Hartree

Unit of energy in the atomic units system

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[1] = 27.211386245981(30) eV.[2]

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.

Other relationships

E h = 2 m e a 0 2 = m e ( e 2 4 π ε 0 ) 2 = m e c 2 α 2 = c α a 0 {\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
= 27.211386245981(30) eV[2]
= 4.3597447222060(48)×10−18 J[1]
= 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 {\displaystyle e^{2}} is replaced by e 2 / ε {\displaystyle e^{2}/\varepsilon } and ε {\displaystyle \varepsilon } is the static dielectric constant. Also, the electron mass is replaced by the effective band mass m {\displaystyle m^{*}} . The effective hartree in semiconductors becomes small enough to be measured in millielectronvolts (meV).[3]

References

  1. ^ a b "2022 CODATA Value: Hartree energy". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18.
  2. ^ a b "2022 CODATA Value: Hartree energy in eV". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18.
  3. ^ Tsuneya Ando, Alan B. Fowler, and Frank Stern Rev. Mod. Phys. 54, 437 (1982)