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

3. 3 Isotopic Substitution Experimentally, a 13 C atom is systematically substituted in place of a 12 C atom in a molecule. Experimentally, a 13 C atom is systematically substituted in place of a 12 C atom in a molecule. 12 1312 1312

4. 4 Illustration of the comparison between observed and predicted isotopic spectra of the ν 3 (σ u ) mode of linear C 5 c2 c1 c3 2130 2140 2150 2160 Frequency (cm -1 ) Absorbance 90% 12 C / 10% 13 C 12 C 12, v 7 c1c2c3c4c5 Experiment Theory R. Cárdenas experimental spectrum

5. 5 90% 12 C / 10% 13 C Frequency (cm -1 ) C 10, v 6 ? Absorbance ? 2045 2055 2065 2075 C8,v6C8,v6 ? ? ? Illustration of the comparison between observed and predicted isotopic spectra of the ν 5 (σ u ) mode of linear C 9 C9,v5C9,v5 R. Cárdenas experimental spectrum

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

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

8. 8 Frequency (cm -1 ) Absorbance 12 C 12, v 7 2130 2140 2150 2160 90% 12 C / 10% 13 C c2 c1 c3 10% 12 C / 90% 13 C 2080 2090 2100 2110 2120 c2 c1 c3 c1c2c3c4c5 Illustration of the complementary isotopic spectra of the ν 3 (σ u ) mode of linear C 5 90/10 spectrum 10/90 spectrum

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

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

11. 11 13-13-13-13-13 Frequency Application of deperturbation method to isotopic shifts of carbon clusters 12-13-13-13-13 13-12-12-12-12 12-12-12-12-12 10/90 Spectrum90/10 Spectrum

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

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

14. 14 Deperturbation Method Using the previous example of the ν 3 (σ u ) mode of linear C 5, the deperturbation method consists of the following steps: Using the previous example of the ν 3 (σ u ) mode of linear C 5, the deperturbation method consists of the following steps:

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

16. 16 to obtain a 10/90 mirrored simulated spectrum

17. 17 90/10 and mirrored simulated isotopic spectra

18. 18 Simulated isotopic spectra of the ν 3 (σ u ) mode of linear C 5 displayed for the application of the deperturbation method

19. 19 Frequency (cm -1 ) Absorbance 12 C 12,v 7 2130 2140 2150 2160 90% 12 C / 10% 13 C c2 c1 c3 10% 12 C / 90% 13 C 2080 2090 2100 2110 2120 c2 c1 c3 Application of the same linear transformation to the isotopic shifts of the 10/90 experimental spectrum

20. 20

21. 21

22. 22 c1c2c3c4c5

23. 23 Results The deperturbation method has been applied to the interpretation of the isotopic spectra of longer carbon chains like linear C 7 and linear C 9. The deperturbation method has been applied to the interpretation of the isotopic spectra of longer carbon chains like linear C 7 and linear C 9.

24. 24 Absorbance 1998.0 2005 2015 2025 2035 C3C3 C3C3 ? 2078.2 2045 2055 2065 2075 Frequency (cm -1 ) C 10, v 6 C8,v6C8,v6 ? ? ? 10% 12 C / 90% 13 C90% 12 C / 10% 13 C 13 C 9 12 C 9 The ν 5 (σ u ) mode of linear C 9

25. 25 Absorbance 1998.0 1999.1 2000.6 2015.6 2033.1 2005 2015 2025 2035 C3C3 C3C3 ? 2045.9 2048.7 2053.7 2075.7 2077.1 2078.2 2045 2055 2065 2075 Frequency (cm -1 ) C 10, v 6 C8,v6C8,v6 ? ? ? ? 10% 12 C / 90% 13 C90% 12 C / 10% 13 C 13 C 9 12 C 9 c5 c1 c4 c5 c1 c3 c4 c2 The ν 5 (σ u ) mode of linear C 9

26. 26 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. 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.