Double Harmonic Approximation IR intensties

[DinosaurChemi]

This feels silly asking but I have a question about units using the double harmonic approximation to determine IR spectral intensities. In the double harmonic approximation the intensity is given by
the square of the derivative of the dipole with respect to a normal mode coordinate times a scaling constant. Numerically this can be done by taking let say a 0.01 step along a mass scaled coordinates. The standard units of dipole are debye and mass scaled coordinates are unit-less so total units of debye squared. The scaling factor is Avagadro's constant divided by the speed of light squared. This gets me in units of times² current². Intensities are reported in km/mol. If anyone can give me a little help here I would appreciate it

Again the equation is:

$I=(\frac{\delta \mu}{\delta Q})^{2}\frac{\pi N_{A}}{3c^{2}}$

 

[azntoon]

Where I is the intensity, \mu is the dipole moment, Q is the normal mode coordinate, N_{A} is Avogadro's constant, and c is the speed of light. To convert from debye squared to km/mol, you need to multiply your expression by 6.022x10^23 (Avogadro's constant) and then divide by 3x10^10 (the speed of light squared). This will give you the intensity in km/mol.