Atomic units

Atomic units (au or a.u.) form a system of natural units which is especially convenient for atomic physics calculations. There are two different kinds of atomic units, Hartree atomic units and Rydberg atomic units, which differ in the choice of the unit of mass and charge. This article deals with Hartree atomic units, where the numerical values of the following four fundamental physical constants are all unity by definition:

In Hartree units, the speed of light is approximately ${\displaystyle 137}$. Atomic units are often abbreviated "a.u." or "au", not to be confused with the same abbreviation used also for astronomical units, arbitrary units, and absorbance units in different contexts.

Atomic units, like SI units, have a unit of mass, a unit of length, and so on. However, the use and notation is somewhat different from SI.

Suppose a particle with a mass of m has 3.4 times the mass of electron. The value of m can be written in three ways:

These four fundamental constants form the basis of the atomic units (see above). Therefore, their numerical values in the atomic units are unity by definition.

Dimensionless physical constants retain their values in any system of units. Of particular importance is the fine-structure constant ${\displaystyle \alpha ={\frac {e^{2}}{(4\pi \epsilon _{0})\hbar c}}\approx 1/137}$. This immediately gives the value of the speed of light, expressed in atomic units.

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