harmonic and combination analysis

[Leeser]

Hi all,

I wish to inspect InfraRed spectra and determine/assign the fundamental vibrational frequencies. Once this is done I wish to pick a peak in the spectrum and return a list of suggested possible combinations and overtones of the previously assigned vibrational frequencies and add this new one to the list to check on next iteration.

 eg some pseudo code:

v1=100

v2=350

v3=500

v4=600

vibration at 800

suggestions:

2v2+1v1

3v1+v3

v5

pick v5 (ie a fundamental vibration in its own right and not a combination of fundamentals)

vibration at 1400

suggestions:

v4+v5

2v2+1v1+v4

3v1+v3+v4

v6

pick v4+v5

etc

Has anybody any suggestions about how to check all combinations of numbers upto a certain value?

Regards,

Leeser

[DFGray]

This particular problem is difficult and whole toolkits have been developed around doing this sort of thing (check out the National Instruments Sound and Vibration Analysis System, for example, which includes a variety of octave and harmonic analysis tools).  It may help to look at how the spectrum was created to give you an idea of what is possible.  For example, if you used a broadband IR source to generate an absorption spectrum, multi-photon events will be unlikely.  Swept laser excitation could change this dramatically.  If you are looking at excitation spectra, similar issues occur.

How many lines does your typical spectrum have?  This is a factorial level problem, so more than a few will rapidly overwhelm you with possibilities.  Brute force may or may not work.  Knowing the physics behind the process can help you pare it down by using probabilities and peak heights.

Good luck!

[Leeser]

Thanks for the reply. I remember a post-doc in my group when I was doing my PhD had an interactive program written in Pascal (or was it Fortran?!) but didn't manage to swipe a copy of the exe file when finished. I think it was a brute force program that tried the harmonics first and then went to combinations.  Basically, we assigned vibrations as we picked peaks and suggestions were made, ultimately though the user selected a combination or a new vibration. I don't think there was any regard for the symmetry of the vibration and whether the harmonics/combinations would be allowed or not (ie overall sym must contain the sym of an IR active mode, eg a1,b1,b2 in C2V symmetry group). Obviously the more additions of modes the lower the probability so a cut off of number of combining elements could reduce the work load. We have broadband IR and NIR sources but also have the capability for laser excitation and multiphoton processes eg REMPI. The number of lines would be on the order of maybe 30 - 40. I will look at the sound and vibration toolkit and maybe bodge something together from that and go from there if successful.

Cheers.