Special case of full correlation

Remarkably, application of the above theory (Hagen et al. 1985d Hearshen 1986) has revealed that many spectra of biological S = 1/2 systems can be excellently fit by a special case of Equation 9.8, namely the case of full (positive or negative) correlation Iryl = 1. This unexpected finding leads to a linewidth equation that is not only much simpler than Equation 9.8, but also very much more easy to use in simulations. 

We will now define this equation and discuss practical aspects of its implementation in computer simulators. Furthermore, in the next section we will develop a biomolecular interpretation of the fully correlated distributions of the p-tensor elements. For Ir J = 1 Equation 9.8 simplifies to (Hagen et al. 1985c) 

The three-matrix product D, / , D is a symmetrical matrix with real elements and can thus be written as 

Implementation of Equation 9.18 in spectral simulators requires some extra precautions (Hagen 1981 Hagen et al. 1985d) (A) The increased periodicity now requires one half of the unit sphere to be scanned. (B) The fact that the term within the absolute-value bars in Equation 9.18 can change sign as a function of molecular orientation implies the possibility that for specific orientations the linewidth becomes equal to zero. To avoid a program crash due to a zero divide, e.g., in the expression for the lineshape in Equation 4.8, a residual linewidth W0 has to be introduced  

INPUT n-point array Xg(n) (amplitudes of absorption spectrum in g-space) INPUT g-space limits gmln, gmax, gstep = (gmax - gmln) / (n-1) 

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