Davydov splitting anthracene

The effect that is dominant in pure crystals, the Davydov splitting, is missing in mixed crystals. There are no first order effects of the crystal field. Second order coupling terms like (3.3), where the superscripts refer to the lowest transitions in the host and guest molecules, cause intensity transfers. In the b direction the tetracene intensity is increased by a factor of 3 by transfer from the anthracene 250 nm and 380 nm systems in the a direction there is little change. 

As shown by Choi et al. (40) contributions of ionized states and of the exchange interaction to the width of triplet excitonic band are of the same order of magnitude. When ionized states are taken into account, the Davydov splitting in anthracene and naphthalene increases by about 50%. 

Davydov splitting for exciton resonance in anthracene, and for the first time obtained reasonable agreement with available experimental data. He used a dipole approximation for the intermolecular interaction and the only ingredients in his theory were the resonance frequencies and oscillator strength. In contrast to quantum theory described in this chapter the classical dipole theory does not take into account the contribution of the nondipole interaction, which are important in the majority of solids. It is clear that also multiexciton states including states with few quantum of excitations on the same molecule (what is forbidden for the two-level model) in classical harmonic oscillator theory contribute to the energy of excitons. However, in the framework of the classical theory it is impossible to develop the estimation of corrections which we discussed here. 

As explained previously, the so-called polarization ratio, being the relation of the oscillator strengths of different bands of the Davydov splitting, is an important characteristic of excitonic spectra. In the case of anthracene, where one of the multiplets is always polarized along the b-axis (representation Au) and the other perpendicular to it (representation Bu), the following expression describes the polarization ratio27... 

Table 3.4 The results of experiments by Brodin and Marisova and Wolf (79), (80) for the polarization ratio P b/a) and the Davydov splitting Ad in anthracene...

Table 5.1 Intramolecular normal vibrations in anthracene crystals vibrational modes, symmetry notation and wavenumbers. Where two different wavenumbers are given for a single normal vibration, a Davydov splitting was observed. From [1-3]. Non-planar (out-of-plane) vibrations are marked with. ...

In the following 20 years, a group of physicists in the Ukraine [2] studied a series of other aromatic crystals spectroscopically. It developed that there are also very characteristic differences from the spectra of free molecules. In the year 1948, A. S. Davydov [3] formulated the basic theoretical explanation for the observable interaction processes in the crystal spectra, between the molecules in electronically excited states within the crystal. He made use of the model of Frenkel excitons [4] and was able in particular to give a quantitative explanation of a characteristic line splitting, the Davydov splitting, as a fundamental property of organic molecular crystals. Fig. 6.1 shows as an example the splitting of the 0,0-transition in the Ti So absorption spectrum of anthracene at room temperature. 

Fig. 6.1 The Davydov splitting Aq = 21.5 cm of the 0.0-transition in the T] So absorption spectrum of anthracene at 300 K. This is the excitation spectrum of the triplet excitons. The absorption was detected via the intensity of the delayed fluorescence...

In triplet transitions, the resonance interaction and thus the Davydov splitting can, as mentioned, no longer be understood in terms of a dipole interaction, but rather as an exchange betv een orbitals which overlap. Measured values are available only for Ti states. Figure 6.10 shows as an example, similar to Fig. 6.1, the two 0,0 components of the excitation spectrum Ti So, of the triplet exciton Ti in an anthracene crystal here, however, the spectrum was taken at 1.8 K. 0,0 transition means that the excitation affects only excitons and that no additional phonons or vibrons are excited. In anthracene, the Davydov splitting of the Ti excitonic state is 21.5 cm" (cf Fig. 6.10). In naphthalene, it is 9.8 cm [34]. 

Fig. 6.10 The Davydov splitting of the 0,0 transition in the T- Sq spectrum of anthracene at 1.8 K. This excitation spectrum was detected with an extremely narrow-band laser. The Davydov splitting is 21.5 cm"h These are the same transitions shown in Fig. 6.1 at 300 K there, however, they have a half-width of...

In the usual crystals, surface excitons are hard to observe. Their absorption is naturally weak compared to that of the bulk and it lies in an energy range in which the bulk also absorbs. They are therefore best observed in reflection. For naphthalene and anthracene, Davydov splittings and solvent shifts are seen in the 0,0 transitions Si So which are about 10-20% smaller than the known bulk transitions in these crystals. See also [39]. 

At T = 2 K, in the jt-polarised reflection spectrum of the (OOl)-cleavage planes of anthracene crystals, one observes spectrally-resolved surface excitons (Fig. 6.17). The Davydov splittings of their 0,0 transitions are only 10-20% smaller than those of the volume excitons (Sect. 6.7 and Ref [39]). Discuss this experimental result qualitatively (cf Sect. 6.5.2). 

Anthracene has two molecules in the unit cell, and according to the Davydov theory in dipole approximation, the splitting between the two components, corresponding to... 

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