Numerics.AtomicUnits
All WavePacket codes are using atomic units throughout. These units are adapted to the classical Bohr model of the hydrogen atom in its ground state, orbiting the hydrogen nucleus, see also the corresponding article in Wikipedia
Fundamental atomic units
In atomic units, Planck's (reduced) constant, electron rest mass, elementary charge, and the Coulomb constant are normalized to unity, see the following table
| quantity | name | symbol | value |
|---|---|---|---|
| mass | electron rest mass | me | 9.109 382 15(45) E-31 kg |
| electric charge | elementary charge | e | 1.602 176 6208(98) E-19 C |
| angular momentum | Planck's constant | ℏ = h/(2π) | 1.054 571 800(13) E-34 Js |
| electric constant | Coulomb constant | ke = 1/(4πε0) | 8.987 551 787 3682 E9 kg·m3·s-2·C-2 |
where ε0 = 8.854 187 817 E−12 As/(Vm) is the electric permittivity of vacuum.
Note that the atomic unit of mass (me) should not be confused with the '''atomic mass unit''' (or Dalton) 1u = 1g/mol = 1/12 m12C = 1822.88839 me frequently used in atomic/molecular physics and in chemistry.
Derived atomic units
This allows to derive the atomic units for all other quantities used in the WavePacket software, see the following table
| quantity | definition | value |
|---|---|---|
| length (Bohr unit) |  |
52.917721 pm |
| energy (Hartree unit) |  |
4.359744 aJ |
| energy (electric potential) | Eh/e | 27.211384 eV |
| energy (per amount of material) | EhNA | 2625499.4 J/mol |
| temperature | Eh/kB | 315774.6 K |
| wavenumber | 1/λ = Eh/(hc) = ω/(2πc) | 21947463 1/m |
| time | ℏ/Eh | 24.188843 as |
| frequency | ν = Eh/ h | 6.5796839 PHz |
| angular frequency | ω = Eh/ ℏ | 41.341373 PHz |
| dipole moment | μ = ea0 | 8.4783531 aC pm [ =2.541 746 D ] |
| electric field: F | Eh/(ea0) | 514.22064 GV/m |
| light intensity: cε0F2/2 | (Eh/(ea0))2/(8πα) | 35.094 PW/cm2 |
where the following constants have been used
-
c = 299792458 m/s is the vacuum speed of light
-
kB = 1.380 648 52(79) E-23 J/K is Boltzmann's constant
-
NA = 6.022 140 857(74) E23 1/mol is Avogadro's number
-
α = e2/(4πε0ℏc) = 7.297 352 5664(17) E-3 = 1/137.035 999 139(31) is the fine structure constant (dimensionless)
-
note that dipole moments are sometimes given in units of 1 Debye = 1E-21 Cm / c = 3.33564 aC pm
Related
Wiki: Demos.MorseOscillator.Main
Wiki: Numerics.Control.Closed
Wiki: Numerics.Main
Wiki: Numerics.Schroedinger