Complex lineshape functions

Many of the Ni hydrogenases contain an iron-sulfur cluster presumed to be of the [3Fe-xS] type, which is paramagnetic with S = 1/2 in the oxidized state and S = 2 in the reduced state (68, 69). Thi function of these clusters is unknown. In some hydrogenases, typifie< by C. vinosum hydrogenase and the membrane-bound hydrogenase o Alcaligenes eutrophus (70), the EPR spectra of the iron-sulfur cluster and the oxidized nickel center show complex lineshapes (Fig. 8). In C vinosum the nickel is also EPR detectable and its spectrum also shows ... 

Contrary to the point by point approach the diagonalization method consists of the generation of an entire lineshape function in one step. (13, 14, 57-60) Time-consuming calculations are carried out only once. The resulting set of complex numbers can be used for a simple calculation of the lineshape (absorption and dispersion modes) at any desired point on the frequency axis. Thus, the complex matrix from equation (147) can be diagonalized by a similarity transformation using an co-independent complex matrix W ... 

We next evaluate the lineshape function (8.16) for two concrete situations in gases, (The complexity of molecular motions in liquids precludes computation of their dipole correlation functions in a text of this scope.) In the first situation, we imagine that we are examining lineshapes in the far-infrared spectrum of a collision-free, rotating polar molecule. Its dipole moment /Iq is assumed to rotate classically without interruption with angular frequency cwq about an axis normal to /Iq. In a dilute gas, we would then have... 

Noting that the relaxation and lineshape functions should, in principle, be complex, Shaul Mukamel [23, 29, 34] obtained the following more general expression for g(t) ... 

For these complexes, the isotropic and 15N chemical shifts and the 15N chemical shift tensor elements were measured as a function of the hydrogen bond geometry. Lineshape simulations of the static powder 15N NMR spectra revealed the dipolar 2H-15N couplings and hence the corresponding distances. The results revealed several correlations between hydrogen bond geometry and NMR parameters which were analysed in terms of the valence bond order model. It was shown that the isotropic 15N chemical shifts of collidine and other pyridines depend in a characteristic way on the N-H distance. A correlation of the and 15N... 

The membrane-bound cytochrome 655s (Bacillus subtilis) contains, according to secondary structure predictions, five transmembrane helices. It functions to anchor two other subunits of the succinate quinone oxidoreductase complex (complex II, E.C. 1.3.5.1) in the cytoplasmic membrane (68). The 1.3-2.0 hemes per covalently bound flavin have been found with the isolated enzyme. The amino acid residues that bind the heme between the a-helices are likely bis(histidine). The EPR and NIR MCD spectra are consistent with this because the EPR spectra show a g value of 3.4 with a HALS lineshape, and the MCD spectra show a low-spin CT band at 1600 nm with Ae of 380 M cm at 4.2 K and 5 T (69). This appears to be another example of a bis(histi-dine)-coordinated heme with near perpendicular alignment of the ligands. 

In the above discussion we have not considered dissipative processes. To include these processes we can, in the framework of the above applied perturbation theory, aside from the perturbation operator U, include a time-independent operator which induces transitions between states tE o- In this case the tensor ej, ij is again defined by the expression (7.52), where in the resonant denominators the energy Huj must be replaced by a complex quantity tuv + ih ylu , k), 7 = 7 + iy", with I7I -C uj. Knowledge of the function 7(0 , k) is important, for example, in the analysis of a lineshape. Below we take into account the exciton-phonon interaction and, for simplicity, consider only the first order of perturbation theory. 

Contrast the above situation with that of wide line FT NMR. First, we need the instrumental capabilities mentioned earlier. Secondly, often we are trying to obtain the shape of a single line or those of a small number of lines which may be complex. Therefore, we cannot presume to know the line shape in order to phase it properly. Similarly, an exponential time window function may alter the lineshape information. Third, the delay time used to avoid the pulse breakthrough in the FID is almost certain to be a significant fraction of the total acquisition time and must be taken into account. Let us deal with each of these difficulties in order. 

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