The atomic system is based on a unit of mass, the electron mass (approximately equal to $9.1093897\times {10}^{\mathrm{-31}}$ kilograms), a unit of charge, the electron (approximately equal to $1.60217733\times {10}^{\mathrm{-19}}$ coulombs), a unit of action, the planck (equal to Planck's constant over $2\mathrm{\pi }$), and a unit of electric permittivity written as kappa0 (equal to $\frac{1.\times {10}^7}{c^2}$ farads per meter, or one statfarad per centimeter, where $c$ is the magnitude of the speed of light).

By taking combinations of these four units, one can derive four units corresponding to the base dimensions length, mass, time, and electric current.

To facilitate using atomic units, enter the command Units[UseContext](Atomic) so that the second, volt, and tesla refer to the atomic and not SI context.

When used in conjunction with the UseSystem command, the atomic system sets the following units for the given dimensions.  All units have context Atomic.

All atomic base units have the context Atomic, including the second, where one atomic second is approximately  $2.4188843\times {10}^{\mathrm{-17}}$ SI second.

All units have the context Atomic.

A plus sign (+) indicates an abbreviation.

$\mathrm{convert}\left(1.0\,'\mathrm{units}'\,'\mathrm{bohr}'\,'m'\right)$

$5.291772103\times {10}^{\mathrm{-11}}$

$\mathrm{convert}\left(1.0\,'\mathrm{units}'\,'\mathrm{second}\left[\mathrm{Atomic}\right]'\,'s'\right)$

$2.418884325\times {10}^{\mathrm{-17}}$

$\mathrm{convert}\left(1.0\,'\mathrm{units}'\,'\mathrm{hartree}'\,'J'\right)$

$4.359744652\times {10}^{\mathrm{-18}}$

$\mathrm{convert}\left(1.0\,'\mathrm{units}'\,'\mathrm{volt}\left[\mathrm{Atomic}\right]'\,'V'\right)$

$27.21138603$

$\mathrm{infolevel}\left[\mathrm{Units}\right]≔1\:$

$\mathrm{convert}\left(3.25721\,'\mathrm{system}'\,\frac{'C'}{{'m'}^2}\,'\mathrm{Atomic}'\right)$

convert/system:   "converting to the units e/a0^2"

$0.05692953475$

$\mathrm{convert}\left(5.23421\times {10}^{\mathrm{-10}}\,'\mathrm{system}'\,\frac{{'C'}^2}{'J'}\,'\mathrm{Atomic}'\right)$

convert/system:   "converting to the units e^2/E0"

$8.889788241\times {10}^{10}$

$\mathrm{with}\left(\mathrm{Units}\left[\mathrm{Standard}\right]\right)\:$

$\mathrm{Units}\left[\mathrm{UseSystem}\right]\left('\mathrm{Atomic}'\right)$

$\mathrm{Units}\left[\mathrm{UseContexts}\right]\left('\mathrm{Atomic}'\right)$

To enter a unit in 2-D Math input, select the unit from the appropriate Units palette. If the unit you want is not there, select $\mathrm{unit}$ and then enter the unit.

When you edit a unit, double brackets appear around it.

$2.532\mathrm{Unit}\left(\frac{'\mathrm{a0}'}{'s'}\right)$

$2.532⟦\frac{\mathrm{a0}}{s}⟧$

$2.532\mathrm{Unit}\left(\frac{'\mathrm{a0}'}{'s\left[\mathrm{SI}\right]'}\right)$

$2.532⟦\frac{\mathrm{a0}}{s_{\mathrm{SI}}}⟧$

$\mathrm{combine}\left(\,'\mathrm{units}'\right)$

convert/system:   "converting to the units a0/s"

$6.124615111\times {10}^{\mathrm{-17}}⟦\frac{\mathrm{a0}}{s}⟧$

$5\mathrm{Unit}\left(\frac{'\mathrm{em}'{'\mathrm{a0}'}^2}{'s'}\right)$

$5⟦\frac{\mathrm{em}{\mathrm{a0}}^2}{s}⟧$

$\mathrm{convert}\left(\,'\mathrm{system}'\right)$

convert/system:   "converting to the units h_bar"

$5⟦\mathrm{h\_bar}⟧$

$\frac{\mathrm{Unit}\left('s'\right)}{}$

$5⟦\mathrm{E0}⟧$

$\frac{{\mathrm{Unit}\left('\mathrm{a0}'\right)}^2}{}$

$5⟦\frac{\mathrm{em}}{s^2}⟧$

$\mathrm{combine}\left(3.25323\mathrm{Unit}\left('F'\right)\,'\mathrm{units}'\right)$

convert/system:   "converting to the units e^2/E0"

$5.525289547\times {10}^{20}⟦\frac{e^2}{\mathrm{E0}}⟧$

$\frac{\mathrm{Unit}\left('m'\right)}{}$

$2.923857309\times {10}^{10}⟦\mathrm{\κ0}⟧$