# Tag Info

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I think this question somewhat comes down to what "camp" of DFT progression you subscribe to. I should specify upfront that this summary is mainly centered around molecular systems, so some of the recommendations likely vary for materials where the computational workload can often be much greater. One side really emphasizes accuracy with respect to ...

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2006 (Grimme): Double hybrid functionals The timeline of milestones you have given, includes a hybrid functional called B3LYP, which mixes a Hartree-Fock exchange functional with a GGA exchange-functional. In 2006, Stefan Grimme introduced what later became known as "double hybrid functionals", which not only mix the Hartree-Fock exchange functional with a ...

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2015 (Sun et al.): SCAN functional The SCAN meta-GGA functional is an extension of the popular PBE GGA [1] and the TPSS [2] and revTPSS [3] meta-GGAs, SCAN adheres to all 17 known exact XC constraints and is constructed to be almost exact for the noble gasses and jellium surfaces. Early evidence suggests that SCAN is more accurate than and of comparable ...

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2013: Density-Corrected DFT (DC-DFT) The goal of Density-Corrected DFT (DC-DFT) is not only to get better accuracy but also to understand and correct the true error in the functional approximation.[1,2] In any approximate density functional, the DFT error is $\Delta E = \tilde E[\tilde n] - E[n]$ where $E$ and $n$ are exact functional and density while $\... 22 Dispersion corrected methods (2007/2010) Lots of answers already, I would say the main ones are covered. However, in the spirit of the question, I don't think anyone has done dispersion corrections yet. So, There are many levels of Dispersion corrected methods, but I would say the most common is from Grimme et al. in 2010 (Grimme et. al. 2010 paper.) The ... 20 2004 (Yanai et al.): Range separation Often, the source of DFT improvement comes from Hartree-Fock as is also obvious from the answer involving double hybrid functionals. So too it is with range-separation. The electron-electron Coulomb operator for the exchange contribution is separated into a short and long range contribution. \frac{1}{... 20 B3LYP is still a decent functional at its level of theory (single-hybrid functional), but you're right that there's a general criticism of it, which I largely hear in the form of people saying things like "all they did was B3LYP/6-31G*" to criticize non-experts that blindly use this combination which became the "default" in chemistry for ... 19 1993 (Becke): Hybrid Functionals Axel D. Becke introduced the adiabatic-connection model, which allows for mixing of DFT exchange and Fock-like exchange via the formula $$E_{\text{x}} = a \cdot E^{\text{HF}}_x + b \cdot E^{\text{GGA}}_x$$ to obtain the exchange part of the exchange-correlation energy. Typically, one imposes$a+b = 1$, but some authors ... 18 1995 (Casida): TD-DFRT Time-Dependent Density Functional Response Theory is a linear response formulation of TDDFT for the calculation of excitation energies and corresponding transition amplitudes, that in turn allows to evaluate electronic spectra of molecular and condensed matter systems. The time-dependent density functional theory (TDDFT) in the Kohn–... 18 I'm not entirely sure what you mean by "universal". If you mean a functional that can model a wide variety of materials with reasonable success, probably the closest we have are GGA functionals. They are not necessarily the most accurate, but they are used to regularly model metals and semiconductors. They get decent results, despite their known ... 17 I think this review¹ by Head-Gordon is a useful supplement to Nike's answer. Its combines a review of functional development, a benchmarking of various functionals, and an explanation of the design process for the$\omega$B97 functionals. Its also open access, so its a great resource if you are interested in DFT functionals in general. They benchmarked 200 ... 16 Constraint #13: Size-Extensivity While the Wikipedia page for size-consistency and size-extensivity gives a clear formula for the definition of size-consistency, unfortunately they did not give a definition of size-extensivity, so I had to look deeper into the reference that they provided. They say that size-extensivity was introduced by Bartlett, and they ... 16 I don't have too much to add to the answers of Nike Dattani and Tyberius, but I think the crux is that its capabilities have been historically overestimated. One particular failing of B3LYP is that it tends to underestimate bond energies. However, since the small (and fast) 6-31G* basis set will lead to overbinding, the famous combination B3LYP/6-31G* ended ... 15 This paper published by Bikash Kanungo, Paul M. Zimmerman & Vikram Gavini provide an interesting solution to getting closer to a "universal functional" Exact exchange-correlation potentials from ground-state electron densities They have mapped very accurate electronic densities from ab initio full configuration interaction methods onto an exact ... 13 2005 (Bartlett): ab initio DFT Basically one takes the xc functional from a wave function approach such as MBPT(2), CC, etc. and constructs an xc potential from them using density conditions or a functional derivatives approach. Summary of developments is best captured in the following article: "Adventures in DFT by a wave function theorist." Details on ... 12 I would add some developments in TDDFT that came around 1996 and resonated only later such as: the Casida equation (Casida 1995) that allows to calculate excitation energies and electronic spectra the real-time TDDFT (Yabana & Bertsch 1996) a non-perturbative TDDFT technique in which the time-dependent Kohn–Sham equation is solved by direct propagation ... 12 The main issue here is that the calculated energy is a potential energy, that's why the absolute value is useless. As potential energy always depends on a reference system, you can only use the absolute value in comparison (as you do the calculations using exactly the same conditions) or in quantities that are obtained by substractions of these energies like ... 12 These are called double hybrid functionals. You add a fraction of MP2 correlation on top of the DFT energy. A good reference is e.g. the review by Goerigk and Grimme from 2014 published in WIREs 4, 576 (2014). Note that this is already 7 years old; many double hybrids have appeared since then. However, it should give you a good overview. 11 Since this is a very active research topic the answer here might change regularly. Just within the last few months we've seen updates to the SCAN functional in the form of r2SCAN and the de-orbitalized r2SCAN-L. These are both functionals that attempt to satisfy all known physical constraints that can be in-principle satisfied by a semi-local functional, ... 11 The general question on the accuracy of density functionals for transition metal compounds is highly ambigious due to the effect of static correlation, for which there is no solution at the moment. As to the simpler question on well-behaving TM compounds with organic ligands, a benchmark study on transition metal reaction barrier heights found that Head-... 11 The band gap problem in DFT is not just due to approximate exchange-correlation functionals--it is a reflection of the fact that the Kohn-Sham (K-S) orbitals are a mathematical construction of a non-physical, non-interacting system of electrons that yields the true ground state charge density of the real many-body system. In exact DFT, the derivative of the ... 11 Susi is right that these are called double hybrids, I'll just add a bit more to complement that correct answer. My answer to "What are some recent developments in density functional theory?" was about double hybrids, and it looks like the community here considered that to be one of the most important "recent" developments in DFT. About ... 10 I don't think you will find a reference showing that LDAs are better than GGAs for computing elastic constants. More specifically, I don't think a paper could reasonably offer an explanation of why LDA does better than GGA for any specific case. In principle, a GGA is more physically consistent than an LDA, as we know that the true exchange-correlation ... 10 Most chemists' point of view could be condensed as follows: Implementation of DFT in Gaussian (Pople et al, 1992) LDAs and GGAs were implemented in Gaussian 92/DFT by Pople, Gill and Johnson [Chem Phys Lett 199, 557 (1992)]. DFT better than ab initio (Johnson et al, 1993) BLYP was found to yield more accurate equilibrium geometries, dipole moments, ... 10 Your question is on absolute energies, but all of your physical examples are relative energies. One could also add properties to the list; however, these are again not determined by the total energy, but rather as its derivatives with respect to some perturbation... which are again energy differences, just now between the perturbed and unperturbed system. ... 9 I think for transition metals the best functionals would be MS1-D3(0), ωB97M-V, ωB97X-V, MN15, and B97M-r based on the information from the review article-Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals 9 In terms of the role of chemists for what you call the "most essential task": "What I understand is that the most essential task is the improvement of exchange correlation functionals to give better and more accurate results" "... the development of them is a job for a quantum physicist for example." I am reminded of two ... 9 It is well known that using pseudopotentials generated with a functional which is inconsistent with the functional used in the plane-wave calculation can lead to serious problems, see here for example. It was also shown that for a potential-only meta-GGA (TB), the choice of pseudopotential makes a huge difference in the band gap, and in particular using PBE ... 9 B3LYP My suggestion for you in this case is to simply use the most common funcitonal for basic properties of molecules: B3LYP. I wrote in my answer here that B3LYP is still a decent functional overall, especially considering its relatively low cost for non-periodic systems (e.g. a pesticide molecule). The first figure in that answer is directly from the ... 8 2020 Furness et al: r$^2\$SCAN functional The SCAN functional is the most recent meta-GGA functional constructed from first principles, which satisfies all known bounds. However, SCAN is also numerically pathological: getting converged energies requires huge quadrature grids, and constructing pseudopotentials is difficult. This motivated the construction of ...

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