MANUAL Minnesota Functional Module

Transcription

1 1 MANUAL Minnesota Functional Module Version 4.0 Subroutines for evaluating the following exchange-correlation functionals: GAM, M05, M05-2X, M06, M06-2X, M06-HF, M06-L, M08-HX, M08-SO, M11, M11-L, MN12-L, MN12-SX, MN15, MN15-L, N12, N12-SX, revm06, revm06-l, revm11, SOGGA, SOGGA11, and SOGGA11-X Documentation Haoyu S. Yu, a Yan Zhao, b Roberto Peverati, c Xiao He, d Ying Wang, d Pragya Verma, and Donald G. Truhlar e Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, MN a Present affiliation: Scientific Development, Schrödinger, Inc. b Present affiliation: International School of Materials Science and Engineering, Wuhan University of Technology c Present affiliation: Florida Institute of Technology, Melbourne, Florida d Present affiliation: School of Chemistry and Molecular Engineering, East China Normal University, and NYU-ECNU Center for Computational Chemistry at NYU Shanghai e truhlar@umn.edu Date of code completion: December 1, 2018 Date of most recent change in this manual: December 1, 2018, 3:00 pm

2 2 Contents Executive summary 3 Literature references 3 Original references for functionals 3 References for reviews 5 Input and output 6 Notes 6 Reference energies and gradients 9 Version history 16

3 3 Executive summary Minnesota Functional Module (abbreviated MFM ) is a Fortran77 code for evaluating the GAM, M05, M05-2X, M06, M06-2X, M06-HF, M06-L, M08-HX, M08-SO, M11, M11-L, MN12-L, MN12-SX, MN15, MN15-L, N12, N12-SX, revm06, revm06-l, revm11, SOGGA, SOGGA11, and SOGGA11-X exchangecorrelation functionals for Kohn-Sham density functional theory. The subroutines are in the accompanying tar file. Literature references A. Original references for functionals GAM Yu, H. S.; Zhang, W.; Verma, P.; He, X.; Truhlar, D. G. Phys. Chem. Chem. Phys. 2015, 17, doi.org/ /c5cp01425e M05 Zhao, Y.; Schultz, N. E.; Truhlar, D. G. J. Chem. Phys. 2005, 123, doi.org/ / M05-2X Zhao, Y.; Schultz, N. E.; Truhlar, D. G. J. Chem. Theory Comput. 2006, 2, doi.org/ /ct M06 and M06-2X Zhao, Y.; Truhlar, D. G. Theor. Chem. Acc. 2008, 120, doi.org/ /s x Erratum: 119, 525 (2008). doi.org/ /s M06-HF Zhao, Y.; Truhlar, D. G. J. Phys. Chem. A 2006, 110, doi.org/ /jp066479k M06-L Zhao, Y.; Truhlar, D. G. J. Chem. Phys. 2006, 125, doi.org/ /

4 4 M08-HX and M08-SO Zhao, Y.; Truhlar, D. G. J. Chem. Theory Comput. 2008, 4, doi.org/ /ct800246v M11 Peverati, R.; Truhlar, D. G. J. Phys. Chem. Lett. 2011, 2, doi.org/ /jz201170d Note that in eqs 21 and 22 of the M11 paper, Y should be X/100. M11-L Peverati, R.; Truhlar, D. G. J. Phys. Chem. Lett. 2012, 3, doi.org/ /jz201525m MN12-L Peverati, R.; Truhlar, D. G. Phys. Chem. Chem. Phys. 2012, 14, doi.org/ /c2cp42025b MN12-SX and N12-SX Peverati, R.; Truhlar, D. G. Phys. Chem. Chem. Phys. 2012, 14, doi.org/ /c2cp42576a MN15 Yu, H. S.; He, X.; Li, S.; Truhlar, D. G. Chem. Sci. 2016, 7, doi.org/ /c6sc00705h Correction: 7, (2016). doi.org/ /c6sc90044e MN15-L Yu, H. S.; He, X.; Truhlar, D. G. J. Chem. Theory Comput. 2016, 12, doi.org/ /acs.jctc.5b01082 N12 Peverati, R.; Truhlar, D. G. J. Chem. Theory Comput. 2012, 8, doi.org/ /ct revm06 Wang, Y.; Verma, P.; Jin, X. S.; Truhlar, D. G.; He, X. Proc. Natl. Acad. Sci. U.S.A , doi.org/ /pnas

5 5 revm06-l Wang, Y.; Jin, X. S.; Yu, H. S.; Truhlar, D. G.; He, X. Proc. Natl. Acad. Sci. U.S.A , doi.org/ /pnas revm11 Verma, P.; Wang, Y.; Ghosh, S.; He, X.; Truhlar, D.G. 2018, submitted. SOGGA Zhao, Y.; Truhlar, D. G. J. Chem. Phys. 2008, 128, doi.org/ / SOGGA11 Peverati, R.; Zhao, Y.; Truhlar, D. G. J. Phys. Chem. Lett. 2011, 2, doi.org/ /jz200616w Note that there is a typo in eq. 3 of the SOGGA11 paper. The correct expression is: m x g 1 = x 1 ai 1 1+ µ i=0 κ s2 i SOGGA11-X Peverati, R.; D. G. Truhlar, J. Chem. Phys. 2011, 135, doi.org/ / B. Reviews Zhao, Y.; Truhlar, D. G. Acc. Chem. Res. 2008, 41, doi.org/ /ar700111a Y. Zhao and D. G. Truhlar, Chemical Physics Letters 502, 1-13 (2011). doi.org/ /j.cplett

6 6 Input and output INPUT: RA, RB - Spin densities D1RA, D1RB - Spin density gradients TA, TB - τ σ and τ β NGrid - total number of grid points at which the functional is evaluated. OUTPUT: F - Functional values on the grids D1F - First derivatives with respect to RA, RB, GA, GB, TA, TB on the grids Notes 1. We used Becke s definition (J. Chem. Phys (1996)) of τ σ and τ β. By this definition they are two times larger than spin kinetic energy densities. 2. The correlation part of all Minnesota functionals uses the local spin density part of the Perdew- Wang-91 correlation functional (J. P. Perdew and Y. Wang, Phys. Rev. B 45, (1992)), which is a fit to the correlation energy of a uniform electron gas (lsdac subroutine). Since we are not allowed to distribute the work of others, users should provide their own subroutine for this LSDA correlation functional, or they may find help on Kieron Burke s web site at: The correlation part of all M08-class functionals also needs to use the H(r s,ζ,t) function in the PBE correlation (PBEH0 subroutine). As for the previous point, we are not allowed to distribute this subroutine and users should provide their own, or they may find help on the author s (Kieron Burke) web site at:

7 7 4. The correlation parts of the N12, GAM, and N12-SX are obtained from B97-like expansion E cαβ = E cσσ = truncated at the fourth order, with the opposite spin contribution calculated as: UEG drε cαβ n i=0 i b i u cαβ and the same spin contribution calculated as: UEG drε cσσ n i=0 i c i u cσσ once again, users should provide their own subroutine for this, and use the parameters in Table 1. Note that there is a typo in the N12 paper, the corrected values for b i and c i have been showed below. Table 1. Parameters of the B97-like expansion for the N12, GAM, and N12-SX correlation functionals. N12 GAM N12-SX b D D D+00 b D D D+00 b D D D-01 b D D D+00 b D D D+00 c D D D-01 c D D D+00 c D D D+01 c D D D+01 c D D D One needs to add a portion of the Hartree-Fock exchange energy to the total exchange-correlation energy for the M05, M05-2X, M06, M06-2X, M06-HF, M08-HX, M08-SO, SOGGA11-X, MN15, revm06, and revm11 functionals. See the details in Table The exchange part of M11 and rev M11 requires range-separation with the error function with M11: 42.8% short-range HF exchange, and 100% long-range HF exchange. The range parameter ω is a 1 0. revm11: 22.5% short-range HF exchange and 100% long-range exchange. The range parameter ω is 0.40 a 1 0.

8 8 7. The exchange part of N12-SX and MN12-SX requires 25% of screened exchange, which is: 25% short-range HF exchange and 0% long-range HF exchange. The range parameter µ is Table 2. Hartree-Fock exchange energies in the Minnesota functionals a Functional Fraction of Hartree-Fock exchange energy M E HFE M05-2X 0.56E HFE M E HFE M06-2X 0.54E HFE M06-HF 1.0E HFE M08-HX E HFE M08-SO E HFE M E SR-HFE + 1.0E LR-HFE (ω = 0.25) N12-SX, MN12-SX 0.25E SX (µ = 0.11) SOGGA, SOGGA11, M06-L, 0 M11-L, MN15 MN12-L, N E HFE SOGGA11-X E HFE revm E HFE revm E SR-HFE + 1.0E LR-HFE (ω = 0.40) a E HFE is the Hartree-Fock exchange energy, E SR-HFE and E LR-HFE are the short-range and longrange Hartree Fock exchange energies respectively, and ESX is the short-range Hartree Fock screened exchange in a screened functional

9 9 Reference energies and gradients Table 3 and 4 present reference energies and forces of CH 3 (open shell, doublet) and H 2 O (closed shell, singlet) with the 6-31+G** basis set and a pruned (99,590) grid. Geometries of CH 3 (in angstrom) ***************************************************** C H H H ***************************************************** Table 3. Reference energies (E h ) and forces (X,Y,Z, E h /a 0 ) for CH 3 PW6B95 E= C H H H PWB6K E= C H H H SOGGA E= C H H H SOGGA11 E= C H H H SOGGA11-X E= C H

10 10 H H N12 E= C H H H N12-SX E= C H H H M08-HX E= C H H H M11 E= C H H H M11-L E= C H H H MN12-L E= C H H H MN12-SX E= C H H H GAM E=

11 11 C H H H MN15-L E= C H H H MN15 E= C H H H revm06-l E= C H H H revm06 E= C H H H revm11 E= C H H H PBEsol E= C H H H WC06 E= C H H H

12 12 RPBE E= C H H H revpbe E= C H H H B97-3 E= C H H H

13 13 Geometries of H 2 O (in Å) ***************************************************** O H H ***************************************************** Table 4. Reference energies (E h ) and forces (X,Y,Z, E h /a 0 ) for H 2 O M06 E= O H H M06-L E= O H H M06-2X E= O H H M06-HF E= O H H M05-2X E= O H H M05 E= O H H M08-HX E= O H H

14 14 M08-SO E= O H H M11 E= O H H M11-L E= O H H MN12-L E= O H H MN12-SX E= O H H SOGGA11 E= O H H SOGGA11-X E= O H H N12 E= O H H N12-SX E= O H H GAM E=

15 15 O H H MN15-L E= O H H MN15 E= O H H revm06-l E= O H H revm06 E= O H H revm11 E= O H H M08-HX E= Exchange-only with O E HFE included H H M08-HX E= Correlation and E HFE O only (no meta exchange) H H M08-HX E= Correlation-only with O no meta or HF exchange H H Note: the final three entries in the above table are for developers.

16 16 Version history Version 1, December 31, 2008 Original version Version 1.1, April 23, 2009 Added SOGGA Version 1.2, May 14, 2009 Fixed some bugs, added reference energies and forces in the manual Version 1.3, May 12, 2011 Added SOGGA11 Version 1.4 October 07, 2011 Fixed some bugs, added reference citation for SOGGA11. Version 1.5 November 07, 2011 Added SOGGA11-X and M11 Version 1.6 December 05, 2011 Added M11-L, fixed some bugs Version 1.7 April 18, 2012 Added N12, fixed some bugs Version 1.8 September 05, 2012 Added MN12-L, N12-SX and MN12-SX, fixed some bugs Version 2.0 January 27, 2016 Added GAM, MN15-L and MN15

17 17 Version 3.0 March 16, 2018 Added revm06-l and revm06 Version 4.0 December 1, 2018 Added revm11