DFT2013. Density functionals poll. List of density functionals included in the poll. News-item, History and rules: Results: Appendices:
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1 DFT2013 Density functionals poll Organized by M. Swart, F.M. Bickelhaupt and M. Duran News-item, 2013 History and rules: The origin of the popularity poll, as it was created after a visit of Matthias Bickelhaupt to the IQCC in Girona 2 The rules of the poll, and how the poll results are transformed into a measure how the computational chemistry community does Results: 3 Results from the online popularity poll (including a disqualification), giving a ranking and a PACO2013 functional 4 Performance of the PACO201x functionals for a variety of diverse chemical interactions Appendices: Density Functional Theory in a nutshell References The non-empirical PBE functional remains the clear winner of this year. List of density functionals included in the poll Primera divisió 2013: ωb97x-d, B2PLYP, B3LYP, B3LYP-D, B3PW91, B97-D, BLYP, BP86, CAM-B3LYP, HSE, LDA, M06, M06-2X, OLYP, PBE, PBE0 (PBE1PBE), PW91, revpbe, SSB-D, TPSSh Segona divisió 2013: APBE, BHandH, B3LYP*, DSD-BLYP, τ-hcth, LB94, LC-ωPBE, LC-PBE, M05, M05-2X, M06-L, mpw1k, optb88-vdw *, PW6B95, PWPB95-D 3, revtpss, revtpss-d, RPBE, SAOP, VSXC, RPA, S12g, S12h, KT1, DSD-PBEP86, BLOC *disqualified (see p. 4)
2 Origin of the online popularity poll of density functionals Following a presentation by Matthias Bickelhaupt ( Hypervalent versus Nonhypervalent Carbon, ) there was a discussion in Can Paco (the bar at the faculty of Chemistry at the University of Girona). Because the presentation showed the results for quite a number of density functionals, Miquel Duran suggested to take a number of these results, and use appropriate weights for them in order to obtain a consensus density functional result. In order to get the weights needed for this procedure, we have held annual online polls where people could indicate their preferences for a number of density functionals. The polls were announced on the CCL list, on Twitter, Facebook, blogs, etc. in order to get the maximum number of participants. The aims of this poll were: (i) to probe the preference of the community, i.e., setting up a ranking of preferred DFT methods; and (ii) provide a compilation of the de facto quality that this implies for the average DFT computation. Note that this poll does not cover everybody, only those who were motivated to take part in the poll and vote. Yet, we feel that the results do provide some insight in current preferences. And interestingly, these preferences do not always match with the best choice in terms of best agreement with accurate reference data. The aim of the online popularity poll is to probe the preferences of the computational chemistry and physics communities, and compile the quality of the average DFT computation. Prof. Bickelhaupt: a regular visitor to Girona At least 50 research papers have resulted from the collaboration There is a longstanding collaboration between the research groups of Prof. Bickelhaupt at the Vrije Universiteit Amsterdam (VUA), and the IQCC in Girona. Since 1993, Prof. Matthias Bickelhaupt collaborates with Prof. Miquel Solà (IQCC) and has visited the University of Girona (UdG) every year since 1998 for joint investigations on the chemical bond, DNA, organic reactions, etc. Many members of the IQCC have also gone to Amsterdam for short (3-month) or longer (postdoc) research stays, which has led to a very fruitful collaboration. This has recently been recognized by the rectorates of the VUA and UdG, and is now officially a collaboration between the universities. For the UdG, this is an important component of the Campus of Excellence that was awarded to it in
3 Rules for the popularity poll and the PACO functionals 1) Points are given similar to football, i.e. a like gives +3 points, neutral +1 points, no answer at all ( Vot en blanc, None Of The Above ) 0 points, hate -1 points. A ranking of the functionals will be made by taking into account these points. 2) In case there are two or more functionals with the same number of points, the ordering will be decided by the following criteria: (i) most number of like s, (ii) least number of hate s, (iii) results from previous years (for future editions), (iv) year of publication of the functional (the younger, the better), (v) decision by organizers. 3) There will be a Primera Divisió with the 20 most popular functionals. At the end of each year, the 5 least popular of the Primera Divisió will relegate to the Segona Divisió. Each year, only the 20 most popular functionals of the Segona Divisió will be kept. The five most popular ones of the Segona will be promoted to the Primera, while the 15 next will form the Segona for the next year together with the 5 relegated from the Primera. The other functionals will not take part in the poll for the year after (unless suggested again). There is a maximum of 10 additional suggestions for each year, which are added chronologically (after being suggested by mail to M. Swart). 4) A new PACO functional will be constructed each year, by taking a weighted linear combination of the 20 functionals in the Primera Divisió. For those functionals that do not have an energy expression (e.g. SAOP, LB94), a weight of zero (except for the excitation energies) will be used for the construction of PACO20xx. In particular, the following energy expressions are obtained: The weight of each functional is given by its number of points, divided by the total number of points of the 20 functionals in the Primera Divisió (using a value of 0 for those without an energy expression, see above). The sum of the weights is therefore one. Note that with these PACO functionals we do not wish to ridicule the development of density functionals, which is hard and painstaking work, and often underestimated. Neither do we intend to mix different functionals for the sake of mixing, in the hope of reducing discrepancies. However, we do wish to help the community by getting a consensus current opinion on the many functionals, which may help the reader choose a functional for his/her own study on chemistry. As mentioned in the introduction, it can also be enlightening to compare the consensus current opinion with the actual performance. 5) The PACO20xx functionals will be applied to a small number of typical chemical systems: the AE6 set for six atomization energies (SiH 4, SiO, S 2, propyne, glyoxal, cyclobutane) the BH6 set for six barrier heights (forward and reverse reaction of OH+CH 4, H+OH, H+H 2S) the π-π stacking energy of anti-parallel cytosine dimer spin-state splitting of FeFHOH and Ni(EDT) 2 2 excitation energies (singlet, triplet) of CO the hydrogen-bonding energies of four dimers (ammonia, water, formic acid, formamide) For all of these coupled cluster CCSD(T) or experimental (reference) data are available. 6) Each year, a new popularity poll will be held between June 1 and October 1, and will be announced on on the CCL list, etc. and a short news item such as the current one about it will be published. 7) The organization of the DFT-poll reserves the right to disqualify density functionals in case of clear proof of cheating. This disqualification remains effective for the year following the year in which the cheating has been observed. 3
4 Results * of the popularity poll functional year like neutral hate empty points Primera Divisió 1 PBE PBE0 (PBE1PBE) B3LYP LDA PW BP HSE revpbe ωb97x-d B3LYP-D CAM-B3LYP M06-2X B97-D B2PLYP B3PW M TPSSh BLYP OLYP SSB-D Segona Divisió 1 RPA LC-ωPBE RPBE BHandH B3LYP* M05-2X M06-L PWPB95-D revtpss-d LC-PBE revtpss mpw1k SAOP PW6B M DSD-BLYP APBE τ-hcth LB DSD-PBEP S12h KT S12g VSXC BLOC * the optb88-vdw functional has been disqualified from this year s result because of attempts to bias the outcome of the poll through repetitive single-answer entries (with only 1 option liked: optb88-vdw), which often were added at a pace of one per 8 seconds; a total of 56 of these single-answer optb88-vdw entries had been entered. The disqualification will be effective both for 2013 and About the authors Marcel Swart ICREA Research Professor at IQCC (Univ. Girona) PhD 2002, Univ. Groningen Research interests: theory, method development, molecular cages, spin states, (bio)inorganic chemistry Matthias Bickelhaupt Full Professor at Theoretical Chemistry (VU Univ. Amsterdam) & Institute of Molecules and Materials (Radboud Univ. Nijmegen) PhD 1993, VU Univ. Amsterdam Research interests: catalysis, S N2/E2 reactions, chemical bonding, DNA, molecular orbital analysis Miquel Duran Full Professor at IQCC (Univ. Girona) PhD 1984, Univ. Aut. Barcelona Research interests: influence electric fields on structure and reactivity, weak bonding, electron density methodology 4
5 Significance of the popularity poll results For the second time in a row, the non-empirical PBE functional has been selected by the computational chemistry and physics communities as the most popular functional, before the PBE0 (the winner of the 2010 and 2011 editions) and B3LYP functionals. This is the second consecutive year that a GGA functional is beating hybrid functionals in popularity. The total number of valid entries has increased significantly, from 171 in 2012 to 194 in 2013 (+13%). It should also be mentioned that 57 additional entries were not counted (56 because of the disqualification of optb88-vdw, see p. 4, and 1 because it was completely empty). It is remarkable that the ωb97x-d and HSE functionals (both for the first time in the Primera Divisió) continue their upward march, and are now at the 9 th and 7 th place respectively. This exemplifies the popularity of range-separated hybrid functionals in general nowadays. Five functionals will be promoted to the Primera Divisió of 2014: RPA, LC-ωPBE, RPBE, BHandH and B3LYP*, replacing the following functionals: M06, TPSSh, BLYP, OLYP and SSB-D. The composition of the Primera Divisió and Segona Divisió for the year 2014 is given on p. 7. The next online poll will, as usual, be held from June 1 until October 1. The average number of points increases again, from 0.69 to 0.77 Construction of the PACO2013 functional w energy PBE PBE0 (PBE1PBE) B3LYP LDA a PW a - a BP HSE a - a - a revpbe a - a ωb97x-d a - a - a B3LYP-D a - a CAM-B3LYP M06-2X B97-D B2PLYP B3PW M a - a - a TPSSh BLYP OLYP a SSB-D a) not included in earlier editions As usual, we prepared a popularity adapted consensus object, i.e. the PACO2013 functional. It was obtained by taking the points from the online poll for the Primera Divisió, and giving each of the functionals in it a weight corresponding to their points (see Rules on p. 3). These weights are listed here on the left. With these weights, we have carried out an analysis of the performance for a series of chemical interactions within a set of molecules (shown on p. 6). The results of the PACO201x functionals, together with the best and worst performing functionals, are listed on p. 7. 5
6 Chemical systems used for checking interactions 6
7 Check of PACO2013 interactions reference best worst AE6 a,b M06-2X LDA SiH SiO S propyne glyoxal cyclobutane MAD BH6 a,b M06-2X LDA OH+CH 4 (fw) OH+CH 4 (rv) H+OH (fw) H+OH (rv) H+H 2S (fw) H+H 2S (rv) MAD Exc. states CO c,d SAOP B2PLYP 1Π, σ π* Σ, π π* , π π* Π, σ π* Σ +, π π* , π π* MAD π-π stacking a,e ωb97x-d OLYP Cyt MAD Spin-states a FeFHOH 5.4 f?? ???? Ni(EDT) 2 2 > ???? MAD???????????? H-bonding a,g M06-2X OLYP ammonia water formic acid formamide MAD a) in kcal mol -1 ; b) reference data from J. Phys. Chem. A 2003, 107, 8996; c) in ev; d) reference data from J. Chem. Phys. 2000, 112, 1344 and J. Chem. Phys. 2001, 114, 652; e) reference data from J. Phys. Chem. B 2004, 108, 5466; f) from news-item PACO2011; g) reference data from Phys. Chem. Chem. Phys. 2006, 8, 1985 Primera Divisió 2014 ωb97x-d B2PLYP B3LYP B3LYP-D B3LYP* B3PW91 B97-D BHandH BP86 CAM-B3LYP HSE LC-ωPBE LDA M06-2X PBE PBE0 PW91 revpbe RPA RPBE Segona Divisió 2014 APBE BLYP DSD-BLYP DSD-PBEP86 τ-hcth LB94 LC-PBE M05 M05-2X M06 M06-L mpw1k OLYP PW6B95 PWPB95-D 3 revtpss revtpss-d SAOP SSB-D TPSSh 7
8 In 1964, Hohenberg and Kohn published theorems that laid the basis for density functional theory (DFT). Together with the Kohn-Sham scheme published a year later in 1965, these form the basic framework of DFT. In these papers, it was shown that there exists a one-to-one relation between the energy and density, i.e. it is in principle possible to obtain directly the exact energy from the electron density. But, the mathematical formulation that delivers this energy is unknown, although it can be constructed numerically from an exact (accurate) wavefunction Density Functional Theory in a nutshell for a concrete system. It was not until the 1980s that the first reasonable approximations were proposed. Apart from the Local Density Approximation (LDA), the Generalized Gradient Approximation (GGA), hybrid functionals containing a portion of exact (Hartree-Fock) exchange, meta-gga functionals, double hybrid functionals, local hybrid functionals, and the hybrid meta-gga functionals, there are now also the range-separated hybrid functionals. In 1998, Walter Kohn received the Nobel prize in Chemistry for his work on DFT. There exists a one-to-one relationship between the electron density and the exact energy. the total electron density defines the number of electrons in the system; the cusps in the density define the nuclear coordinates; the derivative of the density at a cusp defines the nuclear charge at that cusp and thus the configuration of the elements; therefore, the system is fully defined (Bright-Wilson, 1965) References Hohenberg-Kohn: Phys. Rev. B 1964, 136, 864 APBE: Phys. Rev. Lett. 2011, 106, B2PLYP: J. Chem. Phys. 2006, 124, B3LYP: J. Phys. Chem. 1994, 98, B3LYP-D: J. Phys. Chem. 1994, 98, 11623; J. Comput. Chem. 2006, 27, 1787 B3LYP*: Theor. Chem. Acc. 2001, 107, 48 B3PW91: J. Chem. Phys. 1993, 98, 5648 ωb97x-d: Phys. Chem. Chem. Phys. 2008, 10, 6615 B97-D: J. Comput. Chem. 2006, 27, 1787 BHandH: J. Chem. Phys. 1993, 98, 1372 BLYP: Phys. Rev. A 1988, 38, 3098; Phys. Rev. B 1988, 37, 785 BP86: Phys. Rev. A 1988, 38, 3098; Phys. Rev. B 1986, 33, 8822 CAM-B3LYP: Chem. Phys. Lett. 2004, 393, 51 DSD-BLYP: J. Phys. Chem. C 2010, 114, DSD-PBEP86: Phys. Chem. Chem. Phys. 2011, 13, HSE: J. Chem. Phys. 2003, 118, 8207 KT1: J. Chem. Phys. 2003, 119, 3015 LB94: Phys. Rev. A 1994, 49, 2421 LC-ωPBE: J. Chem. Phys. 2006, 125, LC-PBE: J. Chem. Phys. 2007, 126, LDA: Proc. Roy. Soc. (London) A 1929, 123, 714; Phys. Rev. 1951, 81, 385; Can. J. Phys. 1980, 58, 1200; Phys. Rev. B 1992, 45, Kohn-Sham: Phys. Rev. A 1965, 140, 1133 M05: J. Chem. Phys. 2005, 123, M05-2X: J. Chem. Theory Comput. 2006, 2, 364 M06, M06-2X: Theor. Chem. Acc. 2008, 120, 215 M06-L: J. Chem. Phys. 2006, 125, mpw1k: J. Phys. Chem. A 2000, 104, 4811 OLYP: Mol. Phys. 2001, 99, 403; Phys. Rev. B 1988, 37, 785 optb88-vdw: J. Phys.-Condens. Mat. 2010, 22, PBE: Phys. Rev. Lett. 1996, 77, 3865 PBE0: J. Chem. Phys. 1996, 105, 9982 PW6B95: J. Phys. Chem. A 2005, 109, 5656 PW91: Phys. Rev. B 1992, 46, 6671 PWPB95-D 3: J. Chem. Theory Comput. 2011, 7, 291 revpbe: Phys. Rev. Lett. 1998, 80, 890 revtpss, revtpss-d: Phys. Rev. Lett. 2009, 103, ; s 6= (revtpss-d) RPA: J. Chem. Phys. 2008, 129, RPBE: Phys. Rev. B 1999, 59, 7413 S12g, S12h: Chem. Phys. Lett. 2013, 580, 166 SAOP: J. Chem. Phys. 2000, 112, 1344 SSB-D: J. Chem. Phys. 2009, 131, τ-hcth: J. Chem. Phys. 2002, 116, 9559 TPSSh: Phys. Rev. Lett. 2003, 91, ; J. Chem. Phys. 2003, 119, VSXC: J. Chem. Phys. 1998, 109, 400
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