Atomic units

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The atomic units, abbreviated a.u. is a set of units used in atomic calculations.[1][2] In the a.u. system any four of the five quantities charge e, mass me, action ℏ, length a0, and energy Eh may be taken as base quantities, and other quantities are derived. In particular, time is a derived quantity, ℏ/Eh, with the interpretation as the period of an electron circling in the first Bohr orbit divided by 2π.[3] Because length is a basic unit, the speed of light is a measured quantity in a.u., c=1/α a.u. of velocity where the (dimensionless) fine structure constant is given by (in SI units):

and has the value:[4]

α =7.297 352 5376(50) × 10-3 = 1/137.035 999 679(94).

Here, e is the elementary charge, ε0 is the electric constant, ℏ is the reduced Planck's constant h/(2π), and c0 is the SI units defined speed of light in vacuum.

Units

Basic atomic units [2]
Name Symbol Quantity Value in SI units
elementary charge e charge 1.602 176 53(14) × 10−19 C
Bohr radius (bohr) a0 length 0.529 177 2108(18) × 10−10 m
electron mass me mass 9.109 3826(16) × 10−31 kg
reduced Planck constant action 1.054 571 68(18) × 10−34 Js
Hartree energy (hartree) Eh energy 4.359 744 17(75) × 10−18 J
Derived atomic units [1][5]
Name Formula Quantity Value in SI units
a.u. velocity vB ≡ αc = a0Eh/ℏ velocity 2.187 691 2633(73) × 106 m/s
a.u. time ℏ/Eh time 2.418 884 326 505(16) × 10−17 s
a.u. current eEh/ℏ current 6.623 617 63(17) × 10−3 A
a.u. electric potential Eh/e electric potential 27.211 383 86(68) V
a.u. magnetic flux density ℏ/ea02 magnetic flux density 2.350 517 382(59) × 105 T
a.u. magnetic dipole moment ℏe/me = 2μB magnetic dipole moment 1.854 801 830(46) × 10−23 J T−1
a.u. permittivity e2/a0Eh = 107/c2 permittivity 1.112 650 056... × 10−10 J T−1 (exact)

Here, c = measured speed of light, α = fine structure constant and μB is the Bohr magneton.[6]

Notes

  1. Jump up to: 1.0 1.1 For an introduction, see Gordon W. F. Drake (2006). “§1.2 Atomic units”, Springer handbook of atomic, molecular, and optical physics, Volume 1, 2nd ed. Springer, p. 6. ISBN 038720802X. 
  2. Jump up to: 2.0 2.1 Tabulated values from (2008) Barry N. Taylor, Ambler Thompson: International System of Units (SI), NIST special publication 330 • 2008 ed. DIANE Publishing, Table 7, p.34. ISBN 1437915582. 
  3. Volker Schmidt (1997). “§6.1 Atomic units”, Electron spectrometry of atoms using synchrotron radiation. Cambridge University Press, pp. 273 ff. ISBN 052155053X. 
  4. fine-structure constant. The NIST reference on constants, units, and uncertainty. NIST. Retrieved on 2011-03-14.
  5. PJ Mohr, BN Taylor, and DB Newell (2008). "CODATA recommended values of the fundamental physical constants: 2006; Table LIII". Rev. Mod. Phys. vol. 80 (No. 2): p. 717.
  6. An overview of the importance and determination of the fine structure constant is found in G. Gabrielse (2010). “Determining the fine structure constant”, B. Lee Roberts, William J. Marciano, eds: Lepton dipole moments. World Scientific, pp. 195 ff. ISBN 9814271837.