1. Some interstellar molecules: ab initio theory, laboratory spectroscopy and (radio) astronomy PETER BOTSCHWINA Institut für Physikalische Chemie Universität Göttingen, Tammannstraße 6 D-37077 Göttingen, Germany

2. H. S. P. Müller, F. Schlöder, J. Stutzki and G. Winnewisser, J. Mol. Struct. 742, 215 (2005).

3. Among the ca. 140 different molecules found in the interstellar medium (ISM) carbon chains present the dominating structural motif. These are often very reactive and difficult to investigate in the laboratory. During the past three decades, the identification and characterisation of interstellar molecules has often benefitted from a fruitful interplay between theoretical chemistry, laboratory spectroscopy and (radio) astronomy.

4. Contents of lectures I.Overview of work on cyanopolyynes (HC 2n+1 N) and related species II.Interstellar cations III.Heterocumulenic chains IV.Pure carbon chains C n

5. CYANOPOLYYNES (HC 2n+1 N) Almost ubiquituous in the ISM and CSM Provide largest (in terms of number of atoms) interstellar molecule unambiguously detected by radio astronomy HC 11 N Through the presence of low-lying bending vibrational states observable by radio astronomy in excited vibrational states  important information on dynamical processes

6. Chemically, cyanopolyynes are linear molecules with conjugated triple bonds, an energetically very stable situation (once formed). Organic chemists call the cyano group a strong “electron withdrawing group“, which has the astronomically important consequence that cyanopolyynes have rather large electric dipole moments. Already for cyanoacetylene (HC 3 N), the experimental ground-state dipole moment is as large as  0 = 3.72 D

7. recommended method: combination of experimental and theoretical data exp.: B 0 values for various (as many as possible) isotopomers theor.:  B 0 = B e - B 0 calculated from high-quality ab initio cubic force fields (e.g., CCSD(T) with large basis set) (α i from 2 nd order perturbation theory)  i : vibration-rotation coupling constant d i : degeneracy factor of vibrational mode i Cyanopolyynes: demanding cases for accurate equilibrium structure determinations

8. Equilibrium structure for HC 3 N [1] P. Botschwina, M. Horn, S. Seeger and J. Flügge, Mol. Phys. 78, 191 (1993). [2] P. Botschwina, Mol. Phys. 103, 1441 (2005).

9. D 12 C 5 15 N J = 43  42 (*) Millimeter-wave spectroscopy of rare isotopomers of HC 5 N and DC 5 N: determination of a mixed experimental-theoretical equilibrium structure for cyanobutadiyne L. Bizzocchi, C. Degli Esposti and P. Botschwina J. Mol. Spectrosc. 225, 145 (2004)

10. HC 5 N isotopomers: spectroscopic constants from MMW spectroscopy

11. * P. Botschwina, Ä. Heyl, M. Oswald and T. Hirano, Spectrochim. Acta A 53, 1079 (1997). Equilibrium structures for HC 5 N

12. Geometric structures for linear HC 11 N r 0 structure a r e estimate b CCSD(T)/cc-pVTZ c r e structure c (recommended) r (HC (1) )/Å1.057(1)1.06271.06431.0625 R 1 (C (1) C (2) )/Å1.210(1)1.21041.21691.2105 R 2 (C (2) C (3) )/Å1.360(1)1.36371.36951.3635 R 3 (C (3) C (4) )/Å1.218(2)1.21781.22461.2182 R 4 (C (4) C (5) )/Å1.351(3)1.35641.36161.3556 R 5 (C (5) C (6) )/Å1.217(5)1.21871.22671.2203 R 6 (C (6) C (7) )/Å1.360(8)1.35711.36011.3541 R 7 (C (7) C (8) )/Å1.219(6)1.21531.22611.2197 R 8 (C (8) C (9) )/Å1.350(3)1.36951.36241.3564 R 9 (C (9) C (10) )/Å1.217(2)1.21531.22191.2155 R 10 (C (10) C (11) )/Å1.365(1)1.36951.37531.3693 R 11 (C (11) N)/Å1.161(1)1.16201.16891.1620 a M. C. McCarthy, E. S. Levine, A. J. Apponi and P. Thaddeus, J. Mol. Spectrosc. 203 (2000) 75. Statistical uncertainties (1  ) in terms of the last significant digit are given in parentheses. b See above reference. c P. Botschwina, Phys. Chem. Chem. Phys. 5 (2003) 3337.

13. HC 11 N: Variation of CC equilibrium bond lengths

14. HC 11 N: a story of lost and found 1982 and 1985: weak radio lines observed in IRC+10216 and TMC-1 attributed to HC 11 N (without accurate laboratory data at hand) For more than 10 years no confirmation of assignments successful 1996: FT-MW spectroscopy of HC 11 N by Thaddeus and coworkers (Harvard University); 20 rotational transitions measured spectroscopic constants not compatible with previous assignments of radio lines M. J. Travers, M. C. McCarthy, P. Kalmus, C. A. Gottlieb and P. Thaddeus, Astrophys. J. 469 (1996) L65. 1997: detection of rotational transitions J = 39  38 and 38  37 by means of NRAO 43 m telescope M. B. Bell, P. A. Feldman, M. J. Travers, M. C. McCarthy, C. A. Gottlieb and P. Thaddeus, Astrophys. J, 483 (1997) L61.

17. Dipole moments and column densities of cyanopolyynes (HC 2n+1 N) in TMC-1 a Molecule  (D) N (10 11 cm -2 ) HC 5 N4.33 b 330 HC 7 N4.82 c 110 HC 9 N5.20 c 19 HC 11 N5.47 c 2.8 a M. B. Bell et al., Astrophys. J. 483, L61 (1997). b A. J. Alexander et al., J. Mol. Spectrosc. 62, 175 (1976). c P. Botschwina (1997), unpublished. See also: P. Botschwina, in: Jahrbuch der Akademie der Wissenschaften zu Göttingen 2002

18. Vibrationally excited molecules in “hot cores”: centres of star formation: HC 3 N as a probe for highly excited gas rotational transitions within 11 different excited states observed F. Wyrowski, P. Schilke and C. M. Walmsley, Astron. Astrophys. 341, 882 (1999).

19. SpectroscopicCCSD(T)SpectroscopicCCSD(T) constantcc-pVQZexp.constantcc-pVQZexp.  1 /cm -1 3452  5 /MHz -1.714 -1.563 b  2 /cm -1 2316  6 /MHz -9.233 -9.256  3 /cm -1 2111  7 /MHz -14.389-14.455  4 /cm -1 879q 5 /MHz 2.419 2.538  5 /cm -1 671q 6 /MHz 3.498 3.582  6 /cm -1 501q 7 /MHz 6.394 6.538  7 /cm -1 223 /Hz -1.052 -1.331  1 /MHz 7.030 7.331 b /Hz -1.770 -2.063  2 /MHz 21.58921.572 /Hz-15.516-16.291  3 /MHz 13.76713.895 /kHz 0.506 0.544 a  4 /MHz 10.447 11.100 b a Ground-state value b Deperturbed values from approximate deperturbation procedures Characterisation of vibrationally excited states of HC 3 N

20. Millimeter-wave spectroscopy of HC 5 N in vibrationally excited states below 500 cm -1 K. M. T. Yamada, C. Degli Esposti, P. Botschwina, P. Förster, L. Bizzocchi, S. Thorwirth, and G. Winnewisser Astron. Astrophys. 425 (2004) 767.

21. Calculated a and experimental spectroscopic constants for low-lying singly excited bending vibrational states of HC 5 N a CCSD(T)/cc-pVQZ. Standard 2nd order perturbation theory in normal coordinate space is employed in the calculation of , q t and q t J values. v 11 = 1v 10 = 1v 9 = 1 theor.exp.theor.exp.theor.exp.  (cm -1 ) 106.8 254.0 462.9  (MHz) -2.705-2.786-2.453-2.452-1.594-1.593 q t (MHz) 1.125 1.163 0.490 0.500 0.320 0.329 q t J (Hz)-0.993-1.063-0.176-0.173-0.032-0.039

22. J. Cernicharo, A. M. Heras, J. R. Pardo, A. G. G. M. Tielens, M. Guélin, E. Dartois, R. Neri and L. B. F. M. Waters, Astrophys. J. 546 (2001) L127.

23. Cyanopolyynes: what about isomers? HC 3 N is so far the only interstellar molecule for which two more isomers (HCCNC and HNC 3 ) could be detected in the ISM For one isomer of each HC 5 N and HC 7 N, namely HC 4 NC and HC 6 NC, precise data suitable for radioastronomy are available through FT-MW spectroscopy carried out at Harvard.

24. Interstellar isomers of cyanoacetylene, detected in TMC-1 Linear HCCNC K. Kawaguchi, M. Ohishi, S.-I. Ishikawa and N. Kaifu, Astrophys. J. 386, L51 (1992). quasilinear HNC 3 K. Kawaguchi, S. Takano, M. Ohishi, S.-I. Ishikawa, K. Miyazawa, N. Kaifu, K. Yamashita, S. Yamamoto, S. Saito, Y. Ohshima and Y. Endo, Astrophys. J. 396, L49 (1992). High-energy isomer HCNCC observed through matrix-isolation IR spectroscopy Z. Guennoun, I. Couturier-Tamburelli, N. Piétri and J. P. Aycard, Chem. Phys. Lett. 368, 574 (2003). R. Kolos and J. C. Dobrowolski, Chem. Phys. Lett. 369, 75 (2003).

25. P. Botschwina, Phys. Chem. Chem. Phys. 5 (2003) 3337.

26. HC 4 NC and HC 6 NC P. Botschwina, Ä. Heyl, W. Chen, M. C. McCarthy, J.-U. Grabow, M. J. Travers and P. Thaddeus, J. Chem. Phys., 109, 3108 (1998) Fourier transform microwave spectroscopy in a supersonic jet

27. HC 4 NC B e (HC 4 NC): 1399.7 MHz from corrected equilibrium structure.  B 0 = B e -B 0  ½  i  i d i. → B 0 = 1401.20 MHz. B 0 (exp.) = 1401.18227(7) MHz. Isomerisation energy with respect to HC 5 N (0 K): 114 kJ mol -1

28. B 0 predictions for less abundant isotopomers of HC 4 NC isotopomerB 0 (MHz)isotopomerB 0 (MHz) DCCCCNC1336.05HCCC 13 CNC1399.62 H 13 CCCCNC1364.01HCCCC 15 NC1386.91 HC 13 CCCNC1386.82HCCCCN 13 C1364.69 HCC 13 CCNC1399.89 B 0 values for 13 C and 15 N substituted species are expected to have uncertainties of ca. 0.005 MHz; B 0 value for DC 5 NC is probably less accurate.

29. Radicals of type C 2n+1 N C 3 N:found in IRC+10216 already in 1977 [1], six years prior to its laboratory investigation by millimeter-wave spectroscopy [2]. [1]M. Guélin and P. Thaddeus, Astrophys. J. 212 (1977) L81. [2]C. A. Gottlieb et al., Astrophys. J. 275 (1983) 916. Mixed experimental / theoretical work M. C. McCarthy, C. A. Gottlieb, P. Thaddeus, M. Horn and P. Botschwina, J. Chem. Phys. 103 (1995) 7820.

30. M. C. McCarthy, G. W. Fuchs, J. Kucera, G. Winnewisser and P. Thaddeus, J. Chem. Phys. 118 (2003) 3549.

31. The C 5 N radical Theoretical predictions F. Pauzat, Y. Ellinger and A. D. McLean, Astrophys. J. 369, L13 (1991) UHF-SCF calculations yield 2  ground state with small dipole moment P. Botschwina, Chem. Phys. Lett. 259, 627 (1996) RCCSD(T) yields 2  ground state with large dipole moment Laboratory detection by FTMW Y. Kasai, Y. Sumiyoshi, Y. Endo and K. Kawaguchi, Astrophys. J. 477, L65 (1997) radical generated by discharge in a mixture of HC 5 N and HC 3 N diluted in Ar Radioastronomical detection M. Guélin, N. Neininger and J. Cernicharo, Astron. Astrophys. 335, L1 (1998)

34. upper lines: 2  states lower lines: 2  states Recommended equilibrium structures (RCCSD(T) + corrections) P. Botschwina, Phys. Chem. Chem. Phys. 5 (2003) 3337.

35. Calculated equilibrium excitation energies (in cm -1 ) for the 2  states of radicals of type C 2n+1 N (n = 1-3) a a Basis set: cc-pVQZ. Throughout, the calculations were carried out at the recommended equilibrium structures. nRHFRCCSDRCCSD-TRCCSD(T) 1 508232022852316 2-324 698 455 491 3-612 124 -357 -304

36. Calculated equilibrium dipole moments (in D) for radicals of type C 2n+1 N a radicalstateRHFRCCSDRCCSD-TRCCSD(T) C3NC3N X 2  -3.255-2.901-2.865-2.867 A 2  -0.551 0.046 0.200 C5NC5N X 2  -3.865-3.423-3.409-3.412 A 2  -0.532 0.335 0.567 0.566 C7NC7N X 2  -0.431 0.660 0.958 0.957 A 2  -4.328-3.809-3.824-3.826 a Basis set: aug-cc-pVTZ.

37. II. Interstellar cations Although ion-molecule reactions are believed to play a central role in the synthesis of interstellar molecules, the number of unambiguously detected chemically different cations is still rather small, currently not exceeding 15. Theoretical work at Kaiserslautern (until 1989) and Göttingen (since 1990) provided various predictions for: H 3 +, HN 2 +, HCO + /HOC +, HCS +, HCNH +, H 3 O +, H 2 COH + and HC 3 NH +

38. Interstellar H 3 O + An ion playing a key role in the oxygen chemistry network  1986: tentative assignment of a line found in OMC-1 and Sgr B2 near 307.2 GHz to transition P (2,1) (J, K = 1,1 – 2,1) of H 3 O + A. Wotten et al., Astron. Astrophys. 166 (1986) L15.  1990: Confirming line at 364.8 GHz observed with Caltech Submillimetre Observatory at Mauna Kea in the above two sources A. Wotten et al., Astrophys. J. 380 (1991) L79.  1991: above two lines found in W3 IRS 5 cloud, together with new line at 396.3 GHz T. G. Phillips et al., Astrophys. J. 399 (1992) 533

40. What has been measured? H 3 O + has a pyramidal equilibrium structure with a low barrier height to inversion and consequently an unusually large inversion splitting. Energy level diagram T. G. Pillips et al., Astrophys. J. 399 (1992)533.

41. H 3 O + : ab initio predictions 1983:2-dimensional anharmonic variational treatment of 1 and 2 vibrations, using CEPA-1 potential surface P. Botschwina, P. Rosmus and A. E. Reinsch, Chem. Phys. Lett. 102 (1983) 299. predicted 0 - - 0 + splitting: 46 cm -1 best uncorrected ab initio value for quite some time transition dipole moment: 1.44 D

43. First far-infrared detection of H 3 O + in Sagittarius B2 Using the Infrared Space Observatory (ISO) Long- Wavelength Spectrometer three lines arising from the 2 ground-state inversion mode (0 +  0 - ) at 55.3 cm -1 could be observed toward the Sagittarius B2 molecular cloud, near the Galactic center. All transitions were observed in absorption against the optically thick infrared continuum emission of the dust. Again, the theoretical value for the (0 +  0 - ) transition dipole moment published in 1984 by BRR was employed to arrive at column densities. J. R. Goicoechea and J. Cernicharo, Astrophys. J. 554 (2001) L213

44. HC 3 NH + Following CEPA-1 calculations (Botschwina, 1987) and laser-spectroscopic studies of the 1 and 3 bands (Lee, Amano, 1987; Kawaguchi et al., 1990) two lines of HC 3 NH + (J = 5-4 and J = 4-3) were detected in TMC-1 with the Nobeyama 45 m radio telescope. K. Kawaguchi et al., Astrophys. J. 420 (1994) L95. Using the CEPA-1 dipole moment of Botschwina, the column density of HC 3 NH + was determined to be 1.0 (0.2) · 10 12 cm -2 In TMC-1, HC 3 NH + is thus 160 times less abundant than HC 3 N and 2.6 times more abundant than HNCCC.

46. III. Heterocumulenic chains Another frequent structural motif within the series of known interstellar molecules is provided by cumulenic chains with one or two hetero end groups (“heterocumulenes“) Individual series and known examples with n ≥ 3: C n O:C 3 O C n S:C 3 S, (potentially C 5 S) SiC n :(SiC 3 ), SiC 4, (potentially longer chains) H 2 C n :H 2 C 3, H 2 C 4, H 2 C 5, H 2 C 6

47. C3SC3S 1987:three strong lines at 23.123, 40.465 and 46.246 GHz detected with Nobeyama 45 m telescope in TMC-1 [1]; assigned to J = 4-3, 7-6 and 8-7 transitions after laboratory MW data became available [2]. [1]N. Kaifu et al., Astrophys. J,317 (1987) L111. [2]Y. Yamamoto et al., Astrophys. J. 317 (1987) L119. Theoretical work at Göttingen S. Seeger et al., J. Mol. Struct. 3003 (1994) 213. P. Botschwina, Phys. Chem. Chem. Phys. 5 (2003) 3337.

48. Spectroscopic constant exp.CCSD(T)/ cc-pVQZ  1 (MHz) 14.8314.41  4 (MHz) -5.65 -5.40 q 4 (MHz) 1.51 1.48 (Hz) -0.48 -0.57  5 (MHz) -12.36-11.89 q 5 (MHz) 3.96 3.82 (Hz)-11.4-10.5 For details see: P. Botschwina, Phys. Chem. Chem. Phys. 5 (2003) 337.

49. C5SC5S MW spectra in 5-20 GHz region Y. Kasai et al., Astrophys. J. 410 (1993) L45. Tentative assignment of J = 13-12 transition in IRC+ 10216 (probably wrong) M. B. Bell et al., Astrophys. J. 417 (1993) L37. CCSD(T)/cc-pVQZ + corrections (taken over from C 3 S) P. Botschwina, Phys. Chem. Chem. Phys. 5 (2003) 3337.  e = 5.32 D

50. Linear silicon carbides SiC n n: evenclosed-shell singlet ground-states (X 1 Σ + ) n: oddtriplet ground-states (X 3 Σ - ) SiC 2 and SiC 3 detected in the ISM in their ring forms Linear SiC 4 detected in IRC+10216 M. Ohishi et al., Astrophys. J. 345 (1989) L83 Joint experimental/theoretical work (Harvard/Göttingen) on SiC 4 and SiC 6 : V. D. Gordon et al., J. Chem. Phys. 113 (2000) 5311 SiC 4 and SiC 6 are rather normal semi-rigid linear molecules

53. MethodSiC 4 SiC 6 basis A b basis B c basis Abasis B SCF-7.035-7.042-9.439-9.500 MP2-6.713-6.734-8.475-8.533 CCSD-7.004-7.023-9.312-9.381 CCSD-T-6.408-6.427-8.196-8.248 CCSD(T)-6.401-6.421-8.195-8.249 Calculated equilibrium dipole moments (in D) for SiC 4 and SiC 6 a a Evaluated at the recommended equilibrium structures from this work. The positive end of the dipole is located at the silicon site. b aug-cc-pVTZ basis. c aug-cc-pVQZ basis exclusive of g functions. V. D. Gordon, E. S. Nathan, A. J. Apponi, M. C. McCarthy, P. Thaddeus and P. Botschwina, J. Chem. Phys. 113 (2000) 5311.

54. Recommended equilibrium structures P. Botschwina, Mol. Phys. 103 (2005) 1441.

55. nSCFMP2CCSDCCSD-TCCSD(T) 1-4.178-3.782-3.821-3.781-3.783 2-4.882-4.409-4.427-4.409-4.411 3-5.431-4.923-4.892-4.909-4.910 4-5.855-5.343-5.247-5.305 5-6.181-5.683-5.518-5.618 Calculated equilibrium electric dipole moments (  e, in D) for cyanopolyynes HC 2n+ 1N a a Basis set: aug-cc-pVTZ. Sign of dipole moment corresponds to polarity + HC 2n+1 N -. Throughout, the calculations were carried out at the recommended equilibrium structure.

60. Some interstellar molecules: ab initio theory, laboratory spectroscopy and (radio) astronomy Lecture 3: IV. Pure carbon chains C n PETER BOTSCHWINA Institut für Physikalische Chemie Universität Göttingen, Tammannstraße 6 D-37077 Göttingen, Germany

61. Professorial system in Germany (until recently) C1/C2C3C4 ≈ assistant≈ associatefull professor

62. C 3  astronomically well-known through its electronic transition at 4051.6 Å, discovered in comet spectra, carbon-rich planetary nebulae and diffuse interstellar clouds towards various reddened stars  3 (antisymmetric stretch) and 2 (bend) observed in mid and far IR, respectively C 5 observed in the circumstellar envelope of IRC+10216 (Bernath et al., Science 244, 562 (1989)) through its 3 band (antisymmetric stretching vibration with highest wavenumber)

64. C 4 (?) tentative assignment to 5 band of astronomical feature at 57.5  m (174 cm -1 ) found in five different source (Sgr B2, IRC+10216, CRL 618, CRL 2688 and NGC 7027) C 6 and C 5 (??) admittedly rather speculative assignments of a molecular band found in the young planetary nebula NGC 7027 at ca. 98  m (102 cm -1 ) to bending vibrational transitions ( 9 and/or 7 of C 6 and C 5, respectively)

65. J. R. Goicoechea, J. Cernicharo, H. Masso and M. L. Senent, Astrophys. J., 609 (2004) 225.

66. 1)Linear carbon chains of type C 2n+1 (odd number of carbon atoms) have a ···  4 electronic configuration and an electronic ground-state of symmetry. 2)Linear carbon chains of type C 2n (even number of carbon atoms) have a ···  2 electronic configuration and an electronic ground-state of symmetry.

67. C3C3 M. Mladenović, S. Schmatz and P. Botschwina, 101 (1994) 5891.

69. Vibrations of linear C 5 1, 2:  g (symmetric stretching) 3, 4:  u (antisymmetric stretching) 5:  g (trans bending) 6,7:  u (cis bending)

70. C5C5 13 C 5  3 /cm -1 2221.4 (2214.6)2133.9  7 /cm -1 112.5 108.1  3 /MHz 12.779 (12.59)11.329 (11.07)  5 /MHz -9.939 (-10.24) -8.811  7 /MHz -9.383 (-9.30) -8.318 (-8.14) B0B0 -8.143 -7.219 q 5 /MHz 2.134 (2.36) 1.892 q 7 /MHz 3.900 (3.99) 3.457 (3.49) /Hz119 (161) b 102 (138) b For details and further references see: P. Botschwina, Phys. Chem. Chem. Phys. 5 (2003) 337. CCSD(T)/cc-pVQZ spectroscopic constants for C 5 and 13 C 5 a a Exp. values are given in parentheses. b Ground-state values.

71. IR active bending vibrations of C 2n chains Symmetry coordinates: S i = For details see: P. Botschwina, Chem. Phys. Lett. 421 (2006) 488.

72. Parameters (in a.u.) of near-equilibrium cis-bending potential energy functions for linear C 4 a PEFRHF-SCFRCCSD(T) termcc-pVQZ 0.0280770.020467 0.0010770.002126 0.0003080.000521 a Throughout, the RCCSD(T)/cc-pVQZ equilibrium structure is used as expansion point: R 1e = 1.3135 Å and R 2e = 1.2936 Å. V – V e =

73. First derivative of electric dipole moment with respect to the cis-bending symmetry coordinate (in a.u.) for linear C 4 a basis b RHFRCCSD(T) spd (avtz)-0.641-0.912 sp (avtz) + df (vtz)-0.622-0.905 avtz-0.638-0.918 spdf (avqz)-0.639-0.917 avqz-0.640-0.918 a All calculations are carried out around the recommended equilibrium structure: R 1e (outer) = 1.3098 Å and R 2e (inner) = 1.2899 Å. b An obvious shorthand notation is employed to designate the basis sets.

74. cis-bending potentials

76. n Harmonic wavenumbers (in cm -1 ) and IR intensities (in km mol -1 ) of cis-bending vibrations for linear C 2n species a 2171.1 (44.5) exp. (argon matrix): 172.4 cm -1 3370.1 (6.2), 99.4 (28.3) 4480.7 (0.1), 232.1 (17.1), 60.5 (18.6) 5495.9 (1.0), 354.7 (2.1), 174.6 (20.2), 39.8 (13.3) a Calculated from (RCCSD(T)/vqz) quadratic force constants and RCCSD(T)/avtz dipole moment derivatives. P. Botschwina, Chem. Phys. Lett. 421 (2006) 488.

77. “C 7 possesses a filled  u HOMO, which makes this molecule a candidate for extremely large amplitude bending motion.“ A. Van Orden and R. J. Saykally, Chem. Rev. 98 (1998) 2313. Review wisdom

78. Linear C 7 : floppy or not? According to the interpretation of experimental data obtained by Saykally and coworkers, linear C 7 was described as a highly flexible species with an “extremely large amplitude bending motion about the central carbon atom”. (J. R. Heath and R.J. Saykally, J. Chem. Phys. 94, 1724 (1991)).

80. Comparison of CCSD(T)/cc-pVQZ potentials of C 7 and C 3 for bending about the central carbon atom (bond lengths and other angles kept fixed at their equilibrium values).

81. Spectroscopic constants for linear C 7 a  1 /cm -1 2169.5  1 /MHz 2.588q e 7 /MHz 0.140  2 /cm -1 1565.1  2 /MHz 1.602 q e 8 /MHz 0.368  3 /cm -1 574.6  3 /MHz 0.454 q e 9 /MHz 0.131  4 /cm -1 2203.8  4 /MHz 3.411 q e 10 /MHz 0.248  5 /cm -1 1933.3  5 /MHz 2.018 q e 11 /MHz 0.804  6 /cm -1 1088.6  6 /MHz 1.098 q J 7 /Hz -0.01  7 /cm -1 493.7  7 /MHz -1.012 q J 8 /Hz -0.15  8 /cm -1 156.5  8 /MHz -1.816 q J 9 /Hz -0.01  9 /cm -1 528.6  9 /MHz -1.067 q J 10 /Hz -0.07  10 /cm -1 237.5  10 /MHz -1.930 q J 11 /Hz -0.76  11 /cm -1 70.0  11 /MHz -1.952D J e /Hz10.1 a CCSD(T)/cc-pVQZ. Vibrations 1-3 are totally symmetric (  g ), 4-6 belong to symmetry species  u, 7-8 to  g and 9-11 to  u symmetry.

82. Theoretical results (CCSD(T)/cc-pVQZ) are contradictory:  Linear C 7 is a fairly normal semirigid linear molecule with no evidence of floppiness.  Excitation of the 11 bending vibration changes the rotational constant by only 0.2 % (Heath and Saykally: 9.3 %!!)  No unusually large negative value for centrifugal distortion constant.

86. Spectroscopic constants of linear C 7 : comparison of theory and experiment CCSD(T)/cc-pVQZexp. a  4 /MHz 3.411 3.47 (32) b  5 /MHz 2.018 1.71 (87) c  8 /MHz -1.816-1.56 (26) b  11 /MHz -1.952-1.67 (32) b q 8 /MHz 0.3680.618 (213) b q 11 /MHz 0.804 1.15 (35) b a Standard derivations in terms of the last digit in parentheses. b Neubauer-Guenther et al., unpublished (2006). c J. R. Heath, A. Van Orden, E. Kuo and R. J. Saykally, Chem. Phys. Lett., 182, 17 (1991).

88. CCSD(T)/cc-pVQZ bending potential curves for C 2n+1 chains P. Botschwina and R. Oswald, Chem. Phys. 325 (2006) 485.

89. P. Botschwina, Theor. Chem. Acc. 114 (2005) 350.

90. Equilibrium bond lengths (CCSD(T)/cc-pVQZ + corrections

91. No.  (cm -1 ) A (km mol -1 ) 2150612.6 22483 4.2 23453 0.0 24281 1.9 2518811.3 26 8812.5 27 17 7.6 CCSD(T) harmonic wavenumbers and IR intensities for  u vibrations of linear C 15

92. Conclusions High-level ab initio calculations, mostly by CCSD(T) with cc-pVQZ basis set, yield rather accurate values for various spectroscopic properties of (potential) interstellar molecules important quantities for astronomers: rotational constants and centrifugal distortion constants electric dipole moments (ro)vibrational frequencies vibration-rotation coupling constants l-type doubling constants

93. Acknowledgement Present and former Coworkers at Göttingen Drs. J. Flügge, Ä. Heyl, M. Horn, M. Mladenović, M. Oswald, R. Oswald, S. Schmatz and S. Seeger International coworkers (selection) Profs. C. Degli Esposti, T. Hirano, P. Thaddeus and G. Winnewisser Drs. L. Bizzocchi, M. C. McCarthy and K. T. M. Yamada Profs. H.-J. Werner (Stuttgart) and P. J. Knowles (Cardiff) for various versions of MOLPRO Financial support through DFG and Fonds der Chemischen Industrie

94. Ongoing theoretical work on antisymmetric stretching vibrations of C 2n+1 chains Absolute IR intensities for strongest stretching vibrations of linear C 2n+1 chains. In parentheses: wavenumber in cm -1 /A max. P. Botschwina, J. Mol. Struct. 795 (2006) 230.