Atomic units

Atomic units are a natural unit system for atomic physics in which the elementary charge, electron mass, reduced Planck constant, and Coulomb constant are set to one.

Elementary charge: The positive charge of a proton, equal in magnitude to the negative charge of an electron. Its value is set to one, fixing the charge scale for atomic interactions.
Natural units: A unit system that assigns selected fundamental constants the numerical value one. Atomic units are a specialized natural-unit system tailored to atomic physics.
Hartree–Fock method: An approximation that models each electron as moving in the average field of the others. Its electronic energies and equations are commonly expressed in atomic units.
SI units: The International System of Units, a coherent system based on seven defined base units. Unlike atomic units, SI retains explicit conversion factors for atomic-scale constants.
Electron mass: The rest mass of an electron, approximately 9.109 × 10⁻³¹ kilograms. Setting it to one makes the electron the reference mass in this system.
Dimensional analysis: The study of physical dimensions and how they constrain equations and unit conversions. It tracks which dimensions remain after the defining constants are normalized.
Density functional theory: A quantum method that uses electron density to calculate the properties of many-electron systems. Atomic units simplify the equations and numerical scales used in many implementations.
Gaussian units: A centimeter–gram–second electromagnetic unit system that places factors of 4π differently from SI. Its electrostatic conventions differ, while atomic units set the Coulomb constant to one.
Reduced Planck constant: Planck’s constant divided by 2π, denoted ħ, which sets the scale of quantum action. Its value is one, simplifying quantum equations in atomic units.
Atomic unit of length: The Bohr radius expressed as one unit of length in the atomic-unit system. This derived unit replaces meters in many atomic-scale calculations.

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