# Hartree

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Hartree
> Markdown URL: https://mediated.wiki/source/Hartree.md
> Source: https://en.wikipedia.org/wiki/Hartree
> Source revision: 1340624078
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

{{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](/source/measurement_unit) of [energy](/source/energy) in the [atomic units](/source/atomic_units) system, named after the British physicist [Douglas Hartree](/source/Douglas_Hartree). Its [CODATA](/source/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](/source/electric_potential_energy) of the electron in a [hydrogen](/source/hydrogen) [atom](/source/atom) in its [ground state](/source/ground_state) and, by the [virial theorem](/source/virial_theorem), approximately twice its [ionization energy](/source/ionization_energy); the relationships are not exact because of the finite [mass](/source/mass) of the [nucleus](/source/Atomic_nucleus) of the hydrogen atom and [relativistic corrections](/source/Quantum_electrodynamics).

The hartree is usually used as a unit of energy in [atomic physics](/source/atomic_physics) and [computational chemistry](/source/computational_chemistry): for experimental measurements at the atomic scale, the [electronvolt](/source/electronvolt) (eV) or the [reciprocal centimetre](/source/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&thinsp;[Ry](/source/Rydberg_constant) = 2&thinsp;[''R''<sub>∞</sub>](/source/Rydberg_constant)''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](/source/reduced_Planck_constant),
* ''m''<sub>e</sub> is the [electron mass](/source/electron_mass),
* ''e'' is the [elementary charge](/source/elementary_charge),
* ''a''<sub>0</sub> is the [Bohr radius](/source/Bohr_radius),
* ''ε''<sub>0</sub> is the [electric constant](/source/electric_constant), 
* ''c'' is the [speed of light](/source/speed_of_light) in vacuum, and
* ''α'' is the [fine-structure constant](/source/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 [millielectronvolt](/source/millielectronvolt)s (meV).<ref> Tsuneya Ando, Alan B. Fowler, and Frank Stern Rev. Mod. Phys. '''54''', 437 (1982) </ref>

== See also ==

* [Rydberg constant](/source/Rydberg_constant)

== References ==
{{reflist}}

Category:Units of energy
Category:Physical constants

---
Adapted from the Wikipedia article [Hartree](https://en.wikipedia.org/wiki/Hartree) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Hartree?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.