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A Deperturbation Method to Aid in the Interpretation of Infrared Isotopic Spectra

A Deperturbation Method to Aid in the Interpretation of Infrared Isotopic Spectra. G. Garcia and C. M. L. Rittby Texas Christian University Fort Worth, TX 76129 June 20, 2007. Introduction.

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A Deperturbation Method to Aid in the Interpretation of Infrared Isotopic Spectra

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  1. A Deperturbation Method to Aid in the Interpretation of Infrared Isotopic Spectra G. Garcia and C. M. L. Rittby Texas Christian University Fort Worth, TX 76129 June 20, 2007

  2. Introduction • Identification of new molecular species based on the comparison between observed and predicted vibrational fundamentals and isotopic shifts. • Linear carbon chains represent one group of molecules under study.

  3. 13 12 12 12 12 12 12 13 12 Isotopic Substitution • Experimentally, a 13C atom is systematically substituted in place of a 12C atom in a molecule.

  4. 90% 12C / 10% 13C c1 c2 c3 c4 c5 c1 Absorbance c2 12C12,v7 c3 Experiment Theory 2130 2140 2150 2160 Frequency (cm-1) Illustration of the comparison between observed and predicted isotopic spectra of the ν3(σu) mode of linear C5 R. Cárdenas experimental spectrum

  5. Illustration of the comparison between observed and predicted isotopic spectra of the ν5(σu) mode of linear C9 C10,v6 ? C9,v5 90% 12C / 10% 13C ? ? Absorbance C8,v6 ? ? R. Cárdenas experimental spectrum 2045 2055 2065 2075 Frequency (cm-1)

  6. The method of isotopic substitution introduces interactions between vibrational modes. • Strength of the interactions increases as the separation between vibrational fundamentals decreases.

  7. Carbon Chains • Long carbon chains have a larger number of stretching modes with near-lying fundamental frequencies. • Therefore, their vibrational modes experience stronger interactions upon isotopic substitution.

  8. c1 c2 c3 c4 c5 2080 2090 2100 2110 2120 2130 2140 2150 2160 Illustration of the complementary isotopic spectra of the ν3(σu) mode of linear C5 10% 12C / 90% 13C 90% 12C / 10% 13C 10/90 spectrum 90/10 spectrum c1 c1 c2 c2 Absorbance c3 c3 12C12,v7 Frequency (cm-1)

  9. Deperturbation Model • Two-level system • Energies described to 2nd order in perturbation theory • System can be subjected to a positive or a negative perturbation: Negative perturbation Positive perturbation

  10. unperturbed energies energies to 1st order energies to 2nd order

  11. Application of deperturbation method to isotopic shifts of carbon clusters 10/90 Spectrum 90/10 Spectrum 13-13-13-13-13 12-12-12-12-12 13-12-12-12-12 12-13-13-13-13 Frequency

  12. Diagram representing 12C and 13C isotopic shifts to second order in perturbation theory all 13C all 12C 2nd order 2nd order 1st order Frequency

  13. Average frequency 1st order Diagram representing the reduction of coupling effects exhibited by 12C and 13C isotopic shifts all 13C all 12C

  14. Deperturbation Method • Using the previous example of theν3(σu) mode of linear C5 , the deperturbation method consists of the following steps:

  15. Application of a linear transformation that mirrors the simulated 10/90 spectrum

  16. to obtain a 10/90 mirrored simulated spectrum

  17. 90/10 and mirrored simulated isotopic spectra

  18. Simulated isotopic spectra of theν3(σu)mode of linear C5 displayed for the application of the deperturbation method

  19. Application of the same linear transformation to the isotopic shifts of the 10/90 experimental spectrum 10% 12C / 90% 13C 90% 12C / 10% 13C c1 c1 c2 c2 Absorbance c3 c3 12C12,v7 2080 2090 2100 2110 2120 2130 2140 2150 2160 Frequency (cm-1)

  20. c1 c2 c3 c4 c5

  21. Results • The deperturbation method has been applied to the interpretation of the isotopic spectra of longer carbon chains like linear C7 and linear C9.

  22. 10% 12C / 90% 13C 90% 12C / 10% 13C The ν5(σu) mode of linear C9 13C9 C10,v6 12C9 C3 1998.0 2078.2 ? ? Absorbance C8,v6 ? C3 ? 2045 2055 2065 2075 2005 2015 2025 2035 Frequency (cm-1)

  23. 10% 12C / 90% 13C 90% 12C / 10% 13C The ν5(σu) mode of linear C9 c1 13C9 c1 C10,v6 12C9 C3 1998.0 2078.2 c2 c2 ? 1999.1 2077.1 ? 2048.7 ? c3 c3 Absorbance c4 C8,v6 c4 2000.6 c5 2015.6 2053.7 c5 2075.7 ? 2033.1 2045.9 C3 ? 2045 2055 2065 2075 2005 2015 2025 2035 Frequency (cm-1)

  24. Conclusions • The deperturbation method can be applied to interpret isotopic spectra by comparing the effects of the interactions between vibrational modes exhibited by the experimental and predicted isotopic shifts.

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