Electric and Magnetic Fields
****************************


Electric Field
==============

The external electric field is handled at the AMS level, see the
documentation there.

The effect of a magnetic filed can be **approximated** by the
following potential: \mu_B \vec{\sigma}_i \vec{B}, where \mu_B is the
Bohr magneton, \vec{\sigma}_i are the Pauli matrices and \vec{B} is
the magnetic field. For Spin-unrestricted collinear calculations, the
spin is assumed to be aligned with the z-axis.


Magnetic Field
==============

   BField
      Bx float
      By float
      Bz float
      Dipole Yes/No
      DipoleAtom integer
      Method [NR_SDOTB | NR_LDOTB | NR_SDOTB_LDOTB]
      Unit [tesla | a.u.]
   End

"BField"
   Type:
      Block

   Description:
      The effect of a magnetic filed can be approximated by the
      following potential: mu * sigma_i * B, where mu is the Bohr
      magneton, sigma_i are the Pauli matrices and B is the magnetic
      field

   "Bx"
      Type:
         Float

      Default value:
         0.0

      Unit:
         Tesla

      Description:
         Value of the x component of the BField

   "By"
      Type:
         Float

      Default value:
         0.0

      Unit:
         Tesla

      Description:
         Value of the y component of the BField

   "Bz"
      Type:
         Float

      Default value:
         0.0

      Unit:
         Tesla

      Description:
         Value of the z component of the BField

   "Dipole"
      Type:
         Bool

      Default value:
         No

      GUI name:
         Bfield is: Atomic dipole

      Description:
         Use an atomic dipole as magnetic field instead of a uniform
         magnetic field.

   "DipoleAtom"
      Type:
         Integer

      Default value:
         1

      GUI name:
         on atom number

      Description:
         Atom on which the magnetic dipole should be centered (if
         using the dipole option)

   "Method"
      Type:
         Multiple Choice

      Default value:
         NR_SDOTB

      Options:
         [NR_SDOTB, NR_LDOTB, NR_SDOTB_LDOTB]

      Description:
         There are two terms coupling to an external magnetic field.
         One is the intrinsic spin of the electron, called S-dot-B,
         the other one is the orbital momentum call L-dot-B.
         The L.B is implemented non-relativistically, using GIAOs in
         the case of a homogeneous magnetic field (not for the dipole
         case).

   "Unit"
      Type:
         Multiple Choice

      Default value:
         tesla

      Options:
         [tesla, a.u.]

      Description:
         Unit of magnetic filed. The a.u. is the SI version of a.u.


Atom-wise fuzzy potential
=========================

   FuzzyPotential # Non-standard block. See details.
      ...
   End

"FuzzyPotential"
   Type:
      Non-standard block

   Description:
      Atomic (fuzzy cell) based, external, electric potential. See
      example.

Example:

   FuzzyPotential
      scale $scale
      a1 v1   ! atom with index a1 gets potential coefficient v1 (a.u.)
      a2 v2   ! atom a2 gets potential v2
      ...
   End

"scale"
   Overall scaling factor to be applied.

   If an atom is not in the list it gets a coefficient of zero. The
   potential of an atom is its number (v_i) as specified on input
   times its fuzzy cell

      V(r)  = \sum_i^\text{atoms} v_i \mathcal{P}_{i,U} (r)

   using the same partition function \mathcal{P} as for the BeckeGrid.
   A partition function (or fuzzy cell) of an atom is close to one in
   the neighborhood of this atom.

   The sign convention is: negative is favorable for electrons. (Unit:
   a.u.)
