Hartree

The hartree energy is equal to the absolute value of the electric potential energy of the hydrogen atom in its ground state. This is also almost exactly twice the absolute value of the binding energy (or ionization energy) of the electron in the ground state hydrogen atom, |W₁| (it is not exactly equal to twice the ionization energy, because of the finite mass of the proton; see reduced mass).

$E\_mathrm\{h\}\; =\; \{hbar^2\; over\; \{m\_e\; a^2\_0\}\}\; =\; m\_ec^2alpha^2\; =\; \{hbar\; c\; alpha\; over\; \{a\_0\}\}$

= 4.359 744 17(75) J

= 2625.5 kJ/mol

= 27.211 3845(23) eV

= 2 Ry

= 627.509 391 kcal/mol

where:

$hbar$ is the reduced Planck constant,

$m\_e$ is the electron rest mass,

$a\_0$ is the Bohr radius,

$c$ is the speed of light in a vacuum, and

$alpha$ is the fine structure constant.