Minnesota functionals

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Minnesota Functionals (Myz) are a group of highly parameterized approximate exchange-correlation energy functionals in density functional theory (DFT). They are developed by the group of Donald Truhlar at the University of Minnesota. The Minnesota functionals are available in a large number of popular quantum chemistry computer programs, and can be used for traditional quantum chemistry and solid-state physics calculations.

Contents

These functionals are based on the meta-GGA approximation, i.e. they include terms that depend on the kinetic energy density, and are all based on complicated functional forms parametrized on high-quality benchmark databases. The Myz functionals are widely used and tested in the quantum chemistry community. [1] [2] [3] [4]

Controversies

Independent evaluations of the strengths and limitations of the Minnesota functionals with respect to various chemical properties cast doubts on their accuracy. [5] [6] [7] [8] [9] Some regard this criticism to be unfair. In this view, because Minnesota functionals are aiming for a balanced description for both main-group and transition-metal chemistry, the studies assessing Minnesota functionals solely based on the performance on main-group databases [5] [6] [7] [8] yield biased information, as the functionals that work well for main-group chemistry may fail for transition metal chemistry.

A study in 2017 highlighted what appeared to be the poor performance of Minnesota functionals on atomic densities. [10] Others subsequently refuted this criticism, claiming that focusing only on atomic densities (including chemically unimportant, highly charged cations) is hardly relevant to real applications of density functional theory in computational chemistry. Another study found this to be the case: for Minnesota functionals, the errors in atomic densities and in energetics are indeed decoupled, and the Minnesota functionals perform better for diatomic densities than for the atomic densities. [11] The study concludes that atomic densities do not yield an accurate judgement of the performance of density functionals. [11] Minnesota functionals have also been shown to reproduce chemically relevant Fukui functions better than they do the atomic densities. [12]

Family of functionals

Minnesota 05

The first family of Minnesota functionals, published in 2005, is composed by:

In addition to the fraction of HF exchange, the M05 family of functionals includes 22 additional empirical parameters. [14] A range-separated functional based on the M05 form, ωM05-D which includes empirical atomic dispersion corrections, has been reported by Chai and coworkers. [15]

Minnesota 06

The '06 family represent a general improvement[ citation needed ] over the 05 family and is composed of:

The M06 and M06-2X functionals introduce 35 and 32 empirically optimized parameters, respectively, into the exchange-correlation functional. [18] A range-separated functional based on the M06 form, ωM06-D3 which includes empirical atomic dispersion corrections, has been reported by Chai and coworkers. [22]

Minnesota 08

The '08 family was created with the primary intent to improve the M06-2X functional form, retaining the performances for main group thermochemistry, kinetics and non-covalent interactions. This family is composed by two functionals with a high percentage of HF exchange, with performances similar to those of M06-2X[ citation needed ]:

Minnesota 11

The '11 family introduces range-separation in the Minnesota functionals and modifications in the functional form and in the training databases. These modifications also cut the number of functionals in a complete family from 4 (M06-L, M06, M06-2X and M06-HF) to just 2:

Minnesota 12

The 12 family uses a nonseparable [27] (N in MN) functional form aiming to provide balanced performance for both chemistry and solid-state physics applications. It is composed by:

Minnesota 15

The 15 functionals are the newest addition to the Minnesota family. Like the 12 family, the functionals are based on a non-separable form, but unlike the 11 or 12 families the hybrid functional doesn't use range separation: MN15 is a global hybrid like in the pre-11 families. The 15 family consists of two functionals

Main Software with Implementation of the Minnesota Functionals

PackageM05M05-2XM06-LrevM06-LM06M06-2XM06-HFM08-HXM08-SOM11-LM11MN12-LMN12-SXMN15MN15-L
ADF Yes*Yes*YesNoYesYesYesYes*Yes*Yes*Yes*Yes*Yes*Yes*Yes*
CPMD YesYesYesNoYesYesYesYesYesYesYesNoNoNoNo
GAMESS (US) YesYesYesNoYesYesYesYesYesYesYesYesYesYesYes
Gaussian 16 YesYesYesNoYesYesYesYesYesYesYesYesYesYesYes
Jaguar YesYesYesNoYesYesYesYesYesYesYesYesNoYesYes
Libxc YesYesYesYesYesYesYesYesYesYesYesYesYesYesYes
MOLCAS YesYesYesNoYesYesYesYesYesNoNoNoNoNoNo
MOLPRO YesYesYesNoYesYesYesYesYesYesNoNoNoNoNo
NWChem YesYesYesNoYesYesYesYesYesYesYesNoNoNoNo
Orca Yes*Yes*YesYes*YesYesYes*Yes*Yes*Yes*Yes*Yes*Yes*Yes*Yes*
PSI4 Yes*Yes*Yes*NoYes*Yes*Yes*Yes*Yes*Yes*Yes*Yes*Yes*Yes*Yes*
Q-Chem YesYesYesYesYesYesYesYesYesYesYesYesYesNoYes
Quantum ESPRESSO NoNoYesNoNoNoNoNoNoNoNoNoNoNoNo
TURBOMOLE Yes*Yes*YesYes*YesYesYesYes*Yes*Yes*Yes*Yes*Yes*Yes*Yes*
VASP NoNoYesNoNoNoNoNoNoNoNoNoNoNoNo

* Using LibXC.

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References

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  2. ↑ E.G. Hohenstein, S.T. Chill & C.D. Sherrill (2008). "Assessment of the Performance of the M05−2X and M06−2X Exchange-Correlation Functionals for Noncovalent Interactions in Biomolecules". Journal of Chemical Theory and Computation. 4 (12): 1996–2000. doi:10.1021/ct800308k. PMID   26620472.
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  12. ↑ Gould, Tim (2017). "What Makes a Density Functional Approximation Good? Insights from the Left Fukui Function". J. Chem. Theory Comput. 13 (6): 2373–2377. doi:10.1021/acs.jctc.7b00231. hdl: 10072/348655 . PMID   28493684.
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  17. ↑ Ying Wang; Xinsheng Jin; Haoyu S. Yu; Donald G. Truhlar & Xiao Hea (2017). "Revised M06-L functional for improved accuracy on chemical reaction barrier heights, noncovalent interactions, and solid-state physics". Proc. Natl. Acad. Sci. U.S.A. 114 (32): 8487–8492. Bibcode:2017PNAS..114.8487W. doi: 10.1073/pnas.1705670114 . PMC   5559035 . PMID   28739954.
  18. 1 2 3 Y. Zhao & D.G. Truhlar (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-class functionals and 12 other functionals". Theor Chem Acc. 120 (1–3): 215–241. doi: 10.1007/s00214-007-0310-x .
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  23. 1 2 Y. Zhao & D.G. Truhlar (2008). "Exploring the Limit of Accuracy of the Global Hybrid Meta Density Functional for Main-Group Thermochemistry, Kinetics, and Noncovalent Interactions". Journal of Chemical Theory and Computation. 4 (11): 1849–1868. doi:10.1021/ct800246v. PMID   26620329.
  24. ↑ R. Peverati & D.G. Truhlar (2012). "M11-L: A Local Density Functional That Provides Improved Accuracy for Electronic Structure Calculations in Chemistry and Physics". Journal of Physical Chemistry Letters. 3 (1): 117–124. doi: 10.1021/jz201525m .
  25. ↑ R. Peverati & D.G. Truhlar (2011). "Improving the Accuracy of Hybrid Meta-GGA Density Functionals by Range Separation". Journal of Physical Chemistry Letters. 2 (21): 2810–2817. doi: 10.1021/jz201170d .
  26. ↑ P. Verma; Y. Wang; S. Ghosh; X. He & D. G. Truhlar (2019). "Revised M11 Exchange-Correlation Functional for Electronic Excitation Energies and Ground-State Properties". Journal of Physical Chemistry A. 123 (13): 2966–2990. Bibcode:2019JPCA..123.2966V. doi:10.1021/acs.jpca.8b11499. PMID   30707029. S2CID   73431138.
  27. ↑ R. Peverati & D.G. Truhlar (2012). "Exchange–Correlation Functional with Good Accuracy for Both Structural and Energetic Properties while Depending Only on the Density and Its Gradient". Journal of Chemical Theory and Computation. 8 (7): 2310–2319. doi: 10.1021/ct3002656 . PMID   26588964.
  28. ↑ R. Peverati & D.G. Truhlar (2012). "An improved and broadly accurate local approximation to the exchange–correlation density functional: The MN12-L functional for electronic structure calculations in chemistry and physics". Physical Chemistry Chemical Physics. 14 (38): 13171–13174. Bibcode:2012PCCP...1413171P. doi:10.1039/c2cp42025b. PMID   22910998.
  29. ↑ R. Peverati & D.G. Truhlar (2012). "Screened-exchange density functionals with broad accuracy for chemistry and solid-state physics". Physical Chemistry Chemical Physics. 14 (47): 16187–91. Bibcode:2012PCCP...1416187P. doi:10.1039/c2cp42576a. PMID   23132141.
  30. ↑ Yu, Haoyu S.; He, Xiao; Li, Shaohong L. & Truhlar, Donald 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". Chem. Sci. 7 (8): 5032–5051. doi:10.1039/C6SC00705H. PMC   6018516 . PMID   30155154.
  31. ↑ Yu, Haoyu S.; He, Xiao & Truhlar, Donald G. (2016). "MN15-L: A New Local Exchange-Correlation Functional for Kohn–Sham Density Functional Theory with Broad Accuracy for Atoms, Molecules, and Solids". J. Chem. Theory Comput. 12 (3): 1280–1293. doi:10.1021/acs.jctc.5b01082. PMID   26722866.
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