{{for|other articles and the surname|Hartree (disambiguation)}} {{Short description|Unit of energy in the atomic units system}}
The '''hartree''' (symbol: ''E''<sub>h</sub>), also known as the '''Hartree energy''', is the unit of energy in the atomic units system, named after the British physicist Douglas Hartree. Its CODATA recommended value is {{physconst|Eh|symbol=yes}} = {{physconst|Eh_eV|after=.}} The name "hartree" was suggested for this unit of energy.<ref>{{cite journal |last1=Shull |first1=H. |last2=Hall |first2=G.G. |title=Atomic Units |year=1959 |journal=Nature |volume=184 |issue=4698 |publisher=Nature Publishing Group |pages=1559–1560 |doi=10.1038/1841559a0 |bibcode=1959Natur.184.1559S }}</ref><ref>{{cite journal |last1=McWeeny |first1=R. |date=May 1973 |title=Natural Units in Atomic and Molecular Physics |url=https://www.nature.com/articles/243196a0 |journal=Nature |language=en |volume=243 |issue=5404 |pages=196–198 |doi=10.1038/243196a0 |bibcode=1973Natur.243..196M |s2cid=4164851 |issn=0028-0836|url-access=subscription }}</ref>
The hartree is approximately the negative electric potential energy of the electron in a hydrogen atom in its ground state and, by the virial theorem, approximately twice its ionization energy; the relationships are not exact because of the finite mass of the nucleus of the hydrogen atom and relativistic corrections.
The hartree is usually used as a unit of energy in atomic physics and computational chemistry: for experimental measurements at the atomic scale, the electronvolt (eV) or the reciprocal centimetre (cm<sup>−1</sup>) are much more widely used.
== Other relationships ==
: <math>E_\mathrm{h} = {\hbar^2 \over {m_\mathrm{e} a^2_0}} = m_\mathrm{e}\left(\frac{e^2}{4\pi\varepsilon_0\hbar}\right)^2 = m_\mathrm{e} c^2 \alpha^2 = {\hbar c \alpha \over {a_0}} </math> :: = 2 Ry = 2 ''R''<sub>∞</sub>''hc'' :: = {{physconst|Eh_eV|unit={{val|ul=eV}}}} :: = {{physconst|Eh|unit={{val|ul=J}}}} :: = {{val|4.3597447222060|(48)|e=-11|ul=erg}} :: ≘ {{val|2625.4996394799|(50)|ul=kJ/mol}} <!-- to be recalculated or {{physconst}} used --> :: ≘ {{val|627.5094740631|(12)|ul=kcal/mol}} <!-- to be recalculated or {{physconst}} used --> :: ≘ {{val|219474.63136320|(43)|ul=cm-1}} <!-- to be recalculated or {{physconst}} used --> :: ≘ {{val|6579.683920502|(13)|ul=THz}} <!-- to be recalculated or {{physconst}} used --> where: * ''ħ'' is the reduced Planck constant, * ''m''<sub>e</sub> is the electron mass, * ''e'' is the elementary charge, * ''a''<sub>0</sub> is the Bohr radius, * ''ε''<sub>0</sub> is the electric constant, * ''c'' is the speed of light in vacuum, and * ''α'' is the fine-structure constant.
Effective hartree units are used in semiconductor physics where <math>e^2</math> is replaced by <math>e^2/\varepsilon</math> and <math>\varepsilon </math> is the static dielectric constant. Also, the electron mass is replaced by the effective band mass <math>m^*</math>. The effective hartree in semiconductors becomes small enough to be measured in millielectronvolts (meV).<ref> Tsuneya Ando, Alan B. Fowler, and Frank Stern Rev. Mod. Phys. '''54''', 437 (1982) </ref>
== See also ==
== References == {{reflist}}
Category:Units of energy Category:Physical constants