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
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 | m_{e} | 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·m^{3}·s^{-2}·C^{-2} |
where ε_{0}=8.854 187 817 E−12 As/(Vm) is the electric permittivity of vacuum.
Note that the atomic unit of mass (m_{e}) should not be confused with the '''atomic mass unit''' (or Dalton) 1u = 1g/mol = 1/12 m_{12C} = 1822.9 m_{e} frequently used in atomic/molecular physics and in chemistry.
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 | |
E_{h}/e | 27.211384 eV | ||
E_{h}N_{A} | 2.6254994 MJ/mol | ||
E_{h}/k_{B} | 315.92349 kK | ||
wavenumber | 1/λ=E_{h}/(hc)=ω/(2πc) | 21.947463 1/μ m | |
time | ℏ/E_{h} | 24.188843 as | |
frequency | ν = E_{h}/ h | 6.5796839 PHz | |
angular frequency | ω = E_{h}/ ℏ | 41.341373 PHz | |
dipole moment | μ=ea_{0} | 8.4783531 aC pm [ =2.541 746 D ] | |
electric field | E_{h}/(ea_{0}) | 514.22064 GV/m | |
light intensity | (E_{h}/(ea_{0}))^{2}/(8πα) | 35.094 PW/cm^{2} |
where the following constants have been used
c=299792458 m/s is the vacuum speed of light
k_{B}=1.380 650 4(24) E-23 J/K is Boltzmann's constant
N_{A}=6.022 141 79(30) E23 1/mol is Avogadro's number
α=e^{2}/(4πε_{0}ℏc) = 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 cε_{0}F^{2}/2
note that dipole moments are sometimes given in units of 1 Debye = 3.33564 aC pm
Wiki: Numerics.Main
Wiki: Numerics.Schroedinger