# Hartree

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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[1] = 27.211386245988(53) eV.[2]

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

${\displaystyle E_{\mathrm {h} }={\hbar ^{2} \over {m_{\mathrm {e} }a_{0}^{2}}}=m_{\mathrm {e} }\left({\frac {e^{2}}{4\pi \varepsilon _{0}\hbar }}\right)^{2}=m_{\mathrm {e} }c^{2}\alpha ^{2}={\hbar c\alpha \over {a_{0}}}}$
= 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 ${\displaystyle a_{0}}$ 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 ${\displaystyle E_{\mathrm {h} }=e^{2}/a_{0}}$ in Gaussian units where ${\displaystyle 4\pi \varepsilon _{0}=1}$.

Effective hartree units are used in semiconductor physics where ${\displaystyle e^{2}}$ is replaced by ${\displaystyle e^{2}/\varepsilon }$ and ${\displaystyle \varepsilon }$ is the static dielectric constant. Also, the electron mass is replaced by the effective band mass ${\displaystyle m^{*}}$. The effective hartree in semiconductors becomes small enough to be measured in millielectronvolts (meV).[3]

## References

1. ^ "2018 CODATA Value: Hartree energy". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
2. ^ "2018 CODATA Value: Hartree energy in eV". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-09-01.
3. ^ Tsuneya Ando, Alan B. Fowler, and Frank Stern Rev. Mod. Phys. 54, 437 (1982)