-
Functions
- GOBands
- GOBondCharges
- GOBonds
- GOBravais
- GOClasses
- GOColorScheme
- GODCMethod
- GODecimals
- GOEigenvectors
- GOGroupOrder
- GOlmax
- GOMolPlot
- GONames
- GOPhPol
- GOSpecMode
- GOTbBasis
- GOTbEquivalence
- GTAbelianQ
- GTAdjacencyMatrix
- GTAllSymbols
- GTAngularMomentumChars
- GTAngularMomentumRep
- GTBands
- GTBandsPlot
- GTBandStructure
- GTBlueRed
- GTBravaisLattice
- GTBSTOperator
- GTBuckyBall
- GTBZPath
- GTBZPointMesh
- GTCartesianSphericalHarmonicY
- GTCartesianTesseralHarmonicY
- GTCFDatabaseInfo
- GTChangeRepresentation
- GTCharacterTable
- GTCharProjectionOperator
- GTClasses
- GTClassMult
- GTClassMultTable
- GTClebschGordanCoefficients
- GTClebschGordanSum
- GTCluster
- GTClusterFilter
- GTClusterManipulate
- GTCompactStore
- GTCrystalData
- GTCrystalField
- GTCrystalFieldParameter
- GTCrystalFieldSplitting
- GTCrystalSystem
- GTCyclicQ
- GTDensityOfStates
- GTDensityOfStatesPlot
- GTDiracMatrix
- GTDirectProductChars
- GTDirectProductRep
- GTEulerAnglesQ
- GTFermiSurface
- GTGenerators
- GTGetEulerAngles
- GTGetIrep
- GTGetMatrix
- GTGetSubGroups
- GTGroupConnection
- GTGroupFromGenerators
- GTGroupGlp
- GTGroupHierarchy
- GTGroupOrder
- GTGroupQ
- GTHamiltonianList
- GTHamiltonianPlot
- GTInstallAxis
- GTInstallGroup
- GTIrep
- GTJminus
- GTJplus
- GTJx
- GTJy
- GTJz
- GTLatCluster
- GTLatShells
- GTLoadStructures
- GTMolChemicalData
- GTMolDatabaseInfo
- GTMolPermutationRep
- GTMolToCluster
- GTMultTable
- GTPhDielectric
- GTPhFields
- GTPhMaster
- GTPhMasterEquation
- GTPhMasterObjects
- GTPhMPBBands
- GTPhMPBFields
- GTPhPixelStructure
- GTPhShowStructure
- GTPhSymmetryBands
- GTPhSymmetryField
- GTPhSymmetryPoint
- GTPlotCluster
- GTPlotStructure
- GTPointGroups
- GTProjectionOperator
- GTPwDatabaseInfo
- GTPwDatabaseRetrieve
- GTPwDielectricF
- GTPwEmptyLatticeIrep
- GTPwHamiltonian
- GTPwModelPotential
- GTPwSymmetrizePW
- GTQAbs
- GTQConjugate
- GTQInverse
- GTQuaternionQ
- GTReadFromFile
- GTReciprocalBasis
- GTReinstallAxes
- GTSaveStructures
- GTSetTableColors
- GTSGCharacterTable
- GTSGClasses
- GTSGCosetRepresentative
- GTSGGetInvSubGroup
- GTSGGetIreps
- GTSGgmat
- GTSGLeftCosets
- GTSGOrderOfElement
- GTSGRightCosets
- GTShells
- GTShellVectorsQlp
- GTSOCSplitting
- GTStevensOperator
- GTStevensTheta
- GTStrucExport
- GTSU2Matrix
- GTSymbolQ
- GTSymmetryBasisFunctions
- GTTbAtomicWaveFunction
- GTTbDatabaseInfo
- GTTbGetParameter
- GTTbHamiltonian
- GTTbHamiltonianElement
- GTTbHamiltonianRS
- GTTbMatrixElement
- GTTbParmExport
- GTTbReadWannier90
- GTTbRealSpaceMatrix
- GTTbSymbol3C
- GTTbSymmetryBands
- GTTbSymmetryBandStructure
- GTTbSymmetryPoint
- GTTbToFortran
- GTTbToFortranList
- GTTbTubeBands
- GTTbWannier90Hamiltonian
- GTTransformation
- GTTransformationOperator
- GTTransformToQlp
- GTTubeParameters
- GTTubeStructure
- GTVibDisplacementRep
- GTVibDynamicalMatrix
- GTVibLatticeModes
- GTVibModeSymmetry
- GTVibSpectroscopy
- GTVoronoiCell
- GTWhichAxes
- GTWhichRepresentation
- GTWriteToFile
-
Tutorials
- Angular Momentum Operations
- Crystal Field Theory – Stevens Operators and Ho/Pt(111)
- Handling of symmetry elements: multiplication, symbols, matrices, etc.
- Installation of double groups
- Installation of point groups
- Installation of point groups and character tables
- Representation matrices and projection operators
- Standard representations – O(3), SU(2), SU(2)xS
- Tight-binding electronic structure of graphene
- Working with characters and irreducible representations
- Working with crystal structures
- Working with Quaternions
The Mathematica Group Theory Package GTPack, V 1.3
The Mathematica group theory package GTPack contains more than 200 additional modules dedicated to applications in solid state physics and photonics. It can be loaded by Needs["GroupTheory`"].
An introduction into group theory as well as examples using GTPack can be found in the book: [1] W. Hergert, R. M. Geilhufe, Group Theory in Solid State Physics and Photonics: Problem Solving with Mathematica, Wiley-VCH, ISBN: 978-3-527-41133-7 (2018).
A short description of the package including examples and comments about the implementation of the package can be found in: [2] R. M. Geilhufe, W. Hergert, GTPack: A Mathematica group theory package for applications in solid-state physics and photonics, Frontiers in Physics, 6:86, 2018
The development of GTPack is an academic project. To support the development of GTPack we ask you to cite both references [1,2].
We acknowledge the help of Sebastian Schenk who significantly contributed to creating a Mathematica documentation for GTPack.
Version release date December 15th, 2020
ReferenceReference
Angular Momentum »
GTJx ▪ GTJy ▪ GTJz ▪ GTJplus ▪ GTJminus ▪ ...
GTAngularMomentumChars ▪ GTAngularMomentumRep ▪ ...
Auxiliary »
GTQAbs ▪ GTQConjugate ▪ GTQInverse ▪ ...
GTEulerAnglesQ ▪ GTQuaternionQ ▪ GTSymbolQ
Graphic representation of point group relationships
GTPointGroups ▪ GTGroupConnection ▪ GTGroupHierarchy
GTCartesianSphericalHarmonicY ▪ GTCartesianTesseralHarmonicY ▪ ...
GTReadFromFile ▪ GTWriteToFile ▪ ...
GTClusterFilter ▪ GTCompactStore ▪ ...
GTSU2Matrix ▪ GTDiracMatrix ▪ ...
GTBlueRed ▪ GTSetTableColors ▪ ...
Basic »
GTClasses ▪ GTClassMult ▪ GTClassMultTable
Characterization of groups and elements
GTGenerators ▪ GTGetSubGroups ▪ GTGroupOrder ▪ GTMultTable ▪ ...
GTAbelianQ ▪ GTCyclicQ ▪ GTGroupQ ▪ ...
Symbols, matrices, quaternions and Euler angles
GTAllSymbols ▪ GTGetEulerAngles ▪ GTGetMatrix ▪ ...
GTTransformation ▪ GTTransformationOperator
Crystal Structure »
Load and save and modify structures
GTLoadStructures ▪ GTSaveStructures ▪ ...
Plot and manipulate crystsl strucutre
GTClusterManipulate ▪ GTPlotCluster ▪ GTPlotStructure ▪ ...
Point and space group information
GTBravaisLattice ▪ GTCrystalData ▪ GTCrystalSystem ▪ ...
GTBuckyBall ▪ GTTubeParameters ▪ GTTubeStructure
Crystal Field Theory »
Qualitative Crystal Field Theory
Quantitative Crystal Field Theory
GTCrystalField ▪ GTStevensOperator ▪ GTBSTOperator ▪ ...
Crystal field Parameters and Database
GTCrystalFieldParameter ▪ GTStevensTheta ▪ GTCFDatabaseInfo ▪ ...
Electronic Structure »
Calculations of Band Structures
GTBandStructure ▪ GTBands ▪ GTBandsPlot ▪ ...
Calculations of Density of States
GTDensityOfStates ▪ GTDensityOfStatesPlot ▪ GTFermiSurface ▪ ...
Install »
Installation of symmetry elements
GTInstallAxis ▪ GTReinstallAxes ▪ GTWhichAxes
GTGroupFromGenerators ▪ GTInstallAxis ▪ GTInstallGroup ▪ ...
GTChangeRepresentation ▪ GTWhichRepresentation
Lattice »
Cluster construction and analysis
GTCluster ▪ GTShells ▪ GTAdjacencyMatrix
Lattices in Real Space or Reciprocal Space
Symmetry Analysis of Real Structure Clusters
GTShellVectorsQlp ▪ GTGroupGlp ▪ GTTransformToQlp
GTBZPointMesh ▪ GTBZPath ▪ GTVoronoiCell ▪ ...
Molecules »
Parameter Sets and Libraries for Molecules
GTMolChemicalData ▪ GTMolDatabaseInfo ▪ GTMolToCluster ▪ ...
Representation Theory for Molecules
Photonics »
Structure Factors and Fourier Transforms of inverse Permittivity
GTPhDielectric ▪ GTPhFields ▪ GTPhMasterEquation ▪ ...
Visualization of permittivity distributions
GTPhPixelStructure ▪ GTPhShowStructure
GTPhMaster ▪ GTPhMasterObjects ▪ ...
GTPhSymmetryBands ▪ GTPhSymmetryPoint ▪ GTPhSymmetryField ▪ ...
Pseudopotential »
GTPwDatabaseInfo ▪ GTPwDatabaseRetrieve ▪ ...
Model-Pseudopotential Hamiltonians
GTPwHamiltonian ▪ GTPwDielectricF ▪ GTPwModelPotential
GTPwEmptyLatticeIrep ▪ GTPwSymmetrizePW
Representation Theory »
GTCharacterTable ▪ GTSOCSplitting ▪ ...
GTCharProjectionOperator ▪ GTProjectionOperator ▪ ...
GTClebschGordanSum ▪ GTGetIrep ▪ GTIrep ▪ ...
Direct product of representations
GTClebschGordanCoefficients ▪ GTDirectProductChars ▪ GTDirectProductRep
Representation Theory of Space Groups »
GTSGCharacterTable ▪ GTSGGetIreps
GTSGLeftCosets ▪ GTSGRightCosets ▪ GTSGClasses ▪ GTSGGetInvSubGroup ▪ GTSGCosetRepresentative
Simpack ≫
GTTbParmExport ▪ GTStrucExport ▪ ...
TightBinding »
Construction of two-center tight-binding Hamiltonians
GTTbHamiltonian ▪ GTTbHamiltonianElement ▪ GTTbMatrixElement ▪ ...
Construction of three-center tight-binding Hamiltonians
GTSymmetryBasisFunctions ▪ GTTbSymbol3C ▪ ...
GTTbRealSpaceMatrix ▪ GTTbHamiltonianRS ▪ ...
Parameter Sets and Libraries for tight-binding Models
GTTbGetParameter ▪ GTTbDatabaseInfo ▪ ...
GTTbAtomicWaveFunction ▪ ...
Symmetry Analysis of Band Structures
GTTbSymmetryBands ▪ GTTbSymmetryPoint ▪ ...
GTTbSymmetryBandStructure ▪ GTTbSymmetryBands ▪
Output of Hamiltonians as FORTRAN Modules
GTTbToFortran ▪ GTTbToFortranList
GTTbReadWannier90 ▪ GTTbWannier90Hamiltonian
GTHamiltonianPlot ▪ GTHamiltonianList ▪
Vibrations »
Vibrational Modes of Molecules
GTVibDisplacementRep ▪ GTVibModeSymmetry ▪ GTVibSpectroscopy
GTVibDynamicalMatrix ▪ GTVibLatticeModes ▪ ...
Options »
GOColorScheme ▪ GODecimals ▪ ...
GOClasses ▪ GOGroupOrder ▪ ...
GOBands ▪ GOEigenvectors ▪ ...
GODCMethod ▪ GOPhPol ▪ ...
GOTbBasis ▪ GOTbEquivalence ▪ ...