Atomic Units

Atomic units are convenient units to describe the properties of electrons. The atomic units have been chosen such that the fundamental electron properties are all equal to one atomic unit. For example, mass (m_e=1), charge (e=1), angular momentum ( = h/2 = 1), radius in the hydrogen atom (a_o=1), and the potential energy in the hydrogen atom (e²/a_o = 1).

Atomic Units and Their SI Equivalents

Quantity	Conversion Factor	Name
Mass	1 au = 9.10939 x 10-31 kg	Electron mass
	= 5.48580 x 10-4 g/mol
Charge	1 au = 1.60218 x 10-19 C	Electron charge
Length	1 au = 5.29177 x 10-11 m	Bohr radius
Energy	1 au = 4.35975 x 10-18 J	Hartree
	= 27.2114 eV
	= 219475 cm-1
	= 2625.50 kJ/mol
	= 2 Rydbergs
Angular Momentum	1 au = 1.05457 x 10-34 J s/rad

In atomic units the mass of a proton (1.6726 x 10-27 kg) would be 1836.15 au, and the reduced mass of the hydrogen molecule (.503913 g/mol) would be 925.260 au.

The use of atomic units also simplifies Schrödinger's equation. For example the Hamiltonian for an electron in the Hydrogen atom would be: