Parameters for calculating bandStructure

Parameters here are for band structure calculations.

calculation.bandStructure.crystalStructure

key word	:	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.
		zero dimensional system:
		0D is for a molecular system.
		one dimensional system:
		1D is for a system extended along the third
		direction defined in the unitCellVectors.
		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.
		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

key word	:	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.primitiveCellVectors

key word	:	calculation.bandStructure.primitiveCellVectors
possible values	:	3\(\times\)3 or 1\(\times\)6 or 1\(\times\)3 double matrix
default value	:	determined by nanodcal
description	:	The matrix format of the calculated Hamiltonian depends
		on the central cell chosen in the calculation. Normally
		the central cell is a supercell, and one needs
		primitiveCellVectors to convert the Hamiltonian
		matrix in the format of the super cell to that of the
		primitive cell. See also the description of
		system.centralCellVectors.
		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.
an example	:	calculation.bandStructure.primitiveCellVectors = …
		[0 1 1; 1 0 1; 1 1 0]/2*10.2612164268616

calculation.bandStructure.symmetryKPoints

key word	:	calculation.bandStructure.symmetryKPoints
possible values	:	cell array of a combination of the following commonly
		used symbols:
		G for bandStructure.crystalStructure = 0D;
		G, X, for 1D;
		G, M, K, for 2D HEXAGON;
		G, M, X, for 2D SQUARE;
		G, X, M, R, for SC;
		G, X, W, L, K, for FCC;
		G, H, N, P, for BCC;
		G, M, K, A, L for HCP;
		or user defined symbols.
default value	:	{G} for bandStructure.crystalStructure = 0D;
		{G, X} for 1D;
		{G, M, K, G} for 2D HEXAGON;
		{G, X, M, G} for 2D SQUARE;
		{G, X, M, G, R, X} for SC;
		{G, X, W, L, G, K, X} for FCC;
		{G, H, N, P, G, N} for BCC;
		{G, M, K, G, A, L} for HCP;
		{A, B, C, D, …} for other structures or
		coordinatesOfTheSymmetryKPoints is given.
description	:	Each symbol in the cell array corresponds to a high
		symmetry k-point for the given crystal structure. The
		band structure will be calculated along the line
		segments which connect those high symmetry points one
		by one, from the first all the way to the last.
		Please note that for other symbols not listed above,
		the parameter coordinatesOfTheSymmetryKPoints must be
		given explicitly.
an example	:	calculation.bandStructure.symmetryKPoints = …
		{G X W L G K X}
		calculation.bandStructure.symmetryKPoints = …
		{A B C D}

calculation.bandStructure.coordinatesOfTheSymmetryKPoints

key word	:	calculation.bandStructure.coordinatesOfTheSymmetryKPoints
possible values	:	3\(\times\)n double array where n is the number of symmetry
		k-points defined in bandStructure.symmetryKPoints.
default value	:	calculated by nanodcal for those listed structures and
		listed symmetry points. No default value for other
		structures or high symmetry points.
description	:	The k-space fractional coordinates of those high
		symmetry k-points listed in symmetryKPoints, each
		column corresponds to one of them.
		For a k-point with coordinates k1, k2, and k3, the
		corresponding k-vector is
		k-vector = k1\(\times\)b1 + k2\(\times\)b2 + k3\(\times\)b3,
		where b1, b2, and b3 are defined through
		dot(b_i, a_j) = 2\(\pi\)\(\times\)\(\delta_{ij}\),
		and a1, a2, a3 are the unit cell vectors defined
		in unitCellVectors.
		Please note that this parameter must be given explicitly
		if either the crystal structures or any of the high
		symmetry k-points is not among those listed above.
		Note also that the unit cell vectors, normally, can not
		be uniquely determined by nanodcal. Therefore it is
		recommended to input the parameter unitCellVectors
		explicitly when coordinatesOfTheSymmetryKPoints is
		used explicitly.
an example	:	calculation …
		.bandStructure.coordinatesOfTheSymmetryKPoints …
		= [0 0 0; 1 0 0; 0 1 0; 0 0 1]/2

calculation.bandStructure.numberOfKPoints

key word	:	calculation.bandStructure.numberOfKPoints
possible values	:	an integer or an integer array
default value	:	determined using the value of
		bandStructure.kInterval
description	:	If an integer, it is the total number of k points
		(including the two end points) used to represent the
		entire band structure. If an integer array, the number
		of k points (including the two end points) used to
		represent each section of the band structure between
		those high symmetry points.
an example	:	calculation.bandStructure.numberOfKPoints = 100

calculation.bandStructure.kInterval

key word	:	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.isProjected

key word	:	calculation.bandStructure.isProjected
possible values	:	true or false
default value	:	false
description	:	If true, the contributions of the orbitals to the band
		states will be calculated.
an example	:	calculation.bandStructure.isProjected = true

calculation.bandStructure.plot

key word	:	calculation.bandStructure.plot
possible values	:	true or false
default value	:	false
description	:	If true, a plot will be given after the calculation.
an example	:	calculation.bandStructure.plot = true

calculation.bandStructure.eMin

key word	:	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

key word	:	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