Sophe Grid

In the SOPHE grid there are TV curves in each set, with the number of grid points varying from 2 to TV + 1 in steps of 1. In order to produce simulated spectra of high quality, the unit sphere is often required to be finely partitioned, in other words, a large number of vertex points are required to reduce computational noise 

Brute Force Matrix Diagonalization and Field Segmentation Algorithms 

The contribution of a Gaussian distribution, of halfwidth A6[ to the linewidth can then be calculated with the following equation  

In the simulation of powder speetra each point in the SOPHE grid is eonsidered to be a mieroerystallite with a Gaussian distribution of orientations (Fig. 42a), such that there is an overlap between adjacent grid points (Fig. 42b)  

---

Figure 3. The XSophe (v 1.1.4) main Window. The interface allows creation and execution of multiple input files on local or remote hosts. There are macro task buttons to guide the novice through the various menus and two button bars to allow easy access to the menus. For example, the bottom bar (left to right), Experimental Parameters, Spin System, Spin Hamiltonian, Instrumental Parameters, Single Crystal Settings, Lineshape Parameters, Transition Labels/Probabilities, File Parameters, Sophe Grid Parameters, Optimisation Parameters, Execution Parameters and Batch Parameters.

The Sophe tab (Fig. 29) allows the user to input various parameters required for the computational calculation, definition of the SOPHE Grid ( 3.1), and determination of the transition probability (selection rules to be used). In the Calculation Panel, matrix diagonalization is currently the only method available for performing continuous wave and pulsed EPR simulations. The field segmentation algorithm... 

The SOPHE grid ( 3.1) is defined by the number of orientations between flic z and x global coordinate system. The number of gamma steps, used in flic simulation of pulsed EPR experiments, is used to calculate the transition probabilities of the echo intensities. 

Figure 41. A schematic representation of the SOPHE partition scheme (a) SOPHE partition grid in which the three sets of curves are described hy Eq. (8) SOPHE partition number N equals 10 (b) subpartitioning into smaller triangles ean be performed by using either Eq. (8) or alternatively the points along the edge of the triangle are interpolated by the eubie spline interpolation method and each point inside the triangle is linearly interpolated three times and an average is taken.

---