Hartree

The hartree (symbol: E_h 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 2010 CODATA recommended value is E_h = 4.359 744 650(54)×10⁻¹⁸ J = 27.211 386 02(17) eV. The 2006 CODATA recommended value was E_h = 4.359 743 94 (22)×10⁻¹⁸ J = 27.211 383 86(68) eV.

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

$E_\mathrm{h} = {\hbar^2 \over {m_\mathrm{e} a^2_0}} = m_\mathrm{e}\left(\frac{e^2}{4\pi\epsilon_0\hbar}\right)^2 = m_\mathrm{e}c^2\alpha^2 = {\hbar c \alpha \over {a_0}}$

= 2 Ry

≜ 4.359 744 34(19)×10⁻¹⁸ J

≜ 27.211 385 05(60) 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

≜ 3.157 746 46 x 10⁵ K

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.