Two molecules in the unit cell

When the unit cell of an organic crystal contains two or more molecules, the spectrum of the cavity polaritons strongly depends on the relation between (i) the detuning u = coc — u ly (ii) the energy of the Rabi splittings W1 and W2, and 

Applying the results of the previous subsection to each of the two brackets on the left-hand side of this equation, we find that for q C Q the solutions of eqn (10.10) are two pairs of independent polaritonic branches with the total in-plane electric fields parallel to the transition dipole moments Pi and P2  

Typical examples of the dispersion curves are shown in Fig. 10.2 for 99 = 7t/4, small positive detuning u = ivc — d i = 35 meV, and different relations between Wy, W2 and Ac = 2 — uq. It is clear that when one of the coupling parameters IF is small, the spectrum consists of a doublet of polariton branches and of two branches which are close to the bare cavity photon and the bare exciton (Fig. 10.2a). When the Davydov splitting is small and W W2, then the pairs of the dispersion curves almost overlap (Fig. 10.2b). The electric fields in the overlapping curves are (with accuracy up to terms of the order of q2 IQ2) perpendicular to each other (see the discussion in Subsection 10.2.4). When all the parameters are of the same order, the spectrum consists of four well-pronounced polaritonic branches (Fig. 10.2c). 

The predicted in-plane isotropization of the polariton dispersion in an anisotro -pic crystalline organic microcavity can be observed in the spectra of reflection, transmission and photoluminescence. 

---

In that respect we have recently discovered a new compound, namely NPP (20), which crystallizes also in a monoclinic P2jStruc-ture. Moreover, as shown on figure 7 the angle between the charge-transfer axis of any of the two molecules in the unit cell with the binary axis is only at 4° from the optimum orientation (respectively 58 and 54°). 

The molecular planes of the two molecules in the unit cell are nearly parallel to each other and the binary axis which makes the actual 2 point group symmetry close to mm2 symmetry. The crystal is thus near to uniaxial and the "quasi-optical axis" close to the direction perpendicular to the molecular planes (assuming that the... 

In certain complexes, even though the coordination number is the same, two molecules in the same unit cell exhibit different conformations. Thus, in Eu(thd)3 DMSO, the gross geometry around Eu(III) is a distorted pentagonal bipyramid with the oxygen of the DMSO occupying one of the apices 283, 284), but the structure of the two molecules in the unit cell differs in detail. A similar situation also exists in Eu(thd)3(DMF)2 283, 284). 

To understand how the value of g and g are obtained from the experimental spectra, we shall consider their determination for Ti3+ in a single crystal of aluminium (III) acetylacetonate. This crystal is monoclinic with two molecules per unit cell. The trigonal axes of the two molecules in the unit cell point in different directions, and thus in general two absorption lines will be seen. In Fig. 6 are shown the orientations of the appropriate... 

This allows H to become parallel to the trigonal axis of each molecule in the unit cell during the rotation. In this rotation g2 for the two molecules in the unit cell is given by... 

In Fig. 11 is plotted the angular dependence of the resonant magnetic field for chromium(lll) acetylacetonate in a single crystal of the cobalt(III) compound. This system has hv0 D for an -band spectrometer. The orientation of the crystal was that of orientation II in Fig. 6, in which the magnetic field is in the plane defined by the threefold symmetry axes of the two molecules in the unit cell. The angle given in Fig. 11 is the angle between... 

There are occasionally more subtle traps. Some arise out of faulty reasoning and are thus, in principle, entirely avoidable. If, for example, a crystal is found to contain a number of molecules equal to the multiplicity of the general position for its space group, that does not necessarily mean that the molecules must be on general positions. Consider the simplest possible case, a crystal in space group PI with two molecules in the unit cell. While in most instances there are two equivalent molecules on the twofold general position, cases are also known in which each molecule resides on a different center of inversion. In every such case this is a logical possibility and only an actual structure solution can rule it in or out. 

The two molecules in the unit cell are then related by symmetry, consequently only two packing parameters (y and w) defining the orientation and height of one molecule in the unit cell are needed. 

Phenazine (39) is found in two crystalline modifications, a- and jS-(Herbstein and Schmidt, 1955a). The a-form (space group P2ja, with two molecules in the unit cell) has been studied at room temperature (Herbstein and Schmidt, 1955a, b) and at about 90°K (Hirshfeld and Schmidt, 1957). The more accurate low-temperature analysis using partial three-dimensional data indicates that the deviations from the expected mmm molecular symmetry only exceed the estimated experimental accuracy ( + 0-003 A) in a direction normal to the mean molecular plane, the maximum deviation being 0-010 A. This slight non-planarity of the molecule is ascribed to the action of intermolecular forces. 

Preliminary X-ray investigations of crystals of 9,10-dihydro-anthracene (66) (Iball, 1938) showed that the most likely space group was P2X which, with two molecules in the unit cell, gave no indication of the molecular symmetry. A non-planar conformation for 9,10-dihydroanthracene has been established by Ferrier and Iball (1954). Their crystal structure analysis, using two-dimensional Fourier methods, shows clearly that the molecule is not planar but is bent about the line joining the carbon atoms 9 and 10. Each half of the molecule appears to be planar, the two halves being inclined to each other at approximately 145°. 

Cuproscheelite, CuWCh, is triclinic, Cj, PI, a = 4.7026, b = 5.8389, c = 4.8784 A, a = 91.677°, (3 = 92.469°, and y = 82.805°, with two molecules in the unit cell. In Figure 5.12a, the oxygen atoms are in AB close-packed layers with the packing direction along b. Cu and W occupy half of alternate O layers. O sites occur only at C layers, but the metal ions occupy two sites alternating with two vacancies along b. The occupied sites for W are above and below the vacancies in the Cu layer. The CuC>6 and WC>6 octahedra share edges in... 

Montmorillonite, KMgAlSi40io(OH)2 nH20, is a clay mineral closely related to pyrophyllite (Section 10.3.25). Mg replaces some A1 and K is added between the TOT layers. The clay mineral expands when water is absorbed between TOT layers. Figure 10.39 shows the unit cell with ABC labels for the oxygen layers. It is monoclinic, C, C2/m, a = 5.2, b = 9.2, c = 10.15 A, (3 = 99.0° with two molecules in the unit cell. Montmorillonite commonly contains Na and Ca. The mismatch of oxygen layers forming octahedral and bases of tetrahedra is shown by differences in O—O distances, 2.818-2.868 A for oxygen layers bonded to Mg and A1 and 2.631-2.655 A for tetrahedral base... 

The 15N CP/MAS NMR spectra of compounds 41-43 have also been recorded.107 The results indicated that compounds 41 and 42 exist practically completely in the hydrazone form. For compound 43, evidence for an equilibrium mixture of azo and hydrazone forms was found. In this case, two 15N chemical shifts were detected in the 15N CP/MAS NMR spectrum. A possible explanation for this is the existence of two molecules in the unit cell that differ in their hydrazone content as a result of different orientations of the ester methyl group. 

---