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
correlation()
Returns:The correlation functional class
Return type:Correlation
dftHalfEnabled()
Returns:Whether DFT-1/2 is enabled.
Type:bool
exchange()
Returns:The exchange functional class
Return type:Exchange
hubbardTerm()
Returns:The Hubbard term used.
Return type:Onsite | OnsiteShell | Dual | DualShell | None
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
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

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 [TB09]. 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 [BJ06]):

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 23 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 24 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 25 Available abbreviations for MGGA functionals. Note that the correlation is LDA-based for TB09.
XCTYPE Exchange Correlation
TB09LDA TB09Exchange PerdewZunger
SCAN SCANExchange SCANCorrelation

Table 26 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 27 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 28 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 29 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 30 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 31 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 32 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 33 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)

[BJ06]Axel D. Becke and Erin R. Johnson. A simple effective potential for exchange. J. Chemi. Phys., 2006. doi:http://dx.doi.org/10.1063/1.2213970.
[TB09]F. Tran and P. Blaha. Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential. Phys. Rev. Lett., 102:226401, 2009. doi:10.1103/PhysRevLett.102.226401.