Hartree Approximation

The hartree (symbol: ''E''_h or Ha), also known as the Hartree energy, is the unit of energy in the Hartree atomic units system, named after the British physicist Douglas Hartree. Its CODATA recommended value is =

The hartree energy is approximately the electric potential energy of the 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

:$E_\mathrm = = m_\mathrm\left(\frac\right)^2 = m_\mathrm c^2 \alpha^2 =$
::= 2  Ry = 2  ''R''_∞''hc''
::≜
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where:
*''ħ'' is the reduced Planck constant,
*''m''_e is the electron rest mass,
*''e'' is the elementary charge,
*''a''₀ is the Bohr radius,
*''ε''₀ is the electric constant,
*''c'' is the speed of light in vacuum, and
*''α'' is the fine-structure constant.

Note that since the Bohr radius $a_0$ is defined as one may write the Hartree energy as $E_\mathrm = e^2/a_0$ in Gaussian units where $4\pi \varepsilon_0=1$.

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). Tsuneya Ando, Alan B. Fowler, and Frank Stern Rev. Mod. Phys. 54, 437 (1982)

References

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Units of energy
Physical constants