Hartree Explained

The hartree (symbol: E_h), 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 _{h} = {\hbar ^{2} \over {m _{e} a ^{2} _{0 }}} = m _{e \left( (e ^{2})/(4 \pi\varepsilon _{0\hbar})} \right) ^{2} = m _{e} c ^{2} \alpha ^{2} = {\hbar c \alpha \over {a _{0}}}

= 2 Ry = 2 R_∞hc

=

=

=

≘

≘

≘

≘ 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

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).^[1]

Notes and References

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