Computes ENDOR frequencies and transition amplitudes.
Pos = endorfrq(Sys,Par,Ori) Pos = endorfrq(Sys,Par,Ori,Opt) [Pos,Int] = endorfrq(...) [Pos,Int,Tra] = endorfrq(...)
endorfrq
computes ENDOR
frequencies and intensities, which can be used to build single-crystal
spectra or crystal rotation patterns. endorfrq
is used by
salt, the solid-state ENDOR spectrum simulation function, to obtain
ENDOR positions and intensities. The calling syntax of endorfrq
is very similar to that of resfields, its EPR analogue.
The three mandatory input parameters characterise the spin system
(Sys
), the experiment parameters (Par
) and the spin system's
orientations in the external field (Ori
). A fourth parameter
Opt
can be used to modify and tune endorfrq
's computations.
Sys
is a spin system structure. In addition to
all the fields necessary to construct a spin Hamiltonian, endorfrq
only
uses the EPR line width field HStrain
.
Par
is a structure containing information related to the ENDOR
experiment.
mwFreq
|
Microwave frequency used in the ENDOR experiment, in GHz. |
Field
|
Magnetic field at which the ENDOR spectrum is to be computed, in mT. |
Temperature
|
Temperature of the spin system in the ENDOR experiment, in Kelvin. If
it is given, thermal equilibrium populations are assumed, and their
effect is included in the intensity computation. By default,
Temperature is inf , and populations are not included in the
intensity computation.
|
ExciteWidth
|
The excitation width of the microwave in MHz (responsible
for orientation selection). The excitation profile is assumed to be
Gaussian, and ExciteWidth is its FWHM. The default is
inf .
|
Ori
gives a list of orientations for which ENDOR spectra should
be computed. It can be either a 2xn or a 3xn array, giving either two
(φ, θ) or three (φ, θ, χ) Euler angles in
radians to 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 molecular 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 molecular axes system. The optional χ, in the third row, specifies the third Euler angle and fixes the x axis of the laboratory in the molecular system.
Altogether, these three angles define the relative orientation between the molecular and the laboratory coordinate system. The external field is along the lab z axis, and the excitation field is along the lab x axis. The detection field can be either along lab x (perpendicular mode) or along lab z (parallel mode). ENDOR frequencies depend only on the first two angles, intensities also on the third. If the third angle is not given, ENDOR intensities are integrated over all possible values of χ.
Opt
contains a set of optional parameters used to adjust the
computation to one's needs. If a field or the entire structure is
omitted, default values are used. One part of the fields concerns the
automatic or manual selection of transitions to include in the ENDOR
computation, the other one allows to modify the ENDOR intensity
calculation.
Verbosity
|
Level of display. Opt.Verbosity=0 (default) means that endorfrq
does not print to the command window. Opt.Verbosity=1 prints some
log messages, higher values are given ever more details.
|
Transitions
|
mx2 vector of integer Determines manually the level pairs which are used in the spectrum calculation. If given, endorfrq uses them and skips its automatic
transition selection scheme. Level pairs are specified in
Transitions(k,:) by the level numbers, starting with 1 for the
lowest-energy state.
|
Threshold
|
Specifies the relative threshold for endorfrq 's
automatic 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 ENDOR transition found is 1. If levl pairs
are manually specified in Transitions , the threshold setting
is ignored.
|
Nuclei
|
vector Determines which nuclear Zeeman terms should be included in the automatic transition selection procedure. If a system contains two different types of nuclei, this allows the user to tune endorfrq
to select only transitions belonging to a certain type of nuclei. 1 is
the first nucleus in the spin system, 2 the second, and so on. If this
field is absent, all nuclei are included by default. E.g. Opt.Nuclei=2
for a spin system with Sys.Nucs='63Cu,1H' will only include 1H
ENDOR transitions.
|
Intensity
|
'on' (default) or 'off' By default, ENDOR intensities are computed from ENDOR and EPR transition amplitudes between states and the EPR excitation width. If Intensity is set to off , no intensities are computed. If the
endorfrq output parameter Int is given, it is set to empty.
You can also switch off intensity computations by not giving the
corresponding output parameter.
|
Enhancement
|
'off' (default) or 'on' If on , endorfrq includes the hyperfine enhancement effect in
the intensity computations by using the full Zeeman part of the spin
Hamiltonian as detection operator. Otherwise only the nuclear Zeeman
terms are used. The hyperfine enhancement effect causes intensity
asymmetries of ENDOR lines at low fields, but it is often canceled by
the amplitude characteristics of the RF amplifiers used in ENDOR
experiments.
|
There are three output parameters to endorfrq
, only the first one
is mandatory.
Pos
contains the positions of the ENDOR lines (in Megahertz). One
column in the output corresponds to one orientation.
Int
returns the ENDOR intensities, in an array the same size as
Pos
. If intensity computations have been switched off, this array
is empty. If Int
is omitted, intensities are not computed at all.
Tra
is a list of the transitions included in the computation. It
is a nx2 array containing pairs of level numbers along rows. Levels
numbers relate to their energy: the lowest state in energy has number
1, the second lowest is 2, etc. See also the Transitions
field
in Opt
.
The following code produces a plot of ENDOR frequencies and amplitudes
as a function of the Q tensor axial parameter eqQ. First we define the
three input structures to endorfrq
and the range of eqQ values.
S = struct('S',.5,'g',[2 2 2],'Nucs','14N','A',[8 9 10]); Params = struct('mwFreq',9.5,'Field',350); Opt = struct('Enhancement','on','Threshold',1e-6); eqQ = 0.01:.02:4;
Next we loop over all eqQ
values and compute the associated ENDOR
positions and amplitudes for an arbitrary orientation. The results are
stored along columns in the array p
and w
.
for ieqQ = 1:length(eqQ) S.Q = [-1 -1 2]*eqQ(ieqQ); [p(:,ieqQ) w(:,ieqQ)] = endorfrq(S,Params,[10;40]*pi/180,Opt); end
At the end, we plot the results. The ENDOR frequencies are scaled with the Larmor frequency of the nucleus.
NZ = larmorfrq('14N',Params.Field); subplot(1,2,1); plot(eqQ/NZ,sort(p/NZ).','k'); axis tight, xlabel('eqQ/wnuc'); ylabel('frequency/wnuc'); subplot(1,2,2); plot(eqQ/NZ,sort(w).','k'); axis tight, ylabel('amplitude'); xlabel('eqQ/wnuc');
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