The atomic units are a system of natural units of measurement that is especially convenient for calculations in atomic physics and related scientific fields, such as computational chemistry and atomic spectroscopy.
They were originally suggested and named by the physicist Douglas Hartree.
In the context of atomic physics, using the atomic units system can be a convenient shortcut, eliminating symbols and numbers and reducing the order of magnitude of most numbers involved.
For example, the Hamiltonian operator in the Schrödinger equation for the helium atom with standard quantities, such as when using SI units, is[2] but adopting the convention associated with atomic units that transforms quantities into dimensionless equivalents, it becomes In this convention, the constants
The distances relevant to the physics expressed in SI units are naturally on the order of
, while expressed in atomic units distances are on the order of
(one Bohr radius, the atomic unit of length).
An additional benefit of expressing quantities using atomic units is that their values calculated and reported in atomic units do not change when values of fundamental constants are revised, since the fundamental constants are built into the conversion factors between atomic units and SI.
Hartree defined units based on three physical constants:[1]: 91 Both in order to eliminate various universal constants from the equations and also to avoid high powers of 10 in numerical work, it is convenient to express quantities in terms of units, which may be called 'atomic units', defined as follows: Consistent with these are: Here, the modern equivalent of
is the reduced Planck constant
differ from the modern form due to a change in the definition of
In 1957, Bethe and Salpeter's book Quantum mechanics of one-and two-electron atoms[3] built on Hartree's units, which they called atomic units abbreviated "a.u.".
, their unit of action and angular momentum in place of Hartree's length as the base units.
They noted that the unit of length in this system is the radius of the first Bohr orbit and their velocity is the electron velocity in Bohr's model of the first orbit.
In 1959, Shull and Hall[4] advocated atomic units based on Hartree's model but again chose to use
They explicitly named the distance unit a "Bohr radius"; in addition, they wrote the unit of energy as
These terms came to be used widely in quantum chemistry.
[5]: 349 In 1973 McWeeny extended the system of Shull and Hall by adding permittivity in the form of
[6][7] Simultaneously he adopted the SI definition of
so that his expression for energy in atomic units is
, matching the expression in the 8th SI brochure.
[8] A set of base units in the atomic system as in one proposal are the electron rest mass, the magnitude of the electronic charge, the Planck constant, and the permittivity.
[6][9] In the atomic units system, each of these takes the value 1; the corresponding values in the International System of Units[10]: 132 are given in the table.
Three of the defining constants (reduced Planck constant, elementary charge, and electron rest mass) are atomic units themselves – of action,[15] electric charge,[16] and mass,[17] respectively.
Two named units are those of length (Bohr radius
: Bohr magneton, ≘: correspondence Different conventions are adopted in the use of atomic units, which vary in presentation, formality and convenience.
In atomic physics, it is common to simplify mathematical expressions by a transformation of all quantities: Dimensionless physical constants retain their values in any system of units.
, which appears in expressions as a consequence of the choice of units.
For example, the numeric value of the speed of light, expressed in atomic units, is
[44]: 597 Atomic units are chosen to reflect the properties of electrons in atoms, which is particularly clear in the classical Bohr model of the hydrogen atom for the bound electron in its ground state: