BlochState¶

class BlochState(configuration=None, quantum_number=None, spin=None, k_point=None, density_mesh_cutoff=None)¶

A class for calculating the wave function of a Bloch state.

Parameters:

configuration (BulkConfiguration) – The configuration for which the Bloch state should be calculated. quantum_number (int) – The quantum number of the desired Bloch state. Default: 0 spin (Spin.Up | Spin.Down | Spin.All) – The spin to calculate the Bloch state for. Default: Spin.All k_point (list(3) of floats) – The k-point in fractional coordinates that the Bloch state should be calculated for. Default: [0.0, 0.0, 0.0] density_mesh_cutoff (PhysicalQuantity of type energy | GridSampling | OptimizedFFTGridSampling) – The mesh cutoff to be used to determine the grid sampling. The mesh cutoff must be a positive energy or a GridSampling object. Default: Specific for each calculator.

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 grid 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
Returns:	A 2-tuple of 1D numpy.arrays containing the axis values and the projected data. For Cartesian coordinate type the grid offset is added to the axis values.
Return type:	tuple.

derivatives(x, y, z, spin=None)¶

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

Parameters:	x (PhysicalQuantity of type length) – The Cartesian x coordinate. y (PhysicalQuantity of type length) – The Cartesian y coordinate. z (PhysicalQuantity of type length) – The Cartesian z coordinate. spin (Spin.Up | Spin.Down | Spin.All) – The spin component to project on. Default: The spin of this Bloch state object.
Returns:	The gradient at the specified point for the given spin. For Spin.All, a tuple with (Spin.Up, Spin.Down) components is returned if the calculation is not unpolarized.
Return type:	PhysicalQuantity of type energy-3/2 × length-1

evaluate(x, y, z, spin=None)¶

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

Parameters:	x (PhysicalQuantity of type length) – The Cartesian x coordinate. y (PhysicalQuantity of type length) – The Cartesian y coordinate. z (PhysicalQuantity of type length) – The Cartesian z coordinate. spin (Spin.Up | Spin.Down | Spin.All) – The spin component to project on. Default: The spin of this Bloch state object.
Returns:	The value at the specified point for the given spin. For Spin.All, a tuple with (Spin.Up, Spin.Down) components is returned if the calculation is not unpolarized.
Return type:	PhysicalQuantity of type energy-3/2

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.
Returns:	The Cartesian coordinate of the given grid index.
Return type:	PhysicalQuantity of type length.

kPoint()¶

Returns:	The k-point to calculate the Bloch state for.
Return type:	list(3) of floats

metatext()¶

Returns:	The metatext of the object or None if no metatext is present.
Return type:	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.
Return type:	PhysicalQuantity of type length.

quantumNumber()¶

Returns:	The quantum number of the desired eigenstate.
Return type:	int

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.
Return type:	tuple of three int.

spin()¶

Returns:	The spin the Bloch state is calculated for.
Return type:	Spin.Up | Spin.Down | 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 | Spin.Up | Spin.Down | Spin.RealUpDown | Spin.ImagUpDown) – The spin component to project on. Default: The spin the object was created with. If the spin was Spin.All, Spin.Sum will be used for the projection.
Returns:	A new GridValues object for the specified spin.
Return type:	GridValues

toArray()¶

Returns:	The values of the grid as a numpy array slicing off any units.
Return type:	numpy.array

unit()¶

Returns:	The unit of the data in the grid.
Return type:	A physical unit.

unitCell()¶

Returns:	The unit cell of the grid.
Return type:	PhysicalQuantity of type length.

volumeElement()¶

Returns:	The volume element of the grid represented by three vectors.
Return type:	PhysicalQuantity of type length.

# Define lattice
lattice = FaceCenteredCubic(4.08*Angstrom)

# Define elements
elements = [Gold]

# Define coordinates
coordinates = [[2.0, 2.0, 2.0]]*Angstrom

# Set up configuration
bulk_configuration = BulkConfiguration(
    lattice,
    elements,
    coordinates
    )

# Define a a calculator
bulk_configuration.setCalculator(LCAOCalculator())

# Calculate and save the Bloch state with quantum number 5
bloch_state = BlochState(bulk_configuration, quantum_number=5,
                         k_point=[0.0, 0.5, 0.5])
nlsave('bloch_state.nc', bloch_state)