Some interstellar molecules: ab initio theory, laboratory spectroscopy and (radio) astronomy

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

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

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.

Contents of lectures

I. Overview of work on cyanopolyynes (HC2n+1N) and related species

II. Interstellar cations

III. Heterocumulenic chains

IV. Pure carbon chains Cn

CYANOPOLYYNES (HC2n+1N)

• Almost ubiquituous in the ISM and CSM• Provide largest (in terms of number of atoms)

interstellar molecule unambiguously detected by radio astronomy HC11N

• Through the presence of low-lying bending vibrational states observable by radio astronomy in excited vibrational states

important information on dynamical processes

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 (HC3N), the experimental ground-state dipole moment is as large as 0 = 3.72 D

recommended method: combination of experimental and theoretical data

exp.: B0 values for various (as many as possible) isotopomers

theor.: B0 = Be- B0 calculated from high-quality ab initio cubic

force fields (e.g., CCSD(T) with large basis set)

(αi from 2nd order perturbation theory)

i : vibration-rotation coupling constant

di : degeneracy factor of vibrational mode i

Cyanopolyynes: demanding cases for accurate equilibrium structure determinations

i

ii0 d21

B

Equilibrium structure for HC3N

[1] P. Botschwina, M. Horn, S. Seeger and J. Flügge, Mol. Phys. 78, 191 (1993).

[2] P. Botschwina, Mol. Phys. 103, 1441 (2005).

D12C515N

J = 43 42 (*)Millimeter-wave spectroscopy

of rare isotopomers of HC5N and DC5N: determination

of a mixed experimental-theoretical equilibrium

structure for cyanobutadiyne

L. Bizzocchi, C. Degli Esposti and P. Botschwina

J. Mol. Spectrosc. 225, 145 (2004)

HC5N isotopomers: spectroscopic constants from MMW spectroscopy

* P. Botschwina, Ä. Heyl, M. Oswald and T. Hirano, Spectrochim. Acta A 53, 1079 (1997).

Equilibrium structures for HC5N

Geometric structures for linear HC11N

r0 structure a re estimate b CCSD(T)/cc-pVTZ cre structure c

(recommended)

r (HC(1))/Å 1.057(1) 1.0627 1.0643 1.0625

R1 (C(1)C(2))/Å 1.210(1) 1.2104 1.2169 1.2105

R2 (C(2)C(3))/Å 1.360(1) 1.3637 1.3695 1.3635

R3 (C(3)C(4))/Å 1.218(2) 1.2178 1.2246 1.2182

R4 (C(4)C(5))/Å 1.351(3) 1.3564 1.3616 1.3556

R5 (C(5)C(6))/Å 1.217(5) 1.2187 1.2267 1.2203

R6 (C(6)C(7))/Å 1.360(8) 1.3571 1.3601 1.3541

R7 (C(7)C(8))/Å 1.219(6) 1.2153 1.2261 1.2197

R8 (C(8)C(9))/Å 1.350(3) 1.3695 1.3624 1.3564

R9 (C(9)C(10))/Å 1.217(2) 1.2153 1.2219 1.2155

R10 (C(10)C(11))/Å 1.365(1) 1.3695 1.3753 1.3693

R11 (C(11)N)/Å 1.161(1) 1.1620 1.1689 1.1620a 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.

HCHC1111N: Variation of CC equilibrium bond lengthsN: Variation of CC equilibrium bond lengths

HC11N: a story of lost and found

• 1982 and 1985: weak radio lines observed in IRC+10216 and TMC-1 attributed to HC11N (without accurate laboratory data at hand)

• For more than 10 years no confirmation of assignments successful

• 1996: FT-MW spectroscopy of HC11N by Thaddeus and coworkers (Harvard University); 20 rotational transitions measuredspectroscopic 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.

Dipole moments and column densities of cyanopolyynes (HC2n+1N) in TMC-1 a

Molecule (D) N (1011 cm-2)

HC5N 4.33 b 330

HC7N 4.82 c 110

HC9N 5.20 c 19

HC11N 5.47 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

Vibrationally excited molecules in “hot cores”: centres of star formation:

HC3N 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).

Spectroscopic CCSD(T) Spectroscopic CCSD(T)

constant cc-pVQZ exp. constant cc-pVQZ exp.

1 /cm-1 3452 5 /MHz -1.714 -1.563b

2 /cm-1 2316 6 /MHz -9.233 -9.256

3 /cm-1 2111 7 /MHz -14.389 -14.455

4 /cm-1 879 q5 /MHz 2.419 2.538

5 /cm-1 671 q6 /MHz 3.498 3.582

6 /cm-1 501 q7 /MHz 6.394 6.538

7 /cm-1 223 /Hz -1.052 -1.331

1 /MHz 7.030 7.331b /Hz -1.770 -2.063

2 /MHz 21.589 21.572 /Hz -15.516 -16.291

3 /MHz 13.767 13.895 /kHz 0.506 0.544a

4 /MHz 10.447 11.100b

a Ground-state value b Deperturbed values from approximate deperturbation procedures

Characterisation of vibrationally excited states of HC3N

J5qJ6qJ7qJeD

Millimeter-wave spectroscopy of HC5N 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.

Calculateda and experimental spectroscopic constants for

low-lying singly excited bending vibrational states of HC5N

a CCSD(T)/cc-pVQZ. Standard 2nd order perturbation theory in normal coordinate space is employed in the calculation of , qt and qt

J values.

v11 = 1 v10 = 1 v9 = 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

qt (MHz) 1.125 1.163 0.490 0.500 0.320 0.329

qtJ (Hz) -0.993 -1.063 -0.176 -0.173 -0.032 -0.039

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.

Cyanopolyynes: what about isomers?

• HC3N is so far the only interstellar molecule for which two more isomers (HCCNC and HNC3) could be detected in the ISM

• For one isomer of each HC5N and HC7N, namely HC4NC and HC6NC, precise data suitable for radioastronomy are available through FT-MW spectroscopy carried out at Harvard.

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 HNC3

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).

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

HC4NC and HC6NC

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

HC4NC

Be (HC4NC): 1399.7 MHz from corrected equilibrium structure.

B0 = Be-B0 ½ iidi. → B0 = 1401.20 MHz.

B0 (exp.) = 1401.18227(7) MHz.

Isomerisation energy with respect to HC5N (0 K): 114 kJ mol-1

B0 predictions for less abundant isotopomers of HC4NC

isotopomer B0 (MHz) isotopomer B0 (MHz)

DCCCCNC 1336.05 HCCC13CNC 1399.62

H13CCCCNC 1364.01 HCCCC15NC 1386.91

HC13CCCNC 1386.82 HCCCCN13C 1364.69

HCC13CCNC 1399.89

B0 values for 13C and 15N substituted species are

expected to have uncertainties of ca. 0.005 MHz;

B0 value for DC5NC is probably less accurate.

Radicals of type C2n+1N

C3N: 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.

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

The C5N radical

Theoretical predictionsF. 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 FTMWY. Kasai, Y. Sumiyoshi, Y. Endo and K. Kawaguchi,

Astrophys. J. 477, L65 (1997)

radical generated by discharge in a mixture of HC5N and HC3N diluted in Ar

Radioastronomical detectionM. Guélin, N. Neininger and J. Cernicharo, Astron. Astrophys. 335, L1 (1998)

upper lines: 2 stateslower lines: 2 states

Recommended equilibrium structures(RCCSD(T) + corrections)

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

Calculated equilibrium excitation energies (in cm-1)

for the 2 states of radicals of type C2n+1N (n = 1-3)a

a Basis set: cc-pVQZ. Throughout, the calculations were carried out at the recommended equilibrium structures.

n RHF RCCSD RCCSD-T RCCSD(T)

1 508 2320 2285 2316

2 -324 698 455 491

3 -612 124 -357 -304

Calculated equilibrium dipole moments (in D) for radicals of type C2n+1N

a

radical state RHF RCCSD RCCSD-T RCCSD(T)

C3N X 2 -3.255 -2.901 -2.865 -2.867

A 2 -0.551 0.046 0.200 0.200

C5N X 2 -3.865 -3.423 -3.409 -3.412

A 2 -0.532 0.335 0.567 0.566

C7N 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.

II. Interstellar cationsAlthough 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:

H3+, HN2

+, HCO+/HOC+, HCS+, HCNH+, H3O+, H2COH+ and HC3NH+

Interstellar H3O+

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 H3O+

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

What has been measured?

H3O+ 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.

H3O+: 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

First far-infrared detection of H3O+ 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

HC3NH+

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 HC3NH+ (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 HC3NH+ was determined to be

1.0 (0.2) · 1012 cm-2

In TMC-1, HC3NH+ is thus 160 times less abundant than HC3N and 2.6 times more abundant than HNCCC.

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:

CnO: C3O

CnS: C3S, (potentially C5S)

SiCn: (SiC3), SiC4, (potentially longer chains)

H2Cn: H2C3, H2C4, H2C5, H2C6

C3S

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.

Spectroscopic constant

exp. CCSD(T)/cc-pVQZ

1 (MHz) 14.83 14.41

4 (MHz) -5.65 -5.40

q4 (MHz) 1.51 1.48

(Hz) -0.48 -0.57

5 (MHz) -12.36 -11.89

q5 (MHz) 3.96 3.82

(Hz) -11.4 -10.5

J

4q

J

5q

For details see:P. Botschwina, Phys. Chem. Chem. Phys. 5 (2003) 337.

1.2927 1.5374 exp./theor.

r structuree

1.2810

C5S

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 C3S)

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

1.2926 1.26621.2838 1.2815 1.5448e = 5.32 D

Linear silicon carbides SiCn

n: even closed-shell singlet ground-states (X 1Σ+)n: odd triplet ground-states (X 3Σ-)

SiC2 and SiC3 detected in the ISM in their ring forms

Linear SiC4 detected in IRC+10216M. Ohishi et al., Astrophys. J. 345 (1989) L83

Joint experimental/theoretical work (Harvard/Göttingen) on SiC4 and SiC6:V. D. Gordon et al., J. Chem. Phys. 113 (2000) 5311

SiC4 and SiC6 are rather normal semi-rigid linear molecules

1 .27 26 1 .29 86 1 .28 091 .69 28

Method SiC4 SiC6

basis Ab basis Bc basis A basis 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 SiC4 and SiC6 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.

Recommended equilibrium structures

P. Botschwina, Mol. Phys. 103 (2005) 1441.

n SCF MP2 CCSD CCSD-T CCSD(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 -5.305

5 -6.181 -5.683 -5.518 -5.618 -5.618

Calculated equilibrium electric dipole moments (e, in D) for cyanopolyynes HC2n+1N a

a Basis set: aug-cc-pVTZ. Sign of dipole moment corresponds to polarity +HC2n+1N-. Throughout, the calculations were carried out at the recommended equilibrium structure.

Some interstellar molecules: ab initio theory, laboratory spectroscopy and

(radio) astronomy

Lecture 3: IV. Pure carbon chains Cn

PETER BOTSCHWINA Institut für Physikalische Chemie

Universität Göttingen, Tammannstraße 6 D-37077 Göttingen, Germany

Professorial system in Germany(until recently)

C1/C2 C3 C4

≈ assistant ≈ associate full

professor professor professor

C3 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

C5 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)

C4 (?)

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)

C6 and C5 (??)

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

C6 and C5, respectively)

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

1) Linear carbon chains of type C2n+1

(odd number of carbon atoms) have a ··· 4 electronic configuration and an electronic ground-state of symmetry.

g

1

2) Linear carbon chains of type C2n

(even number of carbon atoms) have a ··· 2 electronic configuration and an electronic ground-state of

g

3symmetry.

C3

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

Vibrations of linear C5

1, 2: g (symmetric stretching)

3, 4: u (antisymmetric stretching)

5: g (trans bending)

6,7: u (cis bending)

C513C5

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 -8.143 -7.219

q5 /MHz 2.134 (2.36) 1.892

q7 /MHz 3.900 (3.99) 3.457 (3.49)

/Hz 119 (161)b 102 (138)b

JeD

For details and further references see:P. Botschwina, Phys. Chem. Chem. Phys. 5 (2003) 337.

CCSD(T)/cc-pVQZ spectroscopic constants for C5 and 13C5 a

a Exp. values are given in parentheses. b Ground-state values.

IR active bending vibrations of C2n chains

Symmetry coordinates: Si = )(21 '

ii

For details see:P. Botschwina, Chem. Phys. Lett. 421 (2006) 488.

1

2

'

2

'

1

Parameters (in a.u.) of near-equilibrium cis-bending potential energy functions for linear C4

a

PEF RHF-SCF RCCSD(T)

term cc-pVQZ cc-pVQZ

0.028077 0.020467

0.001077 0.002126

0.000308 0.000521

a Throughout, the RCCSD(T)/cc-pVQZ equilibrium structure is used as expansion point: R1e = 1.3135 Å and R2e = 1.2936 Å.

2

1S4

1S6

1S

V – Ve =

3

1i

)i2(

1

)i2(

1 SC

First derivative of electric dipole moment with respect to the cis-bending symmetry coordinate (in a.u.) for linear C4

a

basis b RHF RCCSD(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: R1e(outer) = 1.3098 Å and R2e(inner) = 1.2899 Å.

b An obvious shorthand notation is employed to designate the basis sets.

cis-bending potentials

n Harmonic wavenumbers (in cm-1) and IR intensities (in km mol-1)

of cis-bending vibrations for linear C2n speciesa

2 171.1 (44.5) exp. (argon matrix): 172.4 cm-1

3 370.1 (6.2), 99.4 (28.3)

4 480.7 (0.1), 232.1 (17.1), 60.5 (18.6)

5 495.9 (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.

“C7 possesses a filled u HOMO, which makes this moleculea candidate for extremely large amplitude bending motion.“

A. Van Orden and R. J. Saykally, Chem. Rev. 98 (1998) 2313.

Review wisdom

Linear C7 : floppy or not?

According to the interpretation of experimental data obtained by Saykally and coworkers, linear C7 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)).

Comparison of CCSD(T)/cc-pVQZ potentials of C7 and C3 for bending about the central

carbon atom (bond lengths and other angles kept fixed at their equilibrium values).

Spectroscopic constants for linear C7 a

1/cm-1 2169.5 1/MHz 2.588 qe7 /MHz 0.140

2/cm-1 1565.1 2/MHz 1.602 qe8 /MHz 0.368

3/cm-1 574.6 3/MHz 0.454 qe9 /MHz 0.131

4/cm-1 2203.8 4/MHz 3.411 qe10 /MHz 0.248

5/cm-1 1933.3 5/MHz 2.018 qe11 /MHz 0.804

6/cm-1 1088.6 6/MHz 1.098 qJ7 /Hz -0.01

7/cm-1 493.7 7/MHz -1.012 qJ8 /Hz -0.15

8/cm-1 156.5 8/MHz -1.816 qJ9 /Hz -0.01

9/cm-1 528.6 9/MHz -1.067 qJ10 /Hz -0.07

10/cm-1 237.5 10/MHz -1.930 qJ11 /Hz -0.76

11/cm-1 70.0 11/MHz -1.952 DJe /Hz 10.1a 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.

Theoretical results (CCSD(T)/cc-pVQZ) are contradictory:

Linear C7 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.

Spectroscopic constants of linear C7: comparison of theory and experiment

CCSD(T)/cc-pVQZ exp.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

q8/MHz 0.368 0.618 (213)b

q11/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).

CCSD(T)/cc-pVQZ bending potential curves for C2n+1 chains

P. Botschwina and R. Oswald, Chem. Phys. 325 (2006) 485.

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

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

No. (cm-1) A (km mol-1)

21 506 12.6

22 483 4.2

23 453 0.0

24 281 1.9

25 188 11.3

26 88 12.5

27 17 7.6

CCSD(T) harmonic wavenumbers and IR intensities for u vibrations of linear C15

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

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

Ongoing theoretical work on antisymmetric stretching vibrations of C2n+1 chains

Absolute IR intensities for strongest stretching vibrations of linear C2n+1 chains. In parentheses: wavenumber in cm-1/Amax.

P. Botschwina, J. Mol. Struct. 795 (2006) 230.