Editing Hartree

{{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 [[measurement unit|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 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 [[Atomic nucleus|nucleus]] of the hydrogen atom and [[Quantum electrodynamics|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&thinsp;[[Rydberg constant#Rydberg unit of energy|Ry]] = 2&thinsp;[[Rydberg constant|''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 [[millielectronvolt]]s (meV).<ref> Tsuneya Ando, Alan B. Fowler, and Frank Stern Rev. Mod. Phys. '''54''', 437 (1982) </ref>

== References ==
{{reflist}}

[[Category:Units of energy]]
[[Category:Physical constants]]