ExchangeCorrelation

	ExchangeCorrelation
DoubleContourIntegralParameters	HuckelBasisParameters

Name

ExchangeCorrelation — Class for representing Exchange Correlation types

Synopsis

Namespace: NanoLanguage

ExchangeCorrelation(
exchange,
correlation,
hubbard_term,
number_of_spins
)

Description

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.

ExchangeCorrelation Arguments

exchange

The exchange to be used.

Type: keyword

Default:


          must be specified

correlation

The correlation to be used.

Type: keyword

Default:


          must be specified

hubbard_term

The Hubbard term to add.

Type: Onsite | Dual | None

Default:


          None

number_of_spins

The number of spins to be used in the calculation.

Type: positive integer

Default:

ExchangeCorrelation Methods

A ExchangeCorrelation object provides the following methods:

This object supports cloning. See the section called “Cloning of ATK Python objects”.
hubbardTerm(): Query method for getting the Hubbard term used
nlprint(stream): Print a string representation of the ExchangeCorrelation instance.

stream

The stream the bandstructure should be written to.
Type: A stream that supports strings being written to using 'write'.
Default: sys.stdout
numberOfSpins(): Query method for getting the number of spins
spinType(): Query method for getting the spin type

Usage Examples

Define a spin-polarized LDA+U calculation for Nickel with a Hubbard U of 4.6 eV on Nickel and using the Dual representation for the Hubbard term.

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)

Notes

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

The ExchangeCorrelation class can take parameters. Currently, this is only relevant for the TB09 meta-GGA functional, which takes a parameter c (cf. the section called “Meta-GGA”). If no value is specified, the value of c is automatically computed according to Eq. (3) in Ref. [39]. The following piece of code selects the TB09 functional with c=1.0 (recovering the Becke-Johnson potental [40]):

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

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 random initial spin.

Further details of the Hubbard U correction can be found in the section called “XC+U mean-field Hubbard term”

Abbreviations

The most common functionals may be specified through abbreviations of the format L[S]DA[U].XCTYPE or [S][M]GGA[U].XCTYPE, where XCTYPE specifies the parametrization of the functional according to the tables below, S selects the spin-polarized version, and U enables the use of the Hubbard model.

The abbreviations are shorthand notations for a full, predefined ExchangeCorrelation class. Thus setting

exchange_correlation=LSDA.PZ

is identical to specifying

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

Table 15: Available abbreviations for specifying LDA functionals. The exchange part is always DiracBloch.

XCTYPE	Correlation
WIGNER	WignerParametrization
XA	SlatersXAlpha
RPA	RandomPhaseApproximation
HL	HedinLundqvist
PZ	PerdewZunger
PW	PerdewWang

Table 16: Available abbreviations for specifying 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 17: Available abbreviations for specifying meta-GGA functionals. Note that the correlation is LDA-based.

XCTYPE	Exchange	Correlation
TB09LDA	TB09Exchange	PerdewZunger

References

ATK uses the Libxc library for exchange and correlation. In the following tables we list the parameterization that are available in ATK 12.2.0, along with the corresponding entity used in the Libxc documentation, and with references to the original articles.

Table 18: Available LDA Exchange parametrizations in ATK

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)

Table 19: Available LDA Correlation parametrizations in ATK

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
`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)
`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)
`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)
`RandomPhaseApproximation`	XC_LDA_C_RPA	Random Phase Approximation M Gell-Mann and KA Brueckner, Phys. Rev. 106, 364 (1957)
`SlatersXAlpha`	XC_LDA_C_XALPHA	Slater's Xa (X-alpha)
`WignerParametrization`	XC_LDA_C_WIGNER	Wigner parametrization EP Wigner, Trans. Faraday Soc. 34, 678 (1938)
`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)
`VoskoWilkNussairRPA`	XC_LDA_C_VWN_RPA	Vosko, Wilk, & Nussair (RPA) SH Vosko, L Wilk, and M Nusair, Can. J. Phys. 58, 1200 (1980)

Table 20: Available GGA Exchange parametrizations in ATK

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)
`Becke86`	XC_GGA_X_B86	Becke 86 Xalfa,beta,gamma AD Becke, J. Chem. Phys 84, 4524 (1986)
`Becke88`	XC_GGA_X_B88	Becke 88 AD Becke, Phys. Rev. A 38, 3098 (1988)
`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)
`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)
`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)
`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)
`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)
`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
`PerdewWang86`	XC_GGA_X_PW86	Perdew & Wang 86 JP Perdew and Y Wang, Phys. Rev. B 33, 8800 (1986)
`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)
`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 21: Available GGA Correlation parametrizations in ATK

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

Table 22: Available Meta-GGA Exchange parametrizations in ATK

Keyword	Libxc entity	Description and references
`TB09Exchange`	XC_MGGA_X_TB09	Tran & Blaha 89, meta-GGA F Tran and P Blaha, Phys. Rev. Lett. 102, 226401 (2009)


DoubleContourIntegralParameters		HuckelBasisParameters