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 halfwidth at half intensity, γ_{D} :
γ_{D} = 3.581 × 10^{7} ν (T/M )^{1/2},
where ν is the frequency in the same units as γ_{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 × 10^{14} Slp/γ_{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 × 10^{14} Slp/γ_{L}),
where S is the intensity given in the tables, γ_{L} is the Lorentzian halfwidth at half height, l is the pathlength in cm, and p is the pressure in Pa.
