## Numerics.AtomicUnits

Attachments
Hartree.gif (3231 bytes)
Bohr.gif (3116 bytes)
Planck.gif (1547 bytes)
Coulomb.gif (1384 bytes)

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

Planck's (reduced) constant, electronic mass, elementary charge, and electric constant are set to unity, see the following table

quantity name symbol value
mass electron rest mass me 9.109 382 91(40) E-31 kg
electric charge elementary charge e 1.602 176 565(35) E-19 C
angular momentum Planck's constant 1.054 571 726(47) E-34 Js
electric constant Coulomb constant 8.987 551 787 3681 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 = 1822.9 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 name definition value
length Bohr 52.917721 pm
energy Hartree 4.359744 aJ
Eh/e 27.211384 eV
EhNA 2.6254994 MJ/mol
Eh/kB 315.92349 kK
wavenumber 1/λ=Eh/(hc)=ω/(2πc) 21.947463 1/μ 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 Eh/(ea0) 514.22064 GV/m
light intensity (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=1.380 650 4(24) E-23 J/K is Boltzmann's constant

• NA=6.022 141 79(30) E23 1/mol is Avogadro's number

• α=e2/(4πε0ℏc) = 7.297 352 537 6(50) E-3= 1/137.035 999 679(94) is the fine structure constant (dimensionless)

• note that light intensity is defined as cε0F2/2

• note that dipole moments are sometimes given in units of 1 Debye = 3.33564 aC pm