deerlab.dipolarmodel

dipolarmodel(t, r=None, Pmodel=None, Bmodel=<deerlab.model.Model object>, experiment=None, parametrization='reftimes', npathways=1, spins=2, harmonics=None, excbandwidth=inf, orisel=None, g=[2.00231930436256, 2.00231930436256], gridsize=1000, minamp=0.001, samespins=True, triangles=None, interp=True)

Generate a dipolar EPR signal model.

This function generates a model for the dipolar EPR signal arising from the dipolar interactions between the electron spins of the system. The model is defined in terms of the evolution time vector t, the spin-spin distances r, the distance distribution model Pmodel, the intermolecular contribution Bmodel, and an experiment object containing information about the specific experiment. The number of spins in the system spins can be specified, as well as the parametrization strategy parametrization for the dipolar pathway refocusing times.

For multi-spin systems (spins > 2), the function allows for the inclusion of three-spin interactions by specifying the triangles list of interspin triangles and enabling the samespins assumption of spectral permutability. The minamp parameter can be used to threshold the amplitude of the three-spin interactions.

Additional effects such as orientation selection or limited excitation bandwidth can be included via the orisel and excbandwidth arguments, respectively.

Parameters:

tarray_like

Vector of dipolar evolution times, in microseconds.

rarray_like, optional

Vector of spin-spin distances, in nanometers. If not specified, it defaults to the range 1.5nm-8nm with a resolution of 0.05nm. Has no effect on models with spins>2.

Pmodeldeerlab.Model, optional

Model for the distance distribution. If not specified, a non-parametric distance distribution defined over r is used. For models with spins>2 a multivariate Gaussian distance distribution is assumed.

Bmodeldeerlab.Model, optional

Model for the intermolecular (background) contribution. If not specified, a background arising from a homogenous 3D distribution of spins is used.

experimentdeerlab.ExperimentInfo, optional

Experimental information obtained from experiment models (ex_). If specified, the boundaries and start values of the dipolar pathways’ refocusing times and amplitudes are refined based on the specific experiment’s delays.

parametrizationstring, optional

Parametrization strategy of the dipolar pathway refocusing times. Must be one of the following:

• 'reftimes' - Each refocusing time is represented individually as a parameter.

• 'delays' - The pulse delays are introduced as parameters from which the refocusing times are computed. Requires experiment to be specified.

• 'shift' - A time shift is introduced as a parameter to represent the variability of the refocusing times from their theoretical values. Requires experiment to be specified.

The default is 'reftimes'.

npathwaysinteger scalar, optional

Number of dipolar pathways. If not specified, a single dipolar pathway is used.

harmonicslist of integers, optional

Harmonic prefactors of the dipolar pathways. Must be a list with npathways harmonics, one for each pathway.

spinsinteger scalar, optional

Number of spins in system. If not specified it defaults to two-spin systems. For multi-spins systems indicated by spins>2 three-spin interactions are accounted for by the model automatically.

triangleslist of lists, optional

Only required when spins>3. List of (Nspins)!/(3!*(Nspins-3)!) triangles formed by the different interspin distances. Each triangle is specified by a list of indices of the interspin distances forming the triangle, e.g. for a three-spin system triangles=[[1,2,3]] where the first, second, and third interspin distances connect to form a triangle.

samespinsboolean, optional

Only when spins>3. Enables the assumption of spectral permutability, i.e. the assumption that all spins in the system have the same spectral distribution. If enabled, all pairwise pathways of the different dipolar interactions are assumed to have the same amplitude. If disabled, all the individual pathway amplitudes are parametrized separately. Enabled by default.

minampfloat scalar, optional

Only when spins>3. Threshold amplitude for neglecting three-spin interaction pathways. To enhance performance, all dipolar pathways arising from three-spin interactions with an amplitude lam<minamp are approximated as having zero amplitude. The default threshold is 1e-3.

oriselcallable or None, optional

Probability distribution of possible orientations of the interspin vector to account for orientation selection. Must be a function taking a value of the angle θ ∈ [0,π/2] between the interspin vector and the external magnetic field and returning the corresponding probability density. If specified as None (default), a uniform distribution is used.

gridsizescalar, optional

Number of points on the grid of powder orientations to be used in the 'grid' kernel calculation method when evaluating models with orientation selection or multi-spin effects. By default set to 1000 points.

excbandwidthscalar, optional

Excitation bandwidth of the pulses in MHz to account for limited excitation bandwidth. If not specified, an infinite excitation bandwidth is used.

gscalar, 2-element array, optional

Electron g-values of the two spins, [g1, g2]. If a single g is specified, [g, g] is used. If not specified, g = 2.002319… is used for both spins.

interpboolean, optional

Enable dipolar kernel interpolation for computation time reduction. By default enabled.

Returns:

Vmodeldeerlab.Model

Dipolar signal model object.