Hartree

 ( Units Of Energy ) 

The hartree (symbol: E_h), also known as the Hartree energy, is the measurement unit of energy in the atomic units system, named after the British physicist Douglas Hartree. Its CODATA recommended value is = 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 Atomic 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.

$E\_\backslash mathrm\{h\}\; =\; \{\backslash hbar^2\; \backslash over\; \{m\_\backslash mathrm\{e\}\; a^2\_0\}\}\; =\; m\_\backslash mathrm\{e\}\backslash left(\backslash frac\{e^2\}\{4\backslash pi\backslash varepsilon\_0\backslash hbar\}\backslash right)^2\; =\; m\_\backslash mathrm\{e\}\; c^2\; \backslash alpha^2\; =\; \{\backslash hbar\; c\; \backslash alpha\; \backslash over\; \{a\_0\}\}$

: = 2 Ry = 2 Rydberg constant hc

: =

: =

: =

: ≘

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• 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 $e^2$ is replaced by $e^2/\backslash varepsilon$ and $\backslash varepsilon$ is the static dielectric constant. Also, the electron mass is replaced by the effective band mass $m^*$. The effective hartree in semiconductors becomes small enough to be measured in millielectronvolts (meV). Tsuneya Ando, Alan B. Fowler, and Frank Stern Rev. Mod. Phys. 54, 437 (1982)