[anvoice]

Hello,

I am trying to analyze an FTIR spectrum of an HCL/DCl mixture. I'm trying to examine the relative peak intensities for one of the isotopes (H35Cl). The predicted relative spectral intensities can be compared to predicted values by a formula like

I(J1)/I(J2) proportional to (((J1 + 1)/(2J1+1)) * (2J+1) * exp(-T(v,J)/kT))
                                                  / (((J2 + 1)/(221+1)) * (2J+1) * exp(-T(v,J)/kT))     for the R branch

and

I(J1)/I(J2) proportional to ((J1/(2J1+1)) * (2J1+1)) * exp(-T(v,J)/kT) )
                                                 / ((J2/(2J2+1)) * (2J2+1)) * exp(-T(v,J)/kT) )           for the P branch

which if I understand correctly give the relative populations, N(J1)/N(J2) in each state. I'm not sure why it's "proportional to" rather than equal, and also why the (2J + 1)/(2J + 1) is present although it seems to cancel out. I calculated T(v,J) according to the formula

T(v, J) = Ve*(v + ½) -XeVe*(v + ½)^2 + Be*J(J + 1) - De*J^2 (J + 1)^2 - Alpha(e)*(v + ½)*J(J + 1)

from my experimentally obtained parameters for Ve, Ve, De, and Alpha(e) (all of which are very close to literature values), and converted them from wavenumbers (cm-1) to Joules to match the units of kT. However, when I calculated the ratios of the value from one of the first 2 formulas to my observed I(J1)/I(J2), they weren't nearly as constant as I would expect. These are the last columns in the table, after the experimental values/constants.

Vo           2885.928869      h   6.63E-34          T   298        kT   4.11E-21      
Alpha(e)   0.303069792      k   1.38E-23                  
Be           10.59105319      c   3.00E+08                  
De           0.00521708                     
Ie           2.64384E-47                           
Re           1.27485E-10                           
Ve           2990.028869                           
XeVe           52.05                           


v(cm-1)   Intensity   m   j   E(cm-1)   E(J)            ~Nj              Nj/Nj-1      I(j)/I(j-1)   the ratio
3097.649   0.01061   13   12   5.94E+03   1.18E-19   4.64E-12      3.41E-01   4.32E-01   7.88E-01
3085.596   0.02454   12   11   5.70E+03   1.13E-19   1.36E-11      3.77E-01   4.72E-01   7.98E-01
3072.819   0.05197   11   10   5.48E+03   1.09E-19   3.61E-11      4.18E-01   6.06E-01   6.89E-01
3059.26   0.08581   10   9   5.28E+03   1.05E-19   8.65E-11      4.64E-01   6.15E-01   7.55E-01
3045.037   0.13963   9   8   5.10E+03   1.01E-19   1.87E-10      5.17E-01   6.69E-01   7.73E-01
3030.031   0.20885   8   7   4.93E+03   9.80E-20   3.61E-10      5.78E-01   6.74E-01   8.58E-01
3014.362   0.30985   7   6   4.79E+03   9.52E-20   6.25E-10      6.50E-01   7.31E-01   8.89E-01
2998.03   0.42408   6   5   4.67E+03   9.28E-20   9.61E-10      7.37E-01   7.97E-01   9.24E-01
2980.975   0.53218   5   4   4.57E+03   9.08E-20   1.30E-09      8.46E-01   8.74E-01   9.68E-01
2963.257   0.60901   4   3   4.49E+03   8.92E-20   1.54E-09      9.94E-01   9.69E-01  1.03E+00
2944.875   0.62854   3   2   4.43E+03   8.80E-20   1.55E-09      1.23E+00   1.15E+00 1.08E+00
2925.892   0.54878   2   1   4.39E+03   8.72E-20   1.26E-09      1.81E+00   1.33E+00 1.36E+00
2906.245   0.41224   1   0   4.37E+03   8.68E-20   6.94E-10            
R branch ends                                                          Nj/Nj+1   I(j)/I(j+1)   the ratio
2865.084   0.41394   -1   1   4.39E+03   8.72E-20   6.29E-10      6.08E-01   7.77E-01   7.82E-01
2843.569   0.53244   -2   2   4.43E+03   8.80E-20   1.03E-09      8.94E-01   9.21E-01   9.70E-01
2821.512   0.5779   -3   3   4.49E+03   8.92E-20   1.16E-09      1.11E+00   1.03E+00 1.08E+00
2798.912   0.56218   -4   4   4.57E+03   9.08E-20   1.04E-09      1.30E+00   1.21E+00 1.08E+00
2775.71   0.46589   -5   5   4.67E+03   9.28E-20   8.01E-10      1.50E+00   1.29E+00 1.16E+00
2752.026   0.36024   -6   6   4.79E+03   9.52E-20   5.35E-10      1.69E+00   1.41E+00 1.20E+00
2727.739   0.25579   -7   7   4.93E+03   9.80E-20   3.16E-10      1.90E+00   1.48E+00 1.28E+00
2702.97   0.17241   -8   8   5.10E+03   1.01E-19   1.66E-10      2.13E+00   1.48E+00 1.44E+00
2677.719   0.11656   -9   9   5.28E+03   1.05E-19   7.79E-11      2.37E+00   1.61E+00 1.47E+00
2651.925   0.07237   -10   10   5.48E+03   1.09E-19   3.28E-11      2.63E+00   2.03E+00 1.30E+00
2625.709   0.03561   -11   11   5.70E+03   1.13E-19   1.25E-11      2.92E+00   2.29E+00 1.27E+00
2599.012   0.01555   -12   12   5.94E+03   1.18E-19   4.28E-12            
P branch ends

Question: could anyone perhaps point out an error in my formulas/understanding that might be leading to this, or perhaps the Boltzmann approximation in this case isn't accurate enough to give constant ratios, or using peak heights instead of areas (more closely related to intensity) typically gives such results? I've been struggling with this for a while, so I'd appreciate any hints or advice.

Thank you,
Anvoice

[Ross]

Hi,

I was wondering if anyone could help me with some simple FTIR stuff? I have been asked to do a bit of FTIR work for a side project but I am very new to this and any help would be much appreciated.

I have 5 different graphs of the same material for the absorption spectrum's ranging from 1400-400cm-1.

The results display the same generalised peaks/shoulders as I had expected however there is some slight variations in the absorptions recorded. I would thus like to know how to normalise the results to compensate for this? I have read a similar post about normalising using the "peak ratios" however it wasn't explained enough for me. I am examining the results in MS Excel and thus cannot use the FTIR software to do this for me.

If someone could explain how to normalise these results for me it would be very much appreciated! Lastly, I have read papers that show their graphs as either the absorption or relative intensity vs Wavenumber (Cm-1) - would I be right in thinking that absorption and relative intensity are essentially the same thing?

Thanks

Ross