Density Functionals from the Truhlar Group


Our information about functionals is organized both by program and by functional.

This page contains the density functionals developed in the Truhlar group on the second, third, and fourth rungs of the ladder of functionals; our fifth-rung functionals (that is, functionals involving unoccupied orbitals (22,23)) are not considered here. The functionals considered here are classified into nine categories: (i) the generalized gradient approximation (GGA, in which the density functional depends on the up and down spin densities and their reduced gradient), (ii) the nonseparable gradient approximation (NGA, in which the density functional depends on the up/down spin densities and their reduced gradient, and also adopts a nonseparable form), (iii) meta GGA (in which the functional also depends on the up and down spin kinetic energy densities), (iv) meta nonseparable gradient approximation (in which the functional also depends on spin kinetic energy densities, and adopts a nonseparable form), (v) hybrid GGA (a combination of GGA with Hartree-Fock exchange), (vi) range-separated hybrid NGA (a combination of long-range NGA with range-separated Hartree-Fock exchange), (vii) hybrid meta GGA (a combination of meta GGA with Hartree-Fock exchange), (viii) range-separated hybrid meta GGA (a combination of short-range meta GGA with range-separated Hartree-Fock exchange), (ix) range-separated meta-NGA (a combination of long-range meta-NGA with range-separated Hartree-Fock exchange), and (x) hybrid meta nonseparable gradient approximation (a combination of meta NGA with Hartree-Fock exchange)

Generalized gradient approximations (GGA): MPWLYP1W, PBE1W, PBELYP1W, MOHLYP, MOHLYP2, SOGGA, SOGGA11

Nonseparable gradient approximation (NGA):  N12, GAM

Meta-GGA:  TPSSLYP1W, M06-L, M11-L

Meta nonseparable gradient approximation (meta-NGA):  MN12-L, MN15-L

Hybrid GGA:  MPW1K, MPW3LYP, MPWLYP1M, SOGGA11-X

Global-hybrid meta-GGA: BB1K, MPWB1K, MPW1B95,  TPSS1KCIS, MPWKCIS1K, MPW1KCIS, PBE1KCIS,  PW6B95, PWB6K, M05, M05-2X, M06-HF, M06, M06-2X, M08-HX, M08-SO

Range-separated hybrid NGA:  N12-SX

Range-separated hybrid meta-GGA: M11

Range-separated hybrid meta-NGA:  MN12-SX

Hybrid meta-NGA:  MN15

 
References

 


Availability of Density Functionals from the Truhlar Group

The Minnesota density functionals are available in the following codes. 

ABINIT

ADF

BAND

CRYSTAL

GAMESS

Gaussian 03

Gaussian 09

GPAW

HONDOPLUS

Jaguar

libxc

Minnesota-Gaussian Functional Module (MN-GFM)

Minnesota Functional Module (MFM)

MOLCAS

NWChem

octopus

ORCA

Q-Chem 

Spartan

TURBOMOLE

VASP

XCFun

MPW1K

MPW1K (1) is a hybrid density functional that is available in the following programs:

HONDOPLUS

NWChem Version 5.0

Gaussian03

Gaussian09


How to perform an MPW1K calculation with HONDOPLUS

The options in the SCF section to run MPW1K are:

$SCF
    MAXIT=50, ACURCY=1E-8,
    DFTFLG=1, DFTFUN=8
$END


How to perform an MPW1K calculation with NWCHEM

The options in the dft section to run MPW1K are:

dft
   XC  mpw1k    
end

 


How to perform an MPW1K calculation with Gaussian98 or Gaussian03 or Gaussian09

The keywords to run MPW1K/6-31+G(d,p) with Gaussian98 are:

#mpwpw91/6-31+G(d,p)
IOp(5/45=10000428)
IOp(5/46=05720572)
IOp(5/47=10001000)


The keywords to run MPW1K/6-31+G(d,p) with Gaussian03 are:

#mpwpw91/6-31+G(d,p)
IOp(3/76=0572004280)

The keywords to run MPW1K/6-31+G(d,p) with Gaussian09 are:

#mpwpw91/6-31+G(d,p)
IOp(3/76=0572004280)

Note: Always run frequency calculations as a separate job when using MPW1K in Gaussian.

Special note for some experienced users: Some changes were made to the IOps in different revisions of Gaussian03. Below is a table of the IOp combinations that will correctly evaluate MPW1K with the different revisions of Gaussian. If you used the keywords recommended above, please ignore this table.

Gaussian version

MPW1K

Not MPW1K

g98

IOp(5/45=05720428)

IOp(3/76=0572004280)

 

IOp(5/45=10000428)
IOp(5/46=05720572)
IOp(5/47=10001000)

 

g03.b01

IOp(3/76=0572004280)

IOp(5/45=05720428)

 

IOp(3/76=1000004280)
IOp(3/77=0572005720)
IOp(3/78=10001000)

 

g03.b05

IOp(3/76=0572004280)

IOp(5/45=05720428)

 

IOp(3/76=1000004280)
IOp(3/77=0572005720)
IOp(3/78=1000010000)

IOp(3/76=1000004280)
IOp(3/77=0572005720)
IOp(3/78=10001000)

g03.c01

IOp(3/76=0572004280)

IOp(5/45=05720428)

 

IOp(3/76=1000004280)
IOp(3/77=0572005720)
IOp(3/78=1000010000)

IOp(3/76=1000004280)
IOp(3/77=0572005720)
IOp(3/78=10001000)


A note on MPW notation

Note that mPW and MPW are the same functional.  Furthermore, Adamo and Barone italicize the m, but many later workers do not follow this convention.  In our own work we use lower case m for the functionals in the original paper of Adamo and Barone.  We also use lower case m if we simply combine the mPW functional with any standard correlation function, such as in mPWLYP.  However, if any parameters are newly optimized for the combination, then we use capital M, as in MPW1K, MPW3LYP, MPW1B95, MPWB1K, MPWLYP1M, and MPWLYP1W.

mPW bug in Gaussian 98

Versions of GAUSSIAN98 through g98.a11 have an error in the mPW exchange functional; this error was first pointed out in an appendix to a paper using this functional.(2) The bug causes small errors in all energies calculated using hybrid DFT methods that involve the mPW or MPW exchange functional,(3) including MPW1K and mPW1PW91(3) (also known as mPW0 and MPW25).

The typical error in bond energies introduced by the bug is about 0.1 kcal/mol.

The details of the bug are documented here

The bug exists in all versions of Gaussian98 through revision a.11. The bug has been fixed in Gaussian03. Gaussian03 also allows a user to run the old incorrect version of the mPW; the keyword to do this is OmPW.

MPW1K in Jaguar

  Jaguar-version 6.5 has a bug in MPW1K; it has the parameters of the original Adamo-Barone paper, which were in error.  For further discussion of this bug, see the section entitled "mPW bug in Gaussian 98"

 


 

BB1K

BB1K (4) is a hybrid density functional that is available in the following programs:


Gaussian03

Gaussian09

NWChem Version 5.0


How to perform a BB1K calculation with Gaussian03


The input file to run BB1K/6-31+G(d,p) with Gaussian03 for CH3SH  (QCISD/MG3 geometry) is:

CH3SHDIDZ.inp

The calculated energy is -438.704427 hartrees at theBB1K/6-31+G(d,p) level.


The input file to run BB1K/MG3S with Gaussian03 for CH3SH  (QCISD/MG3 geometry) is:

CH3SHMG3S.inp

The calculated energy is -438.7473099 hartrees at the BB1K/MG3S level.

The MG3S basis set can be obtained from Truhlar group basis set webpage.


Note: Always run frequency calculations as a separate job when using BB1K in Gaussian.

 


 

How to perform an BB1K calculation with NWChem Version 5.0

 The options in the dft section to run BB1K are:

 dft
   XC  bb1k

end


B1B95 bug in Gaussian03

The online manual of Gaussian03 says that "the B1B95 gives the hybrid

DFT method employing Becke's functional as defined in the original paper [480]." 

However, in Becke's paper,(5) Becke said to use 28% HF exchange, while in Gaussian03 Rev. B01, this is incorrectly coded as 25%. 

This bug has been fixed in the new release Gaussian03 Rev. C01.


MPWB1K and MPW1B95

MPWB1K (6) is hybrid meta DFT method for kinetics, and MPW1B95 (6)is a hybrid meta DFT method for thermochemistry. Both methods are available in the following programs:


Gaussian03

Gaussian09

NWChem Version 5.0

Q-Chem 3.1


 

How to perform an MPWB1K or MPW1B95 calculation with Gaussian03 or Gaussian09

The keywords to run MPWB1K/6-31+G(d,p) with Gaussian03 or Gaussian09 are:

#mpwb95/6-31+G(d,p)
IOp(3/76=0560004400)

The keywords to run MPW1B95/6-31+G(d,p) with Gaussian03 or Gaussian09  are:

#mpwb95/6-31+G(d,p)
IOp(3/76=0690003100)

Note: Always run frequency calculations as a separate job when using MPWB1K and MPW1B95 in Gaussian.

 


How to perform an MPWB1K or MPW1B95 calculation with NWChem Version 5.0

The options in the dft section to run MPW1B95 are:

dft
   XC  mpw1b95

end

 
The options in the dft section to run MPWB1K are:
dft
   XC  mpwb1k

end

 


 
TPSS1KCIS

TPSS1KCIS (7) is a hybrid meta DFT method for thermochemistry, and it is available in the following program:


Gaussian03

Gaussian09


How to perform a TPSS1KCIS calculation with Gaussian03

The keywords to run TPSS1KCIS/6-31+G(d,p) with Gaussian03 are:

#tpsskcis/6-31+G(d,p)
IOp(3/76=0870001300)

Note: Always run frequency calculations as a separate job when using TPSS1KCIS in Gaussian03.


 

MPW3LYP

MPW3LYP (6) is a hybrid DFT method for thermochemistry, and it is available in the following programs:

Gaussian03

Gaussian09

NWChem


 How to perform an MPW3LYP calculation with Gaussian03 or Gaussian09

The keywords to run MPW3LYP/6-31+G(d,p) with Gaussian03 or Gausian09 are:

#mpwlyp/6-31+G(d,p)
IOp(3/76=1000002180) IOp(3/77=0709007820) IOp(3/78=0871010000)


Note: Always run frequency calculations as a separate job when using MPW3LYP in Gaussian03
or Gausian09.


How to perform an MPW3LYP calculation with NWCHEM

The options in the dft section to run MPW3LYP are:

 dft
   XC  vwn_1_rpa 0.129 lyp 0.871 HFexch 0.218  slater 0.782 mpw91 nonlocal 0.709

end


 

 MPWKCIS1K and MPW1KCIS

MPWKCIS1K (8) and MPW1KCIS (8) are hybrid meta DFT methods for thermochemistry. Both methods are available in the following program:

Gaussian03

Gaussian09


 

How to perform an MPWKCIS1K or MPW1KCIS calculation with Gaussian03 or Gaussian09

The keywords to run MPWKCIS1K/6-31+G(d,p) with Gaussian03 or Gaussian09 are:

#MPWKCIS/6-31+G(d,p)
IOp(3/76= 0590004100)

The keywords to run MPW1KCIS/6-31+G(d,p) with Gaussian03
or Gaussian09 are:

# MPWKCIS/6-31+G(d,p)
IOp(3/76= 0850001500)

Note: Always run frequency calculations as a separate job when using MPWKCIS1K and MPW1KCIS in Gaussian.

Note that Gaussian03 originally had a bug as far as combining the mPW or PBE functional with KCIS one.  Because of this bug, the KCIS functional, when used with mPW or PBE, was evaluated in the tau = 0 limit.  The bug is fixed as of version D01/02. Unfortunately, MPWKCIS1K and MPW1KCIS were parameterized before the bug was fixed.


PBE1KCIS

PBE1KCIS (9) is a hybrid meta DFT method for thermochemistry, and it is available in the following program:


Gaussian03

Gaussian09


 

How to perform a PBE1KCIS calculation with Gaussian03 or Gaussian09

The keywords to run PBE1KCIS/6-31+G(d,p) with Gaussian03 or Gaussian09 are:

#pbekcis/6-31+G(d,p)
IOp(3/76=0780002200)


Note: Always run frequency calculations as a separate job when using PBE1KCIS in Gaussian03 or Gaussian09.

Note that Gaussian03 originally had a bug as far as combining the mPW or PBE functional with KCIS one.  Because of this bug, the KCIS functional, when used with mPW or PBE, was evaluated in the tau = 0 limit.  The bug is fixed as of version G03 D01/02. Unfortunately, PBE1KCIS was parameterized before the bug was fixed.


MPWLYP1W, PBE1W, PBELYP1W, TSSLYP1W

PBE1W, MPWLYP1W, TPSSLYP1W, MPWLYP1W are non-hybrid density functionals parameterized for water (10) .

 All four methods are available in the program:

 Gaussian03

Gaussian09

 How to perform MPWLYP1W, PBE1W, PBELYP1W, TPSSLYP1W in Gaussian03 or Gaussian09:

 
The keywords to run PBE1W/6-31+G(d,p) with Gaussian03 or Gaussian09 are:

 #pbepbe/6-31+G(d,p)

IOp(3/78=0740010000)

 

The keywords to run MPWLYP1W/6-31+G(d,p) with Gaussian03 or Gaussian09 are:

 #mpwv5lyp/6-31+G(d,p)

IOp(3/78=0880010000)

 

The keywords to run PBELYP1W in Gaussian03 or Gaussian09 are:

 #pbev5lyp/6-31+G(d,p)

IOp(3/78=0540010000)

The keywords to run TPSSLYP1W in Gaussian03 or Gaussian09 are:

#tpssv5lyp/6-31+G(d,p)

IOp(3/78=0740010000)

Note :  Always run frequency calculations as a separate job when using any of these functionals in Gaussian03.

 


PWB6K and PW6B95

PWB6K (11) is hybrid meta DFT method for kinetics, and PW6B95 (11) is a hybrid meta DFT method for thermochemistry. Both methods are available in the first four following programs and PW6B95 is also available in the last two programs:


Gaussian03-MN-GFM

Q-Chem 3.1

NWChem Version 5.0

Jaguar

ORCA

TURBOMOLE

How to perform an PWB6K or PW6B95 calculation with Gaussian03-MN-GFM

The keywords to run PWB6K/6-31+G(d,p) with Gaussian03-MN-GFM  are:

#pwb6k/6-31+G(d,p)

The keywords to run MPW1B95/6-31+G(d,p) with Gaussian03-MN-GFM are:

#pw6b95/6-31+G(d,p)


 

How to perform an PWB6K or PW6B95 calculation with NWChem Version 5.0

The options in the dft section to run PWB6K are:

 dft
   XC  pwb6k

end

 The options in the dft section to run PW6B95 are:

dft
   XC  pw6b95

end



M05 and M05-2X

M05 (12) and M05-2X (13, 18) are hybrid meta DFT methods. Both methods are available in the following programs:

ADF

CRYSTAL14

GAMESS

Gaussian03-MN-GFM

Gaussian09

Jaguar

NWChem Version 5.0

Q-Chem 3.1

Spartan

FORTRAN subroutines for this functional are available to users or developers who wish to add it to their own code. These subroutines are available at:

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


How to perform an M05 or M05-2X calculation with Gaussian0 and Gaussian09

The keywords to run M05/6-31+G(d,p) with Gaussian03 and Gaussian09  are:

#m05/6-31+G(d,p) integral=ultrafine

The keywords to run M05-2X/6-31+G(d,p) with Gaussian03 are:

#m052X/6-31+G(d,p) integral=ultrafine

How to perform an M05 or M05-2X calculation with NWChem Version 5.0

The options in the dft section to run M05 are:

dft

   XC  m05
end

The options in the dft section to run M05-2X are:
dft
   XC  m05-2x
end


MPWLYP1M 

MPWLYP1M (14) is a hybrid DFT method for organometallic chemistry, and it is available in the following programs:

 Gaussian03

Gaussian09

NWChem Version 5.0

How to perform an MPWLYP1M calculation with Gaussian03

The keywords to run MPWLYP1M/6-31+G(d,p) with Gaussian03 are:

#mpwlyp/6-31+G(d,p)
IOp(3/76=0950000500)


Note: Always run frequency calculations as a separate job when using MPWLYP1M in Gaussian03.


How to perform an MPWLYP1M calculation with NWChem Version 5.0

dft
   XC  HFexch 0.05  slater 0.95 mpw91 nonlocal 0.95 lyp

end


MOHLYP 

MOHLYP (14) is a GGA functional for organometallic chemistry, and it is available in the following programs:

 GAMESS

 Gaussian03

Gaussian09

How to perform an MOHLYP calculation with Gaussian

The keywords to run MOHLYP/6-31+G(d,p) with Gaussian03 Rev B.05 and C.01 are:

#
OV5LYP/6-31+G(d,p)
 IOp(3/77=1292010000)
  IOp(3/78=0500010000)

The keywords to run MOHLYP/6-31+G(d,p) with Gaussian03 Rev D.01 and E.01 and Gaussian09 Rev A.02 are:

#OV5LYP/6-31+G(d,p)
 IOp(3/77=0902409510)
  IOp(3/78=0500010000)

Note: Always run frequency calculations as a separate job when using MOHLYP in Gaussian03 and Gaussian09.

The explanation for the usage of IOp is available here.

The reference data for MOHLYP is available here.


MOHLYP2 

MOHLYP2 (21) is a GGA functional for barrier heights, and it is available in the following programs:

 GAMESS

 Gaussian03

Gaussian09

How to perform an MOHLYP2 calculation with Gaussian 

The keywords to run MOHLYP2/6-31+G(d,p) with Gaussian03 Rev B.05 and C.01 are:

#
OV5LYP/6-31+G(d,p)
 IOp(3/77=1849810515
)
  IOp(3/78=
0500005000)

The keywords to run MOHLYP2/6-31+G(d,p) with Gaussian03 Rev D.01 and E.01 and Gaussian09 Rev A.02 are:

#OV5LYP/6-31+G(d,p)
 IOp(3/77=1292010000)
  IOp(3/78=0500005000)

Note: Always run frequency calculations as a separate job when using MOHLYP2 in Gaussian03 and Gaussian09.

The explanation for the usage of IOp is available here.

The reference data for MOHLYP2 is available here.

The MOHLYP2 functional cannot be recommended as a general purpose functional; it greatly underestimates bond energies.  For example, with the TZQ basis, the mean unsigned errors for the TMAE4, MLBE4, AE6, and DBE14 bond energy databases are  29.8, 14.9, 17.4, and 20.2 kcal/mol.  In contrast, the true MOHLYP functional has respective values of 6.5, 5.2, 2,2, and 4.3 kcal/mol for these quantities. (In both cases the result is averaged over two possible ways for computing the energies of the V and Zr atoms, namely with the experimental multiplicity or with the predicted multiplicity).

Note that MOHLYP2 was incorrectly labeled as MOHLYP in Ref. 21.


M06-L

M06-L(15, 18) is a meta GGA, and it is available in the following programs:

ABINIT

ADF

BAND

CRYSTAL14

GAMESS

Gaussian03-MN-GFM

Gaussian09

GPAW

Jaguar

libxc

NWChem Version 5.0

octopus

ORCA

Q-Chem 3.1

Spartan

VASP

XCFun

FORTRAN subroutines for this functional are available to users or developers who wish to add it to their own code. These subroutines are available at:

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


How to perform an M06-L calculation with Gaussian03-MN-GFM or Gaussian09

The keywords to run M06-L/6-31+G(d,p) with Gaussian03-MN-GFM or Gaussian09  are:

#m06L/6-31+G(d,p)/auto integral=ultrafine


How to perform an M06-L calculation with Q-Chem 3.1

The keyword to run M06-L with Q-Chem is:

EXCHANGE       m06L


How to perform an M06-L calculation with VASP 5.2

M06-L is available in VASP 5.2.12 and later. To run M06-L calculations, please

1. Download the latest PAW potentials containing kinetic energy densities for meta-GGA calculations.

2. Note that meta-GGA calculations are difficult to converge in VASP, so users are always recommended to converge a PBE calculations first, and then read in the converged wavfunctions as initial guess for M06-L calcualtions.

3. Use the all-band minimization algorithm and accurate integration grid by setting the keywords

ALGO=A

PREC=A


 

M06-HF

M06-HF (16, 18) is a meta GGA, and it is available in the following programs:

CRYSTAL14

GAMESS

Gaussian03-MN-GFM

Gaussian09

Jaguar

NWChem Version 5.0

Q-Chem 3.1

Spartan

XCFun

FORTRAN subroutines for this functional are available to users or developers who wish to add it to their own code. These subroutines are available at:

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


How to perform an M06-HF calculation with Gaussian03-MN-GFM and Gaussian09

The keywords to run M06-HF/6-31+G(d,p) with Gaussian03-MN-GFM and Gaussian09  are:

#m06hf/6-31+G(d,p) integral=ultrafine


How to perform an M06-HF calculation with Q-Chem 3.1

The keywords to run M06-HF with Q-Chem is:

EXCHANGE       m06hf


 

M06 and M06-2X

M06(17, 18) and M06-2X(17, 18)  are hybrid meta DFT methods. Both methods are available in the following programs:

ADF

CRYSTAL14

GAMESS

Gaussian03-MN-GFM

Gaussian09

Jaguar

NWChem Version 5.0

ORCA

Q-Chem 3.1

Spartan

TURBOMOLE

XCFun

FORTRAN subroutines for this functional are available to users or developers who wish to add it to their own code. These subroutines are available at:

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


How to perform an M06 or M06-2X calculation with Gaussian03-MN-GFM and Gaussian09

The keywords to run M06/6-31+G(d,p) with Gaussian03-MN-GFM and Gaussian09  are:

#m06/6-31+G(d,p) integral=ultrafine

The keywords to run M06-2X/6-31+G(d,p) with Gaussian03-MN-GFM are:

#m062X/6-31+G(d,p) integral=ultrafine


 
How to perform an M06 or M06-2X calculation with Q-Chem

The keywords to run M06 with Q-Chem is:

EXCHANGE       m06

The keywords to run M06-2X with Q-Chem is:

EXCHANGE        m062x


How to perform M06 calculations with GAMESS
A GAMESS input file and the output file for the M06/6-31+G(d) caculation on the CO molecule. 

SOGGA

SOGGA (19) is a GGA that is available in

       Gaussian03-MN-GFM

FORTRAN subroutines for this functional are available to users or developers who wish to add it to their own code. These subroutines are available at

      http://comp.chem.umn.edu/mfm/

SOGGA is available in GAMESS as of the March 25, 2010 R2 public release.

SOGGA is available in CRYSTAL09.


SOGGA11

SOGGA11 (24) is a GGA that is available in

       Gaussian09

FORTRAN subroutines for this functional are available to users or developers who wish to add it to their own code. These subroutines are available at

      http://comp.chem.umn.edu/mfm/

SOGGA11 is available also in libxc, Q-Chem 4.0

a developer version with a working implementation of SOGGA11 was sent to GAMESS in December 2011 for inclusion in the next release.

a developer version with a working implementation of SOGGA11 was sent to NWChem in January 2012 for inclusion in the next release.


SOGGA11-X

SOGGA11-X (25) is a hybrid GGA that is available in

       Gaussian09

FORTRAN subroutines for this functional are available to users or developers who wish to add it to their own code. These subroutines are available at

      http://comp.chem.umn.edu/mfm/

SOGGA11-X is available also in libxc, Q-Chem 4.0

a developer version with a working implementation of SOGGA11-X was sent to GAMESS in December 2011 for inclusion in the next release.

a developer version with a working implementation of SOGGA11-X was sent to NWChem in January 2012 for inclusion in the next release.


M08-HX

M08-HX (20) is a hybrid meta-GGA that is available in

      Gaussian03-MN-GFM

FORTRAN subroutines for this functional are available to users or developers who wish to add it to their own code. These subroutines are available at

      http://comp.chem.umn.edu/mfm/

M08-HX is available in GAMESS as of the March 25, 2010 R2 public release.


How to perform an M08-HX calculation with Gaussian-MN-GFM

The keywords to run M08-HX/6-31+G(d,p) with Gaussian-MN-GFM  are:

#m08hx/6-31+G(d,p) integral=ultrafine


M08-SO

M08-SO (20) is a hybrid meta-GGA that is available in

      Gaussian03-MN-GFM

FORTRAN subroutines for this functional are available to users or developers who wish to add it to their own code. These subroutines are available at

      http://comp.chem.umn.edu/mfm/

M08-SO is available in GAMESS as of the March 25, 2010 R2 public release.


How to perform an M08-SO calculation with Gaussian-MN-GFM

The keywords to run M08-SO/6-31+G(d,p) with Gaussian-MN-GFM  are:

#m08so/6-31+G(d,p) integral=ultrafine


M11

M11 (26) is a range-separated hybrid meta-GGA that is available in

      Gaussian09

FORTRAN subroutines for this functional are available to users or developers who wish to add it to their own code. These subroutines are available at

      http://comp.chem.umn.edu/mfm/

M11 is available also in Q-Chem 4.0

a developer version with a working implementation of M11 was sent to GAMESS in December 2011 for inclusion in the next release.

a developer version with a working implementation of M11 was sent to NWChem in January 2012 for inclusion in the next release.


How to perform an M11 calculation with Gaussian09

The keywords to run M11/6-31+G(d,p) with Gaussian09  are:

#m11/6-31+G(d,p) integral=ultrafine


M11-L

M11-L (27) is a dual-range local meta-GGA that is available in

      Gaussian09

FORTRAN subroutines for this functional are available to users or developers who wish to add it to their own code. These subroutines are available at

      http://comp.chem.umn.edu/mfm/

M11-L is available also in Q-Chem 4.0

a developer version with a working implementation of M11-L was sent to GAMESS in December 2011 for inclusion in the next release.

a developer version with a working implementation of M11-L was sent to NWChem in January 2012 for inclusion in the next release.


How to perform an M11-L calculation with Gaussian09

The keywords to run M11-L/6-31+G(d,p) with Gaussian09  are:

#m11L/6-31+G(d,p)/auto integral=ultrafine


N12

N12 (28) is a nonseparable gradient approximation that is available in

      Gaussian09

FORTRAN subroutines for this functional are available to users or developers who wish to add it to their own code. These subroutines are available at

      http://comp.chem.umn.edu/mfm/


How to perform an N12 calculation with Gaussian09

The keywords to run N12/6-31+G(d,p) with Gaussian09  are:

#n12/6-31+G(d,p)/auto integral=ultrafine


MN12-L

MN12-L (29) is a nonseparable local meta-NGA that is available in

      Gaussian09

FORTRAN subroutines for this functional are available to users or developers who wish to add it to their own code. These subroutines are available at

      http://comp.chem.umn.edu/mfm/


How to perform an MN12-L calculation with Gaussian09

The keywords to run MN12-L/6-31+G(d,p) with Gaussian09  are:

#mn12l/6-31+G(d,p)/auto integral=ultrafine


N12-SX

N12-SX (30) is a range-separated hybrid nonseparable gradient approximation that is available in

      Gaussian09

FORTRAN subroutines for this functional are available to users or developers who wish to add it to their own code. These subroutines are available at

      http://comp.chem.umn.edu/mfm/


How to perform an N12-SX calculation with Gaussian09

The keywords to run N12-SX/6-31+G(d,p) with Gaussian09  are:

#n12sx/6-31+G(d,p) integral=ultrafine


MN12-SX

MN12-SX (30) is a range-separated hybrid nonseparable meta-NGA that is available in

      Gaussian09

FORTRAN subroutines for this functional are available to users or developers who wish to add it to their own code. These subroutines are available at

      http://comp.chem.umn.edu/mfm/


How to perform an MN12-SX calculation with Gaussian09

The keywords to run MN12-SX/6-31+G(d,p) with Gaussian09  are:

#mn12sx/6-31+G(d,p) integral=ultrafine


GAM

GAM (31) is a nonseparable gradient approximation that is available in

      MN-GFM (beginning with version 6.5)

FORTRAN subroutines for this functional are available to users or developers who wish to add it to their own code. These subroutines are available at

      http://comp.chem.umn.edu/mfm/


How to perform an GAM calculation with Gaussian09

The keywords to run GAM/6-31+G(d,p) with Gaussian09  are:

#GAMGAM/6-31+G(d,p)/auto integral=ultrafine


MN15-L

MN15-L (32) is a nonseparable local meta-NGA that is available in

      MN-GFM (beginning with version 6.6)

FORTRAN subroutines for this functional are available to users or developers who wish to add it to their own code. These subroutines are available at

      http://comp.chem.umn.edu/mfm/


How to perform an MN15-L calculation with Gaussian09

The keywords to run MN15-L/6-31+G(d,p) with Gaussian09  are:

#MN15L/6-31+G(d,p)/auto integral=ultrafine


MN15

MN15 (33) is a hybrid meta-NGA that is available in

      MN-GFM (beginning with version 6.7)

FORTRAN subroutines for this functional are available to users or developers who wish to add it to their own code. These subroutines are available at

      http://comp.chem.umn.edu/mfm/


How to perform an MN15 calculation with Gaussian09

The keywords to run MN15/6-31+G(d,p) with Gaussian09  are:

#MN15/6-31+G(d,p)/auto integral=ultrafine


 

References 

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2.         Lynch, B. J., Zhao, Y., and Truhlar, D. G. (2003) Effectiveness of Diffuse Basis Functions for Calculating Relative Energies by Density Functional Theory, J. Phys. Chem. A 107, 1384.

3.         Adamo, C. and Barone, V. (1998) Exchange functionals with improved long-range behavior and adiabatic connection methods without adjustable parameters: the mPW and mPW1PW models, J. Chem. Phys. 108, 664.

4.         Zhao, Y., Lynch, B. J., and Truhlar, D. G. (2004) Development and Assessment of a New Hybrid Density Functional Method for Thermochemical Kinetics, J. Phys. Chem. A 108, 2715.

5.         Becke, A. D. (1996) Density-functional thermochemistry. IV. A new dynamic correlation functional and implications for exact-exchange mixing, J. Chem. Phys. 104, 1040.

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7.         Zhao, Y., Lynch, B. J., and Truhlar, D. G. (2005) Multi-Coefficient Extrapolated Density Functional Theory for Thermochemistry and Thermochemical Kinetics, Phys. Chem. Chem. Phys. 7, 43.

8.         Zhao, Y., González-García, N., and Truhlar, D. G. (2005) Benchmark Database of Barrier Heights for Heavy Atom Transfer, Nucleophilic Substitution, Association, and Unimolecular Reactions and Their Use to Test Density Functional Theory, J. Phys. Chem. A 109, 2012.

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10.       Dahlke, E. E. and Truhlar, D. G. (2005) Improved Density Functionals for Water, J. Phys. Chem. B 109, 15677.

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12.       Zhao, Y., Schultz, N. E., and Truhlar, D. G. (2005) Exchange-Correlation Functionals with Broad Accuracy for Metallic and Nonmetallic Compounds, Kinetics, and Noncovalent Interactions, J. Chem. Phys. 123, 161103.

13.       Zhao, Y., Schultz, N. E., and Truhlar, D. G. (2006) Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parametrization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions, J. Chem. Theory Comput. 2, 364.

14.       Schultz, N., Zhao, Y., and Truhlar, D. G. (2005) Density functional for Inorganometallic and Organometallic Chemistry, J. Phys. Chem. A 109, 11127.

15.       Zhao, Y. and Truhlar, D. G. (2006) A New Local Density Functional for Main Group Thermochemistry, Transition Metal Bonding, Thermochemical Kinetics, and Noncovalent Interactions, J. Chem. Phys. 125, 194101.

16.       Zhao, Y. and Truhlar, D. G. (2006) Density Functional for Spectroscopy: No Long-Range Self-Interaction Error, Good Performance for Rydberg and Charge-Transfer States, and Better Performance on Average than B3LYP for Ground States, J. Phys. Chem. A 110, 13126.

17.       Zhao, Y. and Truhlar, D. G. (2008) The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06 Functionals and Twelve Other Functionals, Theor. Chem. Acc. 120, 215. [available at http://dx.doi.org/10.1007/s00214-007-0310-x ] (Contribution to the Mark S. Gordon 65th Birthday Festschrift Issue)

18.       Zhao, Y. and Truhlar, D. G. (2008) Density Functionals with Broad Applicability in Chemistry, Acc. Chem. Res. 41, 157

19.       Zhao,Y. and Truhlar, D. G. (2008) Construction of a Generalized Gradient Approximation by Restoring the Density-Gradient Expansion and Enforcing a Tight Lieb-Oxford Bound, J. Chem. Phys. 128, 184109.

20.       Zhao,Y. and Truhlar, D. G. (2008) Exploring the Limit of Accuracy of the Global Hybrid Density Functional for Main-Group Thermochemistry, Kinetics, and Noncovalent Interactions, J. Chem. Theory Comput. 4, 1849.

21.       Zheng, J., Zhao,Y., and Truhlar, D. G. (2009) The DBH24/08 Database and Its Use to Assess Electronic Structure Model Chemistries for Chemical Reaction Barrier Heights, J. Chem. Theory Comput. 5, 808.  See also unpublished erratum at Ref. 852 on http://comp.chem.umn.edu/Truhlar/JA08_09.htm

22.       Zhao,Y.,B. J. Lynch, and Truhlar, D. G. (2004) Doubly Hybrid Meta DFT: New Multi-Coefficient Correlation and Density Functional Methods for Thermochemistry and Thermochemical Kinetics, J. Phys. Chem. A 108, 4786.

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24.       Peverati, R.; Zhao, Y.; Truhlar, D. G. (2011) Generalized Gradient Approximation that Recovers the Second-Order Density-Gradient Expansion with Optimized Across-the-board Performance J. Phys. Chem. Lett. 2 1991-1997.

25.       Peverati, R.; Truhlar, D. G. (2011) Communication: A Global Hybrid Generalized Gradient Approximation to the Exchange-Correlation Functional that Satisfies the Second-Order Density-Gradient Constraint and Has Broad Applicability in Chemistry J. Chem. Phys. 135, 191102.

26.       Peverati, R.; Truhlar, D. G. (2011) Improving the Accuracy of Hybrid Meta-GGA Density Functionals by Range Separation J. Phys. Chem. Lett. 2, 2810-2817.

27.       Peverati, R.; Truhlar, D. G. (2011) M11-L: A Local Density Functional That Provides Improved Accuracy for Electronic Structure Calculations in Chemistry and Physics J. Phys. Chem. Lett. 3, 117-124.

28.       Peverati, R.; Truhlar, D. G. (2012) Exchange-Correlation Functional with Good Accuracy for Both Structural and Energetic Properties While Depending Only on the Density and its Gradient J. Chem. Theory. Comput. 8, 2310-2319.

29.       Peverati, R.; Truhlar, D. G. (2012) An Improved and Broadly Accurate Approximation to the Exchange-Correlation Density Functioal: The MN12-L Functional for Electronic Structure Calculations in Chemistry and Physics Phys. Chem. Chem. Phys. 14, 13171-13174. (Communication)

30.       Peverati, R.; Truhlar, D. G. (2012) Screened-Exchange Density Functionals with Broad Accuracy for Chemistry and Solid-State Physics Phys. Chem. Chem. Phys. 14, 16187-16191 (Communication)

31.       Yu, H. S.; Zhang, W.; Verma, P.; He, X.; Truhlar, D. G. (2015) Nonseparable exchange-correlation functional for molecules, including homogeneous catalysis involving transition metals Phys. Chem. Chem. Phys. 17, 12146-12160.

32.       Yu, H. S.; He, X.; Truhlar, D. G. (2015) MN15-L: A New Local Exchange-Correlation Functional for Kohn-Sham Density Functional Theory with Broad Accuracy for Atoms, Molecules, and Solids online ASAP,

33.       Yu, H. S.; He, X.; Li, S.; Truhlar, D. G. (2016) MN15: A Kohn-Sham Global-Hybrid Exchange-Correlation Density Functional with Broad Accuracy for Multi-Reference and Single-Reference Systems and Noncovalent Interactions submitted,


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