Hartree

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 =

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

 * $$E_\mathrm{h} = {\hbar^2 \over {m_\mathrm{e} a^2_0}} = m_\mathrm{e}\left(\frac{e^2}{4\pi\varepsilon_0\hbar}\right)^2 = m_\mathrm{e} c^2 \alpha^2 = {\hbar c \alpha \over {a_0}} $$
 * = 2&thinsp;Ry = 2&thinsp;R∞hc

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 $$e^2$$ is replaced by $$e^2/\varepsilon$$ and $$\varepsilon $$ 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).