The magnetic field sweep range can be specified either in CenterSweep or in Range. If both are given, CenterSweep has precedence.

The magnetic field sweep range can be specified either in CenterSweep or in Range. If both are given, CenterSweep has precedence.

This field specifies populations for the states of the spin system, either directly or via a temperature.

Thermal equilibium:
Temperature is the temperature of the spin system in the EPR experiment, in Kelvin. If given, Boltzmann populations are computed and included in the EPR line intensities. E.g., Temperature = 298 corresponds to room temperature. If not given, all states are assumed to be equally populated, corresponding to infinite temperature.

Non-equilibrium populations:
Temperature can also be used to specify non-equilibrium populations. For a spin system with N electron states (e.g. 4 for a biradical), it must be a vector with N elements giving the populations of the zero-field electron states, from lowest to highest in energy.
E.g., if Temperature = [0.85 0.95 1.2] for an S=1 system, the population of the lowest-energy zero-field state is 0.85, and the highest-energy zero-field state has a population of 1.2. The populations of all nuclear sublevels within an electron spin manifold are assumed to be equal.

Exp.Orientations = [0;0;0];              % crystal with z axis aligned with B0
Exp.Orientations = [0;pi/2;0];           % crystal with z axis perpendicular to B0
Exp.Orientations = [0 0 0;0 pi/2 0].';   % two orientations
Exp.Orientations = [];                   % powder

Specifies the symmetry of the crystal, if single-crystal spectra to be simulated (that is, if Exp.Orientations is specified). The crystal symmetry can be either the number of the space group (between 1 and 230), the symbol of the space group (e.g. 'P21212' or the symbol for the point group (e.g. 'C2h' or '2/m').

Exp.CrystalSymmetry = 'P21/m'; % space group symbol
Exp.CrystalSymmetry = 11;      % space group number (between 1 and 230)
Exp.CrystalSymmetry = 'C2h';   % point group, Schönflies notation
Exp.CrystalSymmetry = '2/m';   % point group, Hermann-Mauguin notation

When CrystalSymmetry is given, pepper automatically computes the spectra of all symmetry-related sites in the crystal. If CrystalSymmetry is not given, pepper assumes space group 1 (P1, point group C1), which has only one site per unit cell.

If a number is given in this field, it specifies the orientational distribution of the paramagnetic molecules in the sample.

If not given or set to zero, the distribution is isotropic, i.e. all orientations occur with the same probability. If it is given, the orientational distribution is non-isotropic and computed according to the formula P(θ) = exp(λ(3 cos²θ - 1)/2), where θ is the angle between the molecular z axis and the static magnetic field, and λ is the number specified in Exp.Ordering.

Typical values for λ are between about -20 and +20. For negative values, the orientational distribution function is maximum at θ = 90°, for positive values at θ = 0° and θ = 180°. The larger the magnitude of λ, the sharper the distributions.

To plot a distribution depending on λ, use

lambda = 5;
theta = linspace(0,pi,1001);
p = exp(lambda*plegendre(2,0,cos(theta)));
plot(theta*180/pi,p);

If Exp.Ordering is a function handle, pepper will use the user-supplied function to obtain the orientational distribution. It calls the function with two vector arguments, phi and theta (in radians). The function must return a vector P containing probabilities for each orientation, that is P(k) is the probability of finding the paramagnetic molecules with orientation specified by phi(k) and theta(k). Here is an example with an anonymous function:

Exp.Ordering = @(phi,theta) gaussian(theta,0,15/180*pi);

Of course, the function can also be written and stored in a separate file, e.g. myori.m. Then use Exp.Ordering = @myori.

When using a custom orientational distribution, make sure that the symmetry used in the simulation corresponds to the symmetry of the distribution. If the distribution is very narrow, increase the number of knots in the options structure.

• N1 gives the number of orientations between θ=0° and θ=90° for which spectra are explicitely calculated using the physical theory. Common values for N1 are between 10 (10° increments) and 91 (1° increments). The larger the anisotropy of the spectrum and the narrower the linewidth, the higher N1 must be to yield smooth powder spectra.
• N2 is the refinement factor for the interpolation of the orientational grid. E.g. if N2=4, then between each pair of computed orientations three additional orientations are calculated by spline interpolation. Values higher than 10 are rarely necessary. If N2 is not given, a default value is used.

Opt.nKnots = 91;       % 1° increments, no interpolation
Opt.nKnots = [46 0];   % 2° increments, no interpolation
Opt.nKnots = [31 6];   % 3° increments, 6-fold interpolation (giving 0.5° increments)

Determines how pepper computes the resonance fields.

• 'matrix' indicates matrix diagonalization. This method is very reliable and accurate and works for spin systems with any number of spins. All interactions, including quadrupole, are included in the computation.
• 'perturb1' indicates first-order perturbation theory, and 'perturb' or 'perturb2' indicates second-order perturbation theory. These methods ares limited to spin systems with one electron spin 1/2 (and possibly some nuclei). In addition, nuclear Zeeman and nuclear quadrupole terms are neglected, and only allowed transitions are computed. The resulting spectrum is reasonably correct only for small hyperfine couplings (e.g. organic radicals).

If there are large couplings in the spin system that require matrix diagonalization, but also some nuclei with hyperfine couplings that could be treated perturbationally, use the option Opt.Perturb.

Opt.Perturb = 0;    % no perturbational treatment (default)
Opt.Perturb = 1;    % perturbational treatment for all nuclei

Using this option, simulations for systems containing many nuclei can be several orders of magnitude faster than without. If all nuclei can be treated perturbationally, though, it is more efficient to use perturbation theory with Opt.Method='perturb2'.

In an extended syntax, Perturb can be used to include and exclude nuclei explicitly from perturbational treatment. This might be necessary, if the quadrupole or nuclear Zeeman terms of a nucleus cannot be excluded, because it affects the spectrum. E.g.

Sys.Nucs = '63Cu,14N,1H,1H';
Opt.Perturb = [0 0 1 1];   % exclude 63Cu and 14N from perturbational treatment