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Concept
Hartree atomic units
Summary
The Hartree atomic units are a system of natural units of measurement which is especially convenient for calculations in atomic physics and related scientific fields, such as computational chemistry and atomic spectroscopy. They are named after the physicist Douglas Hartree.
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 other contexts.
By definition, each of the following four fundamental physical constants is expressed as the numeric value 1 multiplied by a coherent unit of this system:
Each unit in this system can be expressed as a product of powers of these four physical constants without a numerical multiplier. This makes it a coherent system of units, as well as making the numerical values of the defining constants in atomic units equal to unity.
Three of the defining constants (reduced Planck constant, elementary charge, and electron rest mass) are atomic units themselves – of action, electric charge, and mass, respectively. The two most important derived units are those of length (Bohr radius ) and energy (hartree ). The table below lists these and many other units that can be derived in the system.
Here,
is the speed of light
is the vacuum permittivity
is the Rydberg constant
is the Planck constant
is the fine-structure constant
is the Bohr magneton
≘ denotes correspondence between quantities since equality does not apply.
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:
"". This is the clearest notation (but least common), where the atomic unit is included explicitly as a symbol.
"" ("a.u." means "expressed in atomic units"). This notation is ambiguous: Here, it means that the mass m is 3.4 times the atomic unit of mass. But if a length L were 3.
Official source
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