Misplaced Pages

Hartree

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.
For other articles and the surname, see Hartree (disambiguation). 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 J‍ = 27.211386245981(30) eV.

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) are much more widely used.

Other relationships

E h = ℏ 2 m e a 0 2 = m e ( e 2 4 π ε 0 ℏ ) 2 = m e c 2 α 2 = ℏ 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 R∞hc
= 27.211386245981(30) eV‍
= 4.3597447222060(48)×10 J‍
= 4.3597447222060(48)×10 erg
≘ 2625.4996394799(50) kJ/mol
≘ 627.5094740631(12) kcal/mol
≘ 219474.63136320(43) cm
≘ 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).

References

  1. ^ "2022 CODATA Value: Hartree energy". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18.
  2. ^ "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)
Categories: