# 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.)