216
Appendix A: Physical Constants and Conversion Factors
Atomic Units
Physical constant or observable a.u. value SI unit
Conversion factor from
a.u. to SI
SI to a.u.
Electron mass, m e
1
Elementary charge, e
1
Planck constant, h
2π
Planck constant/2π ()
1
Proton mass, m p
1836.153
Atomic mass constant
1822.888
Bohr radius, a 0
1
Electric constant, ε 0
(4π) −1
Hartree energy, E h
1
Rydberg energy, Ry
1/2
Speed of light
137.035999
Mass
kg 9.109384 · 10 −31 1.097769 · 10 30
Length
Å 0.529177
1.889726
Time
fs 0.02418884
41.341373
Charge
C 1.602177 · 10 −19 6.241509 · 10 18
Dipole
C·m 8.47835 · 10 −30 1.179475 · 10 29
The atomic unit of energy is also called “hartree” and the unit of length, “bohr.”
The Ångström (1Å = 10
−10 m) is one of the most used units for length in molecular
science.
The debye is a CGS unit, also much used in molecular science, equal to 3.33564 ·
10
−30 C·m. The conversion factor from a.u. to debye is 2.541746, and from debye
to a.u. is 0.3934303.
The angular frequency ω in atomic units is numerically equal to the corresponding
energy ω.