# BlochState¶

class BlochState(configuration=None, quantum_number=None, spin=None, k_point=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]
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 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. 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. 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. 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. 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. The Cartesian coordinate of the given grid index. PhysicalQuantity of type length.
kPoint()
Returns: The k-point to calculate the Bloch state for. list(3) of floats
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.
quantumNumber()
Returns: The quantum number of the desired eigenstate. 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. tuple of three int.
spin()
Returns: The spin the Bloch state is calculated for. 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. 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 and save a Bloch state for a gold FCC crystal:

# 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)


blochstate.py

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