Pos = resfields(Sys,Param)
Pos = resfields(Sys,Param,Opt)
[Pos,Amp] = resfields(...)
[Pos,Amp,Wid] = resfields(...)
[Pos,Amp,Wid,Trans] = resfields(...)
[Pos,Amp,Wid,Trans,Grad] = resfields(...)

Gives the spectrometer's operating frequency in GHz. (resfields and resfields_perturb only.)

Gives the spectrometer's static field, in mT. (resfreqs and resfreqs_perturb only.)

Defines the center and width [center sweep] of the range which is searched for resonances. For field sweeps, the units are mT. For frequency sweeps, the units are GHz. Only resonances within this range are computed.
The range can be specified either in CenterSweep or in Range. If both are given, CenterSweep has precedence.

Defines the start and end [sweepmin sweepmax] of the range which is searched for resonances. For field sweeps, the units are mT. For frequency sweeps, the units are GHz. Only resonances within this range are computed.
The range can be specified either in CenterSweep or in Range. If both are given, CenterSweep has precedence.

This field specifies the temperature of the spin system in the EPR experiment, in kelvin. E.g., Exp.Temperature = 298 corresponds to room temperature. If given, populations are computed for all energy levels assuming thermal (Boltzmann) equilibrium, and the population differences between two levels are included in the line intensities of the corresponding EPR transition. If not given (or set to NaN), the populations are not calculated, and all transitions are assumed to have equal population difference of 1.

To specify non-equilibrium populations, use the spin system field Sys.initState. See the user guide on spin polarization.

An Nx3 array that specifies the sample orientations for which the EPR spectrum should be computed. Each row of SampleFrame contains the three Euler rotation angles that transform the lab frame to the sample/crystal frame.

Exp.SampleFrame = [0 0 0];                   % sample/crystal frame aligned with lab frame
Exp.SampleFrame = [0 pi/2 0];                % sample/crystal frame tilted relative to lab frame
Exp.SampleFrame = [0 pi/2 pi/4];             % sample/crystal frame tilted relative to lab frame
Exp.SampleFrame = [0 0 0; 0 pi/2 pi/4];      % two samples/crystals

Specifies the symmetry of the crystal. You can give either the number of the space group (between 1 and 230), the symbol of the space group, or the symbol for the point group of the space group (in either Schönflies or Hermann-Mauguin notation).

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

When CrystalSymmetry is given, all symmetry-related sites in the crystal are included in the calculation. If CrystalSymmetry is not given, space group 1 (P1, point group C1, one site per unit cell) is assumed.

The three Euler angles, in radians, for the transformation of the crystal frame to the molecular frame. Use this field when specifying a crystal containing spin systems that are tilted with respect to the crystal frame. E.g. Param.MolFrame=[0,pi/4,0] tilts the x and z axis of the spin system's molecular frame (xM, zM), relative to the sample frame (xS,yS,zS).

Specifies the microwave excitation mode. Possible settings are

Exp.mwMode = 'perpendicular';  % default
Exp.mwMode = 'parallel';
Exp.mwMode = {k pol};

Resonator experiments:
For conventional experiments with linearly polarized microwave in a resonator, use 'perpendicular' (default) or 'parallel'. In the perpendicular mode, the microwave magnetic field B₁ is oscillating along the laboratory x axis (xL), perpendicular to the external static magnetic field B₀. In the parallel mode, it is oscillating along the laboratory z axis (zL), parallel to B₀. The perpendicular mode is by far the most common.

Beam experiments:
For experiments with a microwave (or THz) beam, use Exp.mwMode = {k pol}. k specifies the propagation direction, in one of three possible ways: (i) a letter code for the direction, e.g. 'y', 'z', 'xy'; (ii) a 3-element cartesian vector, e.g. [0;1;0] specifies the lab y axis; (iii) two polar angles [phi_k theta_k] that specify the orientation. theta_k is the angle between the microwave propagation direction and the lab z axis, and phi_k is the angle between the lab x axis and the projection of the propagation vector onto the lab xy plane. For example, [pi/2 pi/2] gives the lab y axis.

For linearly polarized mw irradiation, additionally provide pol, the polarization angle of the radiation, in radians. To calculate the microwave propagation direction nk and the B1 direction nB1 from k and pol, use

k = 'y';   % propagation along y lab axis
pol = -pi/2; % B1 along x lab axis
[phi,theta] = vec2ang(k);  % convert to angles
[nB1,~,nk]  = erot([phi,theta,pol],'rows')

For unpolarized excitation, set pol='unpolarized'. For circularly polarized radiation, set pol='circular+' or pol='circular-', depending on the sense of rotation.

Specifies mode of photoexcitation. If photoexcitation is present, photoselection weights will be calculated and included into the spectral line intensities. For this, the transition dipole moment direction must be provided in Sys.tdm (see here).

Possible settings for lightBeam are

• Exp.lightBeam = '' - no photoexcitation (default)
• Exp.lightBeam = 'perpendicular' - polarized light incident along the lab y direction (perpendicular to B₀) with E-field along the lab x direction (also perpendicular to B₀)
• Exp.lightBeam = 'parallel' - polarized light incident along the lab y direction (perpendicular to B₀) with E-field along the lab z direction (parallel to B₀)
• Exp.lightBeam = 'unpolarized' - unpolarized light incident along the lab y direction (perpendicular to B0) with E-field uniformly distributed in the lab xz plane
• Exp.lightBeam = {k alpha} - light incident along propagation direction k with polarization given by alpha. There are three ways to specify k: (i) a letter code for the direction, e.g. 'y', 'z', 'xy'; (ii) a 3-element cartesian vector, e.g. [0;1;0] specifies the lab y axis; (iii) two angles [phi_k theta_k] that specify the orientation. theta_k is the angle between the propagation direction and the lab z axis, and phi_k is the angle between the lab x axis and the projection of the propagation vector onto the lab xy plane. For example, [pi/2 pi/2] gives the lab y axis. alpha is the polarization angle, in radians. To represent an unpolarized beam, set alpha=NaN.

Contribution of isotropically scattered light to photoexcitation (see lightBeam), as a value between 0 and 1. 0 means no isotropic contribution (only direct excitation by polarized or unpolarized beam), 1 indicates 100 percent isotropic contribution (essentially beam direction and polarization have no effect).

Determines whether the frequency-to-field conversion factor is included in the line intensities of field-swept spectra. 1 indicates yes, 0 indicates no. The factor is the generalized 1/g Aasa-Vänngård factor. This setting is ignored for frequency-swept spectra.

mx2 vector of integer, or 'all'
Determines the transitions (state pairs) which are used in the resonance field calculation. If given, resfields uses them and skips its automatic transition selection scheme. State pairs are specified in Transitions(k,:) by the level numbers which start with 1 for the lowest-energy level. E.g., Opt.Transitions=[1 3; 2 6; 4 6]; specifies three transitions, where the third is between levels 4 and 6.
If 'all' is given, all transitions are included.

Specifies the threshold for transition pre-selection. Only transitions with an estimated relative average intensity larger than this number are included. The relative average intensity of the strongest transition is set to 1. The default value for the threshold is 1e-4. The pre-selection is an approximate procedure, and it might miss transitions for complicated spin systems. In these cases, setting it to zero will include all transitions in the simulation. After the intensities of all included transitions are computed, the transition are screened again against this threshold in a post-selection step. If transitions are specified manually in Opt.Transitions, Opt.Threshold is ignored.

In crystal simulations, this gives a list of crystal sites to include in the simulation. If Opt.Sites is empty or not given, all sites are included. If given, it must be a list of site numbers. The number of sites depends on the space group given in Exp.CrystalSymmetry. E.g. the following set limits the simulation to sites 1 and 3 of the 4 magnetically distinct sites in crystal of space group no. 47.

Exp.CrystalSymmetry = 47;  % space group Pmmm
Opt.Sites = [1 3];

In powder simulations, Opt.Sites is ignored.

0 or 1. Determines whether to use sparse or full matrices for the calculations. Sparse matrices reduce memory demands for large spin systems.

Determines how much information is printed to the command window. If Opt.Verbosity=0, nothing is shown. 1 logs relevant information, 2 gives more details.

Determines the perturbation theory order. Can be 1 or 2.

Determines how much information is printed to the command window. If Opt.Verbosity=0, nothing is shown. 1 logs relevant information, 2 gives more details.

The amount of random noise to add to non-zero Hamiltonian matrix elements to break degeneracies. This is needed, since EasySpin cannot handle systems with degeneracies in an exact fashion. The default value is 1e-10. This means each non-zero Hamiltonian matrix element is multiplied by a random number between (1-1e-10) and (1+1e-10). This field is only used when matrix diagonalization is used.

clear
Sys.g = [2.05 2.05 2.2];
Sys.Nucs = '1H';
Sys.A = [10 10 500];
Exp.mwFreq = 9.5;
Exp.Range = [200 400];
grid = sphgrid('Dinfh',201);
angles = [grid.phi; grid.theta].';
Exp.SampleFrame = angles;
B = resfields(Sys,Exp);

Br = resfields_eig(Sys,Exp);
Br = cell2mat(Br);

theta_deg = grid.theta*180/pi;
plot(Br,theta_deg,'k.',B,theta_deg,'r');
xlabel('field (mT)');
ylabel('theta (deg)');