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Hartree

Unit of energy in the atomic units system

Wikipedia contributorsAdapted for Fathomly · View authors
1 min read
Source updated September 4, 2026

The hartree (symbol: Eh), 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 Eh = 4.3597447222060(48)×10−18 J‍ = 27.211386245981(30) eV. The name "hartree" was suggested for this unit of energy.

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−1) are much more widely used.

01Other 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 R∞hc
= 27.211386245981(30) eV‍
= 4.3597447222060(48)×10−18 J‍
= 4.3597447222060(48)×10−11 erg
≘ 2625.4996394799(50) kJ/mol
≘ 627.5094740631(12) kcal/mol
≘ 219474.63136320(43) cm−1
≘ 6579.683920502(13) THz

where:

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).

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Sources and credits

This article is adapted from the Wikipedia article “Hartree”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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Rydberg constant

In spectroscopy, the Rydberg constant, symbol R ∞ {\displaystyle R_{\infty }} for heavy atoms or R H {\displaystyle R_{\text{H}}} for hydrogen, named after the Swedish physicist Johannes Rydberg, is a physical constant relating to the electromagnetic spectra of an atom. The constant first arose as an empirical fitting parameter in the Rydberg formula for the hydrogen spectral series, but Niels Bohr later showed that its value could be calculated from more fundamental constants according to his model of the atom.