ExchangeCorrelation

class ExchangeCorrelation(exchange, correlation, hubbard_term=None, number_of_spins=1, spin_orbit=None, dft_half_enabled=None)

The ExchangeCorrelation class is used to define the type of exchange-correlation used in the calculation, and whether the calculation should be polarized or non-polarized.

Parameters:
  • exchange (Exchange) – The exchange to be used.

  • correlation (Correlation) – The correlation to be used.

  • hubbard_term (Onsite | OnsiteShell | Dual | DualShell | None) – The Hubbard term to add.
    Default: None.

  • number_of_spins (1 | 2 | 4) – The number of spins to be used in the calculation.
    Default: 1.

  • spin_orbit (bool) – If True spin-orbit coupling is considered.
    Default: False.

  • dft_half_enabled (bool) – Whether or not DFT-1/2 should be enabled.
    Default: False.

cParameter(grid_descriptor=None)

return the param C.

Parameters:

grid_descriptor (NLEngine.GridDescriptor) – The grid descriptor.

cloneAsPolarized()

Create a new functional with all the same settings, but polarized spin.

cloneAsSpinOrbit()

Create a new functional with all the same settings, but with Spin-Orbit coupling included.

correlation()
Returns:

The correlation functional class

Return type:

Correlation

densityCheckThreshold()
Returns:

The density safe guard.

Return type:

float

dftHalfEnabled()
Returns:

Whether DFT-1/2 is enabled.

Type:

bool

dielectricDependentHybridFunctional()
Returns:

True, then a dielectric dependent hybrid functional is used.

Return type:

bool

dielectricDependentHybridParameters()
Returns:

The dielectric dependent hybrid hybrid parameters.

Return type:

list

exchange()
Returns:

The exchange functional class

Return type:

Exchange

hubbardTerm()
Returns:

The Hubbard term used.

Return type:

Onsite | OnsiteShell | Dual | DualShell | None

maximumPotential()

Set maximum potential value allowed for the TB09. The value to use as the maximum allowed value for the potential in points with density lower than threshold.

Returns:

The density safe guard.

Return type:

float

minimumPotential()

Set minimum potential value allowed for the TB09. The value to use as the minimum allowed value for the potential in points with density lower than threshold.

Returns:

The density safe guard.

Return type:

float

nlprint(stream=<_io.TextIOWrapper name='<stdout>' mode='w' encoding='utf-8'>)

Print a string representation of the ExchangeCorrelation instance.

Parameters:

stream (A stream that supports strings being written to using write.) – The stream the exchange-correlation should be written to.
Default: sys.stdout

numberOfSpins()
Returns:

The number of spins.

Return type:

1 | 2 | 4

params()

Get the parameters

spinOrbit()
Returns:

Boolean determining if spin-orbit is enabled (True) or not (False).

Return type:

bool.

spinType()
Returns:

The spin type.

Return type:

NLEngine.POLARIZED | NLEngine.NONCOLLINEAR | NLEngine.UNPOLARIZED

uniqueString()

Return a unique string representing the state of the object.

unscreenedExchange()

Whether the exchange functional in use is unscreened.

Usage Examples

Define a spin-polarized LDA+U calculation for nickel with a Hubbard U of 4.6 eV on each nickel atom and using the Dual representation for the Hubbard term (see also Dual representation):

exchange_correlation = ExchangeCorrelation(
    exchange=DiracBloch,
    correlation=PerdewZunger,
    hubbard_term=Dual,
    number_of_spins=2
)
basis_set = [LDABasis.Nickel_SingleZeta(hubbard_u=[4.6, 0.0]*eV)]
calculator = LCAOCalculator(
    exchange_correlation=exchange_correlation,
    basis_set=basis_set
)

Below is a similar calculation as above, but using the DualShell representation for the Hubbard term. In the shellwise Hubbard representation, occupations are summed over all basis set orbitals that have the same angular momentum and the complete basis is orthogonalized (see also DualShell representation). The Hubbard U must be the same for all orbitals that have equal angular momentum:

exchange_correlation = ExchangeCorrelation(
    exchange=DiracBloch,
    correlation=PerdewZunger,
    hubbard_term=DualShell,
    number_of_spins=2
)
basis_set = [LDABasis.Nickel_DoubleZetaPolarized(hubbard_u=[4.6, 0.0, 4.6, 0.0, 0.0]*eV)]
calculator = LCAOCalculator(
    exchange_correlation=exchange_correlation,
    basis_set=basis_set
)

Notes

A complete list of available keywords for the exchange and correlation parameters is available in the section References.

Parameters for TB09-MGGA exchange-correlation

The ExchangeCorrelation class can take parameters. Currently, this is only relevant for the TB09 meta-GGA functional, which takes a parameter c (cf. Meta-GGA).

If no value is specified, the value of c is automatically computed according to Eq. (3) in [1]. The calculated value can then be recovered using the calculateTB09C function.

The following piece of code selects the TB09 functional with c=1.0 (recovering the Becke–Johnson potental [2]):

exchange_correlation = MGGA.TB09LDA(c=1.0)
calculator = LCAOCalculator(exchange_correlation=exchange_correlation)

Simulations of complex systems, e.g. interfaces or two-probe device systems with different materials in the electrodes and the central region, may require setting the c parameter to different values in the various parts of the system, e.g. one c for the left electrode, another c for the central region, and yet another c for the right electrode. In such cases, the c parameter for TB09-MGGA exchange-correlation functionals can be defined as a sequence of BoxRegions (cf. BoxRegion), as demonstrated in the following script. The configuration is a bulk configuration that consists of layers of iron, magnesium-oxide, and again iron. Indeed, it is the central region of a magnetic tunneling junction device configuration.

from QuantumATK import *

# Set up lattice
vector_a = [2.866, 0.0, 0.0]*Angstrom
vector_b = [0.0, 2.866, 0.0]*Angstrom
vector_c = [0.0, 0.0, 34.6764]*Angstrom
lattice = UnitCell(vector_a, vector_b, vector_c)

# Define elements
elements = [Iron, Iron, Iron, Iron, Iron, Iron, Iron, Iron, Magnesium,
            Oxygen, Oxygen, Magnesium, Magnesium, Oxygen, Oxygen, Magnesium,
            Magnesium, Oxygen, Iron, Iron, Iron, Iron, Iron, Iron, Iron,
            Iron]

# Define coordinates
fractional_coordinates = [[ 0.25          ,  0.25          ,  0.020662467846],
                          [ 0.75          ,  0.75          ,  0.061987403537],
                          [ 0.25          ,  0.25          ,  0.103312339228],
                          [ 0.75          ,  0.75          ,  0.144637274919],
                          [ 0.25          ,  0.25          ,  0.18596221061 ],
                          [ 0.75          ,  0.75          ,  0.227287146301],
                          [ 0.25          ,  0.25          ,  0.268612081992],
                          [ 0.75          ,  0.75          ,  0.309937017683],
                          [ 0.25          ,  0.25          ,  0.373380743099],
                          [ 0.75          ,  0.75          ,  0.373380743099],
                          [ 0.25          ,  0.25          ,  0.43669037155 ],
                          [ 0.75          ,  0.75          ,  0.43669037155 ],
                          [ 0.25          ,  0.25          ,  0.5           ],
                          [ 0.75          ,  0.75          ,  0.5           ],
                          [ 0.25          ,  0.25          ,  0.56330962845 ],
                          [ 0.75          ,  0.75          ,  0.56330962845 ],
                          [ 0.25          ,  0.25          ,  0.626619256901],
                          [ 0.75          ,  0.75          ,  0.626619256901],
                          [ 0.75          ,  0.75          ,  0.690062982317],
                          [ 0.25          ,  0.25          ,  0.731387918008],
                          [ 0.75          ,  0.75          ,  0.772712853699],
                          [ 0.25          ,  0.25          ,  0.81403778939 ],
                          [ 0.75          ,  0.75          ,  0.855362725081],
                          [ 0.25          ,  0.25          ,  0.896687660772],
                          [ 0.75          ,  0.75          ,  0.938012596463],
                          [ 0.25          ,  0.25          ,  0.979337532154]]

# Set up configuration
bulk_configuration = BulkConfiguration(
    bravais_lattice=lattice,
    elements=elements,
    fractional_coordinates=fractional_coordinates
    )
# -------------------------------------------------------------
# Calculator
# -------------------------------------------------------------
# c parameter regions.

c_region_0 = BoxRegion(
    0.9,
    xmin = 0.0*Angstrom, xmax = 2.866*Angstrom,
    ymin = 0.0*Angstrom, ymax = 2.866*Angstrom,
    zmin = 0.0*Angstrom, zmax = 12.13674*Angstrom,
)

c_region_1 = BoxRegion(
    1.4,
    xmin = 0.0*Angstrom, xmax = 2.866*Angstrom,
    ymin = 0.0*Angstrom, ymax = 2.866*Angstrom,
    zmin = 12.13674*Angstrom, zmax = 22.53966*Angstrom,
)

c_region_2 = BoxRegion(
    0.9,
    xmin = 0.0*Angstrom, xmax = 2.866*Angstrom,
    ymin = 0.0*Angstrom, ymax = 2.866*Angstrom,
    zmin = 22.53966*Angstrom, zmax = 34.6764*Angstrom,
)

c_regions = [c_region_0, c_region_1, c_region_2]

# Define the exchange correlation with the c regions.
exchange_correlation=MGGA.TB09LDA(c=c_regions)

# Define the calculator.
calculator = LCAOCalculator(
    exchange_correlation=exchange_correlation,
    )

# Attach the calculator on the configuration.
bulk_configuration.setCalculator(calculator)

# Calculate the exchange correlation potential.
exchange_correlation_potential = ExchangeCorrelationPotential(bulk_configuration)

# Save on file.
nlsave('Fe-MgO-Fe.nc', exchange_correlation_potential)

It is important that the regions defining the c parameter cover the entire simulation volume. The parameter is set to c = 1.0 at all points that do not fall into any region. The difference in c between two adjacent regions should not be too large, otherwise problems in the SCF convergence may occur. As a rule of thumb, the jump in the exchange-correlation potential between adjacent regions should be of the same order as the fluctuations of the exchange-correlation potential in a region of constant c.

Potential problems in spin polarized calculations

For molecular systems containing hydrogen, the default initial scaled spin values of 1.0 for a spin polarized calculation may cause the density of one of the spin components to be zero. For some of the GGA functionals, relying for their implementation on the Libxc library, there is a known issue for such systems. This has been confirmed using Becke88 exchange, but may also be present in other functionals. The zero-electron density causes numerical errors in the exchange-correlation potential, resulting in ill-behaved convergence. The practical solution to this issue is to explicitly set the initial scaled spin value to 0.999, or use a random initial spin.

Hubbard U

Further details of the Hubbard U correction can be found in XC+U mean-field Hubbard term.

DFT-1/2

Further details of the DFT-1/2 correction can be found in DFT-1/2 method.

Abbreviations

Most common exchange-correlation functionals may be specified through abbreviations of the format XCFAMILY[U|Half].XCTYPE, where XCFAMILY determines the class of approximation to use, e.g. LDA or GGA, and also determines if the calculation should be spin polarized (collinear or non-collinear), and if it should include spin-orbit coupling. The table below gives all possibilities for XCFAMILY without the Hubbard U or DFT-1/2 models.

Non-polarized

Spin-polarized

Non-collinear

Spin-orbit

LDA

LSDA

NCLDA

SOLDA

GGA

SGGA

NCGGA

SOGGA

MGGA

SMGGA

NCMGGA

SOMGGA

Note

Appending U or Half to XCFAMILY enables the use of the Hubbard U or DFT-1/2 model, respectively: e.g., SGGAU for spin-polarized GGA with Hubbard U parameters, LDAHalf for non-polarized LDA with DFT-1/2 parameters. Half may only be appended to XCFAMILY in the first two rows of the table (LDA and GGA functionals).

Also note that calculations including spin-orbit coupling, e.g. SOGGA, are inherently done using a non-collinear representation of electron spin, like with NCGGA, but add extra computational complexity.

The value of XCTYPE sets the specific parametrization of the functional type according to the abbreviations given in tables below, e.g. GGA.PBE for the PBE variant of GGA. The abbreviations are shorthand notations for a full, predefined ExchangeCorrelation class, creating well-known combinations of exchange and correlation functionals. Therefore, setting

exchange_correlation=LSDA.PZ

is identical to specifying

exchange_correlation=ExchangeCorrelation(
   exchange=DiracBloch,
   correlation=PerdewZunger,
   number_of_spins=2,
)

Table 18 Available abbreviations for LDA functionals. The exchange part is always DiracBloch.

XCTYPE

Correlation

Wigner

Parametrization

XA

SlatersXAlpha_c

RPA

RandomPhaseApproximation

HL

HedinLundqvist

PZ

PerdewZunger

PW

PerdewWang


Table 19 Available abbreviations for GGA functionals.

XCTYPE

Exchange

Correlation

PBE

PerdewBurkeErnzerhofExchange

PerdewBurkeErnzerhofCorrelation

RPBE

RevisedPerdewBurkeErnzerhofExchange

PerdewBurkeErnzerhofCorrelation

PBES

PerdewBurkeErnzerhofSolids

PerdewBurkeErnzerhofCorrelationSolids

BLYP

Becke88

LeeYangParr

XLYP

XuGoddard

LeeYangParr

PW91

PerdewWang91

PerdewWang91Correlation

BPW91

Becke88

PerdewWang91Correlation

BP86

Becke86

Perdew86


Table 20 Available abbreviations for MGGA functionals. Note that the correlation is LDA-based for TB09.

XCTYPE

Exchange

Correlation

TB09LDA

TB09Exchange

PerdewZunger

SCAN

SCANExchange

SCANCorrelation


Table 21 Available exchange functionals.

Exchange

Family

DiracBloch

LDA

Exchange1D

LDA

Exchange2D

LDA

AdamoBarone

GGA

ArmientoKummel

GGA

ArmientoMattsson

GGA

Bayesian

GGA

Becke86

GGA

Becke862D

GGA

Becke86MGC2D

GGA

Becke88

GGA

Becke882D

GGA

Becke88DionVanDerWaals

GGA

Becke88ProtonTransfer

GGA

BerlandHyldgaard

GGA

BPCCAC

GGA

C09xForRutgersChalmersVdW

GGA

ChiodoConstantinFabianoExchange

GGA

ConstantinAiryGas

GGA

ConstantinFabianoLaricchiaSalaExchange

GGA

DelCampoGazquezTrickeyVela

GGA

FabianoConstantinSalaExchange

GGA

FilatovThiel97

GGA

Gill96

GGA

GradientModifiedBecke86

GGA

HaasTranBlahaSchwarz

GGA

HammerHansenNorskov

GGA

HandyCohen

GGA

HJSB88

GGA

HJSB97X

GGA

HJSPBE

GGA

HJSPBESOL

GGA

KealTozer1

GGA

KressDePristo

GGA

LacksGordon93

GGA

LocalAiryGas

GGA

Madsen

GGA

MinisotaN12Exchange

GGA

ModifiedAdamoBarone

GGA

ModifiedFilatovThiel97

GGA

OuYangLevy2

GGA

PedrozaSilvaCapelleJSJR

GGA

PerdewBurkeErnzerhof2D

GGA

PerdewBurkeErnzerhofExchange

GGA

PerdewBurkeErnzerhofRegularizedExchange

GGA

PerdewBurkeErnzerhofSolids

GGA

PerdewBurkeErnzerhofVanDerWaalsK1

GGA

PerdewBurkeErnzerhofVanDerWaalsOpt

GGA

PerdewWang86

GGA

PerdewWang86Refitted

GGA

PerdewWang91

GGA

RevisedBecke86

GGA

RevisedKressDePristo

GGA

RevisedPerdewBurkeErnzerhofExchange

GGA

SecondOrderGGA

GGA

SecondOrderGGA2011Exchange

GGA

ShortRangeGGA

GGA

ShortRangeGGASFAT

GGA

ShortRangePBE

GGA

SwartSolaBickelhauptDispersion

GGA

SwartSolaBickelhauptExchange

GGA

SwartSolaBickelhauptPBEExchange

GGA

TognettiCortonaAdamoExchange

GGA

VanLeeuwenBaerends

GGA

VanLeeuwenBaerendsModified

GGA

VelaMedelTrickey84GE

GGA

VelaMedelTrickey84PBE

GGA

VelaMedelTrickeyGE

GGA

VelaMedelTrickeyPBE

GGA

WuCohen

GGA

XuGoddard

GGA

BalancedLocalization

MGGA

GVT4Exchange

MGGA

LocalTauApproximation

MGGA

M06Local

MGGA

M11LExchange

MGGA

ManbyKnowles

MGGA

ManbyKnowlesB

MGGA

MinisotaMN12LExchange

MGGA

ModifiedTaoPerdewStaroverovScuseriaExchange

MGGA

PerdewKurthZupanBlaha

MGGA

SCANExchange

MGGA

SunXiaoBulikScuseriaPerdewMS1

MGGA

SunXiaoBulikScuseriaPerdewMS2

MGGA

SunXiaoRuzsinszkyMS0

MGGA

TaoPerdewStaroverovScuseriaExchange

MGGA

TaoPerdewStaroverovScuseriaRevisedExchange

MGGA

TB09Exchange

MGGA

TwoDimensionalPRHG

MGGA

TwoDimensionalPRHGCorrected

MGGA


Table 22 Available correlation functionals.

Correlation

Family

Attacalite

LDA

CasulaSorellaSenatore1D

LDA

Gombas

LDA

GunnarssonLundqvist

LDA

HedinLundqvist

LDA

Loos1D

LDA

ModifiedPerdewWang

LDA

ModifiedPerdewZunger

LDA

OrtizBallone

LDA

OrtizBallonePerdewWang

LDA

PerdewWang

LDA

PerdewWangRPA

LDA

PerdewZunger

LDA

PittalisRasanenMarques

LDA

ProynovSalahubModifiedLSD1

LDA

ProynovSalahubModifiedLSD2

LDA

RagotCortona

LDA

RandomPhaseApproximation

LDA

SlatersXAlpha

LDA

VonBarthHedin

LDA

VoskoWilkNussair

LDA

VoskoWilkNussair1

LDA

VoskoWilkNussair2

LDA

VoskoWilkNussair3

LDA

VoskoWilkNussair4

LDA

VoskoWilkNussairRPA

LDA

WignerParametrization

LDA

ArmientoMattssonCorrelation

GGA

ChiodoConstantinFabianoCorrelation

GGA

CohenHandy

GGA

ConstantinFabianoLaricchiaSalaCorrelation

GGA

ConstantinFabianoSalaZPBEINT

GGA

ConstantinFabianoSalaZPBESOL

GGA

ExtendedXuGoddard

GGA

FabianoConstantinSalaCorrelation

GGA

FilatovThiel97Correlation

GGA

LangrethMehl

GGA

LeeYangParr

GGA

MinisotaN12Correlation

GGA

MinisotaN12SXCorrelation

GGA

OneParameterB88

GGA

OneParameterG96

GGA

OneParameterPBE

GGA

OneParameterXAlpha

GGA

PedrozaSilvaCapelleJRGX

GGA

Perdew86

GGA

PerdewBurkeErnzerhofCorrelation

GGA

PerdewBurkeErnzerhofCorrelationSolids

GGA

PerdewBurkeErnzerhofRegularizedCorrelation

GGA

PerdewRuszinszkyCsonkaConstantin

GGA

PerdewWang91Correlation

GGA

SecondOrderGGA2011Correlation

GGA

SwartSolaBickelhauptPBE

GGA

TognettiCortonaAdamo

GGA

TognettiCortonaAdamoRevised

GGA

WilsonIvanov

GGA

WilsonIvanovInitial

GGA

WilsonLevy

GGA

BC95Correlation

MGGA

CancioChou

MGGA

ColleSalvetti

MGGA

M06LocalCorrelation

MGGA

M11LCorrelation

MGGA

MinisotaMN12LCorrelation

MGGA

PerdewKurthZupanBlahaCorrelation

MGGA

SCANCorrelation

MGGA

TaoPerdewStaroverovScuseriaCorrelation

MGGA

TaoPerdewStaroverovScuseriaRevisedCorrelation

MGGA

VSXCCorrelation

MGGA


References

ATK uses the Libxc library for efficient implementations of exchange and correlation functionals. In the following tables, we list the parameterization that are available in QuantumATK, along with the corresponding entity used in the Libxc manual, and with references to the original articles.

Table 23 Available LDA exchange parametrizations in QuantumATK.

Keyword

Libxc entity

Description and references

DiracBloch

XC_LDA_X

Exchange. PAM Dirac, (Mathematical) Proceedings of the Cambridge Philosophical Society 26, 376 (1930) F Bloch, Zeitschrift fuer Physik 57, 545 (1929)

Exchange1D

XC_LDA_X_1D

Exchange in 1D N. Helbig, J. I. Fuks, M. Casula, M. J. Verstraete, M. A. L. Marques, I. V. Tokatly and A. Rubio, Phys. Rev. A 83, 032503 (2011)

Exchange2D

XC_LDA_X_2D

Exchange in 2D PAM Dirac, (Mathematical) Proceedings of the Cambridge Philosophical Society 26, 376 (1930) F Bloch, Zeitschrift fuer Physik 57, 545 (1929)


Table 24 Available LDA correlation parametrizations in QuantumATK.

Keyword

Libxc entity

Description and references

Attacalite

XC_LDA_C_2D_AMGB (was XC_LDA_C_AMGB)

Attacalite et al., for 2D systems C Attacalite et al., Phys. Rev. Lett. 88, 256601 (2002) C Attacalite, PhD thesis

CasulaSorellaSenatore1D

XC_LDA_C_1D_CSC (was XC_LDA_C_AMGB)

Casula, Sorella, and Senatore 1D correlation M Casula, S Sorella, and G Senatore, Phys. Rev. B 74, 245427 (2006)

Gombas

XC_LDA_C_GOMBAS (was XC_LDA_C_AMGB)

Gombas parametrization P. Gombas, Pseudopotentiale (Springer-Verlag, Wien, New York, 1967)

GunnarssonLundqvist

XC_LDA_C_GL

Gunnarson & Lundqvist O Gunnarsson and BI Lundqvist, Phys. Rev. B 13, 4274 (1976)

HedinLundqvist

XC_LDA_C_HL

Hedin & Lundqvist L. Hedin and B.I. Lundqvist, , J. Phys. C 4, 2064 (1971)

Loos1D

XC_LDA_C_1D_LOOS

P-F Loos correlation LDA P-F Loos, arXiv:1207.6849v1 [cond-mat.str-el] (2012)

ModifiedPerdewWang

XC_LDA_C_PW_MOD

Perdew & Wang (Modified) Added extra digits to some constants as in the PBE routine (http://dft.uci.edu/pubs/PBE.asc) JP Perdew and Y Wang, Phys. Rev. B 45, 13244 (1992)

ModifiedPerdewZunger

XC_LDA_C_PZ_MOD

Perdew & Zunger (Modified) Modified to improve the matching between the low and high rs parts Perdew and Zunger, Phys. Rev. B 23, 5048 (1981)

OrtizBallone

XC_LDA_C_OB_PZ

Ortiz & Ballone (PZ). G Ortiz and P Ballone, Phys. Rev. B 50, 1391 (1994) , G Ortiz and P Ballone, Phys. Rev. B 56, 9970(E) (1997) Perdew and Zunger, Phys. Rev. B 23, 5048 (1981)

OrtizBallonePerdewWang

XC_LDA_C_OB_PW

Ortiz & Ballone (PW) G Ortiz and P Ballone, Phys. Rev. B 50, 1391 (1994) G Ortiz and P Ballone, Phys. Rev. B 56, 9970(E) (1997) JP Perdew and Y Wang, Phys. Rev. B 45, 13244 (1992)

PerdewWang

XC_LDA_C_PW

Perdew & Wang JP Perdew and Y Wang, Phys. Rev. B 45, 13244 (1992)

PerdewWangRPA

XC_LDA_C_PW_RPA

Perdew & Wang fit of the RPA JP Perdew and Y Wang, Phys. Rev. B 45, 13244 (1992)

PerdewZunger

XC_LDA_C_PZ

Perdew & Zunger Perdew and Zunger, Phys. Rev. B 23, 5048 (1981)

PittalisRasanenMarques

XC_LDA_C_2D_PRM (was XC_LDA_C_PRM08)

Pittalis, Rasanen & Marques correlation in 2D S Pittalis, E Rasanen, and MAL Marques, Phys. Rev. B 78, 195322 (2008)

ProynovSalahubModifiedLSD1

XC_LDA_C_ML1 (was XC_LDA_C_PRM08)

Modified LSD (version 1) of Proynov and Salahub EI Proynov and D Salahub, Phys. Rev. B 49, 7874 (1994)

ProynovSalahubModifiedLSD2

XC_LDA_C_ML2 (was XC_LDA_C_PRM08)

Modified LSD (version 2) of Proynov and Salahub EI Proynov and D Salahub, Phys. Rev. B 49, 7874 (1994)

RandomPhaseApproximation

XC_LDA_C_RPA

Random Phase Approximation M Gell-Mann and KA Brueckner, Phys. Rev. 106, 364 (1957)

RagotCortona

XC_LDA_C_RC04

Ragot-Cortona S Ragot and P Cortona, J. Chem. Phys. 121, 7671 (2004)

SlatersXAlpha

XC_LDA_C_XALPHA

Slater’s X-alpha JC Slater, Phys. Rev. 81, 385 (1951)

VonBarthHedin

XC_LDA_C_vBH

von Barth & Hedin U von Barth and L Hedin, J. Phys. C: Solid State Phys. 5, 1629 (1972)

VoskoWilkNussair

XC_LDA_C_VWN

Vosko, Wilk, & Nussair SH Vosko, L Wilk, and M Nusair, Can. J. Phys. 58, 1200 (1980)

VoskoWilkNussair1

XC_LDA_C_VWN_1

Vosko, Wilk, & Nussair (1) SH Vosko, L Wilk, and M Nusair, Can. J. Phys. 58, 1200 (1980)

VoskoWilkNussair2

XC_LDA_C_VWN_2

Vosko, Wilk, & Nussair (2) SH Vosko, L Wilk, and M Nusair, Can. J. Phys. 58, 1200 (1980)

VoskoWilkNussair3

XC_LDA_C_VWN_3

Vosko, Wilk, & Nussair (3) SH Vosko, L Wilk, and M Nusair, Can. J. Phys. 58, 1200 (1980)

VoskoWilkNussair4

XC_LDA_C_VWN_4

Vosko, Wilk, & Nussair (4) SH Vosko, L Wilk, and M Nusair, Can. J. Phys. 58, 1200 (1980)

VoskoWilkNussairRPA

XC_LDA_C_VWN_RPA

Vosko, Wilk, & Nussair (RPA) SH Vosko, L Wilk, and M Nusair, Can. J. Phys. 58, 1200 (1980)

WignerParametrization

XC_LDA_C_WIGNER

Wigner parametrization EP Wigner, Trans. Faraday Soc. 34, 678 (1938)


Table 25 Available GGA exchange parametrizations in QuantumATK.

Keyword

Libxc entity

Description and references

AdamoBarone

XC_GGA_X_mPW91

Modified form of PW91 by Adamo & Barone C Adamo and V Barone, J. Chem. Phys. 108, 664 (1998)

ArmientoMattsson

XC_GGA_X_AM05

Armiento & Mattsson 05 exchange R Armiento and AE Mattsson, Phys. Rev. B 72, 085108 (2005) AE Mattsson, R Armiento, J Paier, G Kresse, JM Wills, and TR Mattsson, J. Chem. Phys. 128, 084714 (2008)

Bayesian

XC_GGA_X_BAYESIAN

Bayesian best fit for the enhancement factor JJ Mortensen, K Kaasbjerg, SL Frederiksen, JK Norskov, JP Sethna, and KW Jacobsen, Phys. Rev. Lett. 95, 216401 (2005)

Becke86

XC_GGA_X_B86

Becke 86 AD Becke, J. Chem. Phys 84, 4524 (1986)

Becke862D

XC_GGA_X_2D_B86

Becke 86 in 2D. G Vilhena and MAL Marques, unpublished AD Becke, J. Chem. Phys 84, 4524 (1986)

Becke86MGC2D

XC_GGA_X_2D_B86_MGC

Becke 86 MGC for 2D systems S Pittalis, E Rasanen, JG Vilhena, and MAL Marques, Phys. Rev. A 79, 012503 (2009) AD Becke, J. Chem. Phys 85, 7184 (1986)

Becke88

XC_GGA_X_B88

Becke 88 AD Becke, Phys. Rev. A 38, 3098 (1988)

Becke882D

XC_GGA_X_2D_B88

Becke 88 in 2D. G Vilhena, MAL Marques, unpublished AD Becke, Phys. Rev. A 38, 3098 (1988)

Becke88DionVanDerWaals

XC_GGA_X_OPTB88_VDW

Becke 88 reoptimized to be used with vdW functional of Dion et al J Klimes, DR Bowler, and A Michaelides, J. Phys.: Condens. Matter 22, 022201 (2010)

Becke88ProtonTransfer

XC_GGA_X_MB88

Modified Becke 88 for proton transfer V Tognetti and C Adamo, J. Phys. Chem. A 113, 14415-14419 (2009)

BPCCAC

XC_GGA_X_BPCCAC

BPCCAC (GRAC for the energy) E Bremond, D Pilard, I Ciofini, H Chermette, C Adamo, and P Cortona, Theor Chem Acc 131, 1184 (2012)

C09xForRutgersChalmersVdW

XC_GGA_X_C09X

C09x to be used with the VdW of Rutgers-Chalmers VR Cooper, PRB 81, 161104(R) (2010)

ConstantinAiryGas

XC_GGA_X_AIRY

Constantin et al based on the Airy gas LA Constantin, A Ruzsinszky, and JP Perdew, Phys. Rev. B 80, 035125 (2009)

FilatovThiel97

XC_GGA_X_FT97_A

Filatov & Thiel 97 (version A) M Filatov and W Thiel, Mol. Phys. 91, 847 (1997)

Gill96

XC_GGA_X_G96

Gill 96 PMW Gill, Mol. Phys. 89, 433 (1996)

GradientModifiedBecke86

XC_GGA_X_B86_MGC

Becke 86 Xalfa,beta,gamma (with mod. grad. correction) AD Becke, J. Chem. Phys 84, 4524 (1986) AD Becke, J. Chem. Phys 85, 7184 (1986)

HaasTranBlahaSchwarz

XC_GGA_X_HTBS

Haas, Tran, Blaha, and Schwarz P Haas, F Tran, P Blaha, and K Schwarz, Phys. Rev. B 83, 205117 (2011)

HammerHansenNorskov

XC_GGA_X_RPBE

Hammer, Hansen & Norskov (PBE-like) B Hammer, LB Hansen and JK Noerskov, Phys. Rev. B 59, 7413 (1999)

HandyCohen

XC_GGA_X_OPTX

Handy & Cohen OPTX 01 NC Handy and AJ Cohen, Mol. Phys. 99, 403 (2001)

HJSB88

XC_GGA_X_HJS_B88

HJS screened exchange B88 version NTM Henderson, BG Janesko, and GE Scuseria, J. Chem. Phys. 128, 194105 (2008)

HJSB97X

XC_GGA_X_HJS_B97X

HJS screened exchange B97x version NTM Henderson, BG Janesko, and GE Scuseria, J. Chem. Phys. 128, 194105 (2008)

HJSPBE

XC_GGA_X_HJS_PBE

HJS screened exchange PBE version NTM Henderson, BG Janesko, and GE Scuseria, J. Chem. Phys. 128, 194105 (2008)

HJSPBESOL

XC_GGA_X_HJS_PBE_SOL

HJS screened exchange PBE_SOL version NTM Henderson, BG Janesko, and GE Scuseria, J. Chem. Phys. 128, 194105 (2008)

KealTozer1

XC_GGA_X_KT1

Keal and Tozer version 1 TW Keal and DJ Tozer, J. Chem. Phys. 119, 3015 (2003)

KressDePristo

XC_GGA_X_DK87_R1

dePristo & Kress 87 (version R1) AE DePristo and JD Kress, J. Chem. Phys. 86, 1425 (1987)

LacksGordon93

XC_GGA_X_LG93

Lacks & Gordon 93 DJ Lacks and RG Gordon, Phys. Rev. A 47, 4681 (1993)

LocalAiryGas

XC_GGA_X_LAG

Local Airy Gas L Vitos, B Johansson, J Kollar, and HL Skriver, Phys. Rev. B 62, 10046-10050 (2000)

Madsen

XC_GGA_X_PBEA

Madsen (PBE-like) G Madsen, Phys. Rev. B 75, 195108 (2007)

ModifiedAdamoBarone

XC_GGA_X_MPBE

Adamo & Barone modification to PBE C Adamo and V Barone, J. Chem. Phys., 116, 5933 (2002)

ModifiedFilatovThiel97

XC_GGA_X_FT97_B

Filatov & Thiel 97 (version B) M Filatov and W Thiel, Mol. Phys. 91, 847 (1997)

PedrozaSilvaCapelleJSJR

XC_GGA_X_PBE_JSJR

JSJR reparametrization by Pedroza, Silva & Capelle LS Pedroza, AJR da Silva, and K. Capelle, Phys. Rev. B 79, 201106(R) (2009)

PerdewBurkeErnzerhof2D

XC_GGA_X_2D_PBE

Perdew, Burke & Ernzerhof exchange in 2D. G Vilhena and MAL Marques, unpublished JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996) JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 78, 1396(E) (1997)

PerdewBurkeErnzerhofExchange

XC_GGA_X_PBE

Perdew, Burke & Ernzerhof exchange JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996) JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 78, 1396(E) (1997)

PerdewBurkeErnzerhofRegularizedExchange

XC_GGA_X_RGE2

Regularized PBE A Ruzsinszky, GI Csonka, and G Scuseria, J. Chem. Theory Comput. 5, 763 (2009)

PerdewBurkeErnzerhofSolids

XC_GGA_X_PBE_SOL

Perdew, Burke & Ernzerhof exchange (solids) JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996) JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 78, 1396(E) (1997) JP Perdew, et al., Phys. Rev. Lett. 100, 136406 (2008) arXiv:0707.2088v1

PerdewBurkeErnzerhofVanDerWaalsK1

XC_GGA_X_PBEK1_VDW

PBE reparametrization for vdW J Klimes, DR Bowler, and A Michaelides, J. Phys.: Condens. Matter 22, 022201 (2010)

PerdewBurkeErnzerhofVanDerWaalsOpt

XC_GGA_X_OPTPBE_VDW

PBE reparametrization for vdW J Klimes, DR Bowler, and A Michaelides, J. Phys.: Condens. Matter 22, 022201 (2010)

PerdewWang86

XC_GGA_X_PW86

Perdew & Wang 86. JP Perdew and Y Wang, Phys. Rev. B 33, 8800 (1986)

PerdewWang86Refitted

XC_GGA_X_RPW86

Refitted Perdew & Wang 86 ED Murray, K Lee and DC Langreth, J. Chem. Theory Comput. 5, 2754-2762 (2009)

PerdewWang91

XC_GGA_X_PW91

Perdew & Wang 91 JP Perdew, JA Chevary, SH Vosko, KA Jackson, MR Pederson, and C Fiolhais, Phys. Rev. B 46, 6671 (1992)

RevisedBecke86

XC_GGA_X_B86_R

Becke 86 Xalfa,beta,gamma (reoptimized) AD Becke, J. Chem. Phys 84, 4524 (1986) AD Becke, J. Chem. Phys 107, 8554 (1997)

RevisedKressDePristo

XC_GGA_X_DK87_R2

dePristo & Kress 87 (version R2) AE DePristo and JD Kress, J. Chem. Phys. 86, 1425 (1987)

RevisedPerdewBurkeErnzerhofExchange

XC_GGA_X_PBE_R

Perdew, Burke & Ernzerhof exchange (revised) JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996) JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 78, 1396(E) (1997) Y Zhang and W Yang, Phys. Rev. Lett 80, 890 (1998)

SecondOrderGGA

XC_GGA_X_SOGGA

Second-order generalized gradient approximation Y Zhao and DG Truhlar, J. Chem. Phys. 128, 184109 (2008) Minnesota Functional Module

SecondOrderGGA2011Exchange

XC_GGA_X_SOGGA11

Second-order generalized gradient approximation 2011 R Peverati, Y Zhao, and DG Truhlar, J. Phys. Chem. Lett. 2, 1991-1997 (2011) Minnesota Functional Module

ShortRangeGGA

XC_GGA_X_ITYH

Short-range recipe for exchange GGA functionals H Iikura, T Tsuneda, T Yanai, and K Hirao, J. Chem. Phys. 115, 3540 (2001)

ShortRangePBE

XC_GGA_X_WPBEH

Short-range part of the PBE (default w=0 gives PBEh) J Heyd, GE Scuseria, and M Ernzerhof, J. Chem. Phys. 118, 8207 (2003)

SwartSolaBickelhauptDispersion

XC_GGA_X_SSB_D

Swarta, Sola and Bickelhaupt dispersion M Swart, M Sola, and FM Bickelhaupt, J. Chem. Phys. 131, 094103 (2009)

SwartSolaBickelhauptExchange

XC_GGA_X_SSB

Swarta, Sola and Bickelhaupt M Swart, M Sola, and FM Bickelhaupt, J. Chem. Phys. 131, 094103 (2009)

SwartSolaBickelhauptPBEExchange

XC_GGA_X_SSB_SW

Swarta, Sola and Bickelhaupt correction to PBE M Swart, M Sola, and FM Bickelhaupt, J. Comp. Meth. Sci. Engin. 9, 69 (2009)

WuCohen

XC_GGA_X_WC

Wu & Cohen Z Wu and RE Cohen, Phys. Rev. B 73, 235116 (2006)

XuGoddard

XC_GGA_X_XPBE

xPBE reparametrization by Xu & Goddard X. Xu and WA Goddard III, J. Chem. Phys., 121, 4068 (2004)


Table 26 Available GGA correlation parametrizations in QuantumATK.

Keyword

Libxc entity

Description and references

ArmientoMattssonCorrelation

XC_GGA_C_AM05

Armiento & Mattsson 05 correlation R Armiento and AE Mattsson, Phys. Rev. B 72, 085108 (2005) AE Mattsson, R Armiento, J Paier, G Kresse, JM Wills, and TR Mattsson, J. Chem. Phys. 128, 084714 (2008)

CohenHandy

XC_GGA_C_OPTC

Optimized correlation functional of Cohen and Handy AJ Cohen and NC Handy, Mol. Phys. 99, 607-615 (2001)

ExtendedXuGoddard

XC_GGA_C_XPBE

xPBE reparametrization by Xu & Goddard X. Xu and WA Goddard III, J. Chem. Phys., 121, 4068 (2004)

FilatovThiel97Correlation

XC_GGA_C_FT97

Filatov & Thiel correlation M Filatov & W Thiel, Int. J. Quant. Chem. 62, 603-616 (1997) M Filatov & W Thiel, Mol Phys 91, 847 (1997)

LangrethMehl

XC_GGA_C_LM

Langreth and Mehl correlation DC Langreth and MJ Mehl, Phys. Rev. Lett. 47, 446 (1981)

LeeYangParr

XC_GGA_C_LYP

Lee, Yang & Parr C Lee, W Yang and RG Parr, Phys. Rev. B 37, 785 (1988) B Miehlich, A Savin, H Stoll and H Preuss, Chem. Phys. Lett. 157, 200 (1989)

OneParameterB88

XC_GGA_C_OP_B88

One-parameter progressive functional (B88 version) T Tsuneda, T Suzumura, and K Hirao, J. Chem. Phys. 110, 10664 (1999)

OneParameterG96

XC_GGA_C_OP_G96

One-parameter progressive functional (G96 version) T Tsuneda, T Suzumura, and K Hirao, J. Chem. Phys. 111, 5656 (1999)

OneParameterPBE

XC_GGA_C_OP_PBE

One-parameter progressive functional (PBE version) T Tsuneda, T Suzumura, and K Hirao, J. Chem. Phys. 111, 5656 (1999)

OneParameterXAlpha

XC_GGA_C_OP_XALPHA

One-parameter progressive functional (XALPHA version) T Tsuneda, T Suzumura, and K Hirao, J. Chem. Phys. 111, 5656 (1999)

PedrozaSilvaCapelleJRGX

XC_GGA_C_PBE_JRGX

JRGX reparametrization by Pedroza, Silva & Capelle LS Pedroza, AJR da Silva, and K. Capelle, Phys. Rev. B 79, 201106(R) (2009)

Perdew86

XC_GGA_C_P86

Perdew 86 JP Perdew, Phys. Rev. B 33, 8822 (1986)

PerdewBurkeErnzerhofCorrelation

XC_GGA_C_PBE

Perdew, Burke & Ernzerhof correlation JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996) JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 78, 1396(E) (1997)

PerdewBurkeErnzerhofCorrelationSolids

XC_GGA_C_PBE_SOL

Perdew, Burke & Ernzerhof correlation SOL JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996) JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 78, 1396(E) (1997) JP Perdew, et al., Phys. Rev. Lett. 100, 136406 (2008) arXiv:0707.2088v1

PerdewBurkeErnzerhofRegularizedCorrelation

XC_GGA_C_RGE2

Regularized PBE A Ruzsinszky, GI Csonka, and G Scuseria, J. Chem. Theory Comput. 5, 763 (2009)

PerdewWang91Correlation

XC_GGA_C_PW91

Perdew & Wang 91 JP Perdew, JA Chevary, SH Vosko, KA Jackson, MR Pederson, DJ Singh, and C Fiolhais, Phys. Rev. B 46, 6671 (1992) JP Perdew, JA Chevary, SH Vosko, KA Jackson, MR Pederson, DJ Singh, and C Fiolhais, Phys. Rev. B 48, 4978(E) (1993)

SecondOrderGGA2011Correlation

XC_GGA_C_SOGGA11

Second-order generalized gradient approximation 2011 R Peverati, Y Zhao, and DG Truhlar, J. Phys. Chem. Lett. 2, 1991-1997 (2011) Minnesota Functional Module

SwartSolaBickelhauptPBE

XC_GGA_C_SPBE

PBE correlation to be used with the SSB exchange M Swart, M Sola, and FM Bickelhaupt, J. Chem. Phys. 131, 094103 (2009)

TognettiCortonaAdamo

XC_GGA_C_TCA

Tognetti, Cortona, Adamo V Tognetti, P Cortona, and C Adamo, J. Chem. Phys. 128, 034101 (2008)

TognettiCortonaAdamoRevised

XC_GGA_C_REVTCA

Tognetti, Cortona, Adamo (revised) V Tognetti, P Cortona, and C Adamo, Chem. Phys. Lett. 460, 536-539 (2008)

WilsonIvanov

XC_GGA_C_WI

Wilson & Ivanov LC Wilson & S Ivanov, Int. J. Quantum Chem. 69, 523-532 (1998)

WilsonIvanovInitial

XC_GGA_C_WI0

Wilson & Ivanov initial version LC Wilson & S Ivanov, Int. J. Quantum Chem. 69, 523-532 (1998)

WilsonLevy

XC_GGA_C_WL

Wilson & Levy LC Wilson and M Levy, Phys. Rev. B 41, 12930 (1990)


Table 27 Available MGGA exchange parametrizations in QuantumATK.

Keyword

Libxc entity

Description and references

M05

XC_MGGA_X_M05

M05 functional of Minnesota Y Zhao, NE Schultz, and DG Truhlar, J. Chem. Phys. 123, 161103 (2005)

M052X

XC_MGGA_X_M05_2X

M05-2X functional of Minnesota Y Zhao, NE Schultz, and DG Truhlar, J. Chem. Theory Comput. 2, 364 (2006)

M06

XC_MGGA_X_M06

M06 functional of Minnesota Y Zhao and DG Truhlar, Theor. Chem. Acc. 120, 215 (2008)

M062X

XC_MGGA_X_M06_2X

M06-2X functional of Minnesota Y Zhao and DG Truhlar, Theor. Chem. Acc. 120, 215 (2008)

M06HF

XC_MGGA_X_M06_HF

M06-HF functional of Minnesota Y Zhao and DG Truhlar, J. Phys. Chem. A 110, 13126 (2006)

M06Local

XC_MGGA_X_M06_L

M06-Local functional of Minnesota Y. Zhao and D. G. Truhlar, J. Chem. Phys. 125, 194101 (2006) Y Zhao and DG Truhlar, Theor. Chem. Account 120, 215 (2008)

M08HX

XC_MGGA_X_M08_HX

M08-HX functional of Minnesota Y Zhao and DG Truhlar, J. Chem. Theory Comput. 4, 1849-1868 (2008)

M08SO

XC_MGGA_X_M08_SO

M08-SO functional of Minnesota Y Zhao and DG Truhlar, J. Chem. Theory Comput. 4, 1849-1868 (2008)

PerdewKurthZupanBlaha

XC_MGGA_X_PKZB

Perdew, Kurth, Zupan, and Blaha JP Perdew, S Kurth, A Zupan, and P. Blaha, Phys. Rev. Lett. 82, 2544-2547 (1999)

SCANExchange

XC_MGGA_X_SCAN

J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015)

TaoPerdewStaroverovScuseriaExchange

XC_MGGA_X_TPSS

Perdew, Tao, Staroverov & Scuseria exchange JP Perdew, J Tao, VN Staroverov and GE Scuseria, Phys. Rev. Lett. 91, 146401 (2003) JP Perdew, J Tao, VN Staroverov and GE Scuseria, J. Chem. Phys. 120, 6898 (2004)

TaoPerdewStaroverovScuseriaRevisedExchange

XC_MGGA_X_REVTPSS

Revised Perdew, Tao, Staroverov & Scuseria exchange JP Perdew, A Ruzsinszky, GI Csonka, LA Constantin, and J Sun, Phys. Rev. Lett. 103, 026403 (2009) JP Perdew, A Ruzsinszky, GI Csonka, LA Constantin, and J Sun, Phys. Rev. Lett. 106, 179902(E) (2011)

TB09Exchange

XC_MGGA_X_TB09

Tran & Blaha 89, meta-GGA F Tran and P Blaha, Phys. Rev. Lett. 102, 226401 (2009)


Table 28 Available MGGA correlation parametrizations in QuantumATK.

Keyword

Libxc entity

Description and references

PerdewZungerCorrelation

XC_MGGA_C_M06_L

M06-Local functional of Minnesota Perdew and Zunger, Phys. Rev. B 23, 5048 (1981) Reused from PerdewZunger class in order to allow inclusion in MGGA.

SCANCorrelation

XC_MGGA_C_SCAN

J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015)

TaoPerdewStaroverovScuseriaCorrelation

XC_MGGA_C_TPSS

Perdew, Tao, Staroverov & Scuseria correlation JP Perdew, J Tao, VN Staroverov and GE Scuseria, Phys. Rev. Lett. 91, 146401 (2003) JP Perdew, J Tao, VN Staroverov and GE Scuseria, J. Chem. Phys. 120, 6898 (2004)