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Minnesota functionals
open-in-new
<h2 id="controversies">Controversies</h2> <p>Independent evaluations of the strengths and limitations of the Minnesota functionals with respect to various chemical properties cast doubts on their accuracy.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a><a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a><a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a><a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a><a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> 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<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a><a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a><a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a><a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a> yield biased information, as the functionals that work well for main-group chemistry may fail for transition metal chemistry. </p><p>A study in 2017 highlighted what appeared to be the poor performance of Minnesota functionals on atomic densities.<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a> 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 <a href="/facts/Computational_chemistry/KyuCgRV3">computational chemistry</a>. 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.<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a> The study concludes that atomic densities do not yield an accurate judgement of the performance of density functionals.<a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a> Minnesota functionals have also been shown to reproduce chemically relevant Fukui functions better than they do the atomic densities.<a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a> </p> <h2 id="family-of-functionals">Family of functionals</h2> <h3>Minnesota 05</h3> <p>The first family of Minnesota functionals, published in 2005, is composed by: </p> <ul><li>M05:<a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a> Global hybrid functional with 28% HF exchange.</li> <li>M05-2X<a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a> Global hybrid functional with 56% HF exchange.</li></ul> <p>In addition to the fraction of HF exchange, the M05 family of functionals includes 22 additional empirical parameters.<a class="footnote-ref" id="fnref:20" href="#fn:20"><sup>20</sup></a> A range-separated functional based on the M05 form, ωM05-D which includes empirical atomic dispersion corrections, has been reported by Chai and coworkers.<a class="footnote-ref" id="fnref:21" href="#fn:21"><sup>21</sup></a> </p> <h3>Minnesota 06</h3> <p>The '06 family represent a general improvement over the 05 family and is composed of: </p> <ul><li>M06-L:<a class="footnote-ref" id="fnref:22" href="#fn:22"><sup>22</sup></a> Local functional, 0% HF exchange. Intended to be fast, good for transition metals, inorganic and organometallics.</li> <li>revM06-L:<a class="footnote-ref" id="fnref:23" href="#fn:23"><sup>23</sup></a> Local functional, 0% HF exchange. M06-L revised for smoother potential energy curves and improved overall accuracy.</li> <li>M06:<a class="footnote-ref" id="fnref:24" href="#fn:24"><sup>24</sup></a> Global hybrid functional with 27% HF exchange. Intended 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.</li> <li>revM06:<a class="footnote-ref" id="fnref:25" href="#fn:25"><sup>25</sup></a> Global hybrid functional with 40.4% HF exchange. Intended for a broad range of applications on main-group chemistry, transition-metal chemistry, and molecular structure prediction to replace M06 and M06-2X.</li> <li>M06-2X:<a class="footnote-ref" id="fnref:26" href="#fn:26"><sup>26</sup></a> 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,<a class="footnote-ref" id="fnref:27" href="#fn:27"><sup>27</sup></a> however it cannot be used for cases where multi-reference species are or might be involved,<a class="footnote-ref" id="fnref:28" href="#fn:28"><sup>28</sup></a> such as transition metal thermochemistry and organometallics.</li> <li>M06-HF:<a class="footnote-ref" id="fnref:29" href="#fn:29"><sup>29</sup></a> Global hybrid functional with 100% HF exchange. Intended for charge transfer TD-DFT and systems where self-interaction is pathological.</li></ul> <p>The M06 and M06-2X functionals introduce 35 and 32 empirically optimized parameters, respectively, into the exchange-correlation functional.<a class="footnote-ref" id="fnref:30" href="#fn:30"><sup>30</sup></a> A range-separated functional based on the M06 form, ωM06-D3 which includes empirical atomic dispersion corrections, has been reported by Chai and coworkers.<a class="footnote-ref" id="fnref:31" href="#fn:31"><sup>31</sup></a> </p> <h3>Minnesota 08</h3> <p>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: </p> <ul><li>M08-HX:<a class="footnote-ref" id="fnref:32" href="#fn:32"><sup>32</sup></a> Global hybrid functional with 52.23% HF exchange. Intended for main group thermochemistry, kinetics and non-covalent interactions.</li> <li>M08-SO:<a class="footnote-ref" id="fnref:33" href="#fn:33"><sup>33</sup></a> Global hybrid functional with 56.79% HF exchange. Intended for main group thermochemistry, kinetics and non-covalent interactions.</li></ul> <h3>Minnesota 11</h3> <p>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: </p> <ul><li>M11-L:<a class="footnote-ref" id="fnref:34" href="#fn:34"><sup>34</sup></a> Local functional (0% HF exchange) with dual-range DFT exchange. Intended to be fast, to be good for transition metals, inorganic, organometallics and non-covalent interactions, and to improve much over M06-L.</li> <li>M11:<a class="footnote-ref" id="fnref:35" href="#fn:35"><sup>35</sup></a> Range-separated hybrid functional with 42.8% HF exchange in the short-range and 100% in the long-range. Intended for main group thermochemistry, kinetics and non-covalent interactions, with an intended performance comparable to that of M06-2X, and for TD-DFT applications, with an intended performance comparable to M06-HF.</li> <li>revM11:<a class="footnote-ref" id="fnref:36" href="#fn:36"><sup>36</sup></a> Range-separated hybrid functional with 22.5% HF exchange in the short-range and 100% in the long-range. Intended for good performance for electronic excitations and good predictions across the board for ground-state properties.</li></ul> <h3>Minnesota 12</h3> <p>The 12 family uses a nonseparable<a class="footnote-ref" id="fnref:37" href="#fn:37"><sup>37</sup></a> (N in MN) functional form aiming to provide balanced performance for both chemistry and solid-state physics applications. It is composed by: </p> <ul><li>MN12-L:<a class="footnote-ref" id="fnref:38" href="#fn:38"><sup>38</sup></a> A local functional, 0% HF exchange. The aim of the functional was to be very versatile and provide good computational performance and accuracy for energetic and structural problems in both chemistry and solid-state physics.</li> <li>MN12-SX:<a class="footnote-ref" id="fnref:39" href="#fn:39"><sup>39</sup></a> Screened-exchange (SX) hybrid functional with 25% HF exchange in the short-range and 0% HF exchange in the long-range. MN12-L was intended to be very versatile and provide good performance 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.</li></ul> <h3>Minnesota 15</h3> <p>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 </p> <ul><li>MN15,<a class="footnote-ref" id="fnref:40" href="#fn:40"><sup>40</sup></a> a global hybrid with 44% HF exchange.</li> <li>MN15-L,<a class="footnote-ref" id="fnref:41" href="#fn:41"><sup>41</sup></a> a local functional with 0% HF exchange.</li></ul> <h2 id="main-software-with-implementation-of-the-minnesota-functionals">Main Software with Implementation of the Minnesota Functionals</h2> <table><tbody><tr><th>Package</th><th>M05</th><th>M05-2X</th><th>M06-L</th><th>revM06-L</th><th>M06</th><th>M06-2X</th><th>M06-HF</th><th>M08-HX</th><th>M08-SO</th><th>M11-L</th><th>M11</th><th>MN12-L</th><th>MN12-SX</th><th>MN15</th><th>MN15-L</th></tr><tr><td><a href="/facts/Amsterdam_Density_Functional/moCSv1k2">ADF</a></td><td>Yes*</td><td>Yes*</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td></tr><tr><td><a href="/facts/CPMD/IhUdV435">CPMD</a></td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td></tr><tr><td><a href="/facts/GAMESS_(US)/osohnweB">GAMESS (US)</a></td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td><a href="/facts/Gaussian_(software)/QGQaJ7ug">Gaussian 16</a></td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td><a href="/facts/Jaguar_(software)/QkMalFWT">Jaguar</a></td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td></tr><tr><td><a href="http://www.tddft.org/programs/octopus/wiki/index.php/Libxc">Libxc</a><ul><li><a href="http://www.abinit.org/">Abinit</a></li><li><a href="http://www.scm.com/">ADF</a></li><li><a href="http://www.tddft.org/programs/APE">APE</a></li><li><a href="http://quantumwise.com">Atomistix ToolKit</a></li><li><a href="http://www.wfu.edu/~natalie/papers/pwpaw/man.html">AtomPAW</a></li><li><a href="http://inac.cea.fr/L_Sim/BigDFT/">BigDFT</a></li><li><a href="http://castep.org/">Castep</a></li><li><a href="http://www.cp2k.org/">CP2K</a></li><li><a href="http://www.dp-code.org/">DP</a></li><li><a href="http://elk.sourceforge.net/">Elk</a></li><li><a href="https://archive.today/20130411014100/http://erkale.googlecode.com/">ERKALE</a></li><li><a href="http://exciting-code.org/">exciting</a></li><li><a href="https://wiki.fysik.dtu.dk/gpaw">GPAW</a></li><li><a href="http://sourceforge.net/p/jdftx/wiki/Home/">JDFTx</a></li><li><a href="https://code.google.com/p/molgw/">MOLGW</a></li><li><a href="/facts/Octopus_(software)/W5L3wdT7">Octopus</a></li><li><a href="http://www.yambo-code.org/">Yambo</a></li></ul></td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td><a href="/facts/MOLCAS/B5HdIjFL">MOLCAS</a></td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td></tr><tr><td><a href="/facts/MOLPRO/Xp3IeRhw">MOLPRO</a></td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td></tr><tr><td><a href="/facts/NWChem/XBg0VMhy">NWChem</a></td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td></tr><tr><td><a href="/facts/ORCA_(Quantum_Chemistry_Program)/mNJmDbD7">Orca</a></td><td>Yes*</td><td>Yes*</td><td>Yes</td><td>Yes*</td><td>Yes</td><td>Yes</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td></tr><tr><td><a href="/facts/PSI_(computational_chemistry)/VslQHnfP">PSI4</a></td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>No</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td></tr><tr><td><a href="/facts/Q-Chem/3B8WenkS">Q-Chem</a><ul><li><a href="/facts/Spartan_(chemistry_software)/5I4PGBTa">Spartan</a></li></ul></td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td></tr><tr><td><a href="/facts/Quantum_ESPRESSO/hzDru7DV">Quantum ESPRESSO</a></td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td></tr><tr><td><a href="/facts/TURBOMOLE/osB0XHmR">TURBOMOLE</a><ul><li>using <a href="https://web.archive.org/web/20150402112229/https://repo.ctcc.no/projects/xcfun">XCFun</a></li></ul></td><td>Yes*</td><td>Yes*</td><td>Yes</td><td>Yes*</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td><td>Yes*</td></tr><tr><td><a href="/facts/Vienna_Ab-initio_Simulation_Package/ycjJ9k3A">VASP</a></td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td></tr></tbody></table> <p>* Using LibXC. </p> <h2 id="external-links">External links</h2> <ul><li><a href="http://comp.chem.umn.edu/truhlar/index.htm">The Truhlar Group </a></li> <li><a href="http://comp.chem.umn.edu/db">Minnesota Databases for Chemistry and Physics</a></li> <li><a href="https://arxiv.org/abs/1212.0944">The most recent review article on the performance of the Minnesota functionals</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>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. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>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. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>K.E. Riley; M Pitoňák; P. Jurečka; 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. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>L. Ferrighi; Y. Pan; H. Grönbeck; B. Hammer (2012). "Study of Alkylthiolate Self-assembled Monolayers on Au(111) Using a Semilocal meta-GGA Density Functional". Journal of Physical Chemistry. 116 (13): 7374–7379. doi:10.1021/jp210869r. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>N. Mardirossian; M. Head-Gordon (2013). "Characterizing and Understanding the Remarkably Slow Basis Set Convergence of Several Minnesota Density Functionals for Intermolecular Interaction Energies". Journal of Chemical Theory and Computation. 9 (10): 4453–4461. doi:10.1021/ct400660j. OSTI 1407198. PMID 26589163. S2CID 206908565. <a href="http://www.escholarship.org/uc/item/9rj1t5h8" target="_blank">http://www.escholarship.org/uc/item/9rj1t5h8</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>L. Goerigk (2015). "Treating London-Dispersion Effects with the Latest Minnesota Density Functionals: Problems and Possible Solutions". Journal of Physical Chemistry Letters. 6 (19): 3891–3896. doi:10.1021/acs.jpclett.5b01591. hdl:11343/209007. PMID 26722889. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>N. Mardirossian; M. Head-Gordon (2016). "How accurate are the Minnesota density functionals for non-covalent interactions, isomerization energies, thermochemistry, and barrier heights involving molecules composed of main-group elements?". Journal of Chemical Theory and Computation. 12 (9): 4303–4325. doi:10.1021/acs.jctc.6b00637. OSTI 1377487. PMID 27537680. S2CID 5479661. <a href="http://www.escholarship.org/uc/item/0h6407dj" target="_blank">http://www.escholarship.org/uc/item/0h6407dj</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Taylor, DeCarlos E.; Ángyán, János G.; Galli, Giulia; Zhang, Cui; Gygi, Francois; Hirao, Kimihiko; Song, Jong Won; Rahul, Kar; Anatole von Lilienfeld, O. (2016-09-23). "Blind test of density-functional-based methods on intermolecular interaction energies". The Journal of Chemical Physics. 145 (12): 124105. Bibcode:2016JChPh.145l4105T. doi:10.1063/1.4961095. hdl:1911/94780. ISSN 0021-9606. PMID 27782652. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Kepp, Kasper P. (2017-03-09). "Benchmarking Density Functionals for Chemical Bonds of Gold" (PDF). The Journal of Physical Chemistry A. 121 (9): 2022–2034. Bibcode:2017JPCA..121.2022K. doi:10.1021/acs.jpca.6b12086. ISSN 1089-5639. PMID 28211697. S2CID 206643889. <a href="https://backend.orbit.dtu.dk/ws/files/146461416/Kepp_gold_paper_revised2cleaned.pdf" target="_blank">https://backend.orbit.dtu.dk/ws/files/146461416/Kepp_gold_paper_revised2cleaned.pdf</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>N. Mardirossian; M. Head-Gordon (2013). "Characterizing and Understanding the Remarkably Slow Basis Set Convergence of Several Minnesota Density Functionals for Intermolecular Interaction Energies". Journal of Chemical Theory and Computation. 9 (10): 4453–4461. doi:10.1021/ct400660j. OSTI 1407198. PMID 26589163. S2CID 206908565. <a href="http://www.escholarship.org/uc/item/9rj1t5h8" target="_blank">http://www.escholarship.org/uc/item/9rj1t5h8</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>L. Goerigk (2015). "Treating London-Dispersion Effects with the Latest Minnesota Density Functionals: Problems and Possible Solutions". 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