ESR/EPR
*******

BAND is capable to calculate electron paramagnetic resonance (EPR)
parameters for paramagnetic defects in solids: hyperfine A-tensor and
the Zeeman g-tensor.

The implementation of EPR parameters in BAND is described in the
publications by Kadantsev and co-workers [1] and [2].

**Hyperfine A-tensor**

The A-tensor is implemented within the non-relativistic and scalar
relativistic, spin-polarized Kohn-Sham scheme.

   ATensor
      Enabled Yes/No
   End

"ATensor"
   Type:
      Block

   Description:
      Hyperfine A-tensor.

   "Enabled"
      Type:
         Bool

      Default value:
         No

      GUI name:
         :A-tensor

      Description:
         Compute the hyperfine A-tensor.                      Note:
         Unrestricted calculation is required.

Two methods  are used for A-tensor calculation:

* Method 1: involves the gradient of the spin-polarized density and
  integration by parts. The isotropic component of the A-tensor
  obtained through integration, in a "non-local fashion".

* Method 2: the A-tensor is computed from spin-polarized density and
  does not relies on the integration by parts. The isotropic component
  is obtained in a "local fashion" from the value of the spin-
  polarized density on the grid points near the nuclei.

The user should be aware that numerical integration in A- and g-tensor
routines is carried out over the Wigner-Seitz (WS) cell, and,
therefore, to obtain a meaningful result, the defect in question
should lie at or very close to the WS cell origin. This might require,
on the user's part, some modification of the input geometry.

It also might happen that the size of the WS cell is not large enough
for the adequate description of the paramagnetic defect in question.
In this case, Method 1 will fails, since it relies on the integration
by parts and assumes that the spin-polarized density is localized
inside the WS cell. For the same reason, we recommend that the user
removes diffuse basis set functions that describe the defect
subsystem.

Finally, we note that the final result for A-tensor as presented by
BAND is not scaled by the nuclear spin (as it is done in ADF) and the
user is responsible for making necessary adjustments.

**g-tensor**

The calculation of the Zeeman g-tensor is invoked within the ESR
block:

   ESR
      Enabled Yes/No
   End

"ESR"
   Type:
      Block

   Description:
      Zeeman g-tensor. The Zeeman g-tensor is implemented using two-
      component approach of Van Lenthe and co-workers in which the
      g-tensor is computed from a pair of spinors related to each
      other by time-reversal symmetry. Note: the following options are
      necessary for ESR: 'Relativistic zora spin' and 'Kspace 1'

   "Enabled"
      Type:
         Bool

      Default value:
         No

      GUI name:
         ESR: g-tensor

      Description:
         Compute Zeeman g-tensor.                      The Zeeman
         g-tensor is implemented using two-component approach of Van
         Lenthe and co-workers in which the g-tensor is computed from
         a pair of spinors related to each other by time-reversal
         symmetry.                      Note: the following options
         are necessary for ESR: 'Relativistic zora spin' and 'Kspace
         1'

(\Gamma-only calculation). The g-tensor is then computed from the HOMO
spinor at the \Gamma point. In the output, the user can find two-
contributions to the g-tensor: one that stems from the K_\sigma
operator and a second one, that stems from the orbital angular
momentum. By default, GIAO and spin-Zeeman corrections are **not**
included. From our experience, these corrections are quite small.

[1] E.S. Kadantsev and T. Ziegler,  *Implementation of a Density
    Functional Theory-Based Method for the Calculation of the
    Hyperfine A-tensor in Periodic Systems with the Use of Numerical
    and Slater Type Atomic Orbitals: Application to Paramagnetic
    Defects.*  Journal of Physical Chemistry A 112, 4521 (2008).

[2] E.S. Kadantsev and T. Ziegler,  *Implementation of a DFT Based
    Method for the Calculation of Zeeman g-tensor in Periodic Systems
    with the use of Numerical and Slater Type Atomic Orbitals.*
    Journal of Physical Chemistry A  113, 1327 (2009).
