Keyword VXCTYPE

This keyword specifies the choice of exchange-correlation functional. A keyword option controls the selection of the density (Kohn-Sham or auxiliary) to be used in calculating the exchange-correlation energy and matrix elements of the exchange-correlation potential.
Options:
VWN / PZ81 / PW92 / PW86 / BLYP / OLYP / PW91 / PW91SSF / PBE / PBESSF / PBESOL / KT1 / KT2 / KT3 / CAP / SO11 / N12 / GAM / VS98 / PKZB / TPSS / M06L / M11L / MN12 / B3LYP / BH&H / PBE0 / M062X / M06HF / M06 / XALPHA / FOCK / NONE

	VWN		Dirac exchange with local VWN correlation [79,88].
	PZ81		Dirac exchange with local PZ81 correlation [79,89].
	PW92		Dirac exchange with local PW92 correlation [79,90].
	PW86		PW86 GGA exchange with P86 GGA correlation [80,91].
	BLYP		B88 GGA exchange with LYP GGA correlation [81,93,94,95].
	OLYP		HC01 GGA exchange with LYP GGA correlation [86,93,94,95].
	PW91		PW91 GGA exchange and correlation [82].
	PW91SSF		PW91 with full spin scaling function [82].
	PBE		PBE GGA exchange and correlation [83].
	PBESSF		PBE with full spin scaling function [83].
	PBESOL		PBE GGA exchange and correlation for solids [87,87].
	KT1/2/3		KT1-3 GGA exchange and correlation for NMR shieldings [100,101].
	SO11		SO11 GGA exchange and correlation [102].
	N12		N12 GGA exchange and correlation [103].
	GAM		GAM GGA exchange and correlation [104].
	CAP		CAP GGA exchange and correlation [105].
	VS98		VS98 meta-GGA exchange and correlation [106].
	PKZB		PKZB meta-GGA exchange and correlation [107].
	TPSS		TPSS meta-GGA exchange and correlation [108,109].
	M06L		M06L meta-GGA exchange and correlation [110].
	M11L		M11L meta-GGA exchange and correlation [111].
	MN12		MN12 meta-GGA exchange and correlation [112].
	B3LYP		B3LYP GGA hybrid exchange and correlation [62,63].
	BH&H		Becke half-and-half GGA hybrid exchange and correlation [113].
	PBE0		PBE0 GGA hybrid exchange and correlation [64,65].
	M062X		M062X meta-GGA hybrid exchange and correlation [66].
	M06HF		M06HF meta-GGA hybrid exchange and correlation [66].
	M06		M06 meta-GGA hybrid exchange and correlation [66].
	XALPHA		X$_{\alpha}$ calculation. The default $\alpha$ value is 0.75. A user defined $\alpha$ value can be selected with the X = $<$Real$>$ option [114].
	FOCK		Variational fitted Fock exchange [115].
	NONE		No exchange-correlation functional is used.

AUXIS / BASIS

	AUXIS		The auxiliary function density is used for the calculation of the exchange-correlation energy and matrix elements of the potential. This is the default.
	BASIS		The Kohn-Sham density is used for the calculation of the exchange-correlation energy and matrix elements of the potential.

Description:
The options listed above represent the most common combinations of exchange and correlation functionals. In addition to these combinations, the exchange and correlation functionals listed in Table 5 and 6, respectively, can be combined by the user.

The syntax for user-defined combinations of functionals is $<$Exchange$>$ - $<$Correlation$>$ (e.g. B88 - P86). With the option NONE, the exchange or correlation functional (or both) can be omitted. Distinct from the literature, the PW86 exchange functional is implemented in deMon2k with a cutoff and the local contribution of the P86 correlation functional is calculated with the VWN functional. The BH&H hybrid functional energy is defined in deMon2k as [113]:

$$E^{BH\&H} = {1 \over 2} E_x^{LDA} + {1 \over 2} \delta E_x^{B88} + {1 \over 2} E_x^{HF} + E_c^{LYP}%$$ (1)

Also the M06 correlation functional implementation differs slightly from the original proposed form [66] by modifying the self-correlation correction term inside the VS98 [106] contribution and the M06 part, as suggested by Gräfenstein et al. [116]. All other functionals are implemented according to the literature cited. Where possible, second derivatives of the density were eliminated by integration by parts [117].

Table 5: Exchange functionals available in deMon2k. The option acronym is given in bold.

DIRAC Local Dirac exchange [79].

FOCK Variational fitted Fock exchange [115].

PW86 Perdew and Wang GGA exchange from 1986 [80].

B88 Becke GGA exchange from 1988 [81].

PW91 Perdew and Wang GGA exchange from 1991 [82].

ECMV Engel, Chevary, McDonald, Vosko GGA exchange [96,97].

EV93 Engel and Vosko GGA exchange [98].

LB94 Leeuwen and Baerends model exchange potential with correct asymptotic behavior [99].

PBE96 Original Perdew, Burke and Ernzerhof GGA exchange from 1996 [83].

PBE98 PBE GGA exchange modified by Y. Zhang and W. Yang [84].

PBE99 PBE GGA exchange modified by B. Hammer et al. [85].

PBESOL PBE GGA exchange for solids [87].

OPTX Handy and Cohen GGA exchange [86].

KT1 Keal and Tozer GGA exchange for NMR shielding calculations, formula 1 [100].

KT2 Keal and Tozer GGA exchange for NMR shielding calculations, formula 2 [100].

KT3 Keal and Tozer GGA exchange with improved energetics [101].

VMT Vela, Medel, Trickey GGA exchange [29].

VMTSOL Vela, Medel, Trickey GGA exchange for solids [29].

S011 Peverati et al. GGA exchange from 2011 [102].

N12 Peverati and Truhlar GGA exchange from 2012 [103].

CAP Carmona-Espíndola, Gázquez, Vela, Trickey GGA exchange with correct asymptotic potential [105].

GAM Yu et al. GGA exchange from 2015 [104].

VS98 Voorhis and Scuseria meta-GGA exchange [106].

PKZB Perdew, Kurth, Zupan, Blaha meta-GGA exchange [107].

TPSS Tao, Perdew, Staroverov, Scuseria meta-GGA exchange [108,109].

M06L M06 meta-GGA exchange [66].

M11L Peverati and Truhlar meta GGA exchange from 2011 [111].

MN12 Peverati and Truhlar meta GGA exchange from 2012 [112].

PBE0 PBE0 hybrid exchange [64,65].

The AUXIS and BASIS options specify the density that is used for the calculation of the exchange-correlation energy and matrix elements of the exchange-correlation potential. By default, the auxiliary function density is used for both calculations, i.e. the auxiliary density functional theory approach is employed. The option BASIS invokes the Kohn-Sham methodology. Note that this choice may slow down the calculation significantly. For meta-GGAs the option BASIS must be specified. For Fock exchange the AUXIS and BASIS options are meaningless because it is always calculated by the variational fitting of the Fock potential. For more details and recommendations see Section 1.4, "How to Use deMon2k".

For the PW91 and PBE functionals, two different spin scaling functions are implemented in deMon2k. By default a numerically more stable cutoff function is used. By invoking the extension SSF (options PW91SSF and PBESSF), the originally published form of the spin-scaling function is selected. This choice may change the orbital energies considerably, but for the total energies the effect is usually negligible.

Table 6: Correlation functionals available in deMon2k. The option acronym is given in bold.

VWN Local Vosko, Wilk and Nusair correlation [88].

PVWN Pade interpolated VWN correlation [88].

RVWN RPA interpolated VWN correlation [88].

PZ81 Local Perdew and Zunger correlation [89].

PW92 Local Perdew and Wang correlation from 1992 [90].

KT2 Keal and Tozer local correlation for NMR shielding calculations [100].

P86 Perdew GGA correlation from 1986 with VWN local correlation [92].

PZ86 Perdew GGA correlation from 1986 [91].

LYP Lee, Yang and Parr GGA correlation from 1988 [93,94,95].

PW91 Perdew and Wang GGA correlation from 1991 [82].

PW91SSSF PW91 with full spin scaling function.

PBE Perdew, Burke and Ernzerhof GGA correlation from 1996 [83].

PBESSF PBE with full spin scaling function.

PBESOL PBE GGA correlation for solids [87].

KT3 Keal and Tozer GGA exchange with improved energetics [101].

S011 Peverati et al. GGA correlation from 2011 [102].

N12 Peverati and Truhlar GGA correlation from 2012 [103].

GAM Yu et al. GGA correlation from 2015 [104].

VS98 Voorhis and Scuseria meta-GGA correlation [106].

PKZB Perdew, Kurth, Zupan, Blaha meta-GGA correlation [107].

TPSS Tao, Perdew, Staroverov, Scuseria meta-GGA correlation [108,109].

M11L Peverati and Truhlar meta GGA correlation from 2011 [111].

MN12 Peverati and Truhlar meta GGA correlation from 2012 [112].