Compute cw EPR resonance fields, amplitudes and line widths.
Pos = resfields(Sys,Param,Ori) Pos = resfields(Sys,Param,Ori,Opt) [Pos,Amp] = resfields(...) [Pos,Amp,Wid] = resfields(...) [Pos,Amp,Wid,Trans] = resfields(...) [Pos,Amp,Wid,Trans,Grad] = resfields(...)
resfields
computes resonance fields, line intensities and line widths for
cw EPR spectra.
Sys
is a
spin system structure
containing all parameters of the spin system.
Params
is a
structure containing the following experimental parameters.
Range
|
Defines the field range [Bmin Bmax] which is searched for resonances,
in units of mT. Only resonances within this range are returned by resfields .
|
mwFreq
|
Gives the spectrometer's operating frequency in GHz. |
Temperature
|
scalar (default inf ) or vector
This field specifies populations for the states of the spin system, either directly or via a temperature.
Thermal equilibium:
Non-equilibrium populations: |
Detection
|
'perpendicular' (default) or 'parallel' Determines the cw EPR detection mode. In the perpendicular mode, the mw field B1 is along the laboratory x axis, in the parallel mode it is along the z axis, parallel to the external static field B0. The perpendicular detection mode is by far the more common. |
Ori
gives a list of orientations for which resonance fields
should be computed. It can be either a 2xn or a 3xn array, containing
the orientations along columns. Either two (φ, θ) or three
(φ, θ, χ)
Euler angles
(in radians) characterise
each orientation.
φ, in the first row, is the angle between the x axis and the xy plan projection of the orientation of the external field in the reference frame of the spin system. θ, in the second row, is the angle at which the external field is off the z axis of the reference frame. The optional χ, in the third row, specifies the third Euler angle and fixes the x axis of the laboratory in the reference frame of the spin system.
Altogether, these three angles define the relative orientation between the molecular reference frame and the laboratory coordinate system. Resonance fields depend only on the first two angles, intensities also on the third.
If the third angle is not given, EPR intensities are integrated over all possible values of χ.
The structure Opt
contains computational options. The separate fields as
well as the structure as a whole are optional. If a field or the structure are
missing, the function defaults to standard settings.
Transitions
|
mx2 vector of integer 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.
|
Threshold
|
Specifies the threshold for resfields 's transition selection scheme. Any
transition with a relative average amplitude less than this number is
not included in the calculation. The relative average amplitude of the
strongest transition is 1, the default is 1e-4 .
|
Perturb
|
0 (default) or 1 or 1xm vector
Determines whether nuclei with small hyperfine couplings are treated perturbationally. If set to 1 , pepper automatically
determines the nuclei which can be treated using (degenerate) first-order
perturbation theory without too much error. For those nuclei, the quadrupole
and the Zeeman terms are neglected, and only the hyperfine term is retained.
Using this option, simulations for systems containing many nuclei (e.g. 63Cu and four 14N) can be speeded up by several orders of magnitude! In an extended syntax, Perturb can be used to exclude
some nuclei explicitly from perturbational treatment. E.g., Opt.Perturb
= [1 0 1 1] in a spin system with 4 nuclei means that nucleus 2
will be treated exactly and not perturbationally. This might be necessary,
if the quadrupole or nuclear Zeeman terms of a nucleus cannot be excluded,
because it affects the spectrum.
|
There are five outputs from resfields
. Line positions are returned
in matrix Pos
, in units of mT. The various transitions are along columns,
each column corresponding to a separate orientation. The Int
output
contains the intensities, with the same layout as Pos
. Line widths are in
Wid
, again in mT. Trans
is the list of computed transitions. This list
has the same format as the Transitions
option in Opt
. Grad
contains
the magnitudes of the orientational gradient.
of all the resonance fields
A comparison between the resonance field position obtained from resfields
(spline modelling approach) and eigfields
(exact solution) shows that
differences are negligible.
First we compute the resonance fields for an axial spin system with two equivalent protons.
Sys = struct('S',.5,'g',[2.3,2.3,2],... 'Nucs','1H,1H','A',[10 10 500; 10 10 500]); Exp = struct('mwFreq',9.5,'Range',[200 400]); [p,t] = sphgrid('Dinfh',201); x = resfields(Sys,Exp,[p;t]);
Next we compute line positions using eigfields
, which is much slower.
xr = []; for i=1:length(p) xr(:,i) = eigfields(Sys,Exp,[p(i);t(i)]); end
After plotting the result
h = plot(t*180/pi,xr,'k.',t*180/pi,x,'r'); ylim([290 360]); xlabel('theta [deg]'); ylabel('field [mT]');
we see that the resonances obtained by the two methods are practically identical.
eigfields, garlic, levels, levelsplot, pepper