# Electric Field: Homogeneous, Point Charges, Polarizability¶

A homogeneous external electric field and/or the field due to point charges can be included in the Fock operator. Either can be applied in both a Single-Point calculation (or a Create run) or in geometry optimization. When applied in geometry optimization, it will allow for the molecule to rotate with respect to point charges or the field vector but not translate. Rigid translation is explicitly disabled to avoid drifting of the molecule in the external electric field.

Homogeneous electric field:

EField ex ey ez

ex,ey,ez
Define a homogeneous electric field in atomic units: Hartree/(e bohr) = 27.211 V/bohr; the relation to SI units is: 1 Hartree/(e bohr) = 5.14 ... * 1011 V/m. The units applied by ADF for the interpretation of homogeneous field values are not affected by any units used for specifying atomic coordinates. By default no homogeneous E-field is included.

Point charges:

PointCharges
x y z q
x y z q
...
End

x, y, z, q
The Cartesian coordinates and strength of a point charge (in elementary charge units, +1 for a proton). Each point charge must be specified on a separate line in the data block. The Cartesian coordinates are in the units defined in the Units block (by default, Angstrom). By default no point charges are included.

Orientation of the fields

When the atomic coordinates are input in z-matrix format, the direction of the homogeneous field and the location of the point charges as specified in input are interpreted as referring to the standard Cartesian frame associated with z-matrix input. The standard frame means: the first atom at the origin, the second on the positive x-axis, the third in the xy-plane with positive y.

If the program rotates (and translates, as the case might be) the atoms from the input frame - or the auto-generated frame in case of z-matrix input - to some other frame, for instance to accommodate the internal ADF symmetry orientation requirements, the fields are transformed along with the atoms.

Symmetry

The homogeneous electric field and the point charge fields may polarize the electronic charge density. This must be accounted for in the point group symmetry. If symmetry is not specified in input, the program computes the symmetry from the nuclear frame and the fields.

Bonding energy

The bonding energy is computed as: the energy of the molecule in the field minus the energy of the constituent fragments in the same field. Of course, the fragments may not be polarized and hence not be self-consistent in this field. This depends on how the fragments themselves were computed.

Polarizability and hyperpolarizability

ADF supports a direct calculation of the (hyper) polarizability (see section on Spectroscopic Properties). The static (hyper) polarizabilities can also be computed by applying a small homogeneous field and comparing the results with the field-free data.