The total spin Hamiltonian supported by EasySpin functions is
with the following Hamiltonian terms
This spin Hamiltonian is a linear function of the magnetic field
with the operators
The general term describing the interaction between an electron spin and the external magnetic field is
The matrix is usually symmetric, in which case it can be transformed
into its diagonal form
via a
rotation
parameterized by three
Euler angles.
,
and
are the three principal values of the
matrix.
If
is asymmetric,
the diagonalization gives complex principal values.
In its diagonal form, the matrix is the
sum of an isotropic component
and a "g shift" contribution
.
In EPR, the chemical shift anisotropy is neglected.
In the eigenframe of D, the Hamiltonian term is
The relations between the matrix D in its eigenframe and the commonly used scalar parameters D and E are
The hyperfine interaction term is
The matrix
is usually symmetric and can be transformed to its diagonal form
via a similarity transformation with a orthogonal
rotation matrix
The principal values of can be separated into three
components, an
isotropic contribution
, a dipolar contribution
and an orthorhombicity parameter
.
For a spin system with strong anisotropic ,
the
matrices can be
significantly asymmetric. In this case,
has complex principal
values, and 9 parameters are needed to fully specify
.
The general term describing the interaction between two electrons is
The term describing the nuclear quadrupole interaction is present only of nuclei with I>1/2.
The Q matrix is symmetric and can be diagonalized
where ,
and
are the
three principal values.
is traceless, which means
The relations between the diagonal
matrix and the usual parameters
and
are