Jax implementation#

Here are the JAX function for the simualtion and fitting of EPR cw data.

All functions follow a similar approach to that of its counterparts for the Classic method described in the other sections, but adapted to make use of the JAX advantages, without requiring a large amount of RAM.

Hamiltonian’s functions#

All interactions present in the EPR hamiltonian are described with jax.numpy matricial functions. Here are their definitions and the auxiliary functions for their construction.

Interaction’s functions#

Name	Description
epraya.JHze	Function for the Zeeman interaction.
epraya.JNhze	Function for the nuclear Zeeman interaction.
epraya.JHfi	Function for the hiperfine interaction.
epraya.JQii	Function for the nuclear quadrupolar interaction.
epraya.JIee	Function for the electron-electron interaction.
epraya.JLorbit	Function for the spin orbit interaction.
epraya.JStevensO	Function for the expanded Stevens operators.

Auxiliary functions#

Name	Description
epraya.JKronecker	Function for the Kronecker delta.
epraya.JPauli	Calculates the Pauli matrices for the spin system.
epraya.Jchaframe	Rotates the hamiltonian parameters to the right reference frame using the Euler angles.
epraya.JRotationmat	Creates the rotation matrix for the Lab to sample frame transformation.
epraya.JRotmatrix	Creates the rotation matrix using the Euler angles.
epraya.JConvtarray	Makes sure hamiltonian parameters have the right dimensions.
epraya.JMsmi	Determinates the quantum numbers for the spin, nuclear spin and angular momentum.

Powder samples#

Like its classic counterpart, the process is based in the modificated SOPHE method (using the function epraya.Delaunay), however, the calculation is divided in blocks to keep the processing speed.

Note: By the nature of the JAX framework, the reassigment of values to variables and conditionals evaluations must be performed using JAX functions, which requires modifying the program logic, but the results are equivalent to those of the classic one.

Intensity and resonant fields functions#

Name	Description
epraya.JPowder	Wrap function for the simulation of the EPR spectrum for powder samples.
epraya.JCalpowder	Function for the simulation of the EPR spectrum for powder samples using the JAX functions.
epraya.JMulpol	Wrap function for the simulation of the EPR spectrum for powder samples of two systems.
epraya.Jcalmulta	Determinates the spectrum for a two paramagnetic centers system.
epraya.oneori	Wrap function to use JPadaptarray and JNresina with the JAX.vmap implementation.
epraya.JNresina	Determinates the resonant fields and intensities of the spectrum using the expression for the first order perturbation limit.
epraya.JBoltfactor	Calculates the Boltzmann distribution for the intensity, using states di and dj and their related energies.
epraya.JCaltriangle	Creates a sketch spectrum using a barycentral mesh of triangles to calculate the contribution of the resonant fields and their intensities in the final spectrum.
epraya.Meshtriangle	Creates the baricentral mesh of triangles for the JCaltriangle function.

Line profile functions#

Name	Description
epraya.JLorentzp	Determinates the lorentzian profile of the spectrum.
epraya.JGaussp	Determinates the gaussian profile of the spectrum.
epraya.JVoigtp	Determinates the voigtian profile of the spectrum.

Eigen values and vectors functions#

Name	Description
epraya.JPadaptarray	Constructs the Zeeman hamiltonian, adds it to the complete one and finds the energy values and eigenvectors.
epraya.Hungarian	Solves the assigment problem with the J-V method implemented in Scipy for the eigenvectors and energy values.
epraya.Jungarian	Wrap function to call the Scipy J-V method outside of JAX using ShapeDtypeStruct and pure_callback.
epraya.JPretrack	Organize the eigenvectors and energies to relate them with the quantum numbers of the system.
epraya.containeigh	Wrap function for the eignevalues determination using JAX.

Monocristal samples#

Like its classic counterpart, the process includes the functions for monocristal samples simulation (one fixed orientation), with the implementation of the Stoll Easyspin method for the resonant fields determination. Also includes the energy diagrams generator function.

Intensity and resonant fields functions#

Name	Description
epraya.Jresonant	Wrap function for the simulation of the EPR spectrum for monocrystal samples.
epraya.Calresonant	Function for the calculation of the EPR cw spectrum of monocristal systems.
epraya.JMusic	Wrap function for the simulation of the EPR spectrum for monocristal samples of two systems.
epraya.Jcalmusic	Determinates the spectrum for a two paramagnetic centers monocristal system..