Minnesota functionals

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.

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.

Controversies

Independent evaluations of the strengths and limitations of the Minnesota functionals with respect to various chemical properties cast doubts on their accuracy. 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 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. 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. The study concludes that atomic densities do not yield an accurate judgement of the performance of density functionals. Minnesota functionals have also been shown to reproduce chemically relevant Fukui functions better than they do the atomic densities.

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. A range-separated functional based on the M05 form, ωM05-D which includes empirical atomic dispersion corrections, has been reported by Chai and coworkers.

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. A range-separated functional based on the M06 form, ωM06-D3 which includes empirical atomic dispersion corrections, has been reported by Chai and coworkers.

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 (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*YesNoYesYesYes Yes*Yes*Yes*Yes*Yes*Yes*Yes*Yes*
CPMD YesYesYesNoYesYesYes YesYesYesYesNoNoNoNo
GAMESS (US) YesYesYesNoYesYesYes YesYesYesYesYesYesYesYes
Gaussian 16 YesYesYesNoYesYesYes YesYesYesYesYesYesYesYes
Jaguar YesYesYesNoYesYesYes YesYesYesYesYesNoYesYes
Libxc YesYesYesYesYesYesYes YesYesYesYesYesYesYesYes
MOLCAS YesYesYesNoYesYesYes YesYesNoNoNoNoNoNo
MOLPRO YesYesYesNoYesYesYes YesYesYesNoNoNoNoNo
NWChem YesYesYesNoYesYesYes YesYesYesYesNoNoNoNo
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 YesYesYesYesYesYesYes YesYesYesYesYesYesNoYes
Quantum ESPRESSO NoNoYesNoNoNoNo NoNoNoNoNoNoNoNo
TURBOMOLE Yes*Yes*YesYes*YesYesYes Yes*Yes*Yes*Yes*Yes*Yes*Yes*Yes*
VASP NoNoYesNoNoNoNo NoNoNoNoNoNoNoNo

* Using LibXC.

References

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  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.
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