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 α = 1/137.035 999 11(46).
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 | ℏ | 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][4] | |||
|---|---|---|---|
| Name | Symbol | 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 | current | 27.211 383 86(68) V |
| a.u. magnetic flux density | ℏ/ea02 | magnetic flux density | 2.350 517 382(59) × 105 T |
Here, c = speed of light and α = fine structure constant.[5]
Notes
- ↑ 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.
- ↑ 2.0 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.
- ↑ Volker Schmidt (1997). “§6.1 Atomic units”, Electron spectrometry of atoms using synchrotron radiation. Cambridge University Press, pp. 273 ff. ISBN 052155053X.
- ↑ 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.
- ↑ 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.