# Hartree

The hartree (symbol: Eh or Ha), also known as the Hartree energy, is the unit of energy in the Hartree atomic units system, named after the British physicist Douglas Hartree. Its CODATA recommended value is Eh = 4.3597447222071(85)×10−18 J = 27.211386245988(53) eV.

The hartree energy is approximately the electric potential energy of the 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−1) are much more widely used.

## Other relationships

$E_{\mathrm {h} }={\hbar ^{2} \over {m_{\mathrm {e} }a_{0}^{2}}}=m_{\mathrm {e} }\left({\frac {e^{2}}{4\pi \varepsilon _{0}\hbar }}\right)^{2}=m_{\mathrm {e} }c^{2}\alpha ^{2}={\hbar c\alpha \over {a_{0}}}$ = 2 Ry = 2 Rhc
27.211386245988(53) eV
4.3597447222071(85)×10−18 J
4.3597447222071(85)×10−11 erg
2625.4996394799(50) kJ/mol
627.5094740631(12) kcal/mol
219474.63136320(43) cm−1
6579.683920502(13) THz
315775.02480407(61) K

where:

Note that since the Bohr radius $a_{0}$ is defined as ${\textstyle a_{0}={\frac {4\pi \varepsilon _{0}\hbar ^{2}}{m_{\mathrm {e} }e^{2}}}={\frac {\hbar }{m_{\mathrm {e} }c\alpha }}}$ , one may write the Hartree energy as $E_{\mathrm {h} }=e^{2}/a_{0}$ in Gaussian units where $4\pi \varepsilon _{0}=1$ .

Effective hartree units are used in semiconductor physics where $e^{2}$ is replaced by $e^{2}/\varepsilon$ and $\varepsilon$ is the static dielectric constant. Also, the electron mass is replaced by the effective band mass $m^{*}$ . The effective hartree in semiconductors becomes small enough to be measured in millielectronvolts (meV).