Crystal Davydov splitting

The resonance splitting of intramolecular modes in the crystalline state is often called Davydov splitting or factor group splitting . In contrast to the static field effects of the crystal, this splitting is due to the dynamical interaction of the constituents in the primitive cell... 

Now we pass on the analysis of the relations derived focusing on several particular cases of importance which enable us of correlating the calculated values with the available experimental data. CO molecules adsorbed on the (100) face of a NaCl crystal reside at the sites of a square lattice (a = b/2 = 3.988 A) at sufficiently low temperatures (T < 25 K), they have inclined orientations (B = 25°) with alternating dipole moment projections onto the axes of the neighboring chains (

x = 180°).28 For this system, the Davydov splitting of vibration spectral lines is determined as ... 

Outside of a small region around the center of the Brillouin zone, (the optical region), the retarded interactions are very small. Thus the concept of coulombic exciton may be used, as well the important notions of mixure of molecular states by the crystal field and of Davydov splitting when the unit cell contains many dipoles. On the basis of coulombic excitons, we studied retarded effects in the optical region K 0, introducing the polariton, the mixed exciton-photon quasi-particle, and the transverse dielectric tensor. This allows a quantitative study of the polariton from the properties of the coulombic exciton. 

To first order, we consider the molecular structure of the surface layers to be identical to that of the bulk layers. Consequently, all the characteristics corresponding to short-range intralayer interactions (e.g. Davydov splitting, vibrational frequencies, excitonic band structure, vibronic relaxations are similar for bulk and surface layers). In fact, we shall see that even slight changes may be detected. They will be analyzed in Section III.C, devoted to surface reconstruction. Therefore, our crystal model consists of (a,b) monolayers translated in energy relative to the bulk excitation by 206, 10, and 2cm-1 for the first three layers, as indicated in Fig. 3.5. No other changes are considered in this first-order crystal model. 

Upon gas coating (N2) of the crystal surface, while the b component falls by about 78 cm, the a component falls by only 57 cm see Fig. 3.17. Thus, the Davydov splitting increases by more than 10% upon gas coating, its value... 

These values were determined by high-resolution spectroscopy of excitation spectra of mixed crystal at very low concentrations. They are in good agreement with the Davydov splittings in the pure crystals (the slight difference, - 5%, in the deuterated naphthalene is attributed to an appreciable... 

Several theories have been developed to explain how energy absorbed by one molecule is transferred to a second acceptor molecule of the same or a different species. At first sight exciton theory,20 66 which accounts for excitation transfer in molecular aggregates or crystals and the Davydov splitting effects connected with it, appears to bear little relationship to the treatment of long-range resonance transfer as developed, for example, by Forster.81-32 However, these theories can be shown to arise from the same general considerations treated at different well-defined mathematical limits.33-79... 

Figure 5 (a) Absorption (a) and emission (PL) polarized spectra of tetracene b and Lb Davydov splitting components of a tetracene single crystal seen in the absorption spectrum of a polycrystalline tetracene layer (upper full curve) as double features at 505 and =520 nm the PL spectrum (1) as measured, the PL spectrum (2) corrected for the spatial distribution of excitons in the crystal as shown in part (b). (b) The spatial distribution of singlet excitons [fix)] in a 4.7 pm-thick tetracene single crystal, obtained according to the procedure described elsewhere [53] (see also Sec. 3.1). 

This was the start of a line of theoretical and experimental research that lasted in my group over several years. Davydov [212] had shown that in crystals each transition of a free molecule splits into transitions to sub-levels equal in number to molecules in the unit cell. There were new selection rules for the polarization properties in the crystal. The splitting between sublevels in leading order was proportional to the square of the transition moment. In strong transitions this was a dipole moment. In weak transitions, as we later showed, even the octupole moment could appear. 

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. 

Exciton Shape Dependence and Davydov Splitting in Aromatic Crystals. D.P. Craig and J.R. Walsh. 

Deviations from OGM were recognized early on spectroscopic properties of molecular crystals Davydov shifts and splittings of absorption bands in molecular crystals are clear deviations from OGM and were rationalized based on the excitonic model (EM) [10, 14, 15, 16, 17]. This same model proved extremely successful to describe the complex and technologically relevant spectroscopy of molecular aggregates, i.e. of clusters of molecules that spontaneously self-assemble in solution or in condensed phases [IS]. Much as it occurs in molecular crystals, due to intermolecular electrostatic interactions the local bound electron-hole pair created upon photoexcitation travels in the lattice and the corresponding wave function describes an extended delocalized object called an exciton. We explicitly remark that the Frenkel picture of the exciton, as a bound electron-hole pair, both residing on the same molecule, survives, or better is the basis for the excitonic picture. The delocalization of the exciton refers to the fact that the relevant wave function describes a Frenkel exciton (a bound e-h pair) that travels in the lattice, and this is of course possible even when electrons and/or holes are, separately, totally localized. In other terms, the EM describes localized charges, but delocalized excitations. 

APPLICATIONS OF DAVYDOV SPLITTING FOR STUDIES OF CRYSTAL PROPERTIES, G. N. Zhizhin and A. F. Goncharov... 

Interesting information about the excitonic states can be obtained from studying the Davydov splitting (15). This problem is discussed in Ch. 2 and Ch. 3. Here we only note that the discovery of this phenomenon has stimulated the investigation of molecular crystal spectra and led to many important conclusions on the nature of intermolecular interactions. 

Thus in crystals where unit cells contain a molecules, to any single nondegenerate excited state of a free molecule in the crystal corresponds not one, but a bands of excited states and correspondingly several absorbtion lines. Such a splitting was first discussed by Davydov ((9)—(11)) and is usually called the Davydov splitting,8 to distinguish it from the Bethe splitting (14). 

Let us note that both Bethe and Davydov splittings are not consequences of specific quantum-mechanical properties of molecules. They appear also in the crystals where the molecules are modeled, for example, by classical harmonic oscillators. 

A quite analogous role of the medium polarization can be discussed in the case of more complex crystals, where the unit cell contains more than one molecule. We consider, as an example, the case of two molecules in the unit cell. In the vicinity of a nondegenerate molecular term, however, taking into account the Davydov splitting eqn (2.50) now becomes... 

The role of mixing of molecular states can be particularly important for excitonic bands with a small Davydov splitting in crystals with unit cells containing several molecules. 

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