1. Ethane International Symposium on Molecular Spectroscopy 64th Meeting June 22-26, 2009 U.A.M.-I María Villa Villa Ricardo Hidalgo Olguín DAMIR-C.S.I.C (Madrid) Ma. Luisa Senent Diez

2. Ethane Ĥ rot-int θ Ĥ vib

3. Ethane #MP2/aug-cc-pVTZ r C-H1.095 Å r C-C1.542 Å 1.554 Å  H-C-H 107.837º107.312º  H-C-C 111.065º 111.554º   60º 0º  E(cm -1 )0 1011.134

4. Ethane Ethane characteristic frequencies (cm -1 ) #MP2/aug-cc- pVTZ Experimental Rotatión317.1519288 C-C1026.4447994 Symm C-H3072.70652968 Antisymm C-H3074.55603042 Frecuencias caracteristicas del etano

5. Ethane Ĥ = Ĥ rot-ext + Ĥ rot-int + Ĥ vib

6. Ethane Bidemensional S i, θ potential

7. Ethane Potential scan   = 10° (0-60)  C-C = 0.0050 A° (8±)  C-H = 0.0025 A° (8±)

8. Ethane Internal Rotation potential 500.054 + 505.081 Cos 3θ + 5.4539 Cos 6θ + 0.47624 Cos 9θ

9. Ethane C-C stretching Potential cm -1 θ 01.7679x+36.7953x 2 -1.0969x 3 101.7987x+36.8214x 2 -1.0974x 3 201.7415x+36.8909x 2 -1.1015x 3 301.7383x+36.9812x 2 -1.1029x 3 400.2898x+37.1498x 2 -1.1113x 3 500.0084x+37.1989x 2 -1.1118x 3 600.8080x+37.1855x 2 -1.1119x 3 Cos 3θ Cos 6θ Cos 9θ x 1.0821 1.0155 -0.0188 -0.5217 x 2 37.0038 -0.2170 -0.0036 0.0214 x 3 -1.1048 0.0082 0.0001 -0.0007

10. Ethane

11. C-C Stretching spectra cm -1 30º00ºCoupled 0.0000 0.0064 0.0065 0.0064 0.0065 282.4849 282.1226 1020.00 1018.00 1020.00

12. Ethane C-H symmetric stretching Potential cm -1 θ 00.6266 x + 315.6833 x 2 - 11.4143 x 3 103.0082 x + 315.6554 x 2 - 11.4385 x 3 203.1231 x + 315.2141 x 2 - 11.4112 x 3 302.2313 x + 314.5991 x 2 - 11.3830 x 3 401.1387 x + 313.9756 x 2 - 11.3718 x 3 500.7496 x + 313.5721 x 2 - 11.3490 x 3 603.4795 x + 313.1965 x 2 - 1 1.3512 x 3 Cos 3θ Cos 6θ Cos 9θ x -0.6266 -1.7397 1.6575 -0.0955 x 2 314.5661 1.2261 -0.0666 0.0055 x 3 -11.3886 -0.0411 0.0009 0.0043

13. Ethane

14. C-H Symmetric spectra cm -1 60º30º00ºcoupled 0.0000 …………………. ………. ……….. 282.4849 283.5480 :.:. 3000.7245 3006.0705 3011.8113 3006.1845 3000.7309 3006.0769 3011.8178 3006.1903 3000.7309 3006.0769 3011.8178 3006.1903

15. Ethane C-H anti-symmetric potential cm -1 θ 0-4.0829x10 -13 +315.7138 x 2 +5.3226 x 10 -13 10-4.0829x10 -13 +315.8564 x 2 +5.3226 x 10 -13 20-4.0829x10 -13 +315.8007 x 2 +5.3226 x 10 -13 30-4.0829x10 -13 +315.5397 x 2 +5.3229 x 10 -13 40-3.8634x10 -13 +314.3069 x 2 +5.3243 x 10 -13 50-4.0829x10 -13 +314.0071 x 2 +5.3248 x 10 -13 60-4.0829x10 -13 +313.7660 x 2 +5.3251 x 10 -13 cos 3θ cos 6θ cos 9θ x -4.0464 x 10 -13 -4.3899 x 10 -15 -3.6583 x 10 -15 6.5849 x 10 -15 x 2 315.0424 1.1154 -0.3060 -0.1653 x 3 5.3235 x 10 -13 -1.3505 x 10 -16 4.0242 x 10 -17 1.2867 x 10 -17

16. Ethane

17. 60º30º0.0ºACOPLADO 0.0000 0.0064 0.0062 0.0064 0.0062 282.4849 283.7226 282.4849 283.7226 282.7376 283.9679 533.3629 535.8566 :.:. 3039.4455 3048.6993 3049.5402 3040.8672 3039.4519 3048.7058 3049.5466 3040.8730 3039.4519 3048.7058 3049.5466 3040.8730 C-H anti-symmetric spectra cm -1

18. Ethane

19. 1)N. Moazzen-Ahmadi, H.P. Gush, M. Halpern, H. Jagannath, A. Leung, and Ozzier. J. Chem. Phys., 88 No. 2, (1988) 563. 2)D. Bermejo, J. Santos, P. Cancio, J.M. Fernandez-Sanchez, and S. Montero. J. Chem. Phys., 97 No. 10, (1992) 7055. 3)J.M. Fernandez-Sanchez, and S. Montero. J. Chem. Phys., 118 No. 6, (2003) 2657. 4)G.E. Hansen, D.M. Dennison, J. Chem. Phys. 20 (1951) 313 *L.M. Sverdlov, M.A. Kovner and E. P. Krajnov, Kolebatelnyje spektry mnogoatomnych molekul (Nauka, Moscow, (1970). Armónic #MP2/aug- cc-pVTZ Our method cm -1 Experimental cm -1 Rotación317.1519282.3793288(1),278* C-C1026.44471020.6801994(2),993* C-H Symmetric3072.70653006.19032968.69 (3),2915* C-H Anti-symmetric3074.55603040.873030042.8 (4),2950

20. Ethane Conclusions This method is a propper formalism to introduce the interaction of the normal modes of vibration from the internal rotational variable in the case of non-rigid molecules

21. Ethane Comments It will be interesting to study 1)The umbrella motion which can be more θ dependent. 2)It must be consider a three dimentional potential considering the symmetric C-H and C-H anti-symmetric stretchings.

22. Ethane Thank you for your attention