Atomic units

Lore & Background

Atomic units were motivated by the need for stable and accurate reporting of quantum-mechanical calculations. In early atomic physics, the accepted values of fundamental constants such as ℏ, mₑ, e, and c were not sufficiently stable or accurate, making it difficult to directly compare results from different years. This led to suggestions that results should be reported using units based directly on these constants, eliminating confusion. Douglas Hartree defined atomic units based on three physical constants: the unit of length (a_H = h² / 4π² m e²), the unit of charge (e, the magnitude of the electron's charge), and the unit of mass (m, the mass of the electron). Consistent with these were the unit of action (h / 2π), the unit of energy (e² / a_H = 2 h c R), and the unit of time (1 / 4π c R). Using atomic units simplifies equations by setting ℏ, mₑ, 4πϵ₀, and e all to 1. For example, the Hamiltonian for the helium atom in SI units contains many constants, but in atomic units it becomes a simpler expression with only numerical coefficients and distances. Additionally, values reported in atomic units do not change when fundamental constants are revised, because those constants are built into the conversion factors.

Reader's Guide

Atomic units are significant because they provide a stable and convenient framework for atomic physics calculations. By setting fundamental constants to unity, they eliminate symbols and numbers, reducing the order of magnitude of most numbers involved. This makes calculations easier to perform and compare across different eras, as the values do not shift when the accepted values of constants like ℏ or mₑ are updated. The system was originally suggested by Douglas Hartree and remains widely used in fields such as computational chemistry and atomic spectroscopy. Its abbreviation "a.u." or "au" should not be confused with astronomical units, arbitrary units, or absorbance units. The legacy of atomic units lies in their ability to streamline complex quantum-mechanical equations—such as the Schrödinger equation for multi-electron atoms—while ensuring that reported results remain consistent over time, independent of revisions to fundamental constants.

Did You Know?

• Atomic units were originally suggested and named by physicist Douglas Hartree.
• The abbreviation 'a.u.' or 'au' is also used for astronomical units, arbitrary units, and absorbance units in other contexts.
• In atomic units, the constants ℏ, mₑ, 4πϵ₀, and e all correspond to the value 1.
• Hartree defined the atomic unit of length as a_H = h² / 4π² m e², based on the radius of the 1-quantum circular orbit of the hydrogen atom.