Talk:Density functional theory

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Comments
The page is inconsistent in whether "density-functional" is hyphenated or not. Perhaps most egregiously, the article title is not hyphenated but the bold term right below it that starts the article is hyphenated. I'm partial to hyphenating it, but I'd prefer to leave it to others more familiar with the field and how the term is generally used to make the decision. 172.92.14.139 (talk) 16:51, 26 October 2022 (UTC)

In my opinion, the explanation given for a functional in the second sentence is not complete, because by function of a function it is meant f(g(x)), while a functional can be whatever application defined on a space of functions. This definition includes functions of functions but also other kinds of application (a common one is the integral over an interval [a,b] of the function). Francesco.randi (talk) 15:36, 23 March 2012 (UTC)

Mott insulators are quite an important example of DFT not working as it could in strongly correlated electron systems. Do you think it's worth mentioning specifically. I don't know if it is comparable to the examples given in other fields. Grj23 (talk) 21:01, 1 April 2009 (UTC)

When discussing DFT and dispersion forces I would be more careful in saying that"Despite the improvements in DFT, there are still difficulties in using density functional theory to properly describe intermolecular interactions, especially van der Waals forces (dispersion)". In literature there are some examples of how to address this issue. In particular, it has been shown that the BHandH functional is able of reproducing with great accuracy correlated ab initio performances, see for instance "Hybrid density functional theory for pi-stacking interactions: application to benzenes, pyridines, and DNA bases", Robertazzi et al., Journal of Computional Chemistry, 2006 Mar;27(4):491-504.
 * Thank you for the reference! It seems however that they do not simply treat dispersion interactions, but the special case that is pi-pi stacking. A very interesting problem, of course, but still a special case. -- Mipmip 06:58, 15 November 2006 (UTC)
 * There are also some other derived or ad-hoc (see Grimme's B2PLYP) dispersion-cabable methods that include DFT. Nevertheless, a semi-local KS-DFT functional can, in principle, never describe dispersion interactions properly due to the simple fact that dispersion is intrinsically a non-local correlation effect.129.69.55.52 (talk) 13:35, 4 April 2008 (UTC)

I would explain the different opinions about DFT vs ab initio. While DFT is able to treat bigger, more complex systems, many scientists view it just as a good semiempyrical technique, not to be used if a "proper" ab initio calculation is possible.

True, also should be mentioned are techniques that are less accurate than DFT but can be used for bigger systems still.

DFT is not in itself semi-empirical (Hohenberg-Kohn is in itself just a reformulation of the Schrodinger equation.) LDA and LSDA are ab initio. Many popular functionals are however semi-empirical.

But the debate on true ab initio vs. hybrid DFT may be a bit too specific for a general article such as this though. Although DFT looks somewhat empirical in comparison to wave-based methods, by comparison to the very empirical methods such as MM, DFT looks very 'ab initio' indeed.

I made some changes to the introduction of the article. I felt some statements were incorrect, or at least very vague. For example, the sentence beginning with "Within the framework of DFT, the ..." actually describes Kohn-Sham theory. DFT, of course, can be done without Kohn-Sham (see the original Hohenberg-Kohn paper).

The same sentence says that DFT reduces the many body problem to a "solvable problem of a single electron moving in an averaged effective force field." Being picky and precise, I don't think this is true. DFT does not reduce the N-body problem to a single electron problem, Kohn-Sham reduces it to an effective non-interacting electron problem. Moreover, this is not always solvable: if you have $$10^{23}$$ electrons you still cannot solve the equivalent non-interacting problem. Where, by solve, I mean to numerically solve the problem.

I will probably make more modifications, further down the article, as time goes on. I know that some of the material in the introduction is now repeated later, but that shouldn't be a big deal. Please comment. WikipAcct 07:58, 2 Jan 2005 (UTC)

Also, I think the article needs to emphasize that KS-DFT is a groundstate theory. And it should mention the time-dependent generalization. I will add these to the to-do list.
 * Added TD-DFT to "see also" list Azo bob (talk) 12:59, 3 May 2009 (UTC)

The statement: DFT is an exact theory only for the free electron gas, while for the treatment of extended atomic systems various approximations have to be made, is slightly misleading.

The paradigm of DFT development, starting with Thomas-Fermi and Kohn-Sham has been to work as a series of corrections to the free electron gas model. All functionals I know of use that approach, and can thus be said to be 'exact for the free electron gas'. But this does not mean DFT by necessity is like that. DFT can in principle be exact for any potential fullfilling the criterium of the Hohenberg-Kohn proof.


 * Yes, I agree. To be precise, the sentence in the article refered to
 * by this person is incorrect. Feel free to fix it!  I just stumbled upon
 * the article yesterday. I thought about quickly fixing it to say
 * that "LDA is exact for theuniform gas", but that doesn't help
 * the article much. In fact, in my not so humble opinion, the article
 * needs some work. I'll try to add some improvements. WikipAcct 05:52, 4 Jan 2005 (UTC)

Some of the statements seemed to be still odd, and so i cleaned up some sections, and expanded some. I think it still needs a discussion of time-dependent DFT, as well as some more applications, and maybe some of the work on including dispersion into functionals. Salsb 18:30, 26 July 2005 (UTC)

If I may add something: The Spartan package distributed by Wavefunction, Inc. also supports DFT computations. The version we are running in our laboratory is properly cited as: Spartan'04 for Macintosh; Wavefunction, Inc.; Irvine, CA. Iamthealchemist 22:03, 6 December 2005 (UTC)

I think there needs to be more on the various exchange and correlation functions that are widely used, particularly in programs such as Gaussian. There is a mention of B3LYP without stating that it is a hybrid method and this needs defining as noted on the TODO list above. There is no mention of non-hybrid methods such as BLYP. Elsewhere there is an empty link to B3LYP, so perhaps we need a set of sections on different widely used methods, so they can be used as links for B3LYP and so on. I am rather busy at present with other pages and I am not a real expert on DFT. Anyone else want to do it? Bduke 01:02, 19 December 2005 (UTC)

Kohn-Sham functional
Which part of Kohn-Sham equations is the "Kohn-Sham functional"? --HappyCamper 14:14, 4 October 2006 (UTC)
 * E[ρ] WilliamDParker 15:15, 4 October 2006 (UTC)
 * Thanks. --HappyCamper 20:27, 4 October 2006 (UTC)

Software
I think it might be helpful to separate the list of software that supports DFT into programs available for free (including GPL'd software and proprietary software released gratis) and programs for which a paid site license is required. Does this make sense? --WilliamJenkins09 (talk) 14:02, 4 January 2008 (UTC)
 * It might be better to make it into a table, with columns for license (free etc as you suggest), methods (basis set KS or pure DFT, only DFT or DFT + HF etc) and perhaps other things. This would make it rather large and it might then have to become a separate article like Quantum chemistry computer programs. --Bduke (talk) 00:40, 5 January 2008 (UTC)
 * The section is only somewhat helpful, in that it only informs of the existence of all these programs. A separate article with a big table would allow more useful information to be included, as you have both noted. Also, it's becoming a bit of an eye saw, which is only going to grow with time. THEN WHO WAS PHONE? (talk) 19:43, 2 November 2008 (UTC)

Structuring
Seems like the section, Description of the theory, is out of place. It could be to merged with the lead (which needs beefing up anyway), placed above the Hohenberg-Kohn theorems section, or a bit of both. Part of the last paragraph in that section could be expanded in to a general overview of the issues that are still being worked out with DFT and placed in a section of its own lower down the article. Also the Thomas-Fermi model section could be expanded in to an article of its own having only a brief comment in this article. Any of these suggestions sound reasonable? THEN WHO WAS PHONE? (talk) 19:28, 2 November 2008 (UTC)


 * I basically agree with you. Here's some specific thoughts:
 * Re "Seems like the section, Description of the theory, is out of place." - I agree.
 * Re "It could be to merged with the lead (which needs beefing up anyway), placed above the Hohenberg-Kohn theorems section, or a bit of both." - We could start out by moving it above the Theorems section. Then we could extract some info from it to put in the lead.  However, I think we want to keep the lead relatively simple and not make it too big.
 * Re "Part of the last paragraph in that section could be expanded in to a general overview of the issues that are still being worked out with DFT and placed in a section of its own lower down the article." - Could you be more specific about what part and the place you had in mind for it?
 * Re "Also the Thomas-Fermi model section could be expanded in to an article of its own having only a brief comment in this article." - I've been thinking along similar lines and when I first saw it in the DFT article I was surprised that it wasn't in an article of its own.
 * --Bob K31416 (talk) 21:15, 2 November 2008 (UTC)


 * I moved part of the "Description of the theory" (DOTT) section that gives history, general info related to other subjects, etc., to the Intro where it is more appropriately placed. (For the most part, this is what THEN WHO WAS PHONE? suggested.) Now the DOTT section doesn't seem as much out of place since a disorienting part has been moved. Also, I'm looking into not having the HK theorems section as a section by itself but instead putting it into the DOTT section. --Bob K31416 (talk) 17:14, 5 November 2008 (UTC)


 * I like what you have done, it flows nicely and we just need some others to comment on re moving the Thomas-Fermi section. Your third point above now refers to what is the third paragraph of the lead. I think that it's nice to have a mention in the lead, as many people tend to think DFT (or rather DFA, density functional approximations) can do anything. We should also mention self-interaction error in this regard, but perhaps only in the body. I'll think about tweaking the Overview of the method section – especially the way it begins. THEN WHO WAS PHONE? (talk) 23:53, 9 November 2008 (UTC)


 * It might be better to create a Thomas-Fermi Model article before deciding related changes in this article. --Bob K31416 (talk) 18:03, 11 November 2008 (UTC)


 * It would be easiest for the creation to proceed by splitting the section off directly in to a new article. If nothing else, this provides (appreciative, and GFDL) recognition to all those people that have contributed to it. Doing so would need a commitment to expand the article beyond what is in that section though, since the issue is not that it's too big, but rather (IMO), too significant and too wide ranging to be hidden in a DFT article. I'll pull together something in my sandbox which would build on any split, if it were so to happen. THEN WHO WAS PHONE? (talk) 19:21, 11 November 2008 (UTC)


 * It doesn't seem like "split" is quite appropriate because the TF section in DFT isn't very large and thus doesn't fit into the motive for "split". How about just leaving the DFT article intact for now and starting a new article Thomas-Fermi Model by simply copying the TF section to it? The new TF article can be worked on at leisure and the DFT article can be edited with the new article in mind, just like regular editing.
 * As far as recognition is concerned, from what I've seen it is essentially nonexistent on Wikipedia. There are Barnstars but I don't think anyone keeps track of who did what when, except maybe a few people amongst themselves or on a very short term basis for the purpose of a good working atmosphere. There are no bylines.


 * I think what we want to do is simple and doesn't need to be complicated. Just copy the TF section to a new article and carry on with business-as-usual editing of DFT with the TF section still in it for now. I'm willing to make the new article in this way if you like or you can do it. Either way is fine with me. Or you can do what you suggested above. All these ways seem to end up in the same place so I'm flexible on this. --Bob K31416 (talk) 01:26, 12 November 2008 (UTC)


 * I think were pretty much suggesting the same thing :)


 * In the context of DFT and of this article, the section seems disproportionately large. In the context of itself, it seem too small. It's not that big of an issue, and certainly not something which needs to be dealt with in a hurry. There's no harm in it staying here even if duplicated, with recognition for GFDL, to some extent elsewhere. If you want to quasi-"split" (no hurry in doing so) without deleting I'll would certainly see what I can pull together to expand it. THEN WHO WAS PHONE? (talk) 03:19, 12 November 2008 (UTC)


 * I created the new Thomas-Fermi Model article by copying from DFT and mentioned that it was copied in the edit summary, as we discussed here and on our talk pages.
 * "For unto us a child is born..." Isaiah 9:6 --Bob K31416 (talk) 20:23, 13 November 2008 (UTC)

Text on calculating electron chemical potential within density functional theory
I'm in the process of deleting some text with mathematical details about how to calculate electron chemical potential within DFT. It is this section here. It is too specialized to keep within the general chemical potential article. If someone knows a good home for it, either this article or somewhere else, please feel free to put it there. Thanks! --Steve (talk) 14:13, 27 April 2012 (UTC)

the coordinate where the functional is evaluated
When the article is describing LDA, it says "the functional depends only on the density at the coordinate where the functional is evaluated". However, the functional isn't evaluated at a particular coordinate in space, r. The functional is an integral over all points in space. The "coordinate" of the functional is the density function, not a location, r.Mpalenik (talk) 02:11, 14 March 2013 (UTC)

Split classical Density Functional Theory?
This article is structurally weird, tacking on the whole classical DFT topic after what feels like the end of a complete article on quantum QFT. Plus, wading through all this quantum stuff is frustrating when searching for information on classical DFT. German wikipedia has two separate articles and I found it more readable. However, an ambitious undertaking and I'm personally struggling to understand either. CyreJ (talk) 10:41, 13 January 2022 (UTC)


 * I agree. I would prefer a separate article, too. From Mermin's proof analogous to Hohenberg-Kohn classical DFT has gone its own way. Then there is not even a mentioning of mean field approximations or Fundamental Measure Theory (a successful family of hard sphere fluid functionals) in the classical DFT text, which are discussed in review papers on classical DFT. FNGdM (talk) 18:57, 28 August 2023 (UTC)

Potential mistake in classical DFT section
The dimensions in the equation $$\frac{\delta^s\Omega}{\delta \mu(\boldsymbol{r}_1)\dots\delta \mu(\boldsymbol{r}_s)}=(-1)^sn_s(\boldsymbol{r}_1,\dots,\boldsymbol{r}_s)$$ do not add up.

Also, a clarification, that $$\mu(\boldsymbol{r})$$ is not the chemical potential in the sense of being the intensive variable $$\mu_{\mathrm{thermodynamics}}$$ to particle number, but that $$\mu(\boldsymbol{r})=\mu_{\mathrm{thermodynamics}}-v(\boldsymbol{r})$$, where $$v(\boldsymbol{r})$$ is the external potential, would in my opinion be an improvement. FNGdM (talk) 17:05, 31 August 2023 (UTC)