Minnesota functionals

Minnesota Functionals (Myz) are a group of approximated exchange-correlation energy functionals in density functional theory (DFT). They are developed by the group of Prof. Donald Truhlar at the University of Minnesota. These functionals are based on meta-GGA approximations, since they all include terms that depend on the kinetic energy density, and are all based on flexible functional forms parametrized on high-quality benchmark databases. These functionals are immensely useful for traditional quantum chemistry and solid-state physics calculations. The Myz functionals are widely used and tested in the quantum chemistry community,^[1][2][3][4] and are available in a large number of popular quantum chemistry computer programs.

Family of functionals

Minnesota 05

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

• M05:^[5] Global hybrid functional with 28% HF exchange.
• M05-2X^[6] Global hybrid functional with 56% HF exchange.

Minnesota 06

The 06 family represent a general improvement over the 05 family and is composed by:

• M06-L:^[7] Local functional, 0% HF exchange. Fast, good for transition metals, inorganic and organometallics.
• M06:^[8] Global hybrid functional with 27% HF exchange. For main group thermochemistry and non-covalent interactions, transition metal thermochemistry and organometallics. It is usually the most versatile of the 06 functionals, and because of this large applicability it can be slightly worse than M06-2X for specific properties that require high percentage of HF exchange, such as thermochemistry and kinetics.
• M06-2X:^[8] Global hybrid functional with 54% HF exchange. It is the top performer within the 06 functionals for main group thermochemistry, kinetics and non-covalent interactions, however it cannot be used for cases where multi-reference species are or might be involved, such as transition metal thermochemistry and organometallic.
• M06-HF:^[9] Global hybrid functional with 100% HF exchange. For charge transfer TD-DFT and systems where self interaction is pathological.

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 high-percentage of HF exchange, with performances similar to those of M06-2X:

• M08-HX:^[10] Global hybrid functional with 52.23% HF exchange. For main group thermochemistry, kinetics and non-covalent interactions.
• M08-SO:^[10] Global hybrid functional with 56.79% HF exchange. For main group thermochemistry, kinetics and non-covalent interactions.

Minnesota 11

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

• M11-L:^[11] Local functional (0% HF exchange) with dual-range DFT exchange. Fast, good for transition metals, inorganic, organometallics and non-covalent interactions, with large improvements over M06-L.
• M11:^[12] Range-separated hybrid functional with 42.8% HF exchange in the short-range and 100% in the long-range. For main group thermochemistry, kinetics and non-covalent interactions, with performances comparable to those of M06-2X and for TD-DFT applications, with performances comparable to M06-HF.

Minnesota 12

The 12 family uses a Nonseparable^[13] (MN) functional form in order to provide balanced performance for both chemistry and solid-state physics applications. It is composed by:

• MN12-L:^[14] Local functional, 0% HF exchange. It is very versatile and provides good performances and fast calculations for energetic and structural problems in both chemistry and solid-state physics.
• MN12-SX:^[15] Screened-exchange (SX) hybrid functional with 25% HF exchange in the short-range and 0% HF exchange in the long-range. As MN12-L it is very versatile and provides good performances for energetic and structural problems in both chemistry and solid-state physics, at a computational cost that is intermediate between local and global hybrid functionals.

Main Software with Implementation of the Minnesota Functionals

Package	M05	M05-2X	M06-L	M06	M06-2X	M06-HF	M08-HX	M08-SO	M11-L	M11	MN12-L	MN12-SX	MN15-L
ADF	Yes*	Yes*	Yes	Yes	Yes	Yes	Yes*	Yes*	Yes*	Yes	Yes*	Yes	Yes*
GAMESS (US)	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No
Gaussian	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No
Jaguar	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No
Libxc Abinit ADF APE Atomistix ToolKit AtomPAW BigDFT CP2K DP Elk ERKALE exciting GPAW JDFTx MOLGW Octopus Yambo	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
MOLCAS	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No
MOLPRO	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No
NWChem	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No
Orca	No	No	Yes	Yes	Yes	No	No	No	No	No	No	No	No
PSI	Yes	Yes	No	No	No	No	No	No	No	No	No	No	No
Q-Chem Spartan	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No
Quantum ESPRESSO	No	No	Yes	No	No	No	No	No	No	No	No	No	No
TURBOMOLE using XCFun	No	No	Yes	Yes	Yes	No	No	No	No	No	No	No	No
VASP	No	No	Yes	No	No	No	No	No	No	No	No	No	No

* Using LibXC.

References

1. A.J. Cohen, P. Mori-Sánchez and W. Yang (2012). "Challenges for Density Functional Theory". Chemical Reviews 112 (1): 289–320. doi:10.1021/cr200107z. PMID 22191548.
2. E.G. Hohenstein, S.T. Chill and 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.
3. K.E. Riley, M Pitoňák, P. Jurečka and P. Hobza (2010). "Stabilization and Structure Calculations for Noncovalent Interactions in Extended Molecular Systems Based on Wave Function and Density Functional Theories". Chemical Reviews 110 (9): 5023–63. doi:10.1021/cr1000173. PMID 20486691.
4. L. Ferrighi, Y. Pan, H. Grönbeck and B. Hammer (2012). "Study of Alkylthiolate Self-assembled Monolayers on Au(111) Using a Semilocal meta-GGA Density Functional". Journal of Physical Chemistry 116: 7374–7379. doi:10.1021/jp210869r.
5. Y. Zhao, N.E. Schultz and D.G. Truhlar (2005). "Exchange-correlation functional with broad accuracy for metallic and nonmetallic compounds, kinetics, and noncovalent interactions". Journal of Chemical Physics 123 (16): 161103. doi:10.1063/1.2126975. PMID 16268672.
6. Y. Zhao, N.E. Schultz and D.G. Truhlar (2006). "Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parametrization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions". Journal of Chemical Theory and Computation 2: 364–382. doi:10.1021/ct0502763.
7. Y. Zhao and D.G. Truhlar (2006). "A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions". Journal of Chemical Physics 125 (19): 194101. doi:10.1063/1.2370993. PMID 17129083.
8. Y. Zhao and D.G. Truhlar (2006). "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 Account 120: 215–241. doi:10.1007/s00214-007-0310-x.
9. Y. Zhao and D.G. Truhlar (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". Journal of Physical Chemistry A 110: 13126–13130. doi:10.1021/jp066479k.
10. Y. Zhao and 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.
11. R. Peverati and 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: 117–124. doi:10.1021/jz201525m.
12. R. Peverati and 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.
13. R. Peverati and 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.
14. R. Peverati and 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): 13171–4. doi:10.1039/c2cp42025b. PMID 22910998.
15. R. Peverati and 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. doi:10.1039/c2cp42576a. PMID 23132141.

External links

• The Truhlar Group
• Minnesota Databases for Chemistry and Physics
• The most recent review article on the performance of the Minnesota functionals