Spectral broadenings

Overview

EPR spectra are not infinitely sharp, they are broadened by relaxation, unresolved hyperfine splittings, or distributions in magnetic properties such as g and A values, and others. EasySpin allows you to include broadening in most spectral simulations (solid-state cw EPR with pepper, liquid EPR with garlic, ENDOR with salt).

There are two types of broadenings

The broadenings are given in fields of the spin system structure, which contains the spin system and all associated spin Hamiltonian parameters. Not all types of broadenings are supported by all simulation functions.

Broadenings are treated differently in the simulation of slow-motion cw EPR spectra using chili. See the documentation of chili.

All broadenings are understood to be FWHM (full width at half height) or PP (peak-to-peak), independent of the simulation function, the line shape or the detection harmonic. For the conversion to and from peak-to-peak line widths, see the reference page on line shapes.

Use only broadenings of one type at a time.

Isotropic convolutional broadenings

Warning! This type of broadening should only be used for S=1/2 systems with very small g anisotropy. For systems with higher electron spin or with substantial g anisotropy, it will lead to incorrect results.

The following fields in the spin system structure specify convolutional broadenings.

lwpp
Line width for isotropic broadening (PP, peak-to-peak), used for convolution of a field-swept or frequency-swept liquid or solid-state cw EPR spectrum. Peak-to-peak refers to the horizontal distance between the maximum and the minimum of a first-derivative lineshape.

For field-swept spectra, the unit of lwpp is mT. For frequency-swept spectra, the unit is MHz.

Sys.lwpp = 10;       % Gaussian broadening
Sys.lwpp = [0 12];   % Lorentzian broadening
Sys.lwpp = [10 12];  % Voigtian broadening (Gaussian + Lorentzian)

For conversion between FWHM and PP line widths, see the reference page on line shapes.

lw
Same as lwpp, except that the numbers are assumed to indicate the full width at half maximum (FWHM) instead of the peak-to-peak (PP) width. For conversion between FWHM and PP line widths, see the reference page on line shapes.
lwEndor
Line width (FWHM) for ENDOR broadening. Usage is the same as lw. For lwEndor, no peak-to-peak analogue is available. See the page on line shapes for conversion formulas.
Anisotropic broadenings

Anisotropic broadenings in solid-state cw EPR spectra has two main physical origins:

More than one of these broadenings can be specified. The total broadening for a given orientation is the combination of all individual broadenings

HStrain
Residual line width (full width at half height, FWHM), in MHz, describing broadening due to unresolved hyperfine couplings. The three components are the Gaussian line widths in the x, y and z direction of the molecular frame.
Sys.HStrain = [10 10 10];        % 10 MHz Gaussian FWHM broadening in all directions
Sys.HStrain = [10 10 50];        % larger broadening along the molecular z axis

The line width for a given orientation [eqn] of the static magnetic field is given by [eqn] where [eqn], [eqn] and [eqn] are the three elements of HStrain.

If the spin system contains only one electron spin, it is possible to specify combined g and A strain or D strain.

gStrain
[FWHM_gx FWHM_gy FWHM_gz]
Defines the g strain for the electron spin. It specifies the FWHM widths of the Gaussian distributions of the g principal values (x, y and z). The distributions are assumed to be completely uncorrelated. g strain is not supported for systems with more than one electron spin.
AStrain
[FWHM_Ax FWHM_Ay FWHM_Az], in MHz
Vector of FWHM widths (in Megahertz) of the Gaussian distributions of the corresponding principal values in A (x, y, z) of the first nucleus in the spin system. The distributions are completely uncorrelated. AStrain is not supported for systems with more than one electron spin. To set the correlation between gStrain and AStrain, use the field gAStrainCorr.
gAStrainCorr
+1 (default) or -1
Sets the correlation between gStrain and AStrain. +1 indicates that positive change in gx is correlated with a positive change in Ax etc,whereas -1 indicates anticorrelation.
DStrain
FWHM_D or [FWHM_D FWHM_E]
Widths (FWHM) in MHz of the Gaussian distributions of the scalar parameters D and E that specify the D matrix of the zero-field interaction. If FWHM_E is omitted, it defaults to zero.

If the spin system contains more than one electron spin, DStrain should contain one row for each electron spin.

Examples: DStrain = [10, 5] specifies a Gaussian distribution of D with a FWHM of 10 MHz and a Gaussian distribution of E with a FWHM of 5 MHz. DStrain = [100 33] specifies a Gaussian distribution of D with a FWHM of 100 MHz and a Gaussian distribution of E with a FWHM of 33 MHz. For two electron spins, DStrain = [10 5; 100 20] specifies [10 5] for the first electron spin and [100 20] for the second.

DStrainCorr
+1 (default) or -1
Sets the correlation coefficient between D and E, which can be between -1 and +1. +1 indicates that positive change in D is correlated with a positive change in E, whereas -1 indicates anticorrelation. If not given, it defaults to 0, and the distributions in D and E are uncorrelated.

If the spin system has more than one electron spin, give one correlation coefficient per electron spin.

The broadenings resulting from the various strains are computed in an approximate way. For example, for gStrain, the derivative with respect to g of the resonance field of a given transition is computed, and then the magnitude of this derivative is multiplied by the value from gStrain to give the actual line width. A Gaussian with this line width is then added to the spectrum. A similar procedure is used for all other strains.

This approximation, which corresponds to the first term in a Taylor expansion or to first-order perturbation theory, is valid only as long as the strain distribution width is much smaller than the parameter itself, e.g. a gStrain of 0.02 for a g of 2. If the distributions is wider, an explicit loop (see below) should be used.

Using your own broadening models

When none of the above inhomogeneous broadenings apply to your problem, you can always run a loop over any distribution of spin Hamiltonian parameters, simulate the associated spectra and sum them up (including weights of the distribution function) to obtain an inhomogeneously broadened line.