Real space grid parameters
The parameters here are for generating real space numerical grids.
calculation.realspacegrids.number
keyword: calculation.realspacegrids.number
possible values: 3 x 1 integer vector or a integer number
default value: determined from the value of realspacegrids.E_cutoff
description: the small grid number in each direction. It is used to divide the central cell into the input number of small grids.
an example:
calculation.realspacegrids.number = [64 64 64]'
calculation.realspacegrids.E_cutoff
keyword: calculation.realspacegrids.E_cutoff
possible values: a double number with proper energy unit such as ‘eV’, ‘Ryd’, ‘Ryd.’, ‘Rydberg’, ‘au’, ‘a.u.’, ‘atomic unit’, ‘Hartree’, where ‘au’ ‘a.u.’, and ‘atomic unit’ are for Hartree, ‘Ryd’, ‘Ryd.’ for Rydberg.
default value: 20, 50, or 150 Hartree, depending on the value of the parameter calculation.control.precision.
description: the equivalent energy cut-off of the grid density. E_cutoff ~ (1/2)(pi/grid_length)^2. This input parameter is not used when realspacegrids.number is given. Note that if the number part of the input is missing, it will be considered as 1, and if the unit part is missing, it will be considered to use the unit defined by calculation.control.energyUnit.
an example:
calculation.realspacegrids.E_cutoff = 50
calculation.bandStructure.crystalStructure
keyword: calculation.bandStructure.crystalStructure
possible values: 0D, 1D, HEXAGON, SQUARE SC, FCC, BCC, HCP or any other string representing another / new structure
default value: determined by nanodcal
description: the crystal structure of the system. (1) zero dimensional system: 0D is for a molecular system. (2) one dimensional system: 1D is for a system extended along the third direction defined in the unitCellVectors. (3) two dimensional system: the system extended along the first and second direction defined in the unitCellVectors. HEXAGON is for a system whose unit cell has a hexagonal shape, e.g. graphene. SQUARE is a for a system whose unit cell has a square shape. (4) three dimensional system: SC stands for simple cubic structure; FCC for face center cubic structure; BCC for body center cubic structure, HCP for hexagonal close-packing structure.
Please note that for other structures not listed above, the parameter coordinatesOfTheSymmetryKPoints must be given explicitly.
an example:
calculation.bandStructure.crystalStructure = FCC
calculation.bandStructure.unitCellVectors
keyword: calculation.bandStructure.unitCellVectors
possible values: 3\(\times\)3 or 1\(\times\)6 or 1\(\times\)3 double matrix
default value: determined by nanodcal
description: The band structure will be calculated along line segments connecting some symmetry points in k-space. The coordinates of those symmetry points are, in convention, defined based on the unit cell. The unitCellVectors will be used to calculate the coordinates of the symmetry k-points.
When the parameter is a 3\(\times\)3 double matrix, its each column forms one of the three basis vectors. When the parameter is a 1\(\times\)6 double matrix, it defines the three basis vectors by giving their lengths, a, b, and c, and the angles between them, alpha, beta, and gamma, with the convention that the a-axis is collinear with the x-axis, and the b-axis lies in the xy-plane. When the parameter is a 1\(\times\)3 double matrix, the alpha, beta, and gamma are all assumed to be \(\pi\)/2.
If the unitCellVectors is to be given, but the coordinatesOfTheSymmetryKPoints is not to be given explicitly, the following are the rules to define the unitCellVectors:
For an 1D structure, the unit cell vector along which the system extends, should be defined as the third vector in the unitCellVectors.
For a 2D HEXAGON structure, the unit cell vectors along which the system extends, should be defined as the first and the second vectors in the unitCellVectors. In addition, the angle between the two vectors should be 60 degrees rather than 120 degrees.
For a 2D SQUARE structure, the unit cell vectors along which the system extends, should be defined as the first and the second vectors in the unitCellVectors.
For a 3D HCP structure, the unit cell vector which is perpendicular to the other two vectors, should be defined as the third vector in the unitCellVectors. In addition, the angle between the first and the second vectors should be 60 degrees rather than 120 degrees.
an example:
calculation.bandStructure.unitCellVectors = ...
eye(3)*10.2612164268616
calculation.bandStructure.kInterval
keyword: calculation.bandStructure.kInterval
possible values: a double number
default value: 0.1
description: the small k-space interval between the k-points which are chosen to represent the band structure. It will help as a reference value to interpolate a integer number of k-points between each pair of two adjacent high symmetry points given in symmetryKPoints. Note that the input value will not be used when numberOfKPoints is given, and its unit is 2\(\pi\)/a for cubic unit cell where a is the unit cell length, or 2\(\pi\)/V\(^{1/3}\) for a general unit cell, where V is the unit cell volume.
an example:
calculation.bandStructure.kInterval = 0.01
calculation.bandStructure.eMin
keyword: calculation.bandStructure.eMin
possible values: a double number
default value: -10 eV
description: minimum energy of the band structure plot.
an example:
calculation.bandStructure.eMin = -30
calculation.bandStructure.eMax
keyword: calculation.bandStructure.eMax
possible values: a double number
default value: 10 eV
description: maximum energy of the band structure plot.
an example:
calculation.bandStructure.eMax = 30