# 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 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 0.0 Tesla Value of the x component of the BField
By
Type: Float 0.0 Tesla Value of the y component of the BField
Bz
Type: Float 0.0 Tesla Value of the z component of the BField
Dipole
Type: Bool No Bfield is: Atomic dipole Use an atomic dipole as magnetic field instead of a uniform magnetic field.
DipoleAtom
Type: Integer 1 on atom number Atom on which the magnetic dipole should be centered (if using the dipole option)
Method
Type: Multiple Choice NR_SDOTB [NR_SDOTB, NR_LDOTB, NR_SDOTB_LDOTB] 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 tesla [tesla, a.u.] 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 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.)