Fine structure tensor

The effective operator in Eq. [209] has exactly the same structure as the second term of the Breit-Pauli SSC operator in Eq. [162]. The fine-structure tensor of rank two has thus two major contributions... 

After a transformation into a principal-axis system (X, Y, Z) the fine-structure tensor becomes a traceless symmetric diagonal tensor ... 

Fig. 16. Orientation of the fine structure tensor main axes for a thienyl ligand anion (Cs symmetry). In the x, /, zf axis system of the metal complex cation, a single asterisk refers to the thpy ligand at which the triplet state is localized in [Rh(thpy)2(bpy)]+ and [Rh(thpy) (phpy)(bpy)]+, whereas the double asterisk labels the thpy ligand at which the triplet state is locdized in [Rh(phpy)(thpy)(bpy)]+...

Fo is the fine-structure tensor, which is diagonal in the principal-axis system of the molecule. Then compute the spin Hamiltonian of the exdton, Hs,ab with the aid of Eq. (7.10a). 

Fig. 8. Energy levels for the two possible zero-fieid schemes of (tm ) benzophenone with the magnetic field parallel to the y axis of the fine-structure tensor. Soiid arrows indicate the Ams = 1 transitions and whether they are emissive (f) or absorptive (t) in the absence of SLR dashed arrows indicate the same in the presence of rapid SLR. Arrows designated by ...

The principal values of A, and the direction cosines relating its principal axes to those of the fine-structure tensor, may be determined by fitting the observed ENDOR shift... 

Consider the effect of applying a magnetic field in the direction of one of the principal axes of the fine-structure tensor of (nw ) benzophenone. In that event, off-diagonal Zeeman terms are introduced and two of the electron spin states are mixed. The energy level diagrams for the cases H z and H x are shown in Fig. 15. It is observed that two of the spin states... 

The three sublevels of Ti are split even in the absence of a magnetic field owing to the anisotropic dipolar interaction of the two unpaired electron spins. The sub-levels are labelled 2T), T>, and jZ) and are related to the principal axis of the fine-structure tensor, which by symmetry are constrained to lie parallel to the three twofold symmetry axes of pentacene. The zero-field splitting in the case of pentacene is in the order of 1.5 GHz [14]. 

I, - nuclear spin operator of nucleus i D - fine structure tensor... 

As yet the ODMR experiments have been described without an external Bo field. Fig. 7 shows how the application of a Bq field affects the line position as well as the width of the two ODMR transitions for pentacene in p-terphenyl. Both transitions are shifted to higher frequencies and the lines are broadened considerably. The shift of the ODMR line depends on the magnitude of Bq (Zeeman effect) as well as on its orientation with respect to the principal axes system of the fine-structure tensor. As can be seen in Fig. 7(a) the experimentally observed shifts (triangles) agree well with the calculated curves. The line broadening (30 MHz in Fig. 7(b) is a consequence of... 

By performing a systematic variation of the orientation of the external magnetic held with respect to the sample one is able to determine the orientation of the principal axes system of the fine-structure tensor of an individual molecule with respect to the laboratory reference frame. Since for symmetric molecules such as pentacene this principal axes system coincides with the molecular symmetry axes, one thus can determine the orientation of individual molecules even in macroscopically random samples. 

Figure 9.9 The ESR spectrum of perdeuterated TS after irradiation for 1000 s. The signals marked with T arise from triplet states and those with Q from quintets. The T-lines are microwave saturated. The magnetic field Bq is oriented parallel to the z-axis of the quintet fine structure tensor [28].

Figure 9.11 Angular dependence of die resonance fields Bo of the 4 dicarbene structures DC9, DCjo, DCn, and DC in perdeuterated TS-diacetylene crystals. The crystal is rotated so that the external magnetic field Bq is in the plane of the polymer backbone. The b-axis is the direction of the polymer chain, y and z are the principal axes of the fine structure tensor. The curves are fitted to the experimental points by computer calculations. A and B indicate the two magnetically equivalent directions of the molecular orientation within the monoclinic imit cell. Dots experimental values lines calculated by (Eqs. 4-7) [32, 42].

D and E are the fine structure parameters of the identical triplet carbene chain ends X, y, and z are the principal axes of the corresponding fine structure tensors. The intercar-bene magnetic dipolar interaction is represented by the parameter... 

The geometrical factors A and a are only dependent on the orientation

[Pg.135]

Figure 9.15 ENDOR spectra as detected by the ESR transitions (a-d) Vp is the free proton frequency. (1) to (5) label the NMR transitions illustrated in Fig. 9.14, and 1, 2, 3. .. number the individual protons. The external field Bq is oriented along the y or x-axis of the fine structure tensor [36].

Figure 9.16 ENDOR shift anisotropies for the four strongest coupled protons i= 1, 2, 3 and 4, detected via the ESR transition (b). x, y and z are the principal axes of the fine structure tensor. The experimental values were taken for the rotation of Bq in the jz-plane and in the zx-plane, respectively. The ENDOR shifts Av are calculated for (b)i(2) transitions (drawn out) and the (b)i(3) transitions (dashed), respectively [36].

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