CRYSTAL
Encyclopedia
CRYSTAL is a quantum chemistry
ab initio
program, designed primarily for calculations on crystals (3 dimensions), slabs (2 dimensions) and polymers (1 dimension) using translational symmetry, but it can also be used for single molecules. It is written by V.R. Saunders, R. Dovesi, C. Roetti, R. Orlando, C.M. Zicovich-Wilson, N.M. Harrison, K. Doll, B. Civalleri, I.J. Bush, Ph. D’Arco, and M. Llunell from Theoretical Chemistry Group at the University of Torino and the Computational Materials Science Group at the Daresbury Laboratory
near Warrington
in Cheshire
, England
. The current version is CRYSTAL09, released on February 2010. Earlier versions were CRYSTAL88, CRYSTAL92, CRYSTAL95, CRYSTAL98, CRYSTAL03 and CRYSTAL06.
unit 9, and as formatted data in Fortran unit 98.
One-electron properties and wave function analysis can be computed from the SCF wave function by running the program properties.
The main advantage of the crystal code is due to the deep and optimized exploitation of symmetry, at all levels of calculation (SCF as well gradients and vibrational frequencies calculations). This allows significant reduction of the computational cost for periodic calculations. Note that while the symmetry generally reduces to identity in large molecules, large crystalline system usually show many symmetry operators.
Exact exchange Hartree-Fock
calculations for periodic systems.
I. Illustration of the method.
Int. J. Quantum Chem. 17, 501 (1980).
V.R. Saunders
Ab Initio Hartree-Fock Calculations for periodic systems.
Faraday Symp. Chem. Soc. 19, 79-84 (1984).
C.Pisani, R.Dovesi and C.Roetti
Hartree-Fock ab-initio of crystalline systems,
Lecture Notes in Chemistry, Vol. 48, Spinger Verlag, Heidelberg, 1988
Treatment of Coulomb
interactions in Hartree-Fock calculations of periodic systems.
Phys. Rev. B28, 5781-5792, 1983
V.R.Saunders, C.Freyria Fava, R.Dovesi, L.Salasco and C.Roetti
On the electrostatic potential in crystalline systems where the charge
density is expanded in Gaussian Functions
Molecular Physics, 77, 629-665, 1992
V.R.Saunders, C.Freyria Fava, R.Dovesi and C.Roetti
On the electrostatic potential in linear periodic polymers.
Computer Physics Communications, 84, 156-172, 1994
Treatment of the exchange interaction
s in Hartree-Fock LCAO calculation
of periodic systems.
J. Phys. Chem, 92, 909, 1988
On the role of symmetry in the ab initio Hartree-Fock linear
combination of atomic orbitals treatment of periodic systems.
Int. J. Quantum Chem. 29, 1755 (1986).
C. Zicovich-Wilson and R. Dovesi
On the use of Symmetry Adapted Crystalline Orbitals in SCF-LCAO periodic calculations.
I. The construction of the Symmetrized Orbitals.
Int. J. Quantum Chem. 67, 299-309 (1998).
C. Zicovich-Wilson and R. Dovesi
On the use of Symmetry Adapted Crystalline Orbitals in SCF-LCAO periodic calculations.
II. Implementation of the Self-Consistent-Field scheme and examples.
Int. J. Quantum Chem. 67, 309-320 (1998).
Correlation correction to the Hartree-Fock total energy of solids.
Phys. Rev., B 36, 891, 1987
M.D. Towler, M. Causa' and A. Zupan
Density functional Theory
in periodic systems using local gaussian basis sets.
Comp. Phys. Comm. 98, 181 (1996)
Analytical Hartree-Fock gradients for periodic systems.
Int. J. Quantum Chem. 82, 1-13 (2001)
K. Doll, R. Dovesi, R. Orlando
Analytical Hartree-Fock gradients with respect to the cell parameter
for systems periodic in three dimensions.
Theor. Chem. Acc. 112, 394-402 (2004).
Hartree-Fock geometry optimisation of periodic systems with the CRYSTAL code.
Chem. Phys. Lett. 348, 131-138 (2001)
A general method to obtain well localized Wannier function
s for
composite energy bands in LCAO periodic calculations.
J. Chem. Phys. 115, 9708-9718 (2001).
The calculation of vibrational frequencies of crystalline compounds.
and its implementation in the CRYSTAL code
J. Comput. Chem. 25, 888-897 (2004).
C.M. Zicovich-Wilson, F. Pascale, C. Roetti, V.R. Saunders, R. Orlando, R. Dovesi
Calculation of vibration frequencies of alpha-quartz: the effect of hamiltonian
and basis set.
J. Comput. Chem.25, 1873-1881 (2004).
Implementation of the finite field perturbation method in the CRYSTAL
program for calculating the dielectric constant
of periodic systems.
J. Comp. Chem. 24, 1305-1312 (2003).
Quantum-Mechanical Ab-initio calculation of the Properties of Crystalline Materials,
Lecture Notes in Chemistry, Vol. 67, Spinger Verlag, Heidelberg, 1996
Quantum chemistry
Quantum chemistry is a branch of chemistry whose primary focus is the application of quantum mechanics in physical models and experiments of chemical systems...
ab initio
Ab initio quantum chemistry methods
Ab initio quantum chemistry methods are computational chemistry methods based on quantum chemistry. The term ab initiowas first used in quantum chemistry by Robert Parr and coworkers, including David Craig in a semiempirical study on the excited states of benzene.The background is described by Parr...
program, designed primarily for calculations on crystals (3 dimensions), slabs (2 dimensions) and polymers (1 dimension) using translational symmetry, but it can also be used for single molecules. It is written by V.R. Saunders, R. Dovesi, C. Roetti, R. Orlando, C.M. Zicovich-Wilson, N.M. Harrison, K. Doll, B. Civalleri, I.J. Bush, Ph. D’Arco, and M. Llunell from Theoretical Chemistry Group at the University of Torino and the Computational Materials Science Group at the Daresbury Laboratory
Daresbury Laboratory
Daresbury Laboratory is a scientific research laboratory near Daresbury in Cheshire, England, which began operations in 1962 and was officially opened on 16 June 1967 as the Daresbury Nuclear Physics Laboratory by the then Prime Minister of United Kingdom, Harold Wilson...
near Warrington
Warrington
Warrington is a town, borough and unitary authority area of Cheshire, England. It stands on the banks of the River Mersey, which is tidal to the west of the weir at Howley. It lies 16 miles east of Liverpool, 19 miles west of Manchester and 8 miles south of St Helens...
in Cheshire
Cheshire
Cheshire is a ceremonial county in North West England. Cheshire's county town is the city of Chester, although its largest town is Warrington. Other major towns include Widnes, Congleton, Crewe, Ellesmere Port, Runcorn, Macclesfield, Winsford, Northwich, and Wilmslow...
, England
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
. The current version is CRYSTAL09, released on February 2010. Earlier versions were CRYSTAL88, CRYSTAL92, CRYSTAL95, CRYSTAL98, CRYSTAL03 and CRYSTAL06.
Hamiltonians
- Hartree-FockHartree-FockIn computational physics and chemistry, the Hartree–Fock method is an approximate method for the determination of the ground-state wave function and ground-state energy of a quantum many-body system....
Theory- Restricted
- Unrestricted
- Density Functional TheoryDensity functional theoryDensity functional theory is a quantum mechanical modelling method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular atoms, molecules, and the condensed phases. With this theory, the properties of a many-electron system can be determined by...
- Local functionals [L] and gradient-corrected functionals [G]
- Exchange functionals
- SlaterSlaterSlater is an occupational surname of English origin. A slater is a tradesman.-Surname:* Allana Slater , Australian artistic gymnast* Bert Slater , Scottish football player* Bill Slater , English footballer...
(LDA) [L] - von Barth-Hedin (VBH) [L]
- Becke '88 (BECKE) [G]
- Perdew-Wang '91 (PWGGA) [G]
- Perdew-Burke-Ernzerhof (PBE) [G]
- Revised PBE functional for solids (PBEsol) [G]
- Second-order expansion GGA for solids (SOGGA) [G]
- Wu-Cohen '06 (WCGGA) [G]
- Slater
- Correlation functionals
- VWN (#5 parameterization) (VWN) [L]
- Perdew-Wang '91 (PWLSD) [L]
- Perdew-Zunger '81 (PZ) [L]
- von Barth-Hedin (VBH) [L]
- Lee-Yang-Parr (LYP) [G]
- Perdew '86 (P86) [G]
- Perdew-Wang '91 (PWGGA) [G]
- Perdew-Burke-Ernzerhof (PBE) [G]
- Revised PBE functional for solids (PBEsol) [G]
- Wilson-Levy '90 (WL) [G]
- Hybrid HF-DFT functionalsHybrid functionalHybrid functionals are a class of approximations to the exchange-correlation energy functional in density functional theory that incorporate a portion of exact exchange from Hartree-Fock theory with exchange and correlation from other sources...
- B3PW, B3LYP (using the VWN5 functional)
- User-defined hybrid functionals
- Numerical-grid based numerical quadrature scheme
- London-type empirical correction for dispersion interactions (Grimme scheme)
Energy derivatives
- Analytical first derivatives with respect to the nuclear coordinates and cell parameters
- Hartree-Fock and Density Functional methods
- All-electron and Effective Core Potentials
Type of calculation
- Single-point energy calculation
- Automated geometry optimization
- Uses a modified conjugate gradient algorithm
- Optimizes in symmetry-adapted cartesian coordinates
- Optimizes in redundant coordinates
- Full geometry optimization (cell parameters and atom coordinates)
- Freezes atoms during optimization
- Constant volume or pressure constrained geometry optimization (3D only)
- Transition state search
- Harmonic vibrational frequenciesMolecular vibrationA molecular vibration occurs when atoms in a molecule are in periodic motion while the molecule as a whole has constant translational and rotational motion...
- Harmonic frequencies at Gamma
- Phonon dispersion using a direct approach (efficient supercell scheme)
- IR intensities through either localized Wannier functions or Berry phase
- Calculation of the reflectance spectrum
- Exploration of the energy and geometry along selected normal modes
- AnharmonicAnharmonicityIn classical mechanics, anharmonicity is the deviation of a system from being a harmonic oscillator. An oscillator that is not oscillating in simple harmonic motion is known as an anharmonic oscillator where the system can be approximated to a harmonic oscillator and the anharmonicity can be...
frequencies for X-H bonds - Automated calculation of the elastic tensor of crystalline systems (3D only)
- Automated E vs V calculation for equation of state (3D only)
- Automatic treatment of solid solutions
Basis set
- Gaussian typeGaussian orbitalIn computational chemistry and molecular physics, Gaussian orbitals are functions used as atomic orbitals in the LCAO method for the computation of electron orbitals in molecules and numerous properties that depend on these.- Rationale :The principal reason for the use of Gaussian basis functions...
functions basis setsBasis set (chemistry)A basis set in chemistry is a set of functions used to create the molecular orbitals, which are expanded as a linear combination of such functions with the weights or coefficients to be determined. Usually these functions are atomic orbitals, in that they are centered on atoms. Otherwise, the...
- s, p, d, and f GTFs
- Standard PopleJohn PopleSir John Anthony Pople, KBE, FRS, was a Nobel-Prize winning theoretical chemist. Born in Burnham-on-Sea, Somerset, England, he attended Bristol Grammar School. He won a scholarship to Trinity College, Cambridge in 1943. He received his B. A. in 1946. Between 1945 and 1947 he worked at the Bristol...
Basis Sets- STO-nG n=2-6 (H-Xe), 3-21G (H-Xe), 6-21G (H-Ar)
- polarization and diffuse function extensions
- User-specified basis sets supported
- PseudopotentialPseudopotentialIn physics, a pseudopotential or effective potential is used as an approximation for the simplified description of complex systems. Applications include atomic physics and neutron scattering.- Atomic physics :...
Basis Sets- Hay-Wadt large core
- Hay-Wadt small core
- User-defined pseudopotential basis sets supported
Periodic systems
- Periodicity
- Consistent treatment of all periodic systems
- 3D - Crystalline solids (230 space groups)
- 2D - Films and surfaces (80 layer groups)
- 1D - Polymers, space group derived symmetrySymmetrySymmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection...
(75 rod groups) and helical symmetry (up to order 48) - 0D - Molecules (32 point groups)
- Automated geometry editing
- 3D to 2D - slab parallel to a selected crystalline face (hkl)
- 3D to 0D - cluster from a perfect crystal (H saturated)
- 3D to 0D - extraction of molecules from a molecular crystal
- 3D to n3D - supercell creation
- 2D to 1D - building nanotubesCarbon nanotubeCarbon nanotubes are allotropes of carbon with a cylindrical nanostructure. Nanotubes have been constructed with length-to-diameter ratio of up to 132,000,000:1, significantly larger than for any other material...
from a single-layer slab model - Several geometry manipulations (reduction of symmetry; insertion, displacement, substitution, deletion of atoms)
Wave function analysis and properties
- Band structureElectronic band structureIn solid-state physics, the electronic band structure of a solid describes those ranges of energy an electron is "forbidden" or "allowed" to have. Band structure derives from the diffraction of the quantum mechanical electron waves in a periodic crystal lattice with a specific crystal system and...
- Density of statesDensity of statesIn solid-state and condensed matter physics, the density of states of a system describes the number of states per interval of energy at each energy level that are available to be occupied by electrons. Unlike isolated systems, like atoms or molecules in gas phase, the density distributions are not...
- Band projected DOSS
- AO projected DOSS
- All Electron Charge Density - Spin Density
- Density maps
- Mulliken population analysis
- Density analytical derivatives
- Atomic multipoles
- Electric field
- Electric field gradient
- Structure factorStructure factorIn condensed matter physics and crystallography, the static structure factor is a mathematical description of how a material scatters incident radiation...
s - Compton profiles
- Electron Momentum Density
- Electrostatic potential and its derivatives
- Quantum and classical electrostatic potential and its derivatives
- Electrostatic potential maps
- Fermi contactFermi contact interactionThe Fermi contact interaction is the magnetic interaction between an electron and an atomic nucleus when the electron is inside that nucleus. It is of magnitude...
- Localized Wannier FunctionsWannier functionThe Wannier functions are a complete set of orthogonal functions used in solid-state physics. They were introduced by Gregory Wannier.The Wannier functions for different lattice sites in a crystal are orthogonal, allowing a convenient basis for the expansion of electron states in certain regimes...
(Boys method) - Dielectric properties
- Spontaneous polarization (Berry Phase)
- Spontaneous polarization (Localized Wannier Functions)
- Dielectric constant: new Coupled Perturbed HF(KS) scheme and Finite-field approximation
Software performance
- Memory management: dynamic allocation
- Full parallelization of the code
- parallel SCF and gradients for both HF and DFT methods
- Replicated data version (MPIMessage Passing InterfaceMessage Passing Interface is a standardized and portable message-passing system designed by a group of researchers from academia and industry to function on a wide variety of parallel computers...
) - Massive parallel version (MPIMessage Passing InterfaceMessage Passing Interface is a standardized and portable message-passing system designed by a group of researchers from academia and industry to function on a wide variety of parallel computers...
) (distributed memory)
Program structure
The program is built of two modules: crystal and properties. The crystal program is dedicated to perform the SCF calculations, the geometry optimizations, and the frequency calculations for the structures given in input. At the end of the SCF process, the program crystal writes information on the crystalline system and its wave function as unformatted sequential data in FortranFortran
Fortran is a general-purpose, procedural, imperative programming language that is especially suited to numeric computation and scientific computing...
unit 9, and as formatted data in Fortran unit 98.
One-electron properties and wave function analysis can be computed from the SCF wave function by running the program properties.
The main advantage of the crystal code is due to the deep and optimized exploitation of symmetry, at all levels of calculation (SCF as well gradients and vibrational frequencies calculations). This allows significant reduction of the computational cost for periodic calculations. Note that while the symmetry generally reduces to identity in large molecules, large crystalline system usually show many symmetry operators.
The Hartree-Fock method for periodic systems
C. Pisani and R. DovesiExact exchange Hartree-Fock
Hartree-Fock
In computational physics and chemistry, the Hartree–Fock method is an approximate method for the determination of the ground-state wave function and ground-state energy of a quantum many-body system....
calculations for periodic systems.
I. Illustration of the method.
Int. J. Quantum Chem. 17, 501 (1980).
V.R. Saunders
Ab Initio Hartree-Fock Calculations for periodic systems.
Faraday Symp. Chem. Soc. 19, 79-84 (1984).
C.Pisani, R.Dovesi and C.Roetti
Hartree-Fock ab-initio of crystalline systems,
Lecture Notes in Chemistry, Vol. 48, Spinger Verlag, Heidelberg, 1988
The Coulomb problem
R. Dovesi, C. Pisani, C. Roetti and V.R. SaundersTreatment of Coulomb
Ewald summation
Ewald summation, named after Paul Peter Ewald, is a method for computing the interaction energies of periodic systems , particularly electrostatic energies. Ewald summation is a special case of the Poisson summation formula, replacing the summation of interaction energies in real space with an...
interactions in Hartree-Fock calculations of periodic systems.
Phys. Rev. B28, 5781-5792, 1983
V.R.Saunders, C.Freyria Fava, R.Dovesi, L.Salasco and C.Roetti
On the electrostatic potential in crystalline systems where the charge
density is expanded in Gaussian Functions
Molecular Physics, 77, 629-665, 1992
V.R.Saunders, C.Freyria Fava, R.Dovesi and C.Roetti
On the electrostatic potential in linear periodic polymers.
Computer Physics Communications, 84, 156-172, 1994
The exchange problem
M.Causa`, R.Dovesi, R.Orlando, C.Pisani and V.R.SaundersTreatment of the exchange interaction
Exchange interaction
In physics, the exchange interaction is a quantum mechanical effect without classical analog which increases or decreases the expectation value of the energy or distance between two or more identical particles when their wave functions overlap...
s in Hartree-Fock LCAO calculation
of periodic systems.
J. Phys. Chem, 92, 909, 1988
The symmetry
R. DovesiOn the role of symmetry in the ab initio Hartree-Fock linear
combination of atomic orbitals treatment of periodic systems.
Int. J. Quantum Chem. 29, 1755 (1986).
C. Zicovich-Wilson and R. Dovesi
On the use of Symmetry Adapted Crystalline Orbitals in SCF-LCAO periodic calculations.
I. The construction of the Symmetrized Orbitals.
Int. J. Quantum Chem. 67, 299-309 (1998).
C. Zicovich-Wilson and R. Dovesi
On the use of Symmetry Adapted Crystalline Orbitals in SCF-LCAO periodic calculations.
II. Implementation of the Self-Consistent-Field scheme and examples.
Int. J. Quantum Chem. 67, 309-320 (1998).
DFT implementation
M.Causa`, R.Dovesi, C.Pisani, R.Colle and A.FortunelliCorrelation correction to the Hartree-Fock total energy of solids.
Phys. Rev., B 36, 891, 1987
M.D. Towler, M. Causa' and A. Zupan
Density functional Theory
Density functional theory
Density functional theory is a quantum mechanical modelling method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular atoms, molecules, and the condensed phases. With this theory, the properties of a many-electron system can be determined by...
in periodic systems using local gaussian basis sets.
Comp. Phys. Comm. 98, 181 (1996)
Analytical gradients implementation
K. Doll, V.R. Saunders, N.M. HarrisonAnalytical Hartree-Fock gradients for periodic systems.
Int. J. Quantum Chem. 82, 1-13 (2001)
K. Doll, R. Dovesi, R. Orlando
Analytical Hartree-Fock gradients with respect to the cell parameter
for systems periodic in three dimensions.
Theor. Chem. Acc. 112, 394-402 (2004).
Geometry Optimisation
B. Civalleri, Ph. D'Arco, R. Orlando, V.R. Saunders, R. DovesiHartree-Fock geometry optimisation of periodic systems with the CRYSTAL code.
Chem. Phys. Lett. 348, 131-138 (2001)
Localized Wannier Functions
C.M. Zicovich-Wilson, R. Dovesi and V.R. SaundersA general method to obtain well localized Wannier function
Wannier function
The Wannier functions are a complete set of orthogonal functions used in solid-state physics. They were introduced by Gregory Wannier.The Wannier functions for different lattice sites in a crystal are orthogonal, allowing a convenient basis for the expansion of electron states in certain regimes...
s for
composite energy bands in LCAO periodic calculations.
J. Chem. Phys. 115, 9708-9718 (2001).
Vibration frequencies at Gamma
F. Pascale, C.M. Zicovich-Wilson, F. Lopez Gejo, B. Civalleri, R. Orlando, R. DovesiThe calculation of vibrational frequencies of crystalline compounds.
and its implementation in the CRYSTAL code
J. Comput. Chem. 25, 888-897 (2004).
C.M. Zicovich-Wilson, F. Pascale, C. Roetti, V.R. Saunders, R. Orlando, R. Dovesi
Calculation of vibration frequencies of alpha-quartz: the effect of hamiltonian
and basis set.
J. Comput. Chem.25, 1873-1881 (2004).
Calculation of dielectric constant
C. Darrigan, M. Rerat, G. Mallia, R. DovesiImplementation of the finite field perturbation method in the CRYSTAL
program for calculating the dielectric constant
Dielectric constant
The relative permittivity of a material under given conditions reflects the extent to which it concentrates electrostatic lines of flux. In technical terms, it is the ratio of the amount of electrical energy stored in a material by an applied voltage, relative to that stored in a vacuum...
of periodic systems.
J. Comp. Chem. 24, 1305-1312 (2003).
Calculation of properties of crystalline materials
C.PisaniQuantum-Mechanical Ab-initio calculation of the Properties of Crystalline Materials,
Lecture Notes in Chemistry, Vol. 67, Spinger Verlag, Heidelberg, 1996
See also
- Crystal structureCrystal structureIn mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
- Quantum chemistry programs
External links
- CRYSTAL
- Computational Materials Science Group
- Theoretical Chemistry Group University of Torino