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Powder Simulations
quickly when using first order perturbation theory. All possible
statistical distributions of the isotopes are easily generated. For
third order perturbation theory calculation, all the statistical distributions must be explicitly calculated, hence resulting in a
longer calculation time.
A third advantage of the Fourier method is that different instrument response functions can also be included. For example, SimFonia can simulate the effect of overmodulating your EPR
spectrum or using too long of a time constant.
Powder Simulations
3.2
A powder means a sample composed of many small single crystals or a glass. The paramagnetic species are moving so slowly
that their anisotropic interactions (interactions which change
with the orientation of the magnetic field with respect to the
complex or radical) are not averaged out. The resulting spectrum
is called a powder pattern.
As stated in “Powder Simulations” on page 5, the algorithm used
in the SimFonia program is based on perturbation theory. Historically, perturbation theory has been used in the interpretation of
EPR spectra because of the speed of calculation and the intuitiveness of the results. It is an approximation technique for finding the energy eigenvalues and the eigenvectors of the spin
hamiltonian (the equations used to described the EPR spectrum
of the sample). Perturbation theory is covered in any introductory quantum mechanics text book.
As stated in the previous paragraph, perturbation theory is an
approximation. The assumption made is that there is a dominant
interaction which is much larger than the other interactions. As
the dominant interaction becomes larger compared to the other
interactions, the approximation becomes better. The five interactions which are considered in the SimFonia simulation program
WIN-EPR
SimFonia User’s Manual
3 -5