Editing Density functional theory (section)

==Applications==

[[File:c60 isosurface.png|thumb|right|160px|[[fullerene|C<sub>60</sub>]] with [[isosurface]] of ground-state electron density as calculated with DFT]]

In general, density functional theory finds increasingly broad application in chemistry and materials science for the interpretation and prediction of complex system behavior at an atomic scale. Specifically, DFT computational methods are applied for synthesis-related systems and processing parameters. In such systems, experimental studies are often encumbered by inconsistent results and non-equilibrium conditions. Examples of contemporary DFT applications include studying the effects of dopants on phase transformation behavior in oxides, magnetic behavior in dilute magnetic semiconductor materials, and the study of magnetic and electronic behavior in ferroelectrics and [[Magnetic semiconductor|dilute magnetic semiconductors]].<ref name="dftmag" /><ref>{{cite journal |last1=Segall |first1=M. D. |last2=Lindan |first2=P. J. |title=First-principles simulation: ideas, illustrations and the CASTEP code |journal=Journal of Physics: Condensed Matter |year=2002 |volume=14 |issue=11 |page=2717 |bibcode=2002JPCM...14.2717S |doi=10.1088/0953-8984/14/11/301 |citeseerx=10.1.1.467.6857|s2cid=250828366 }}</ref> It has also been shown that DFT gives good results in the prediction of sensitivity of some nanostructures to environmental pollutants like [[sulfur dioxide]]<ref>{{Cite journal |title = Theoretical investigation on the selective detection of SO2 molecule by AlN nanosheets |journal = Journal of Molecular Modeling |volume = 20 |issue = 9 |page = 2439 |date = 2014-01-01 |first1 = Hamed |last1=Soleymanabadi |first2 = Somayeh F. |last2=Rastegar |doi = 10.1007/s00894-014-2439-6 |pmid = 25201451|s2cid = 26745531 }}</ref> or [[acrolein]],<ref>{{Cite journal |title = DFT studies of acrolein molecule adsorption on pristine and Al-doped graphenes |journal = Journal of Molecular Modeling |volume = 19 |issue = 9 |pages = 3733–3740 |date = 2013-01-01 |first1 = Hamed |last1=Soleymanabadi |first2 = Somayeh F. |last2=Rastegar |doi = 10.1007/s00894-013-1898-5 |pmid = 23793719|s2cid = 41375235 }}</ref> as well as prediction of mechanical properties.<ref>{{cite journal |last1=Music |first1=D. |last2=Geyer |first2=R. W. |last3=Schneider |first3=J. M. |title=Recent progress and new directions in density functional theory based design of hard coatings |journal=Surface & Coatings Technology |volume=286 |pages=178–190 |year=2016 |doi=10.1016/j.surfcoat.2015.12.021}}</ref>

In practice, Kohn–Sham theory can be applied in several distinct ways, depending on what is being investigated. In solid-state calculations, the local density approximations are still commonly used along with [[plane-wave]] basis sets, as an electron-gas approach is more appropriate for electrons delocalised through an infinite solid. In molecular calculations, however, more sophisticated functionals are needed, and a huge variety of exchange–correlation functionals have been developed for chemical applications. Some of these are inconsistent with the uniform electron-gas approximation; however, they must reduce to LDA in the electron-gas limit. Among physicists, one of the most widely used functionals is the revised Perdew–Burke–Ernzerhof exchange model (a direct generalized gradient parameterization of the free-electron gas with no free parameters); however, this is not sufficiently calorimetrically accurate for gas-phase molecular calculations. In the chemistry community, one popular functional is known as BLYP (from the name Becke for the exchange part and Lee, Yang and Parr for the correlation part). Even more widely used is B3LYP, which is a [[hybrid functional]] in which the exchange energy, in this case from Becke's exchange functional, is combined with the exact energy from Hartree–Fock theory. Along with the component exchange and correlation funсtionals, three parameters define the hybrid functional, specifying how much of the exact exchange is mixed in. The adjustable parameters in hybrid functionals are generally fitted to a "training set" of molecules. Although the results obtained with these functionals are usually sufficiently accurate for most applications, there is no systematic way of improving them (in contrast to some of the traditional [[wavefunction]]-based methods like [[configuration interaction]] or [[coupled cluster]] theory). In the current DFT approach it is not possible to estimate the error of the calculations without comparing them to other methods or experiments.

Density functional theory is generally highly accurate but highly computationally-expensive. In recent years, DFT has been used with machine learning techniques - especially graph neural networks - to create [[machine learning potential]]s. These graph neural networks approximate DFT, with the aim of achieving similar accuracies with much less computation, and are especially beneficial for large systems. They are trained using DFT-calculated properties of a known set of molecules. Researchers have been trying to approximate DFT with machine learning for decades, but have only recently made good estimators. Breakthroughs in model architecture and data preprocessing that more heavily encoded theoretical knowledge, especially regarding symmetries and invariances, have enabled huge leaps in model performance. Using backpropagation, the process by which neural networks learn from training errors, to extract meaningful information about forces and densities, has similarly improved machine learning potentials accuracy. By 2023, for example, the DFT approximator [https://matlantis.com/ Matlantis] could simulate 72 elements, handle up to 20,000 atoms at a time, and execute calculations up to 20,000,000 times faster than DFT with similar accuracy, showcasing the power of DFT approximators in the artificial intelligence age. ML approximations of DFT have historically faced substantial transferability issues, with models failing to generalize potentials from some types of elements and compounds to others; improvements in architecture and data have slowly mitigated, but not eliminated, this issue. For very large systems, electrically nonneutral simulations, and intricate reaction pathways, DFT approximators often remain insufficiently computationally-lightweight or insufficiently accurate.<ref>{{cite journal|title=Completing density functional theory by machine learning hidden messages from molecules|last1=Nagai|first1=Ryo|last2=Akashi|last3=Sugino|first3=Osamu|first2=Ryosuke|date=May 5, 2020|volume=6|journal=npj Computational Materials|page=43 |doi=10.1038/s41524-020-0310-0 |arxiv=1903.00238 |bibcode=2020npjCM...6...43N }}</ref><ref>{{cite journal|last1=Schutt|first1=KT|last2=Arbabzadah|first2=F|last3=Chmiela|first3=S|last4=Muller|first4=KR|last5=Tkatchenko|first5=A|date=2017|title=Quantum-chemical insights from deep tensor neural networks|journal=Nature Communications|volume=8 |page=13890 |doi=10.1038/ncomms13890 |pmid=28067221 |pmc=5228054 |arxiv=1609.08259|bibcode=2017NatCo...813890S }}</ref><ref name="ML">{{cite journal|last1=Kocer|last2=Ko|last3=Behler|first1=Emir|first2=Tsz Wai|first3=Jorg|journal=Annual Review of Physical Chemistry|title=Neural Network Potentials: A Concise Overview of Methods|date=2022|volume=73|pages=163–86|doi=10.1146/annurev-physchem-082720-034254 |pmid=34982580 |arxiv=2107.03727 |bibcode=2022ARPC...73..163K }}</ref><ref>{{cite journal|journal=Nature Communications|title=Towards universal neural network potential for material discovery applicable to arbitrary combinations of 45 elements|last1=Takamoto|first1=So|last2=Shinagawa|first2=Chikashi|last3=Motoki|first3=Daisuke|last4=Nakago|first4=Kosuke|volume=13|date=May 30, 2022|page=2991 |doi=10.1038/s41467-022-30687-9 |arxiv=2106.14583 |bibcode=2022NatCo..13.2991T }}</ref><ref>{{cite web|url=https://matlantis.com/|title=Matlantis}}</ref>