Hartree

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 2R_∞hc, where R_∞ is the Rydberg constant, h is the Planck constant and c is the speed of light. The 2006 CODATA recommended value is E_h = 4.359 743 94 (22)×10⁻¹⁸ J = 27.211 383 86 (68) eV. The 2010 CODATA recommended value is E_h = 4.359 744 34 (10)×10⁻¹⁸ J.

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

$E_{\mathrm {h} }={\hbar ^{2} \over {m_{\mathrm {e} }a_{0}^{2}}}=m_{\mathrm {e} }\left({\frac {e^{2}}{4\pi \epsilon _{0}\hbar }}\right)^{2}=m_{\mathrm {e} }c^{2}\alpha ^{2}={\hbar c\alpha \over {a_{0}}}$

= 2 Ry

≜ 4.359 743 94 (22)×10⁻¹⁸ J

≜ 27.211 383 86 (68) eV

≜ 2625.499 62 kJ/mol

≜ 627.509 469 kcal/mol

≜ 219 474.631 3705(15) cm⁻¹

≜ 6 579.683 920 729(33) THz

where:

ħ is the reduced Planck constant,

m_e 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.