Hartree

Its CODATA recommended value is E_h = 4.3597447222071(85)×10⁻¹⁸ J = 27.211386245988(53) 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⁻¹) are much more widely used.

${\displaystyle E_{\mathrm {h} }={\hbar ^{2} \over {m_{\mathrm {e} }a_{0}^{2}}}=m_{\mathrm {e} }\left({\frac {e^{2}}{4\pi \varepsilon _{0}\hbar }}\right)^{2}=m_{\mathrm {e} }c^{2}\alpha ^{2}={\hbar c\alpha \over {a_{0}}}}$ 
= 2 Ry = 2 R_∞hc
= 27.211386245988(53) eV
= 4.3597447222071(85)×10⁻¹⁸ J
= 4.3597447222071(85)×10⁻¹¹ erg
≘ 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,
• m_e 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 ${\displaystyle e^{2}}$  is replaced by ${\displaystyle e^{2}/\varepsilon }$  and ${\displaystyle \varepsilon }$  is the static dielectric constant. Also, the electron mass is replaced by the effective band mass ${\displaystyle m^{*}}$ . The effective hartree in semiconductors becomes small enough to be measured in millielectronvolts (meV).