2Ag state

The exact relative locations of the lowest excited Bu and Ag states are difficult to predict on a theoretical basis. Indeed, they sensitively depend on the interplay between electron correlation effects and bond-length alternation effects, as shown for instance by Soos and his co-workers23. Strong effective bond alternations favour the 1BU state as the S, state this is the case in polyparaphenylene and PPV due to the presence of phenylene rings. The effective bond alternation is much weaker in polyacetylene while it is intermediate in polythiophene where the 2Ag state is found to lie slightly above the 1BU state. 

Another aspect worth mentioning is that it is usually the case that the 2Ag state has a covalent (neutral) character while the 1BU state has a more ionic character. As a result, in polyenes end-capped by strong donor and acceptor groups, the 1 Bu state becomes very much stabilized and passes below the 2Ag state24 substitution of the... 

In symmetric organic molecules the ground state S0 is usually an Ag state. The higher states normally alternate in symmetry. There are only few molecules known, where the 2Ag state has a lower energy than the 1BU state, as for example in elongated polyenes [43]. 

Although the 2Ag state is optically-forbidden , efficient B to 2Ag internal conversion causes fluorescence fromthe 2Ag state when the conjugated chain is short enough, en the conjugated chain becomes longer, the energy gap between the B and 2 A states increases, and then, the crossover from the 2A fluorescence to the B fluorescence takes place. Therefore, the detection of the 2A fluorescence becomes extremely difficult when the number of the conjugated double bonds (n) exceeds 9. 

Based on the U-V model, we first fit the experimental energies of the lowest-lying 1B and 2Ag states for short polyenes we find that the optimal parameters for U and V are U=3t, V=1.2t (with... 

Most interestingly, the N-crossovef" behavior is found in the case of intermediate Ujt and mediiun to large 8 values. We observe that the 1B and 2Ag states cross over for fixed U/t and 5 as a... 

The evolution with chain length of the lowest-lying excited states of polyenes within the PPP model is depicted in Figure 24. For the chosen set of parameters, namely, t==-2.4 eV, 5=0.07, U=11.26 eV (with the widely used Ohno-Klopman potential, see Eq. (8)), there does not exist any N-crossover, namely, for all systems, the covalent 2Ag is always below IBu- (Note that the exotic 2Ag state for N=2 is shown in Fig. 24 it is much higher in energy than both IBu and twice the lowest triplet state). Most interestingly, we find that the... 

Fig. 2 Polyenes and the 2 state, (a) Schematic representation of the singlet 2Ag state in a polyene, showing its equivalent description either as a triplet-triplet or as soliton-antisoliton pair. Adapted from ref. 33. (b) Polyene-type structures discussed in the text. 1 Polydiacetylene [34,35], 2 Poly(diethyldipropargylmalonate) 136], 3 Poly(3-dodecylthienyl-enevinylene) [37], 4 Polyibenzodithiophene thiophene dioxide) [38]. R-groups denote solubilizing chains, (c) Models of singlet fission in polyenes, mediated by formation of 2Ag (left) or directly from IBu (right).

Thus, a particle-hole excitation from the HOMO to the LUMO must have overall odd symmetry. This is the state. The first Ag excitation (the 2Ag state) will be HOMO—1 to LUMO (or, equivalently HOMO to LUMO+1). Such an excitation will lie higher in energy than the 1B state.These transitions are shown in Fig. 3.8. 

These are single-particle states with a definite spatial symmetry. Thus, the overall spatial symmetry of the many body state is determined by the occupation of these states. Figure 4.5 shows the occupancies for the lAg, 1B , and 2Ag states. 

We saw that the soliton in the ground state of an odd-site chain is either neutral with spin-1/2 for the undoped chain (5°), or charged with spin 0 for the singly doped chain S ). We now discuss the types of solitons present in the excited states of an even-site chain. Suppose that an even-site chain is instantaneously excited from the ground state to the or 2Ag states. This is a vertical transition, with the soliton-antisoliton separation initially zero. Within a time 27r/o o a soliton-antisoliton pair is created and separates a distance Their... 

A weak first absorption is found experimentally (AE° ° = 3.59 eV) corresponding to the electric dipole-forbidden lAg 2Ag transition. The second (intense) band results from the allowed lAg 1B transition (AE ° = 4.41 eV). This situation is challenging for any theoretical method because the character of both states is very different (single-configurational, ionic 1B state vs. multiconfigurational, covalent 2Ag state with significant contributions from double excitations). 

All calculations were performed at the (TD)DFT-B3LYP/TZV(d,p) level employing Cih symmetry. In contrast to the experimental data, the TDDFT calculation yields an Si state with B symmetry (AE = = 4.05 eV) and the 2Ag state as the second one (AE = 4.89 eV). This error can be traced to the systematic underestimation of excitation energies for ionic states with TDDFT-B3LYP. Because of the adiabatic approximation used in the... 

TDDFT treatments, the 2Ag state is HOMO LUMO -F 1 and HOMO-1-... 

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