Hartree energy

Eh=4.359744722206×1018 JE_{\mathrm{h}} = 4.359744722206 \times 10^{-18}\ \text{J}
Value4.359744722206e-18 J
StatusMeasured: ± 4.80e-30 J (1.1e-12 relative)
SourceCODATA 2022
CategoriesUniversal & Atomicphysicsquantum
E_h in every energy unit
joule4.3597447e-18 J
kilojoule4.3597447e-21 kJ
megajoule4.3597447e-24 MJ
calorie1.0420040e-18 cal
kilocalorie1.0420040e-21 kcal
watt-hour1.2110402e-21 Wh
kilowatt-hour1.2110402e-24 kWh
British thermal unit4.1322407e-21 BTU
foot-pound3.2155827e-18 ft⋅lb
electron volt27.211386 eV
kiloelectron volt0.027211386 keV
megaelectron volt0.000027211386 MeV

Learning zone

Douglas Hartree built a unit system in which ħ, m_e, e and 4πε₀ all equal one, so that the Schrödinger equation for atoms loses its constants entirely. One hartree is then the natural energy: twice hydrogen's ionisation energy, and equal to the potential energy of two elementary charges one Bohr radius apart. Every serious electronic-structure code — Gaussian, VASP, Quantum ESPRESSO — reports total energies in hartrees.

Conversions worth keeping close: 1 E_h = 27.211 386 eV = 2625.5 kJ/mol = 627.51 kcal/mol = 219 474.6 cm⁻¹. The last one matters because spectroscopists work in wavenumbers while chemists work in kJ/mol. The classic trap remains the factor of two against the Rydberg: a plane-wave code quoting cutoff energies in Ry and a molecular code quoting them in hartree are not describing the same number, and mixing them silently doubles or halves your energy scale.