2.7. LibXC Functionals

The following functionals are available in HORTON through LibXC 2.2.2. [marques2012] (The MGGA functionals are not supported yet in HORTON.)

lda_k_lp

Lee and Parr Gaussian ansatz for the kinetic energy

CL and RG Parr, Phys. Rev. A 35, 2377-2383 (1987)

lda_k_tf

Thomas-Fermi kinetic energy

LH Thomas, Proc. Cambridge Phil. Soc. 23, 542-548 (1927)

E Fermi. Rend. Accad. Naz. Lincei 6, 602-607 (1927)

lda_x

Slater exchange

PAM Dirac, Proceedings of the Cambridge Philosophical Society 26, 376 (1930)

F Bloch, Zeitschrift fuer Physik 57, 545 (1929)

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)

lda_x_2d

Slater exchange

PAM Dirac, Proceedings of the Cambridge Philosophical Society 26, 376 (1930)

F Bloch, Zeitschrift fuer Physik 57, 545 (1929)

lda_c_1d_csc

Casula, Sorella & Senatore

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

lda_c_1d_loos

P-F Loos correlation LDA

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

lda_c_2d_amgb

AMGB (for 2D systems)

C Attaccalite et al, Phys. Rev. Lett. 88, 256601 (2002)

C Attaccalite, PhD thesis

lda_c_2d_prm

PRM (for 2D systems)

S Pittalis, E Rasanen, and MAL Marques, Phys. Rev. B 78, 195322 (2008)

lda_c_gl

Gunnarson & Lundqvist

O Gunnarsson and BI Lundqvist, PRB 13, 4274 (1976)

lda_c_gombas

Gombas

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

lda_c_hl

Hedin & Lundqvist

L Hedin and BI Lundqvist, J. Phys. C 4, 2064 (1971)

lda_c_ml1

Modified LSD (version 1) of Proynov and Salahub

EI Proynov and D Salahub, Phys. Rev. B 49, 7874 (1994)

lda_c_ml2

Modified LSD (version 2) of Proynov and Salahub

EI Proynov and D Salahub, Phys. Rev. B 49, 7874 (1994)

lda_c_ob_pw

Ortiz & Ballone (PW parametrization)

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)

lda_c_ob_pz

Ortiz & Ballone (PZ parametrization)

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)

lda_c_pw

Perdew & Wang

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

lda_c_pw_mod

Perdew & Wang (modified)

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

Added extra digits to some constants as in the PBE routine

http://dft.rutgers.edu/pubs/PBE.asc

lda_c_pw_rpa

Perdew & Wang (fit to the RPA energy)

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

lda_c_pz

Perdew & Zunger

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

lda_c_pz_mod

Perdew & Zunger (Modified)

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

Modified to improve the matching between the low- and high-rs parts

lda_c_rc04

Ragot-Cortona

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

lda_c_rpa

Random Phase Approximation (RPA)

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

lda_c_vbh

von Barth & Hedin

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

lda_c_vwn

Vosko, Wilk & Nusair (VWN5)

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

lda_c_vwn_1

Vosko, Wilk & Nusair (VWN1)

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

lda_c_vwn_2

Vosko, Wilk & Nusair (VWN2)

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

lda_c_vwn_3

Vosko, Wilk & Nusair (VWN3)

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

lda_c_vwn_4

Vosko, Wilk & Nusair (VWN4)

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

lda_c_vwn_rpa

Vosko, Wilk & Nusair (VWN5_RPA)

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

lda_c_wigner

Wigner

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

lda_c_xalpha

Slater’s Xalpha

JC Slater, Phys. Rev. 81, 385 (1951)

lda_xc_teter93

Teter 93

S Goedecker, M Teter, J Hutter, PRB 54, 1703 (1996)

gga_k_absp1

gamma-TFvW form by Acharya et al [g = 1 - 1.412/N^(1/3)]

PK Acharya, LJ Bartolotti, SB Sears, and RG Parr, Proc. Natl. Acad. Sci. USA 77 6978-6982 (1980)

gga_k_absp2

gamma-TFvW form by Acharya et al [g = 1 - 1.332/N^(1/3)]

PK Acharya, LJ Bartolotti, SB Sears, and RG Parr, Proc. Natl. Acad. Sci. USA 77 6978-6982 (1980)

gga_k_apbe

mu fixed from the semiclassical neutral atom

LA Constantin, E Fabiano, S Laricchia, and F Della Sala, Phys. Rev. Lett. 106, 186406 (2011)

gga_k_apbeint

interpolated version of APBE

S Laricchia, E Fabiano, LA Constantin, and F Della Sala, J. Chem. Theory Comput. 7, 2439-2451 (2011)

gga_k_baltin

TF-lambda-vW form by Baltin (l = 5/9)

R Baltin, Z. Naturforsch. A 27, 1176 (1972)

gga_k_dk

DePristo and Kress

AE DePristo and JD Kress, Phys. Rev. A 35, 438-441 (1987)

gga_k_ernzerhof

Ernzerhof

M Ernzerhof, J. Mol. Struct.:THEOCHEM 501-502, 59 (2000)

gga_k_fr_b88

Fuentealba & Reyes (B88 version)

P Fuentealba and O Reyes, Chem. Phys. Lett. 232, 31-34 (1995)

gga_k_fr_pw86

Fuentealba & Reyes (PW86 version)

P Fuentealba and O Reyes, Chem. Phys. Lett. 232, 31-34 (1995)

gga_k_ge2

Second-order gradient expansion of the kinetic energy density

AS Kompaneets and ES Pavlovskii, Zh. Eksp. Teor. Fiz. 31, 427 (1956) [Sov. Phys. JETP 4, 328 (1957)]DA Kirznits, Zh. Eksp. Teor. Fiz. 32, 115 (1957) [Sov. Phys. JETP 5, 64 (1957)]

gga_k_golden

TF-lambda-vW form by Golden (l = 13/45)

S Golden, Phys. Rev. 105, 604-615 (1957)

gga_k_gp85

gamma-TFvW form by Ghosh and Parr

SK Ghosh and RG Parr, J. Chem. Phys. 82, 3307 (1985)

gga_k_gr

gamma-TFvW form by Gázquez and Robles

JL Gázquez and J Robles, J. Chem. Phys. 76, 1467 (1982)

gga_k_lc94

Lembarki & Chermette

A Lembarki and H Chermette, Phys. Rev. A 50, 5328-5331 (1994)

gga_k_lieb

TF-lambda-vW form by Lieb (l = 0.185909191)

EH Lieb, Rev. Mod. Phys. 53, 603-641 (1981)

gga_k_llp

Becke 88

H Lee, C Lee, and RG Parr, Phys. Rev. A 44, 768 (1991)

gga_k_ludena

gamma-TFvW form by Ludeña

EV Ludeña, in Cond. Matt. Theor. Vol 1, ed. by FB Malik (Plenum, New York, 1986), p. 183

gga_k_meyer

Meyer, Wang, and Young

A Meyer, GC Wang and WH Young, Z. Naturforsch. A 31, 898-903 (1976)

gga_k_ol1

Ou-Yang and Levy v.1

H Ou-Yang, M Levy, Int. J. of Quant. Chem. 40, 379-388 (1991)

gga_k_ol2

Ou-Yang and Levy v.2

H Ou-Yang, M Levy, Int. J. of Quant. Chem. 40, 379-388 (1991)

gga_k_pearson

Pearson 1992

DJ Lacks and RG Gordon, J. Chem. Phys. 100, 4446 (1994)

E W Pearson and R G Gordon, J. Chem. Phys. 82, 881 (1985)

E W Pearson, Ph.D. thesis, Harvard University (1983)

gga_k_perdew

Perdew

JP Perdew, Phys. Lett. A 165, 79 (1992)

gga_k_revapbe

revised APBE

LA Constantin, E Fabiano, S Laricchia, and F Della Sala, Phys. Rev. Lett. 106, 186406 (2011)

gga_k_revapbeint

interpolated version of REVAPBE

S Laricchia, E Fabiano, LA Constantin, and F Della Sala, J. Chem. Theory Comput. 7, 2439-2451 (2011)

gga_k_tfvw

Thomas-Fermi plus von Weiszaecker correction

CF von Weiszaecker, Z. Phys. 96, 431 (1935)

gga_k_thakkar

Thakkar 1992

AJ Thakkar, Phys. Rev. A 46, 6920-6924 (1992)

gga_k_tw1

Tran and Wesolowski set 1 (Table II)

F Tran and TA Wesolowski, Int. J. Quant. Chem. 89, 441-446 (2002)

gga_k_tw2

Tran and Wesolowski set 1 (Table II)

F Tran and TA Wesolowski, Int. J. Quant. Chem. 89, 441-446 (2002)

gga_k_tw3

Tran and Wesolowski set 1 (Table II)

F Tran and TA Wesolowski, Int. J. Quant. Chem. 89, 441-446 (2002)

gga_k_tw4

Tran and Wesolowski set 1 (Table II)

F Tran and TA Wesolowski, Int. J. Quant. Chem. 89, 441-446 (2002)

gga_k_vjks

Vitos, Johansson, Kollar, and Skriver

L Vitos, B Johansson, J. Kollár, and HL Skriver, Phys. Rev. A 61, 052511 (2000)

gga_k_vsk

Vitos, Skriver, and Kollar

L Vitos, HL Skriver, and J. Kollár, Phys. Rev. B 57, 12611-12615 (1998)

gga_k_vw

von Weiszaecker correction to Thomas-Fermi

CF von Weiszaecker, Z. Phys. 96, 431 (1935)

gga_k_yt65

TF-lambda-vW form by Yonei and Tomishima (l = 1/5)

K. Yonei and Y. Tomishima, J. Phys. Soc. Jpn. 20, 1051-1057 (1965)

gga_x_2d_b86

Becke 86 in 2D

G Vilhena and MAL Marques, unpublished

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

gga_x_2d_b86_mgc

Becke 86 with modified gradient correction for 2D

S Pittalis, E Rasanen, JG Vilhena, and MAL Marques, Phys. Rev. A 79, 012503 (2009)

AD Becke, J. Chem. Phys 85, 7184 (1986)

gga_x_2d_b88

Becke 88

G Vilhena, MAL Marques, unpublished

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

gga_x_2d_pbe

Perdew, Burke & Ernzerhof 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)

gga_x_airy

Constantin et al based on the Airy gas

LA Constantin, A Ruzsinszky, and JP Perdew, Phys. Rev. B 80, 035125 (2009)

gga_x_ak13

Armiento & Kuemmel 2013

R Armiento and S Kuemmel, PRL 111, 036402 (2013)

gga_x_am05

Armiento & Mattsson 05

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).

gga_x_apbe

mu fixed from the semiclassical neutral atom

LA Constantin, E Fabiano, S Laricchia, and F Della Sala, Phys. Rev. Lett. 106, 186406 (2011)

gga_x_b86

Becke 86

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

gga_x_b86_mgc

Becke 86 with modified gradient correction

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

AD Becke, J. Chem. Phys 85, 7184 (1986)

gga_x_b88

Becke 88

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

gga_x_bayesian

Bayesian best fit for the enhancement factor

JJ Mortensen, K Kaasbjerg, SL Frederiksen, JK Nørskov, JP Sethna, and KW Jacobsen, Phys. Rev. Lett. 95, 216401 (2005)

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)

gga_x_c09x

C09x to be used with the VdW of Rutgers-Chalmers

VR Cooper, Phys. Rev. B 81, 161104(R) (2010)

gga_x_dk87_r1

dePristo & Kress 87 version R1

AE DePristo and JD Kress, J. Chem. Phys. 86, 1425 (1987)

gga_x_dk87_r2

dePristo & Kress 87 version R2

AE DePristo and JD Kress, J. Chem. Phys. 86, 1425 (1987)

gga_x_ft97_a

Filatov & Thiel 97 (version A)

M Filatov and W Thiel, Mol. Phys 91, 847 (1997)

gga_x_ft97_b

Filatov & Thiel 97 (version B)

M Filatov and W Thiel, Mol. Phys 91, 847 (1997)

gga_x_g96

Gill 96

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

gga_x_herman

Herman Xalphabeta GGA

F Herman, JP Van Dyke, and IB Ortenburger, Phys. Rev. Lett. 22, 807 (1969)

F Herman, IB Ortenburger, and JP Van Dyke, Int. J. Quantum Chem. Symp. 3, 827 (1970)

gga_x_hjs_b88

HJS screened exchange B88 version

TM Henderson, BG Janesko, and GE Scuseria, J. Chem. Phys. 128, 194105 (2008)

gga_x_hjs_b97x

HJS screened exchange B97x version

TM Henderson, BG Janesko, and GE Scuseria, J. Chem. Phys. 128, 194105 (2008)

gga_x_hjs_pbe

HJS screened exchange PBE version

TM Henderson, BG Janesko, and GE Scuseria, J. Chem. Phys. 128, 194105 (2008)

gga_x_hjs_pbe_sol

HJS screened exchange PBE_SOL version

TM Henderson, BG Janesko, and GE Scuseria, J. Chem. Phys. 128, 194105 (2008)

gga_x_htbs

Haas, Tran, Blaha, and Schwarz

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

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)

gga_x_kt1

Keal and Tozer, version 1

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

gga_x_lag

Local Airy Gas

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

gga_x_lb

van Leeuwen & Baerends

R van Leeuwen and EJ Baerends, Phys. Rev. A. 49, 2421 (1994)

gga_x_lbm

van Leeuwen & Baerends modified

PRT Schipper, OV Gritsenko, SJA van Gisbergen, and EJ Baerends, J. Chem. Phys. 112, 1344 (2000)

R van Leeuwen and EJ Baerends, Phys. Rev. A. 49, 2421 (1994)

gga_x_lg93

Lacks & Gordon 93

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

gga_x_lv_rpw86

Berland and Hyldgaard

K Berland and P Hyldgaard, arXiv:1309.1756 [cond-mat.mtrl-sci] (2013)

gga_x_mb88

Modified Becke 88 for proton transfer

V Tognetti and C Adamo, J. Phys. Chem. A 113, 14415-14419 (2009)

gga_x_mpbe

Adamo & Barone modification to PBE

C Adamo and V Barone, J. Chem. Phys. 116, 5933 (2002)

gga_x_mpw91

mPW91 of Adamo & Barone

C Adamo and V Barone, J. Chem. Phys. 108, 664 (1998)

gga_x_n12

N12 functional of Minnesota

R Peverati and DG Truhlar, J. Chem. Theory Comput. 8, 2310-2319 (2012)

gga_x_ol2

Exchange form based on Ou-Yang and Levy v.2

P Fuentealba and O Reyes, Chem. Phys. Lett. 232, 31-34 (1995)

H Ou-Yang, M Levy, Int. J. of Quant. Chem. 40, 379-388 (1991)

gga_x_optb88_vdw

opt-Becke 88 for vdW

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

gga_x_optpbe_vdw

Reparametrized PBE for vdW

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

gga_x_optx

Handy & Cohen OPTX 01

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

gga_x_pbe

Perdew, Burke & Ernzerhof

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)

gga_x_pbe_jsjr

Reparametrized PBE by Pedroza, Silva & Capelle

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

gga_x_pbe_mol

Reparametrized PBE by del Campo, Gazquez, Trickey & Vela

JM del Campo, JL Gazquez, SB Trickey, and A Vela, J. Chem. Phys. 136, 104108 (2012)

gga_x_pbe_r

Revised PBE from Zhang & Yang

Y Zhang and W Yang, Phys. Rev. Lett 80, 890 (1998)

gga_x_pbe_sol

Perdew, Burke & Ernzerhof SOL

JP Perdew, et al, Phys. Rev. Lett. 100, 136406 (2008)

gga_x_pbe_tca

PBE revised by Tognetti et al

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

gga_x_pbea

Madsen 07

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

gga_x_pbeint

PBE for hybrid interfaces

E. Fabiano, LA Constantin, and F. Della Sala, Phys. Rev. B 82, 113104 (2010)

gga_x_pbek1_vdw

Reparametrized PBE for vdW

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

gga_x_pw86

Perdew & Wang 86

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

gga_x_pw91

Perdew & Wang 91

JP Perdew, in Proceedings of the 21st Annual International Symposium on the Electronic Structure of Solids, ed. by P Ziesche and H Eschrig (Akademie Verlag, Berlin, 1991), p. 11.

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)

gga_x_q2d

Chiodo et al

L Chiodo, LA Constantin, E Fabiano, and F Della Sala, Phys. Rev. Lett. 108, 126402 (2012)

gga_x_rge2

Regularized PBE

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

gga_x_rpbe

Hammer, Hansen, and Nørskov

B Hammer, LB Hansen and JK Nørskov, Phys. Rev. B 59, 7413 (1999)

gga_x_rpw86

Refitted Perdew & Wang 86

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

gga_x_sfat

Short-range recipe for exchange GGA functionals - Yukawa

A Savin, H-J Flad, J. of Quant. Chem. 56, 327-332 (1995)

Y Akinaga, S Ten-no, Chem. Phys. Lett. 462, 348-351 (2008)

gga_x_sogga

Second-order generalized gradient approximation

Y Zhao and DG Truhlar, J. Chem. Phys. 128, 184109 (2008)

http://comp.chem.umn.edu/mfm/index.html

gga_x_sogga11

Second-order generalized gradient approximation 2011

R Peverati, Y Zhao, and DG Truhlar, J. Phys. Chem. Lett. 2, 1991-1997 (2011)

http://comp.chem.umn.edu/mfm/index.html

gga_x_ssb

Swarta, Sola and Bickelhaupt

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

gga_x_ssb_d

Swarta, Sola and Bickelhaupt dispersion

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

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)

gga_x_vmt84_pbe

VMT{8,4} with constraint satisfaction with mu = mu_GE

A Vela, JC Pacheco-Kato, JL Gazquez, JM del Campo, and SB Trickey, J. Chem. Phys. 136, 144115 (2012)

gga_x_vmt_ge

Vela, Medel, and Trickey with mu = mu_GE

A. Vela, V. Medel, and S. B. Trickey, J. Chem. Phys. 130, 244103 (2009)

gga_x_vmt_pbe

Vela, Medel, and Trickey with mu = mu_PBE

A. Vela, V. Medel, and S. B. Trickey, J. Chem. Phys. 130, 244103 (2009)

gga_x_wc

Wu & Cohen

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

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)

gga_x_xpbe

Extended PBE by Xu & Goddard III

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

gga_c_am05

Armiento & Mattsson 05

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).

gga_c_apbe

mu fixed from the semiclassical neutral atom

LA Constantin, E Fabiano, S Laricchia, and F Della Sala, Phys. Rev. Lett. 106, 186406 (2011)

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)

gga_c_lm

Langreth & Mehl

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

CD Hu and DC Langreth, Phys. Scr. 32, 391 (1985)

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)

gga_c_n12

N12 functional of Minnesota

R Peverati and DG Truhlar, J. Chem. Theory Comput. 8, 2310-2319 (2012)

gga_c_n12_sx

N12-SX functional of Minnesota

R Peverati and DG Truhlar, Phys. Chem. Chem. Phys. 14, 16187-16191 (2012)

gga_c_op_b88

one-parameter progressive functional (B88 version)

T Tsuneda, T Suzumura, and K Hirao, J. Chem. Phys. 110, 10664 (1999)

gga_c_op_g96

one-parameter progressive functional (G96 version)

T Tsuneda, T Suzumura, and K Hirao, J. Chem. Phys. 111, 5656 (1999)

gga_c_op_pbe

one-parameter progressive functional (PBE version)

T Tsuneda, T Suzumura, and K Hirao, J. Chem. Phys. 111, 5656 (1999)

gga_c_op_xalpha

one-parameter progressive functional (Xalpha version)

T Tsuneda, T Suzumura, and K Hirao, J. Chem. Phys. 111, 5656 (1999)

gga_c_optc

Optimized correlation functional of Cohen and Handy

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

gga_c_p86

Perdew 86

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

gga_c_pbe

Perdew, Burke & Ernzerhof

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)

gga_c_pbe_jrgx

Reparametrized PBE by Pedroza, Silva & Capelle

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

gga_c_pbe_sol

Perdew, Burke & Ernzerhof SOL

JP Perdew, et al, Phys. Rev. Lett. 100, 136406 (2008)

gga_c_pbeint

PBE for hybrid interfaces

E. Fabiano, LA Constantin, and F. Della Sala, Phys. Rev. B 82, 113104 (2010)

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)

gga_c_q2d

Chiodo et al

L Chiodo, LA Constantin, E Fabiano, and F Della Sala, Phys. Rev. Lett. 108, 126402 (2012)

gga_c_revtca

Tognetti, Cortona, Adamo (revised)

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

gga_c_rge2

Regularized PBE

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

gga_c_sogga11

Second-order generalized gradient approximation 2011

R Peverati, Y Zhao, and DG Truhlar, J. Phys. Chem. Lett. 2, 1911-1997 (2011)

http://comp.chem.umn.edu/mfm/index.html

gga_c_sogga11_x

To be used with hyb_gga_x_SOGGA11-X

R Peverati and DG Truhlar, J. Chem. Phys. 135, 191102 (2011)

http://comp.chem.umn.edu/mfm/index.html

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)

gga_c_tca

Tognetti, Cortona, Adamo

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

gga_c_vpbe

variant PBE

JP Perdew, A Ruzsinszky, GI Csonka, LA Constantin, and J Sun, Phys. Rev. Lett. 103, 026403 (2009)

gga_c_wi

Wilson & Ivanov

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

gga_c_wi0

Wilson & Ivanov initial version

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

gga_c_wl

Wilson & Levy

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

gga_c_xpbe

Extended PBE by Xu & Goddard III

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

gga_c_zpbeint

spin-dependent gradient correction to PBEint

A Constantin, E Fabiano, and F Della Sala, Phys. Rev. B 84, 233103 (2011)

gga_c_zpbesol

spin-dependent gradient correction to PBEsol

A Constantin, E Fabiano, and F Della Sala, Phys. Rev. B 84, 233103 (2011)

gga_xc_b97

Becke 97

AD Becke, J. Chem. Phys. 107, 8554 (1997)

gga_xc_b97_1

Becke 97-1

FA Hamprecht, AJ Cohen, DJ Tozer, and NC Handy, J. Chem. Phys. 109, 6264 (1998)

gga_xc_b97_2

Becke 97-2

PJ Wilson, TJ Bradley, and DJ Tozer, J. Chem. Phys. 115, 9233 (2001)

gga_xc_b97_3

Becke 97-3

TW Keal and DJ Tozer, J. Chem. Phys. 123, 121103 (2005)

gga_xc_b97_d

Becke 97-D

S Grimme, J. Comput. Chem. 27, 1787 (2006)

gga_xc_b97_gga1

Becke 97 GGA-1

AJ Cohen and NC Handy, Chem. Phys. Lett. 316, 160-166 (2000)

gga_xc_b97_k

Boese-Martin for Kinetics

AD Boese and JML Martin, J. Chem. Phys., Vol. 121, 3405 (2004)

gga_xc_edf1

EDF1

RD Adamson, PMW Gill, and JA Pople, Chem. Phys. Lett. 284 6 (1998)

gga_xc_hcth_120

HCTH/120

AD Boese, NL Doltsinis, NC Handy, and M Sprik, J. Chem. Phys. 112, 1670 (2000)

gga_xc_hcth_147

HCTH/147

AD Boese, NL Doltsinis, NC Handy, and M Sprik, J. Chem. Phys. 112, 1670 (2000)

gga_xc_hcth_407

HCTH/407

AD Boese and NC Handy, J. Chem. Phys. 114, 5497 (2001)

gga_xc_hcth_407p

HCTH/407+

AD Boese, A Chandra, JML Martin, and Dominik Marx, J. Chem. Phys. 119, 5965 (2003)

gga_xc_hcth_93

HCTH/93

FA Hamprecht, AJ Cohen, DJ Tozer, and NC Handy, J. Chem. Phys. 109, 6264 (1998)

gga_xc_hcth_a

HCTH-A

FA Hamprecht, AJ Cohen, DJ Tozer, and NC Handy, J. Chem. Phys. 109, 6264 (1998)

gga_xc_hcth_p14

HCTH p=1/4

G Menconi, PJ Wilson, and DJ Tozer, J. Chem. Phys. 114, 3958 (2001)

gga_xc_hcth_p76

HCTH p=1/4

G Menconi, PJ Wilson, and DJ Tozer, J. Chem. Phys. 114, 3958 (2001)

gga_xc_kt2

Keal and Tozer, version 2

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

gga_xc_mohlyp

Functional for organometallic chemistry

NE Schultz, Y Zhao, DGJ Truhlar, Phys. Chem. A, 109, 11127 (2005)

gga_xc_mohlyp2

Functional for barrier heights

J Zheng, Y Zhao, DGJ Truhlar, Chem. Theory. Comput. 5, 808 (2009)

gga_xc_mpwlyp1w

mPWLYP1w

EE Dahlke and DG Truhlar, J. Phys. Chem. B 109, 15677 (2005)

gga_xc_oblyp_d

oBLYP-D functional of Goerigk and Grimme

L Goerigk and S Grimme, J. Chem. Theory Comput. 6, 107-126 (2010)

gga_xc_opbe_d

oBLYP-D functional of Goerigk and Grimme

L Goerigk and S Grimme, J. Chem. Theory Comput. 6, 107-126 (2010)

gga_xc_opwlyp_d

oPWLYP-D functional of Goerigk and Grimme

L Goerigk and S Grimme, J. Chem. Theory Comput. 6, 107-126 (2010)

gga_xc_pbe1w

PBE1W

EE Dahlke and DG Truhlar, J. Phys. Chem. B 109, 15677 (2005)

gga_xc_pbelyp1w

PBELYP1W

EE Dahlke and DG Truhlar, J. Phys. Chem. B 109, 15677 (2005)

gga_xc_sb98_1a

SB98 (1a)

HL Schmider and AD Becke, J. Chem. Phys. 108, 9624 (1998)

gga_xc_sb98_1b

SB98 (1b)

HL Schmider and AD Becke, J. Chem. Phys. 108, 9624 (1998)

gga_xc_sb98_1c

SB98 (1c)

HL Schmider and AD Becke, J. Chem. Phys. 108, 9624 (1998)

gga_xc_sb98_2a

SB98 (2a)

HL Schmider and AD Becke, J. Chem. Phys. 108, 9624 (1998)

gga_xc_sb98_2b

SB98 (2b)

HL Schmider and AD Becke, J. Chem. Phys. 108, 9624 (1998)

gga_xc_sb98_2c

SB98 (2c)

HL Schmider and AD Becke, J. Chem. Phys. 108, 9624 (1998)

gga_xc_th1

Tozer and Handy v. 1

DJ Tozer and NC Handy, J. Chem. Phys. 108, 2545 (1998)

gga_xc_th2

Tozer and Handy v. 2

DJ Tozer and NC Handy, J. Phys. Chem. A 102, 3162 (1998)

gga_xc_th3

Tozer and Handy v. 3

DJ Tozer and NC Handy, Mol. Phys. 94, 707 (1998)

gga_xc_th4

Tozer and Handy v. 4

DJ Tozer and NC Handy, Mol. Phys. 94, 707 (1998)

gga_xc_th_fc

Tozer and Handy v. FC

DJ Tozer, NC Handy, amd WH Green, Chem. Phys. Lett. 273, 183-194 (1997)

gga_xc_th_fcfo

Tozer and Handy v. FCFO

DJ Tozer, NC Handy, amd WH Green, Chem. Phys. Lett. 273, 183-194 (1997)

gga_xc_th_fco

Tozer and Handy v. FCO

DJ Tozer, NC Handy, amd WH Green, Chem. Phys. Lett. 273, 183-194 (1997)

gga_xc_th_fl

Tozer and Handy v. FL

DJ Tozer, NC Handy, amd WH Green, Chem. Phys. Lett. 273, 183-194 (1997)

gga_xc_xlyp

XLYP

X Xu and WA Goddard, III, PNAS 101, 2673 (2004)

hyb_gga_x_n12_sx

N12-SX functional of Minnesota

R Peverati and DG Truhlar, Phys. Chem. Chem. Phys. 14, 16187-16191 (2012)

hyb_gga_x_sogga11_x

Hybrid based on SOGGA11 form

R Peverati and DG Truhlar, J. Chem. Phys. 135, 191102 (2011)

http://comp.chem.umn.edu/mfm/index.html

hyb_gga_xc_b1lyp

B1LYP

C. Adamo, V. Barone, Chem. Phys. Lett. 274, 242 (1997)

hyb_gga_xc_b1pw91

B1PW91

C. Adamo, V. Barone, Chem. Phys. Lett. 274, 242 (1997)

hyb_gga_xc_b1wc

B1WC

DI Bilc, R Orlando, R Shaltaf, G-M Rignanese, J Iniguez, and Ph Ghosez, Phys. Rev. B 77, 165107 (2008)

hyb_gga_xc_b3lyp

B3LYP

PJ Stephens, FJ Devlin, CF Chabalowski, MJ Frisch, J. Phys. Chem. 98 11623 (1994)

hyb_gga_xc_b3p86

B3P86

Defined through Gaussian implementation

hyb_gga_xc_b3pw91

The original (ACM, B3PW91) hybrid of Becke

AD Becke, J. Chem. Phys. 98, 5648 (1993)

hyb_gga_xc_b97

Becke 97

AD Becke, J. Chem. Phys. 107, 8554 (1997)

hyb_gga_xc_b97_1

Becke 97-1

FA Hamprecht, AJ Cohen, DJ Tozer, and NC Handy, J. Chem. Phys. 109, 6264 (1998)

hyb_gga_xc_b97_2

Becke 97-2

PJ Wilson, TJ Bradley, and DJ Tozer, J. Chem. Phys. 115, 9233 (2001)

hyb_gga_xc_b97_3

Becke 97-3

TW Keal and DJ Tozer, J. Chem. Phys. 123, 121103 (2005)

hyb_gga_xc_b97_k

Boese-Martin for Kinetics

AD Boese and JML Martin, J. Chem. Phys., Vol. 121, 3405 (2004)

hyb_gga_xc_bhandh

BHandH

AD Becke, J. Chem. Phys., 98 1372-77 (1993)

hyb_gga_xc_bhandhlyp

BHandHLYP

AD Becke, J. Chem. Phys., 98 1372-77 (1993)

hyb_gga_xc_cam_b3lyp

CAM version of B3LYP

T Yanai, DP Tew, NC Handy, Chem. Phys. Lett. 393, 51-57 (2004)

hyb_gga_xc_camy_blyp

CAMY version of BLYP

Y Akinaga, S Ten-no, Chem. Phys. Lett. 462, 348-351 (2008)

hyb_gga_xc_hjs_b88

HJS hybrid screened exchange B88 version

TM Henderson, BG Janesko, and GE Scuseria, J. Chem. Phys. 128, 194105 (2008)

hyb_gga_xc_hjs_b97x

HJS hybrid screened exchange B97x version

TM Henderson, BG Janesko, and GE Scuseria, J. Chem. Phys. 128, 194105 (2008)

hyb_gga_xc_hjs_pbe

HJS hybrid screened exchange PBE version

TM Henderson, BG Janesko, and GE Scuseria, J. Chem. Phys. 128, 194105 (2008)

hyb_gga_xc_hjs_pbe_sol

HJS hybrid screened exchange PBE_SOL version

TM Henderson, BG Janesko, and GE Scuseria, J. Chem. Phys. 128, 194105 (2008)

hyb_gga_xc_hse03

HSE03

J Heyd, GE Scuseria, and M Ernzerhof, J. Chem. Phys. 118, 8207 (2003)

J Heyd, GE Scuseria, and M Ernzerhof, J. Chem. Phys. 124, 219906 (2006)

hyb_gga_xc_hse06

HSE06

J Heyd, GE Scuseria, and M Ernzerhof, J. Chem. Phys. 118, 8207 (2003)

J Heyd, GE Scuseria, and M Ernzerhof, J. Chem. Phys. 124, 219906 (2006)

AV Krukau, OA Vydrov, AF Izmaylov, and GE Scuseria, J. Chem. Phys. 125, 224106 (2006)

hyb_gga_xc_mb3lyp_rc04

B3LYP with RC04 LDA

V Tognetti, P Cortona, and C Adamo, Chem. Phys. Lett. 439, 381-385 (2007)

hyb_gga_xc_mpw1k

mPW1K

BJ Lynch, PL Fast, M Harris, DGJ Truhlar, Phys. Chem. A 104, 4811 (2000)

hyb_gga_xc_mpw1pw

mPW1PW

C. Adamo, V. Barone, J. Chem. Phys. 108, 664 (1998)

hyb_gga_xc_mpw3lyp

MPW3LYP

Y Zhao and DGJ Truhlar, Phys. Chem. A 108, 6908-6918 (2004)

hyb_gga_xc_mpw3pw

MPW3PW of Adamo & Barone

C Adamo and V Barone, J. Chem. Phys. 108, 664 (1998)

hyb_gga_xc_mpwlyp1m

MPW with 1 par. for metals/LYP

NE Schultz, Y Zhao, and DG Truhlar, J. Phys. Chem. A 109, 11127-11143 (2005)

hyb_gga_xc_o3lyp

O3LYP

AJ Cohen, NC Handy, Mol. Phys. 99 607 (2001)

hyb_gga_xc_pbe0_13

PBE0-1/3

P Cortona, J. Chem. Phys. 136, 086101 (2012)

hyb_gga_xc_pbeh

PBEH (PBE0)

C Adamo and V Barone, J. Chem. Phys. 110, 6158 (1999)

M. Ernzerhof, G. E. Scuseria, J. Chem. Phys. 110, 5029 (1999)

hyb_gga_xc_revb3lyp

Revised B3LYP

L Lua, H Hua, H Houa, B Wang, Comput. Theor. Chem. 1015, 64-71 (2013)

hyb_gga_xc_sb98_1a

SB98 (1a)

HL Schmider and AD Becke, J. Chem. Phys. 108, 9624 (1998)

hyb_gga_xc_sb98_1b

SB98 (1b)

HL Schmider and AD Becke, J. Chem. Phys. 108, 9624 (1998)

hyb_gga_xc_sb98_1c

SB98 (1c)

HL Schmider and AD Becke, J. Chem. Phys. 108, 9624 (1998)

hyb_gga_xc_sb98_2a

SB98 (2a)

HL Schmider and AD Becke, J. Chem. Phys. 108, 9624 (1998)

hyb_gga_xc_sb98_2b

SB98 (2b)

HL Schmider and AD Becke, J. Chem. Phys. 108, 9624 (1998)

hyb_gga_xc_sb98_2c

SB98 (2c)

HL Schmider and AD Becke, J. Chem. Phys. 108, 9624 (1998)

hyb_gga_xc_tuned_cam_b3lyp

CAM version of B3LYP

K Okuno, Y Shigeta, R Kishi, H Miyasaka, M Nakano, J. Photochem. Photobiol., A 235, 29-34 (2012)

hyb_gga_xc_x3lyp

X3LYP

X Xu, WA Goddard, III, PNAS 101, 2673 (2004)