Molecular orientation, electronic couplings

The most important interactions between the unpaired electron and the magnetic nuclei can be of two kinds dipole-dipole (anisotropic) interactions, that depend on the molecular orientation with respect to the external field, and Fermi contact or isotropic interactions (spherically symmetric). The latter are purely quantum mechanical, and arise when there is a non-zero probability of finding the electron at a particular magnetic nucleus. Hence, the interaction (coupling) will in principle be larger the more s-character there is in the singly occupied molecular orbital on the particular atom (JV). 

Molecular orientation can also alter electronic couplings and therefore control ET rates (44-47). Experiments by Zeng and Zimmt (48, 49) and McLendon and co-workers (50) indicate the possibility of substantial orientation effects in ET. Again, both methods should be effective, but photoexcitation has an advantage because high time resolution is often valuable. 

Under potentiostatic conditions, photoinduced heterogeneous electron transfer between specifically adsorbed porphyrins and redox couples confined to the organic phase manifests itself by photocurrent responses. As in the case of dynamic photoelectrochemistry, these photoresponses provide information on the dynamics of heterogeneous electron transfer and recombination processes. In addition, we shall demonstrate that photocurrent measurements can be used to characterise the interfacial coverage of the specifically adsorbed porphyrins as well as their molecular orientation. 

The calculation of collisional cross sections for phenomena involving atoms and molecules is particularly difficult because many quantum states of the colliding partners are coupled by the interaction forces. Even in cases involving electronically adiabatic phenomena, where one can assume that the electronic states of the system remain the same while the nuclei move, one must yet deal with the coupling of translational, rotational and vibrational degrees of freedom of the nuclei. The interaction forces furthermore depend intricately on the molecular orientations and on the atomic displacements within molecules, and change extensively with the atomic composition of molecules. It is therefore usually impossible to invoke physical considerations to make a preliminary selection of the quantum states that are relevant to the collision. We describe here the computational aspects of an alternative approach, based on the time evolution of operators for scattering, and on their time-correlation functions, which eliminates the need for basis set expansions. 

Hq, Hd, Hcs and Hj describe the quadrupolar, dipolar, chemical shift and indirect electron coupled interactions, respectively, and are listed according to their typical magnitude. The Zeeman term was given by equ. (1) and is not influenced by the local environment. Quadrupolar interactions occur for nuclei with I> A only and are described in the next chapter for the case of 2H with 1=1, thus the dominant interaction for IH and 13C is given by Ho and Hcs. The dipole-dipole interaction between spins is a strongly anisotropic interaction. Similarly, the chemical shift depends on the orientation of the molecule with respect to Bq, this part is the so-called chemical shift anisotropy (CSA). In a static sample without any molecular motions... 

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