constants

Atomic units and constants

All constants taken from CODATA:

http://physics.nist.gov/cuu/Constants/index.html

See also:

http://en.wikipedia.org/wiki/Atomic_units http://en.wikipedia.org/wiki/Natural_units

hbar  = h/(2*pi)
h     = Planck constant
m0    = electron mass
e0    = (electron) unit charge
mu0   = magnetic constant = 4*pi * 1e-7 (exact)
c0    = speed of light (exact)
eps0  = electric field constant (exact)

Bohr radius (also “Bohr” as length unit):

a0 = 4*pi*eps0*hbar**2/(m0*e0**2)

fine structure constant:

alpha = e0**2 / (4*pi*eps0*hbar*c0)

Hartree units

hbar = m0 = e0 = 1
4*pi*eps0 = 1

length:

a0

energy:

Eh = e0**2 / (4*pi**eps0*a0) = alpha**2*m0*c0**2

time (“atomic time unit”):

th = hbar/Eh # J*s/J = s

unit of mass   = m0 = 1
unit of charge = e0 = 1

Rydberg units

hbar = 2*m0 = e0**2/2 = 1
4*pi*eps0 = 1

unit of mass   = 2*m0       = 1
unit of charge = e0/sqrt(2) = 1

In all Hartree-definitions, replace:

e0**2 -> e0**2/2
m0    -> 2*m0

length:

a0 (the same, b/c in a0 formula: m0*e0**2 -> 2*m0*e0**2/2)

energy:

Eryd = e0**2/2 / (4*pi**eps0*a0) = 1/4*alpha**2*2*m0*c0**2
       ^^^^^^^                     ^^^          ^^^^

time:

tryd = hbar/Eryd

m0(Rydberg) = 1/2*m0(Hartree)
Eryd        = 1/2*Eh
tryd = hbar/Eryd = 2*th

Atomic mass unit

amu = 1/12 * mass of C-12 isotope, mass in periodic table * amu = mass [kg]

Useful conversions

pressure:

dyn / cm**2 = 0.1 Pa
1 Mbar      = 100 GPa
1 kbar      = 0.1 GPa

energy/frequency:

1 cm^-1     = 2.998e10 Hz = 0.02998 THz

Ang	Convert a string or number to a floating point number, if possible.
Angstrom	Convert a string or number to a floating point number, if possible.
Bohr	Convert a string or number to a floating point number, if possible.
Bohr_to_Ang	Convert a string or number to a floating point number, if possible.
Eh	Convert a string or number to a floating point number, if possible.
Eryd	Convert a string or number to a floating point number, if possible.
GPa	Convert a string or number to a floating point number, if possible.
Ha	Convert a string or number to a floating point number, if possible.
Ha_to_eV	Convert a string or number to a floating point number, if possible.
Hartree	Convert a string or number to a floating point number, if possible.
J_to_eV	Convert a string or number to a floating point number, if possible.
J_to_rcm	Convert a string or number to a floating point number, if possible.
R	Convert a string or number to a floating point number, if possible.
Ry	Convert a string or number to a floating point number, if possible.
Ry_to_Ha	Convert a string or number to a floating point number, if possible.
Ry_to_Hz	Convert a string or number to a floating point number, if possible.
Ry_to_J	Convert a string or number to a floating point number, if possible.
Ry_to_eV	Convert a string or number to a floating point number, if possible.
Ry_to_rcm	Convert a string or number to a floating point number, if possible.
Rydberg	Convert a string or number to a floating point number, if possible.
a0	Convert a string or number to a floating point number, if possible.
a0_to_A	Convert a string or number to a floating point number, if possible.
alpha	Convert a string or number to a floating point number, if possible.
amu	Convert a string or number to a floating point number, if possible.
avo	Convert a string or number to a floating point number, if possible.
c0	Convert a string or number to a floating point number, if possible.
dyn	Convert a string or number to a floating point number, if possible.
e0	Convert a string or number to a floating point number, if possible.
eV	Convert a string or number to a floating point number, if possible.
eV_by_Ang3_to_GPa	Convert a string or number to a floating point number, if possible.
eV_by_Ang3_to_Pa	Convert a string or number to a floating point number, if possible.
eps0	Convert a string or number to a floating point number, if possible.
fs	Convert a string or number to a floating point number, if possible.
h	Convert a string or number to a floating point number, if possible.
hbar	Convert a string or number to a floating point number, if possible.
hplanck	Convert a string or number to a floating point number, if possible.
kb	Convert a string or number to a floating point number, if possible.
m0	Convert a string or number to a floating point number, if possible.
mu0	Convert a string or number to a floating point number, if possible.
pi	Convert a string or number to a floating point number, if possible.
ps	Convert a string or number to a floating point number, if possible.
rcm_to_Hz	Convert a string or number to a floating point number, if possible.
th	Convert a string or number to a floating point number, if possible.
thart	Convert a string or number to a floating point number, if possible.
tryd	Convert a string or number to a floating point number, if possible.