Exact resonance fields (eigenfields) of a spin system.
B = eigfields(Sys,Par,Ori) B = eigfields(sys,Par,Ori,Opt) [B,Int] = eigfields(...)
Given a spin system Sys
and a set of orientations Ori
,
eigfields
computes exact resonance fields (so called eigenfields)
for a cw EPR experiment.
Sys
is a spin system structure.
Par
is a structure containing fields for the experimental parameters.
mwFreq | Required parameter giving the spectrometer frequency in GHz. |
Detection |
'perpendicular' (default) or 'parallel' Determines the cw EPR detection mode. In the perpendicular mode, the excitation and detection mw fields are along the laboratory x axis, in the parallel mode they are along the z axis, parallel to the external static field. The perpendicular detection mode is the most common, and it is the default here. |
Range |
2-element vector [Bmin Bmax] If set, eigfields will only return eigenfields falling between Bmin
and Bmax (both in mT).
|
Ori
gives a list of orientations for which resonance fields
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 describe 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 frame. The optional χ, in the third row, specifies the third Euler angle and fixes the x axis of the laboratory in the molecular frame.
Altogether, these three angles define the relative orientation between the molecular frame and the laboratory frame. The external field is along the lab z axis, and the excitation/detection field is along the lab x axis. Resonance fields depend only on the first two angles, intensities also on the third.
If the third angle is not given, intensities are integrated over all possible values of χ.
The structure Opt
contains computational options.
Threshold | Relative threshold for eigenfields. Only eigenfields with a relative transition intensity above the threshold are returned. Works only if transition intensities are computed, i.e. if two output arguments are requested. The relative intensity of the strongest transition is 1. |
eigfields
returns the resonance fields (mT) in B
and,
optionally,
transition intensities (MHz^2/mT^2) in Int
.
The intensities returned are integrated over the plane normal to the external
magnetic field direction if only two of the three Euler angles are
specified in Ori
(see above).
The resonance fields of an S=3/2 system with orthorhombic zero-field splitting for an arbitrary orientation are
B = 59.5729 123.0851 148.9710 253.3805 387.0805 512.8191
These values are exact within the numerical accuracy of MATLAB's generalised
eigenproblem solver eig(A,B)
.
eigfields
solves a generalised eigenproblem in Liouville space describing
the fixed-frequency swept-field situation in cw EPR experiments. This approach
was first described in R.L. Belford et al., J.Magn.Reson. 11, 251-265 (1973).