Unit of energy in the atomic units system
The hartree (symbol: E h ), 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 E h = 744 722 2060 (48)× 10−18 J [ 1] 386 245 981 (30) eV[ 2] [ 3] [ 4]
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
=
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
= 386 245 981 (30) eV [ 2]
= 744 722 2060 (48)× 10−18 J [ 1]
= 744 722 2060 (48)× 10−11 erg
≘ 625 .499639 4799 (50) kJ/mol
≘ 474 0631 (12) kcal/mol
≘ 474 .631363 20 (43) cm−1
≘ 579 .683920 502 (13) THz where:
Effective hartree units are used in semiconductor physics where
e
2
{\displaystyle e^{2}}
e
2
/
ε
{\displaystyle e^{2}/\varepsilon }
ε
{\displaystyle \varepsilon }
m
∗
{\displaystyle m^{*}}
millielectronvolts (meV).[ 5]
References
^ a b "2022 CODATA Value: Hartree energy" . The NIST Reference on Constants, Units, and Uncertainty . NIST . May 2024. Retrieved 2024-05-18 .^ a b "2022 CODATA Value: Hartree energy in eV" . The NIST Reference on Constants, Units, and Uncertainty . NIST . May 2024. Retrieved 2024-05-18 .^ Shull, H.; Hall, G.G. (1959). "Atomic Units". Nature . 184 (4698). Nature Publishing Group: 1559– 1560. Bibcode :1959Natur.184.1559S . doi :10.1038/1841559a0 . ^ McWeeny, R. (May 1973). "Natural Units in Atomic and Molecular Physics" Nature . 243 (5404): 196– 198. Bibcode :1973Natur.243..196M . doi :10.1038/243196a0 . ISSN 0028-0836 . S2CID 4164851 . ^ Tsuneya Ando, Alan B. Fowler, and Frank Stern Rev. Mod. Phys. 54 , 437 (1982)
