Appendix: Useful Equations and Formulas

Conversion factors

dipole moment or transition moment:

1 debye = 3.335 64 × 10^-30 C·m

wavenumber:

1 cm^-1 = 29 979.2458 MHz

pressure:

1 atm = 101 325. Pa (pascal)
1 torr = 133.322 Pa

absorption intensity:

1 cm^-2 atm^-1 at 296 K = 4.033 × 10^-20 cm/molecule

Useful equations:

Boltzmann factor:

N_i = N_j exp(-1.439 E_ij / T),

where N_i is the population of the i^th level and N_j is the population of the j^th level with energy difference in cm^-1 of E_ij at a temperature of T kelvin.

Doppler half-width at half intensity,  _D :

_D = 3.581 × 10^-7 (T/M )^1/2,

where is the frequency in the same units as _D , T is the temperature in kelvin, and M is the mass of the molecule in atomic mass units.

Peak intensity of a Doppler shaped line:

% transmission = 100 exp(-1.1494 × 10¹⁴ Slp/_D),

where S is the intensity given in the tables, l is the pathlength in cm, and p is the pressure in Pa.

Peak intensity of a Lorentzian line:

% transmission = 100 exp(-0.7789 × 10¹⁴ Slp/_L),

where S is the intensity given in the tables, _L is the Lorentzian half-width at half height, l is the pathlength in cm, and p is the pressure in Pa.