# ExternalPotential¶

class ExternalPotential(configuration)

A class for calculating the external potential for a configuration.

Parameters: configuration (MoleculeConfiguration | BulkConfiguration | DeviceConfiguration | SurfaceConfiguration) – The configuration for which the external potential should be calculated.
axisProjection(projection_type='sum', axis='c', spin=None, projection_point=None, coordinate_type=<class 'NL.ComputerScienceUtilities.NLFlag._NLFlag.Fractional'>)

Get the values projected on one of the Cartesian axes.

Parameters: projection_type (str) – The type of projection to perform. Should be either ‘sum’ for the sum over the plane spanned by the two other axes. ‘average’ or ‘avg’ for the average value over the plane spanned by the two other axes. ‘line’ for the value along a line parallel to the axis and through a point specified by the projection_point parameter. Default: ‘sum’ axis (str) – The axis to project the data onto. Should be either ‘a’, ‘b’ or ‘c’. Default: ‘c’ spin (Spin.Sum | Spin.Z | Spin.X | Spin.Y | Spin.Up | Spin.Down | Spin.RealUpDown | Spin.ImagUpDown) – Which spin component to project on. Default: Spin.All projection_point (sequence, PhysicalQuantity) – Axis coordinates of the point through which to take a line if projection_type is ‘projection_point’. Must be given as a sequence of three coordinates [a, b, c]. It the numbers have units of length, they are first divided by the length of the respective primitive vectors [A, B, C], and then interpreted as fractional coordinates. Unitless coordinates are immidiately interpreted as fractional. coordinate_type (Fractional | Cartesian) – Flag to toggle if the returned axis values should be given in units of Angstrom (NLFlag.Cartesian) or in units of the norm of the axis primitive vector (NLFlag.Fractional). Default: Fractional A 2-tuple of 1D numpy.arrays containing the axis values and the projected data. tuple.
derivatives(x, y, z, spin=None)

Calculate the derivative in the point (x, y, z).

Parameters: x (PhysicalQuantity with type length) – The Cartesian x coordinate. y (PhysicalQuantity with type length) – The Cartesian y coordinate. z (PhysicalQuantity with type length) – The Cartesian z coordinate. spin (Spin.All | Spin.Sum | Spin.Up | Spin.Down | Spin.X | Spin.Y | Spin.Z) – The spin component to project on. Default: Spin.All The gradient at the specified point for the given spin. For Spin.All, a tuple with (Spin.Sum, Spin.X, Spin.Y, Spin.Z) components is returned. PhysicalQuantity of type energy × length-1
evaluate(x, y, z, spin=None)

Evaluate in the point (x, y, z).

Parameters: x (PhysicalQuantity with type length) – The Cartesian x coordinate. y (PhysicalQuantity with type length) – The Cartesian y coordinate. z (PhysicalQuantity with type length) – The Cartesian z coordinate. spin (Spin.All | Spin.Sum | Spin.Up | Spin.Down | Spin.X | Spin.Y | Spin.Z) – The spin component to project on. Default: Spin.All The value at the specified point for the given spin. For Spin.All, a tuple with (Spin.Sum, Spin.X, Spin.Y, Spin.Z) components is returned. PhysicalQuantity of type energy
gridCoordinate(i, j, k)

Return the coordinate for a given grid index.

Parameters: i (int) – The grid index in the A direction. j (int) – The grid index in the B direction. k (int) – The grid index in the C direction. The Cartesian coordinate of the given grid index. PhysicalQuantity of type length.
metatext()
Returns: The metatext of the object or None if no metatext is present. str | unicode | None
nlprint(stream=None)

Print a string containing an ASCII table useful for plotting the AnalysisSpin object.

Parameters: stream (python stream) – The stream the table should be written to. Default: NLPrintLogger()
primitiveVectors()
Returns: The primitive vectors of the grid. PhysicalQuantity of type length.
scale(scale)

Scale the field with a float.

Parameters: scale (float) – The parameter to scale with.
setMetatext(metatext)

Set a given metatext string on the object.

Parameters: metatext (str | unicode | None) – The metatext string that should be set. A value of “None” can be given to remove the current metatext.
shape()
Returns: The number of grid points in each direction. tuple of three int.
spin()
Returns: The spin the external potential is calculated for, always Spin.All. Spin.All
spinProjection(spin=None)

Construct a new GridValues object with the values of this object projected on a given spin component.

Parameters: spin (Spin.All | Spin.Sum | Spin.X | Spin.Y | Spin.Z) – The spin component to project on. Default: Spin.All A new GridValues object for the specified spin. GridValues
toArray()
Returns: The values of the grid as a numpy array slicing off any units. numpy.array
unit()
Returns: The unit of the data in the grid. A physical unit.
unitCell()
Returns: The unit cell of the grid. PhysicalQuantity of type length.
volumeElement()
Returns: The volume element of the grid represented by three vectors. PhysicalQuantity of type length.

## Usage Examples¶

Calculate the external potential and save it to a file:

# Set up configuration
molecule_configuration = MoleculeConfiguration(
elements=[Nitrogen, Hydrogen, Hydrogen, Hydrogen],
cartesian_coordinates=[[ 6.13508 ,  5.790587,  2.75    ],
[ 6.13508 ,  6.73176 ,  2.336663],
[ 6.95016 ,  5.32    ,  2.336663],
[ 5.32    ,  5.32    ,  2.336663]]*Angstrom
)

# Add metallic regions (without them the external potential would be constant)
metallic_region_0 = BoxRegion(
0*Volt,
xmin = 0*Angstrom, xmax = 12*Angstrom,
ymin = 0*Angstrom, ymax = 12*Angstrom,
zmin = 0*Angstrom, zmax = 1*Angstrom
)

metallic_region_1 = BoxRegion(
1*Volt,
xmin = 0*Angstrom, xmax = 12*Angstrom,
ymin = 0*Angstrom, ymax = 12*Angstrom,
zmin = 5*Angstrom, zmax = 6*Angstrom
)

metallic_regions = [metallic_region_0, metallic_region_1]
molecule_configuration.setMetallicRegions(metallic_regions)

# Define the calculator
calculator = HuckelCalculator()
molecule_configuration.setCalculator(calculator)

# Calculate and save the effective potential
external_potential = ExternalPotential(molecule_configuration)
nlsave('results.nc', molecule_configuration)
nlsave('results.nc', external_potential)


nh3_external_potential.py

For examples on working with 3D grids, see HartreePotential and ElectronDensity.

## Notes¶

• This class inherits from the GridValues class.
• Returns the electrostatic potential due to the electrodes and gates in the system. Note that other external electrostatic potentials, e.g. from pseudopotentials, are not included.
• See External potential (for ATK-DFT calculators) or Tight-binding total energy (for ATK-SE calculators) for more information on the theoretical background.