RealSpaceSelfEnergyPDOS¶
- class RealSpaceSelfEnergyPDOS(configuration, primitive_configuration, kpoints=None, energies=None, infinitesimal=None, projections=None, primitive_layer_extensions=None, automatic_primitive_layer_extensions=True, use_recursive_method=None)¶
- Parameters:
configuration (
BulkConfiguration) – The configuration of the supercell with attached calculator for which to calculate the projected DOS.primitive_configuration (
BulkConfiguration) – The configuration to be used for self-energy calculations.kpoints – The k-points for which to calculate the projected density of states. The kpoints are used to sample the real-space self-energy for the primitive configuration in the A- and B directions only. Default: KpointDensity(30 * Ang)
energies (PhysicalQuantity of type energy) – The energies for which to calculate the projected density of states. The energies are relative to the Fermi energy of the primitive configuration. Default:
numpy.linspace(-1.0, 1.0, 101) * eVinfinitesimal (PhysicalQuantity of type energy.) – Small positive energy, used to move the transmission calculation away from the real axis. Default:
1.0e-4*eVprojections (list of
Projection|Projection|ProjectionGenerator) – The projections used for the calculating the weights. Default:ProjectOnElements.primitive_layer_extensions – The number of times the primitive cell is repeated inwards. This determines where the self-energy is added to the configuration. Given as a list of int for A, B, and C direction.
automatic_primitive_layer_extensions (bool) – Boolean controlling if the primitive_layer_extensions should be determined automatically based on the range of the Hamiltonian.
use_recursive_method (bool) – Boolean to determine if the recursive method should be used or not.
- automaticPrimitiveLayerExtensions()¶
- Returns:
Boolean determining if the recursive method should be used or not.
- Return type:
bool.
- bandsAboveFermiLevel()¶
- Returns:
The number of bands above the Fermi level per principal spin channel.
- Return type:
int
- densityOfStates(normalization=None)¶
Returns the possible normalized density of states.
- Parameters:
normalization (False` | NormalizeByVolume() | NormalizeByNumberOfAtoms()) – Normalization scheme to use for the DOS. Default:
False- Returns:
The full density of states as a vector of the length of the number of energies.
- Return type:
PhysicalQuantity of type reciprocal energy
- directBandGap()¶
- Returns:
The direct band gap.
- Return type:
PhysicalQuantity of type energy
- energies()¶
- Returns:
The energies.
- Return type:
PhysicalQuantity of type energy
- energyZero()¶
- Returns:
The energy zero.
- Return type:
PhysicalQuantity of type energy.
- evaluate(projection_index=None, normalization=None)¶
The projected density of states for a given projection.
- Parameters:
projection_index (int) – The index of the projection to query the projected density of states for. Negative indexing can be used such that e.g. projection_index=-1 will return the projected density of states for the last projection. Default: The projected density of states for each projection is returned.
normalization (False` | NormalizeByVolume() | NormalizeByNumberOfAtoms()) – Normalization scheme to use for the DOS. Default:
False
- Returns:
The projected density of states as a vector of the length of the number of energies, e. If
projection_indexis not specified, an array of shape (p, e) is returned, where p is the number of projections.- Return type:
PhysicalQuantity of type reciprocal energy
- fermiLevel(spin=None)¶
- Parameters:
spin (
Spin.Up|Spin.Down|Spin.All) – The spin the Fermi level should be returned for. Must be eitherSpin.Up,Spin.Down, orSpin.All. Only when the band structure is calculated with a fixed spin moment will the Fermi level depend on spin. Default:Spin.Up- Returns:
The Fermi level in absolute energy.
- Return type:
PhysicalQuantityof type energy
- indirectBandGap()¶
- Returns:
The indirect band gap.
- Return type:
PhysicalQuantity of type energy
- infinitesimal()¶
- Returns:
The imaginary energy part.
- Return type:
PhysicalQuantity of type energy
- kpoints()¶
- Returns:
The k-point sampling used for calculating the projected density of states.
- Return type:
- metatext()¶
- Returns:
The metatext of the object or None if no metatext is present.
- Return type:
str | None
- nlinfo()¶
- Returns:
Structured information about the PDOS.
- Return type:
dict
- 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()
- primitiveLayerExtensions()¶
- Returns:
The number of times the primitive cell is repeated inwards. This determines where the self-energy is added to the configuration.
- Return type:
int
- projections()¶
- Returns:
The projections used for the calculated projected density of states.
- Return type:
list of class:~.Projection | class:~.Projection
- setMetatext(metatext)¶
Set a given metatext string on the object.
- Parameters:
metatext (str | None) – The metatext string that should be set. A value of “None” can be given to remove the current metatext.
- uniqueString()¶
Return a unique string representing the state of the object.
- useRecursiveMethod()¶
- Returns:
Boolean determining if the recursive method should be used or not.
- Return type:
bool.
Usage Examples¶
Calculate the RealSpaceSelfEnergyPDOS for a graphene sheet with a Stone-Wales defect in the middle.
# Set up lattice
lattice = SimpleOrthorhombic(4.26258*Angstrom, 15.0*Angstrom, 4.922*Angstrom)
# Define elements
elements = [Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon]
# Define coordinates
fractional_coordinates = [[ 0.083333333333, 0.5 , 0.124999739368],
[ 0.083333333333, 0.5 , 0.625000086877],
[ 0.416666666667, 0.5 , 0.124999739368],
[ 0.416666666667, 0.5 , 0.625000086877],
[ 0.583333333333, 0.5 , 0.374999913123],
[ 0.583333333333, 0.5 , 0.875000260632],
[ 0.916666666667, 0.5 , 0.374999913123],
[ 0.916666666667, 0.5 , 0.875000260632]]
# Set up configuration
primitive_configuration = BulkConfiguration(
bravais_lattice=lattice,
elements=elements,
fractional_coordinates=fractional_coordinates
)
# %% SemiEmpiricalCalculator
hamiltonian_parametrization = SlaterKosterHamiltonianParametrization(
basis_set=Hancock.C_Basis)
k_point_sampling = KpointDensity(
density_a=4.0*Angstrom,
density_b=4.0*Angstrom,
density_c=4.0*Angstrom
)
numerical_accuracy_parameters = NumericalAccuracyParameters(
k_point_sampling=k_point_sampling
)
calculator = SemiEmpiricalCalculator(
hamiltonian_parametrization=hamiltonian_parametrization,
numerical_accuracy_parameters=numerical_accuracy_parameters,
checkpoint_handler=NoCheckpointHandler
)
# %% Set Calculator
primitive_configuration.setCalculator(calculator)
primitive_configuration.update()
# Set up lattice
lattice = SimpleOrthorhombic(46.88838*Angstrom, 15.0*Angstrom, 54.141999999999996*Angstrom)
# Define elements
elements = [Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon,
Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon, Carbon]
# Define coordinates
fractional_coordinates = [[ 0.007575757576, 0.5 , 0.01136361267 ],
[ 0.007575757576, 0.5 , 0.056818189716],
[ 0.037878787879, 0.5 , 0.01136361267 ],
[ 0.037878787879, 0.5 , 0.056818189716],
[ 0.05303030303 , 0.5 , 0.034090901193],
[ 0.05303030303 , 0.5 , 0.079545478239],
[ 0.083333333333, 0.5 , 0.034090901193],
[ 0.083333333333, 0.5 , 0.079545478239],
[ 0.007575757576, 0.5 , 0.102272703579],
[ 0.007575757576, 0.5 , 0.147727280625],
[ 0.037878787879, 0.5 , 0.102272703579],
[ 0.037878787879, 0.5 , 0.147727280625],
[ 0.05303030303 , 0.5 , 0.124999992102],
[ 0.05303030303 , 0.5 , 0.170454569148],
[ 0.083333333333, 0.5 , 0.124999992102],
[ 0.083333333333, 0.5 , 0.170454569148],
[ 0.007575757576, 0.5 , 0.193181794488],
[ 0.007575757576, 0.5 , 0.238636371534],
[ 0.037878787879, 0.5 , 0.193181794488],
[ 0.037878787879, 0.5 , 0.238636371534],
[ 0.05303030303 , 0.5 , 0.215909083011],
[ 0.05303030303 , 0.5 , 0.261363660057],
[ 0.083333333333, 0.5 , 0.215909083011],
[ 0.083333333333, 0.5 , 0.261363660057],
[ 0.007575757576, 0.5 , 0.284090885397],
[ 0.007575757576, 0.5 , 0.329545462443],
[ 0.037878787879, 0.5 , 0.284090885397],
[ 0.037878787879, 0.5 , 0.329545462443],
[ 0.05303030303 , 0.5 , 0.30681817392 ],
[ 0.05303030303 , 0.5 , 0.352272750967],
[ 0.083333333333, 0.5 , 0.30681817392 ],
[ 0.083333333333, 0.5 , 0.352272750967],
[ 0.007575757576, 0.5 , 0.374999976306],
[ 0.007575757576, 0.5 , 0.420454553352],
[ 0.037878787879, 0.5 , 0.374999976306],
[ 0.037878787879, 0.5 , 0.420454553352],
[ 0.05303030303 , 0.5 , 0.397727264829],
[ 0.05303030303 , 0.5 , 0.443181841876],
[ 0.083333333333, 0.5 , 0.397727264829],
[ 0.083333333333, 0.5 , 0.443181841876],
[ 0.007575757576, 0.5 , 0.465909067215],
[ 0.007575757576, 0.5 , 0.511363644262],
[ 0.037878787879, 0.5 , 0.465909067215],
[ 0.037878787879, 0.5 , 0.511363644262],
[ 0.05303030303 , 0.5 , 0.488636355738],
[ 0.05303030303 , 0.5 , 0.534090932785],
[ 0.083333333333, 0.5 , 0.488636355738],
[ 0.083333333333, 0.5 , 0.534090932785],
[ 0.007575757576, 0.5 , 0.556818158124],
[ 0.007575757576, 0.5 , 0.602272735171],
[ 0.037878787879, 0.5 , 0.556818158124],
[ 0.037878787879, 0.5 , 0.602272735171],
[ 0.05303030303 , 0.5 , 0.579545446648],
[ 0.05303030303 , 0.5 , 0.625000023694],
[ 0.083333333333, 0.5 , 0.579545446648],
[ 0.083333333333, 0.5 , 0.625000023694],
[ 0.007575757576, 0.5 , 0.647727249033],
[ 0.007575757576, 0.5 , 0.69318182608 ],
[ 0.037878787879, 0.5 , 0.647727249033],
[ 0.037878787879, 0.5 , 0.69318182608 ],
[ 0.05303030303 , 0.5 , 0.670454537557],
[ 0.05303030303 , 0.5 , 0.715909114603],
[ 0.083333333333, 0.5 , 0.670454537557],
[ 0.083333333333, 0.5 , 0.715909114603],
[ 0.007575757576, 0.5 , 0.738636339943],
[ 0.007575757576, 0.5 , 0.784090916989],
[ 0.037878787879, 0.5 , 0.738636339943],
[ 0.037878787879, 0.5 , 0.784090916989],
[ 0.05303030303 , 0.5 , 0.761363628466],
[ 0.05303030303 , 0.5 , 0.806818205512],
[ 0.083333333333, 0.5 , 0.761363628466],
[ 0.083333333333, 0.5 , 0.806818205512],
[ 0.007575757576, 0.5 , 0.829545430852],
[ 0.007575757576, 0.5 , 0.875000007898],
[ 0.037878787879, 0.5 , 0.829545430852],
[ 0.037878787879, 0.5 , 0.875000007898],
[ 0.05303030303 , 0.5 , 0.852272719375],
[ 0.05303030303 , 0.5 , 0.897727296421],
[ 0.083333333333, 0.5 , 0.852272719375],
[ 0.083333333333, 0.5 , 0.897727296421],
[ 0.007575757576, 0.5 , 0.920454521761],
[ 0.007575757576, 0.5 , 0.965909098807],
[ 0.037878787879, 0.5 , 0.920454521761],
[ 0.037878787879, 0.5 , 0.965909098807],
[ 0.05303030303 , 0.5 , 0.943181810284],
[ 0.05303030303 , 0.5 , 0.98863638733 ],
[ 0.083333333333, 0.5 , 0.943181810284],
[ 0.083333333333, 0.5 , 0.98863638733 ],
[ 0.098484848485, 0.5 , 0.01136361267 ],
[ 0.098484848485, 0.5 , 0.056818189716],
[ 0.128787878788, 0.5 , 0.01136361267 ],
[ 0.128787878788, 0.5 , 0.056818189716],
[ 0.143939393939, 0.5 , 0.034090901193],
[ 0.143939393939, 0.5 , 0.079545478239],
[ 0.174242424242, 0.5 , 0.034090901193],
[ 0.174242424242, 0.5 , 0.079545478239],
[ 0.098484848485, 0.5 , 0.102272703579],
[ 0.098484848485, 0.5 , 0.147727280625],
[ 0.128787878788, 0.5 , 0.102272703579],
[ 0.128787878788, 0.5 , 0.147727280625],
[ 0.143939393939, 0.5 , 0.124999992102],
[ 0.143939393939, 0.5 , 0.170454569148],
[ 0.174242424242, 0.5 , 0.124999992102],
[ 0.174242424242, 0.5 , 0.170454569148],
[ 0.098484848485, 0.5 , 0.193181794488],
[ 0.098484848485, 0.5 , 0.238636371534],
[ 0.128787878788, 0.5 , 0.193181794488],
[ 0.128787878788, 0.5 , 0.238636371534],
[ 0.143939393939, 0.5 , 0.215909083011],
[ 0.143939393939, 0.5 , 0.261363660057],
[ 0.174242424242, 0.5 , 0.215909083011],
[ 0.174242424242, 0.5 , 0.261363660057],
[ 0.098484848485, 0.5 , 0.284090885397],
[ 0.098484848485, 0.5 , 0.329545462443],
[ 0.128787878788, 0.5 , 0.284090885397],
[ 0.128787878788, 0.5 , 0.329545462443],
[ 0.143939393939, 0.5 , 0.30681817392 ],
[ 0.143939393939, 0.5 , 0.352272750967],
[ 0.174242424242, 0.5 , 0.30681817392 ],
[ 0.174242424242, 0.5 , 0.352272750967],
[ 0.098484848485, 0.5 , 0.374999976306],
[ 0.098484848485, 0.5 , 0.420454553352],
[ 0.128787878788, 0.5 , 0.374999976306],
[ 0.128787878788, 0.5 , 0.420454553352],
[ 0.143939393939, 0.5 , 0.397727264829],
[ 0.143939393939, 0.5 , 0.443181841876],
[ 0.174242424242, 0.5 , 0.397727264829],
[ 0.174242424242, 0.5 , 0.443181841876],
[ 0.098484848485, 0.5 , 0.465909067215],
[ 0.098484848485, 0.5 , 0.511363644262],
[ 0.128787878788, 0.5 , 0.465909067215],
[ 0.128787878788, 0.5 , 0.511363644262],
[ 0.143939393939, 0.5 , 0.488636355738],
[ 0.143939393939, 0.5 , 0.534090932785],
[ 0.174242424242, 0.5 , 0.488636355738],
[ 0.174242424242, 0.5 , 0.534090932785],
[ 0.098484848485, 0.5 , 0.556818158124],
[ 0.098484848485, 0.5 , 0.602272735171],
[ 0.128787878788, 0.5 , 0.556818158124],
[ 0.128787878788, 0.5 , 0.602272735171],
[ 0.143939393939, 0.5 , 0.579545446648],
[ 0.143939393939, 0.5 , 0.625000023694],
[ 0.174242424242, 0.5 , 0.579545446648],
[ 0.174242424242, 0.5 , 0.625000023694],
[ 0.098484848485, 0.5 , 0.647727249033],
[ 0.098484848485, 0.5 , 0.69318182608 ],
[ 0.128787878788, 0.5 , 0.647727249033],
[ 0.128787878788, 0.5 , 0.69318182608 ],
[ 0.143939393939, 0.5 , 0.670454537557],
[ 0.143939393939, 0.5 , 0.715909114603],
[ 0.174242424242, 0.5 , 0.670454537557],
[ 0.174242424242, 0.5 , 0.715909114603],
[ 0.098484848485, 0.5 , 0.738636339943],
[ 0.098484848485, 0.5 , 0.784090916989],
[ 0.128787878788, 0.5 , 0.738636339943],
[ 0.128787878788, 0.5 , 0.784090916989],
[ 0.143939393939, 0.5 , 0.761363628466],
[ 0.143939393939, 0.5 , 0.806818205512],
[ 0.174242424242, 0.5 , 0.761363628466],
[ 0.174242424242, 0.5 , 0.806818205512],
[ 0.098484848485, 0.5 , 0.829545430852],
[ 0.098484848485, 0.5 , 0.875000007898],
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[ 0.856060606061, 0.5 , 0.738636339943],
[ 0.856060606061, 0.5 , 0.784090916989],
[ 0.871212121212, 0.5 , 0.761363628466],
[ 0.871212121212, 0.5 , 0.806818205512],
[ 0.901515151515, 0.5 , 0.761363628466],
[ 0.901515151515, 0.5 , 0.806818205512],
[ 0.825757575758, 0.5 , 0.829545430852],
[ 0.825757575758, 0.5 , 0.875000007898],
[ 0.856060606061, 0.5 , 0.829545430852],
[ 0.856060606061, 0.5 , 0.875000007898],
[ 0.871212121212, 0.5 , 0.852272719375],
[ 0.871212121212, 0.5 , 0.897727296421],
[ 0.901515151515, 0.5 , 0.852272719375],
[ 0.901515151515, 0.5 , 0.897727296421],
[ 0.825757575758, 0.5 , 0.920454521761],
[ 0.825757575758, 0.5 , 0.965909098807],
[ 0.856060606061, 0.5 , 0.920454521761],
[ 0.856060606061, 0.5 , 0.965909098807],
[ 0.871212121212, 0.5 , 0.943181810284],
[ 0.871212121212, 0.5 , 0.98863638733 ],
[ 0.901515151515, 0.5 , 0.943181810284],
[ 0.901515151515, 0.5 , 0.98863638733 ],
[ 0.916666666667, 0.5 , 0.01136361267 ],
[ 0.916666666667, 0.5 , 0.056818189716],
[ 0.94696969697 , 0.5 , 0.01136361267 ],
[ 0.94696969697 , 0.5 , 0.056818189716],
[ 0.962121212121, 0.5 , 0.034090901193],
[ 0.962121212121, 0.5 , 0.079545478239],
[ 0.992424242424, 0.5 , 0.034090901193],
[ 0.992424242424, 0.5 , 0.079545478239],
[ 0.916666666667, 0.5 , 0.102272703579],
[ 0.916666666667, 0.5 , 0.147727280625],
[ 0.94696969697 , 0.5 , 0.102272703579],
[ 0.94696969697 , 0.5 , 0.147727280625],
[ 0.962121212121, 0.5 , 0.124999992102],
[ 0.962121212121, 0.5 , 0.170454569148],
[ 0.992424242424, 0.5 , 0.124999992102],
[ 0.992424242424, 0.5 , 0.170454569148],
[ 0.916666666667, 0.5 , 0.193181794488],
[ 0.916666666667, 0.5 , 0.238636371534],
[ 0.94696969697 , 0.5 , 0.193181794488],
[ 0.94696969697 , 0.5 , 0.238636371534],
[ 0.962121212121, 0.5 , 0.215909083011],
[ 0.962121212121, 0.5 , 0.261363660057],
[ 0.992424242424, 0.5 , 0.215909083011],
[ 0.992424242424, 0.5 , 0.261363660057],
[ 0.916666666667, 0.5 , 0.284090885397],
[ 0.916666666667, 0.5 , 0.329545462443],
[ 0.94696969697 , 0.5 , 0.284090885397],
[ 0.94696969697 , 0.5 , 0.329545462443],
[ 0.962121212121, 0.5 , 0.30681817392 ],
[ 0.962121212121, 0.5 , 0.352272750967],
[ 0.992424242424, 0.5 , 0.30681817392 ],
[ 0.992424242424, 0.5 , 0.352272750967],
[ 0.916666666667, 0.5 , 0.374999976306],
[ 0.916666666667, 0.5 , 0.420454553352],
[ 0.94696969697 , 0.5 , 0.374999976306],
[ 0.94696969697 , 0.5 , 0.420454553352],
[ 0.962121212121, 0.5 , 0.397727264829],
[ 0.962121212121, 0.5 , 0.443181841876],
[ 0.992424242424, 0.5 , 0.397727264829],
[ 0.992424242424, 0.5 , 0.443181841876],
[ 0.916666666667, 0.5 , 0.465909067215],
[ 0.916666666667, 0.5 , 0.511363644262],
[ 0.94696969697 , 0.5 , 0.465909067215],
[ 0.94696969697 , 0.5 , 0.511363644262],
[ 0.962121212121, 0.5 , 0.488636355738],
[ 0.962121212121, 0.5 , 0.534090932785],
[ 0.992424242424, 0.5 , 0.488636355738],
[ 0.992424242424, 0.5 , 0.534090932785],
[ 0.916666666667, 0.5 , 0.556818158124],
[ 0.916666666667, 0.5 , 0.602272735171],
[ 0.94696969697 , 0.5 , 0.556818158124],
[ 0.94696969697 , 0.5 , 0.602272735171],
[ 0.962121212121, 0.5 , 0.579545446648],
[ 0.962121212121, 0.5 , 0.625000023694],
[ 0.992424242424, 0.5 , 0.579545446648],
[ 0.992424242424, 0.5 , 0.625000023694],
[ 0.916666666667, 0.5 , 0.647727249033],
[ 0.916666666667, 0.5 , 0.69318182608 ],
[ 0.94696969697 , 0.5 , 0.647727249033],
[ 0.94696969697 , 0.5 , 0.69318182608 ],
[ 0.962121212121, 0.5 , 0.670454537557],
[ 0.962121212121, 0.5 , 0.715909114603],
[ 0.992424242424, 0.5 , 0.670454537557],
[ 0.992424242424, 0.5 , 0.715909114603],
[ 0.916666666667, 0.5 , 0.738636339943],
[ 0.916666666667, 0.5 , 0.784090916989],
[ 0.94696969697 , 0.5 , 0.738636339943],
[ 0.94696969697 , 0.5 , 0.784090916989],
[ 0.962121212121, 0.5 , 0.761363628466],
[ 0.962121212121, 0.5 , 0.806818205512],
[ 0.992424242424, 0.5 , 0.761363628466],
[ 0.992424242424, 0.5 , 0.806818205512],
[ 0.916666666667, 0.5 , 0.829545430852],
[ 0.916666666667, 0.5 , 0.875000007898],
[ 0.94696969697 , 0.5 , 0.829545430852],
[ 0.94696969697 , 0.5 , 0.875000007898],
[ 0.962121212121, 0.5 , 0.852272719375],
[ 0.962121212121, 0.5 , 0.897727296421],
[ 0.992424242424, 0.5 , 0.852272719375],
[ 0.992424242424, 0.5 , 0.897727296421],
[ 0.916666666667, 0.5 , 0.920454521761],
[ 0.916666666667, 0.5 , 0.965909098807],
[ 0.94696969697 , 0.5 , 0.920454521761],
[ 0.94696969697 , 0.5 , 0.965909098807],
[ 0.962121212121, 0.5 , 0.943181810284],
[ 0.962121212121, 0.5 , 0.98863638733 ],
[ 0.992424242424, 0.5 , 0.943181810284],
[ 0.992424242424, 0.5 , 0.98863638733 ]]
# Set up configuration
bulk_configuration = BulkConfiguration(
bravais_lattice=lattice,
elements=elements,
fractional_coordinates=fractional_coordinates
)
# Add tags
bulk_configuration.addTags('5-ring', [399, 481, 485, 488, 490])
bulk_configuration.addTags('6-ring', [397, 399, 402, 404, 406, 488])
bulk_configuration.addTags('6-ring-bulk', [77, 79, 82, 84, 86, 168])
bulk_configuration.addTags('7-ring', [481, 483, 484, 485, 486, 487, 569])
# Add tags
bulk_configuration.setCalculator(calculator)
bulk_configuration.update()
# RealSpaceSelfEnergyPDOS
real_space_self_energy_pdos = RealSpaceSelfEnergyPDOS(
bulk_configuration,
primitive_configuration,
kpoints=MonkhorstPackGrid(1001, 1, 1),
energies=numpy.linspace(-1, 1, 201) * eV,
infinitesimal=2e-3*eV,
primitive_layer_extensions=(1,1,1),
automatic_primitive_layer_extensions=True,
projections=ProjectOnTags,
use_recursive_method=True
)
nlsave('analysis.hdf5', real_space_self_energy_pdos)
Notes¶
The RealSpaceSelfEnergyPDOS object calculates the projected density of states (PDOS) using the real-space self-energy (RSSE) method described in [1]. The method is intended to be used to study the PDOS of isolated defects in an other-wise crystalline environment.
In the RSSE method, the interaction between periodic repeated images is removed such that one obtains the PDOS for a single defect in an infinite crystal. In a normal PDOS calculation performed with the ProjectedDensityOfStates object, the eigen-states and -energies are obtained from repeated super cells containing the defect. The interaction between the periodic images can affect the results and it often requires very large super cells to converge the results to the isolated defect limit.
The RealSpaceSelfEnergyPDOS improves on this since the interactions between periodic images is removed by the use of real-space self energies as explained in [1].
When performing a RealSpaceSelfEnergyPDOS calculation, it is implicitly assumed that the effective potential in the boundary regions of the super-cell are converged to it’s bulk value (except maybe for a rigid energy shift). Before performing the RealSpaceSelfEnergyPDOS calculation it is advised to inspect the EffectivePotential or HartreeDifferencePotential to assure that the potential in the boundary regions is converged. This it particularly important in systems where a significant charge transfer takes place around the defect.
System setup and k-point sampling¶
When performing a RealSpaceSelfEnergyPDOS calculation there are some particular requirements to how the configuration is setup and in which directions it is needed to perform k-point averaging.
The self-energy is calculated from the provided primitive configuration.
The configuration containing the defect must have a unit cell, which is an integer repetition of the primitive configuration.
The configuration containing the defect must have a boundary region, where the atoms are in the same positions as the repeated primitive configuration. In practice it is advised to setup the configuration containing the defect in the following steps (see figure below):
Start with the primitive configuration for the bulk host material.
Repeat the primitive configuration a suitable number of times in the desired directions.
Create the defect of interest in the center of the repeated configuration.
Optimize the geometry while constraining the atoms in the boundary region (usually 1-2 repetitions of the primitive configuration).
The configuration must always be extended along the C-direction as this is the axis along which the self-energy is being calculated initially. This is similar to a NEGF calculation for a DeviceConfiguration. The C-direction is thus treated as a truly infinite direction and no k-point sampling is needed along the C-axis.
k-point averaging should be performed along the other extended directions. In the graphene example above the graphene sheet is extended in the (A,C) plane and the RealSpaceSelfEnergyPDOS must therefore be k-point sampled along the A-direction only.
The required number of k-points depends on the configuration and on the infinitesimal input. The infinitesimal is similar to a Gaussian broadening in ProjectedDensityOfStates. The most accurate results are obtained for high k-point sampling and small infinitesimal.
Fig. 170 Illustration of primitive configuration and configuration with the defect from the usage example above.¶