Editing Computational chemistry (section)

=== Hartree-Fock method ===
{{See also|Hartree–Fock method}}

==== Algorithm ====
Finds a single Fock state that minimizes the energy.<ref name="Lucas-2014">{{Cite journal |last=Lucas |first=Andrew |date=2014 |title=Ising formulations of many NP problems |journal=Frontiers in Physics |volume=2 |page=5 |arxiv=1302.5843 |bibcode=2014FrP.....2....5L |doi=10.3389/fphy.2014.00005 |issn=2296-424X |doi-access=free}}</ref>

==== Complexity ====

NP-hard or NP-complete as demonstrated by embedding instances of the [[Ising model]] into Hartree-Fock calculations. The Hartree-Fock method involves solving the Roothaan-Hall equations, which scales as <math>\mathcal{O}(N^3)</math> to <math>\mathcal{O}(N)</math> depending on implementation, with <math>N</math> being the number of basis functions. The computational cost mainly comes from evaluating and transforming the two-electron integrals. This proof of NP-hardness or NP-completeness comes from embedding problems like the Ising model into the Hartree-Fock formalism.<ref name="Lucas-2014" />
[[File:Acrolein-s-trans-GED-MW-3D-sf.png|thumb|An [[acrolein]] molecule. DFT gives good results in the prediction of sensitivity of some nanostructures to environmental pollutants such as Acrolein.<ref>{{Cite journal |last1=Rastegar |first1=Somayeh F. |last2=Hadipour |first2=Nasser L. |last3=Tabar |first3=Mohammad Bigdeli |last4=Soleymanabadi |first4=Hamed |date=2013-09-01 |title=DFT studies of acrolein molecule adsorption on pristine and Al- doped graphenes |url=http://link.springer.com/10.1007/s00894-013-1898-5 |journal=Journal of Molecular Modeling |language=en |volume=19 |issue=9 |pages=3733–3740 |doi=10.1007/s00894-013-1898-5 |pmid=23793719 |s2cid=41375235 |issn=1610-2940}}</ref>]]