Crystal Class Reference

Object to store the information on the crystal unit cell, such as atomic positions, crystal lattice vectors, etc... More...

#include <crystal.h>

Public Member Functions
	Crystal (Context &context, Eigen::Matrix3d &directUnitCell_, Eigen::MatrixXd &atomicPositions_, Eigen::VectorXi &atomicSpecies_, std::vector< std::string > &speciesNames_, Eigen::VectorXd &speciesMasses_, Eigen::Tensor< double, 3 > &bornCharges_, Eigen::Matrix3d &dielectricMatrix)
	Class containing the information on the crystal structure Note: a number of important quantities used throughout the code are referenced here, so check if it does go out of scope. More...
	Crystal ()
	Empty constructor.
	Crystal (const Crystal &obj)
	Copy constructor.
Crystal &	operator= (const Crystal &obj)
	Copy assignment operator.
void	print () const
	Print the crystal information.
const Eigen::Matrix3d &	getDirectUnitCell ()
	Returns the crystal unit cell in real space, in Bohr. More...
const Eigen::Matrix3d &	getReciprocalUnitCell ()
	Returns the reciprocal lattice vectors, in units of Bohr^-1/tpi. More...
const int &	getNumAtoms ()
	get the number of atoms in the unit cell
const Eigen::Tensor< double, 3 >	getBornEffectiveCharges ()
	Return the born effective charges for the crystal object.
const Eigen::Matrix3d	getDielectricMatrix ()
	Return the dielectric matrix for the crystal object. More...
double	getVolumeUnitCell (int dimensionality_=3) const
	get the volume of the crystal unit cell in Bohr^3 More...
const std::vector< SymmetryOperation > &	getSymmetryOperations ()
	get the symmetry operations of the crystal, in cartesian coordinates. More...
int	getNumSymmetries () const
	get the number of symmetries operations that are used by phoebe. More...
const Eigen::MatrixXd &	getAtomicPositions ()
	get the atomic positions, in cartesian coordinates we return an array of size (numAtoms,3)
const Eigen::VectorXi &	getAtomicSpecies ()
	get the species of each atom in the unit cell. More...
const std::vector< std::string > &	getAtomicNames ()
	get the vector of atomic names vector has size (numAtoms)
const Eigen::VectorXd &	getAtomicMasses ()
	get the vector of atomic masses the vector has size (numAtoms)
const std::vector< std::string > &	getSpeciesNames ()
	get the vector of names of atomic species the vector has size (numSpecies)
const Eigen::VectorXd &	getSpeciesMasses ()
	get the vector of masses of atomic species, in rydberg the vector has size (numSpecies)
int	getDimensionality () const
	return the dimensionality of the crystal, i.e. More...
int	getNumSpecies () const
	Return the number of atomic species present in the crystal.
const Eigen::VectorXd &	getAtomicIsotopeCouplings ()
Eigen::Vector3d	crystalToCartesian (const Eigen::Vector3d &point)
	Change of basis method to convert crystal wavevector to cartesian coordinates. More...
Eigen::Vector3d	cartesianToCrystal (const Eigen::Vector3d &point)
	Change of basis method to convert crystal wavevector to cartesian coordinates. More...
std::tuple< Eigen::MatrixXd, Eigen::VectorXd >	buildWignerSeitzVectors (const Eigen::Vector3i &grid, const int &superCellFactor=2)
	Build the list of Bravais lattice vectors (real space) that live within the Wigner Seitz zone of a super cell which is grid(0) x grid(1) x grid(2) bigger than the unitCell. More...
std::tuple< Eigen::MatrixXd, Eigen::Tensor< double, 3 > >	buildWignerSeitzVectorsWithShift (const Eigen::Vector3i &grid, const Eigen::MatrixXd &shift, const int &superCellFactor=2)
	Similar to buildWignerSeitzVectors, we build the list of Bravais lattice vectors (real space) that live within the Wigner Seitz zone of a super cell which is grid(0) x grid(1) x grid(2) bigger than the unitCell. More...
void	generateSymmetryInformation (Context &context)
	A function to set up the symmetry rotation matrices for a crystal, which are then stored in this object.

Protected Member Functions
void	setDirectUnitCell (const Eigen::Matrix3d &directUnitCell_)
	Internal utility to set the crystal unit cell and the reciprocal cell.

Static Protected Member Functions
static Eigen::Matrix3d	calcReciprocalCell (const Eigen::Matrix3d &directUnitCell)
	utility function to invert the direct unit cell

Protected Attributes
Eigen::Matrix3d	directUnitCell
	These are the internal quantities used to store. More...
Eigen::Matrix3d	reciprocalUnitCell
double	volumeUnitCell
int	numAtoms
int	numSpecies
int	dimensionality
Eigen::MatrixXd	atomicPositions
Eigen::VectorXi	atomicSpecies
std::vector< std::string >	atomicNames
Eigen::VectorXd	atomicMasses
Eigen::VectorXd	atomicIsotopeCouplings
Eigen::Tensor< double, 3 >	bornCharges
Eigen::Matrix3d	dielectricMatrix
std::vector< std::string >	speciesNames
Eigen::VectorXd	speciesMasses
Eigen::VectorXd	speciesIsotopeCouplings
std::vector< SymmetryOperation >	symmetryOperations
int	numSymmetries

Detailed Description

Note that fractional occupancies are not supported.

Constructor & Destructor Documentation

Crystal()

Crystal::Crystal	(	Context &	context,
		Eigen::Matrix3d &	directUnitCell_,
		Eigen::MatrixXd &	atomicPositions_,
		Eigen::VectorXi &	atomicSpecies_,
		std::vector< std::string > &	speciesNames_,
		Eigen::VectorXd &	speciesMasses_,
		Eigen::Tensor< double, 3 > &	bornCharges_,
		Eigen::Matrix3d &	dielectricMatrix
	)

Parameters

directUnitCell	a matrix containing the crystal lattice vectors in Bohr.
atomicPositions(numAtoms,3)	list of atomic positions in cartesian coordinates.
atomicSpecies(numAtoms)	list of integers identifying the species of each atom.
speciesNames(numSpecies)	list of names of species. The position should match the indices of the parameter atomicSpecies.
speciesMasses(numSpecies)	array with the masses of each species, in rydberg.

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Member Function Documentation

buildWignerSeitzVectors()

std::tuple< Eigen::MatrixXd, Eigen::VectorXd > Crystal::buildWignerSeitzVectors	(	const Eigen::Vector3i &	grid,
		const int &	superCellFactor = 2
	)

Parameters

grid	size of the super cell for the WS construction.
superCellFactor	in order to do the correct folding of wavevectors, we look for wavevectors in a slightly bigger super cell. A factor 2 should be enough, but could be increased if the code fails to find all vectors.

Returns

: a tuple with bravaisLatticeVectors(3,numVectors) in cartesian coordinates and their degeneracies(numVectors). Note: the weights to be used for integrations are 1/degeneracies.

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buildWignerSeitzVectorsWithShift()

std::tuple< Eigen::MatrixXd, Eigen::Tensor< double, 3 > > Crystal::buildWignerSeitzVectorsWithShift	(	const Eigen::Vector3i &	grid,
		const Eigen::MatrixXd &	shift,
		const int &	superCellFactor = 2
	)

However, the vectors are slightly shifted. For example, for phonons, we want the vectors R+tau(3,na)-tau(3,nb), where tau are atomic positions. A similar transform may be used for the Wannier transformation, where the WS is centered on the Wannier-functions' centers.

Note: for a well-converged calculation, the difference between with and without shift shouldn't make a difference when used in Fourier transforms. This is because the interactions should decay quickly.

Parameters

grid	size of the super cell for the WS construction.
shift	a shift in cartesian coordinates of shape(3,nDim).
superCellFactor	in order to do the correct folding of wavevectors, we look for wavevectors in a slightly bigger super cell. A factor 2 should be enough, but could be increased if the code fails to find all vectors.

Returns

: a tuple with bravaisLatticeVectors(3,numVectors) in cartesian coordinates and their degeneracies(numVectors,nDim,nDim), where the last two indices must be used in conjunction with the meaning of shift. Some weights might be set to zero if they don't fall in the WS zone. Note: the weights to be used for integrations are 1/degeneracies.

cartesianToCrystal()

Eigen::Vector3d Crystal::cartesianToCrystal

(

const Eigen::Vector3d &

point

)

Parameters

point

a point in cartesian coordinates

Returns

the point in crystal coordiantes

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crystalToCartesian()

Eigen::Vector3d Crystal::crystalToCartesian

(

const Eigen::Vector3d &

point

)

Parameters

point

a point in crystal coordinates

Returns

the point in cartesian coordiantes

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getAtomicSpecies()

const Eigen::VectorXi & Crystal::getAtomicSpecies

(

)

The atomic species are simply identified by an integer id The vector returned has size (numAtoms)

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getDielectricMatrix()

const Eigen::Matrix3d Crystal::getDielectricMatrix ( )

inline

Returns

dielectricMatrix: crystal structure's dielectric matrix. Zero if non-polar

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getDimensionality()

int Crystal::getDimensionality

(

)

const

a number from 1 to 3

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getDirectUnitCell()

const Eigen::Matrix3d & Crystal::getDirectUnitCell

(

)

Lattice vectors are rows (e.g. a0 = cell.row(0), ...)

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getNumSymmetries()

int Crystal::getNumSymmetries

(

)

const

For the time being, we only retain symmetry operations that don't use a translation.

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getReciprocalUnitCell()

const Eigen::Matrix3d & Crystal::getReciprocalUnitCell

(

)

Lattice vectors are rows (e.g. a0 = cell.row(0), ...) must be multiplied by twoPi to be complete

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getSymmetryOperations()

const std::vector< SymmetryOperation > & Crystal::getSymmetryOperations

(

)

Returns a vector of SymmetryOperation. A SymmetryOperation is a structure containing the rotation matrix and the translation vector for the given symmetry. The size of the vector is equal to getNumSymmetries().

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getVolumeUnitCell()

double Crystal::getVolumeUnitCell

(

int

dimensionality_ = 3

)

const

Parameters

dimensionality

returns the volume of the unit cell on a reduced dimensionality. If 2D, it is ASSUMED that the z-direction is the non periodic direction. If 1D, it's assumed that z is the periodic direction

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Member Data Documentation

directUnitCell

Eigen::Matrix3d Crystal::directUnitCell

protected

• lattice vectors
• reciprocal lattice vectors
• (real space) crystal unit cell volume
• number of atoms in unit cell
• number of atomic species in the crystal
• dimensionality (to log whether we work in 1, 2, or 3D.