Numerics.AtomicUnits

Burkhard Schmidt
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Bohr.gif (3116 bytes)
Hartree.gif (2786 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

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) a_0=klzzwxh:0085rac{4klzzwxh:0086iklzzwxh:0087psilon_0klzzwxh:0088bar^2}{m_ee^2}=klzzwxh:0089rac{klzzwxh:0090bar}{m_e klzzwxh:0091lpha c} 52.917721 pm
energy (Hartree unit) E_h=klzzwxh:0079rac{m_e e^4}{(4klzzwxh:0080iklzzwxh:0081psilon_0klzzwxh:0082bar)^2}=klzzwxh:0083lpha^2 m_e c^2 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


Related

Wiki: Demos.MorseOscillator.Main
Wiki: Numerics.Control.Closed
Wiki: Numerics.Main
Wiki: Numerics.Schroedinger