From Wikipedia, the free encyclopedia
Jump to navigation Jump to search

The hartree (symbol: Eh or Ha), also known as the Hartree energy, is the atomic unit of energy, named after the British physicist Douglas Hartree. It is defined as 2Rhc, where R is the Rydberg constant, h is the Planck constant and c is the speed of light. The 2014 CODATA recommended value is Eh = 4.359 744 650(54)×10−18 J = 27.211 386 02(17) eV.[1]

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[edit]

= 2 Ry
27.21138602(17) eV
4.359744650(54)×10−18 J
4.359744650(54)×10−11 erg
2625.499638(65) kJ/mol
627.509474(15) kcal/mol
219474.6313702(13) cm−1
6579.683920711(39) THz
315775.13(18) K


ħ is the reduced Planck constant,
me is the electron rest 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.

Note that since the Bohr radius is defined as , one may write the Hartree energy as in Gaussian units where . Effective Hartree units are used in semiconductor physics where is replaced by and is the static dielectric constant. Also, the electron mass is replaced by the effective band mass . The effective Hartree in semiconductors becomes small enough to be measured in millielectronvolts (meV).[2]


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