Hartree
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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)×10−18J = 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.
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}}}} = 2Ry = 2R∞hc = 27.211386245981(30)eV = 4.3597447222060(48)×10−18J = 4.3597447222060(48)×10−11erg ≘ 2625.4996394799(50)kJ/mol ≘ 627.5094740631(12)kcal/mol ≘ 219474.63136320(43)cm−1 ≘ 6579.683920502(13)THz
where:
- ħ is the reduced Planck constant,
- me is the electron mass,
- e is the elementary charge,
- a0 is the Bohr radius,
- ε0 is the electric constant,
- c is the speed of light in vacuum, and
- α is the fine-structure constant.
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).