Hartree energy

Eh=4.359744722206×10−18 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 & AtomicQuantum
Hartree energy in every energy unit
electron volt27.211386 eV
hartree1 Eh
kiloelectron volt0.027211386 keV
megaelectron volt0.000027211386 MeV
gigaelectron volt2.7211386e-08 GeV
nanojoule4.3597447e-09 nJ
erg4.3597447e-11 erg
teraelectron volt2.7211386e-11 TeV
microjoule4.3597447e-12 µJ
millijoule4.3597447e-15 mJ
inch-pound3.8586992e-17 in·lb
joule4.3597447e-18 J
foot-pound3.2155827e-18 ft⋅lb
calorie1.0420040e-18 cal
calorie (International Table)1.0413071e-18 cal IT
kilojoule4.3597447e-21 kJ
BTU (thermochemical)4.1350060e-21 BTU th
British thermal unit4.1322407e-21 BTU
watt-hour1.2110402e-21 Wh
kilocalorie1.0420040e-21 kcal
megajoule4.3597447e-24 MJ
horsepower-hour1.6240317e-24 hp·h
kilowatt-hour1.2110402e-24 kWh
therm4.1322407e-26 therm
gigajoule4.3597447e-27 GJ
million BTU4.1322407e-27 MMBTU
megawatt-hour1.2110402e-27 MWh
ton of TNT1.0420040e-27 t TNT
tonne of oil equivalent1.0413071e-28 toe
terajoule4.3597447e-30 TJ
gigawatt-hour1.2110402e-30 GWh
kiloton of TNT1.0420040e-30 kt TNT
petajoule4.3597447e-33 PJ
terawatt-hour1.2110402e-33 TWh
megaton of TNT1.0420040e-33 Mt TNT
quad4.1322407e-36 quad

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.