Editing Atomic units (section)

== Units ==
Three of the defining constants (reduced Planck constant, elementary charge, and electron rest mass) are atomic units themselves – of [[action (physics)|action]],<ref>{{cite web |title=atomic unit of action |work={{harvnb|CODATA}} |url=http://physics.nist.gov/cgi-bin/cuu/Value?Ahbar }}</ref> [[electric charge]],<ref>{{cite web |title=atomic unit of charge |work={{harvnb|CODATA}} |url=http://physics.nist.gov/cgi-bin/cuu/Value?Ae }}</ref> and [[mass]],<ref>{{cite web |title=atomic unit of mass |url=http://physics.nist.gov/cgi-bin/cuu/Value?Ame |work={{harvnb|CODATA}} }}</ref> respectively. Two named units are those of [[length]] ([[Bohr radius]] {{tmath|1= a_0 \equiv 4 \pi \epsilon_0 \hbar^2 / m_\text{e} e^2 }}) and [[energy]] ([[hartree]] {{tmath|1= E_\text{h} \equiv \hbar^2 / m_\text{e} a_0^2 }}).

{|class="wikitable"
|+ Defined atomic units
|-
!scope="col"| Atomic unit of
!scope="col"| Expression
!scope="col"| Value in SI units
!scope="col"| Other equivalents
|-
| [[charge density|electric charge density]] || <math> e/a_0^3 </math>
| {{physconst|auecd|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of charge density |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?aucd }}</ref>
|
|-
| [[electric current]] || <math> e E_\text{h} / \hbar </math>
| {{physconst|aucur|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of current |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?aucur }}</ref>
|
|-
| [[electric charge]] || <math>e</math>
| {{physconst|auec|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of charge | work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?Ae }}</ref>
|
|-
| [[electric dipole moment]] || <math> e a_0 </math>
| {{physconst|auedm|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of electric dipole moment |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?auedm }}</ref>
| {{math|≘}} {{val|2.541746473|u=[[debye|D]]}}
|-
| [[electric quadrupole]] moment || <math> e a_0^2 </math>
| {{physconst|aueqm|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of electric quadrupole moment |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?aueqm }}</ref>
|
|-
| [[electric potential]] || <math> E_\text{h} / e </math>
| {{physconst|auepot|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of electric potential |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?auep }}</ref>
| 
|-
| [[electric field]] || <math>E_\text{h} / e a_0 </math>
| {{physconst|auef|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of electric field |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?auefld }}</ref>
| 
|-
| [[electric field gradient]] || <math>E_\text{h} / e a_0^2 </math>
| {{physconst|auefg|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of electric field gradient |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?auefg }}</ref>
|
|-
| [[permittivity]] || <math> e^2 / a_0 E_\text{h} </math>
| {{physconst|auperm|ref=no}}&nbsp;<ref name="auperm">
  {{cite web |title=atomic unit of permittivity |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?auperm }}</ref>
| {{tmath|1= 4 \pi \epsilon_0 }}
|-
| [[electric polarizability]] || <math> e^2 a_0^2 / E_\text{h} </math>
| {{physconst|auepol|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of electric polarizability |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?auepol }}</ref>
|
|-
| 1st [[hyperpolarizability]] || <math>e^3 a_0^3 / E_\text{h}^2</math>
| {{physconst|au1hypol|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of 1st hyperpolarizability | work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?auhypol }}</ref>
|
|-
| 2nd hyperpolarizability || <math>e^4 a_0^4 / E_\text{h}^3</math>
|{{physconst|au2hypol|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of 2nd hyperpolarizability | work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?au2hypol }}</ref>
|
|-
| [[magnetic dipole moment]] || <math> \hbar e / m_\text{e} </math>
| {{physconst|aumdm|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of magnetic dipole moment |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?aumdm }}</ref>
| {{tmath|1= 2 \mu_\text{B} }}
|-
| [[magnetic flux density]] || <math> \hbar/e a_0^2 </math> 
| {{physconst|aumfd|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of magnetic flux density |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?aumfd }}</ref>
| {{math|≘}} {{val|2.3505|e=9|ul=G}}
|-
| [[magnetizability]] || <math> e^2 a_0^2 / m_\text{e}</math>
| {{physconst|aumag|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of magnetizability |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?aumag }}</ref>
|
|-
| [[action (physics)|action]] || <math>\hbar</math>
| {{physconst|auact|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of action | work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?Ahbar }}</ref>
|
|-
| [[energy]] || <math> E_\text{h} </math>
| {{physconst|auener|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of energy |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?Ahr }}</ref>
| {{tmath|1= 2 h c R_\infty }}, {{tmath|1= \alpha^2 m_\text{e} c^2 }}, {{val|27.211386245988|(53)|ul=eV}}&nbsp;<ref>
  {{cite web |title=Hartree energy in eV |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?hrev }}</ref>
|-
| [[force]] || <math>E_\text{h} / a_0 </math>
| {{physconst|auforce|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of force |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?auforce }}</ref>
| {{val|82.387|u=nN}}, {{val|51.421|u=eV·Å<sup>−1</sup>}}
|-
| [[length]] || <math> a_0 </math>
| {{physconst|aulen|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of length |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?Abohrrada0 }}</ref>
| {{tmath|1= \hbar / \alpha m_\text{e} c }}, {{val|0.529177|ul=Å}}
|-
| [[mass]] || <math>m_\text{e}</math>
| {{physconst|aumass|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of mass |work={{harvnb|CODATA}} |
    url=http://physics.nist.gov/cgi-bin/cuu/Value?Ame }}</ref>
|
|-
| [[momentum]] || <math> \hbar/a_0 </math>
| {{physconst|aumom|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of momentum |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?aumom }}</ref>
|
|-
| [[time]] || <math>\hbar / E_\text{h}</math>
| {{physconst|autime|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of time |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?aut }}</ref>
|
|-
| [[velocity]] || <math> a_0 E_\text{h} / \hbar </math>
| {{physconst|auvel|ref=no}}&nbsp;<ref>
  {{cite web |title=atomic unit of velocity |work={{harvnb|CODATA}}
    |url=http://physics.nist.gov/cgi-bin/cuu/Value?auvel }}</ref>
| {{tmath|1= \alpha c }}
|-
| colspan=4 | 
{{tmath|1= c }}:&nbsp;[[speed&nbsp;of&nbsp;light]],
{{tmath|1= \epsilon_0 }}:&nbsp;[[vacuum&nbsp;permittivity]],
{{tmath|1= R_\infty }}:&nbsp;[[Rydberg&nbsp;constant]],
{{tmath|1= h }}: [[Planck constant]],
{{tmath|1= \alpha }}:&nbsp;[[fine-structure&nbsp;constant]],
{{tmath|1= \mu_\text{B} }}:&nbsp;[[Bohr&nbsp;magneton]],
{{math|≘}}:&nbsp;''correspondence''
|-
|}