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In general (at least for molecular calculations) basis sets and DFT functionals are fit to some high level calculation or experimental energy. It is speculated that an accurate energy will result in an accurate wavefunction and thus accurate properties, but this is not guaranteed. There have been papers looking at how different functionals perform at computing properties as well as basis sets optimized to compute particular nonenergetic properties.

Are there any functionals/basis sets optimized to calculate bulk material properties rather than the energy? Say polarizablity or refractive index (I'm not certain what properties would be of most interest to material scientists in general, as I have more of a molecular chemistry background).

To clarify, I'm not necessarily interested in functionals that were intended to be better for some property, but were still fit using minimization of error in the energy as a criteria. I'm hoping to find cases where the fitting was done explicitly to minimize the error of some property within a test set, rather than cases where the functional was implicitly improved by, for example, using a different test set.

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    $\begingroup$ You might get a better answer if you specify what kind of properties you are interested in. There are many functionals that have been benchmarked and/or parameterized for reproducing accurate quantities beyond (relative) energies. $\endgroup$ – Andrew Rosen May 3 at 23:11
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    $\begingroup$ rev-vdW-DF2 was specifically designed to improve the poor performance of lattice constant prediction in vdw-DF2. revM06-L was designed in part to reproduce issues with integration grids but also a similar issue regarding lattice constant predictions with M06-L. There are also several functionals specifically made to reproduce spin states, if you count that. $\endgroup$ – Andrew Rosen May 3 at 23:25
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    $\begingroup$ Also, there are many functionals that are fit to experimental energies (in addition to "high level" calculations), in particular many of the Minnesota functionals. $\endgroup$ – Andrew Rosen May 3 at 23:28
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    $\begingroup$ @AndrewRosen I should have specified that fits to energies high level or experimental. The example functionals you list are interesting. My background is in molecular simulation, almost all functionals used there are just fit to some energy (theory or experiment) $\endgroup$ – Tyberius May 3 at 23:40
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    $\begingroup$ It would be great if you suggest what type of "bulk material properties" and what materials... Rule of thumb I use is, I usually search for other DFT papers for the material of interest, and check what other researchers used for their own study and material properties. Or at least the materials in the same group or period in periodic table. $\endgroup$ – exsonic01 May 4 at 0:15
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On the basis set side, e.g. completeness-optimized basis sets are usually optimized for properties, there's a bunch of papers on them for magnetic properties from Juha Vaara's group; I've also published a few. One could also mention the augmented Karlsruhe sets which are optimized for polarizabilities instead of the description of anions, as well as Sadlej's basis sets which are also aimed for electric properties.

On the DFT side, hundreds of functionals have been proposed, and several semiempirical ones are fit for properties. E.g. the Keal-Tozer functionals KT1, KT2, KT3, B97-2, and B97-3 are optimized for NMR shieldings. There are also functionals fitted to band gaps.

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