bonding-antibonding pattern of the HOMO and beautifully exemplified in the field of conducting polymers LUMO levels. with the emergence of concepts such as solitons, polarons, and bipolarons.16-17 Consider again octatetraene, Figure after (e.g., luminescence, electron-hole separation, non- 1b, and suppose that, in a first step, only the σ backbone linear optical response) require a proper description of is taken into account. The geometry would then be such electronic excited states and interchain interactions, for that all carbon-carbon bond lengths are roughly the same which the role of many-body effects is large. In this and equal to ca. 1.51 Å (the typical single bond length context, the theoretical treatment of π-conjugated systems between two sp2 carbons). When the π electrons are often becomes very elaborate because of the need (i) to thrown in, the main aspect is that they distribute unevenly incorporate electron correlation effects and (ii) to take over the bonds and in such a way that alternating larger account of the strong connection between, and mutual and smaller π bond densities appear when starting from influence of, the electronic and geometric structures. one end of the molecule; this results in alternating That electron correlation effects are important can be (physicists would say ªdimerizedº) double-like carbon- seen from an analysis of the ordering of the lowest singlet carbon bonds (ca.