Antisymmetric excitons

In electroluminescent applications, electrons and holes are injected from opposite electrodes into the conjugated polymers to form excitons. Due to the spin symmetry, only the antisymmetric excitons known as singlets could induce fluorescent emission. The spin-symmetric excitons known as triplets could not decay radiatively to the ground state in most organic molecules [65], Spin statistics predicts that the maximum internal quantum efficiency for EL cannot exceed 25% of the PL efficiency, since the ratio of triplets to singlets is 3 1. This was confirmed by the performance data obtained from OLEDs made with fluorescent organic... 

The classical formalism quantifies the above observations by assuming that both the ground-state wave functions and the excited state wave function can be written in terms of antisymmetrized product wave functions in which the basis functions are the presumed known wave functions of the isolated molecules. The requirements of translational symmetry lead to an excited state wave function in which product wave functions representing localized excitations are combined linearly, each being modulated by a phase factor exp (ik / ,) where k is the exciton wave vector and Rt describes the location of the ith lattice site. When there are several molecules in the unit cell, the crystal symmetry imposes further transformation properties on the wave function of the excited state. Using group theory, appropriate linear combinations of the localized excitations may be found and then these are combined with the phase factor representing translational symmetry to obtain the crystal wave function for the excited state. The application of perturbation theory then leads to the E/k dependence for the exciton. It is found that the crystal absorption spectrum differs from that of the free molecule as follows ... 

When the two dipoles occupy symmetrical positions in the cell, as for instance in the case of the anthracene crystal, (1.70) may be further simplified by introducing symmetric and antisymmetric states for all directions of K, with respect to the assumed symmetry. Then (1.70) reduces to 2 x 2 determinants for the two (symmetric and antisymmetric) transitions. The solution of (1.70) leads to four values of co for each wave vector K, i.e. to four excitonic branches. In general, the crystal field is assumed weak compared to intramolecular forces, so that coupling between excitonic branches may be neglected. To a first approximation, each of the excitonic branches, symmetric and antisymmetric, is given by the equation... 

For purely imaginary solutions of re (Re re = 0, re = ik, fc-real), the function un becomes proportional to cos(kn) for symmetrical solutions, and proportional to sin (kn) for antisymmetrical solutions, respectively. In these cases we obtain bulk symmetrical and antisymmetrical solutions which are similar to the solutions in chains with Frenkel excitons only. 

Of these eight interchain two-particle correlation functions, only the q=0 excitonic insulator (El) responses are divergent. There are both symmetric and antisymmetric forms of El (from the sum and difference of the two operators), and the magnitude of the symmetric form is larger. The regions in which the various two-particle correlation functions are divergent are shown in Fig. (2). We note that El diverges for g a 0 and - g /2 + < k/5 (for finite but... 

The exciton states on both chromophores are interchanged by the twofold axis and can be recombined to yield a symmetric and an antisymmetric combination, denoted as A and B, respectively. One has ... 

Xii(o>) = magnetic susceptibility x(q, a>) = electronic susceptibility XzziQ ") = longitudinal susceptibility 1/ (2) = trigamma function ip z) = digamma function o) = Matsubara frequencies op(fl) = dispersion of optical phonons oj(q) = dispersion of magnetic excitons phonon mode frequencies = antisymmetric part of deformation tensor... 

---