1. Carbon dioxide clusters: (CO 2 ) 6 to (CO 2 ) 13 J. Norooz Oliaee, M. Dehghany, N. Moazzen-Ahmadi Department of Physics and Astronomy University of Calgary A.R.W. McKellar Steacie Institute for Molecular Sciences National Research Council of Canada

2. TDL Jet Trigger Ref. Gas 12 bit DAQ Card Timer Controller Card (CTR05) Laser Sweep Trigger DAQ Trigger Gas Supply Jet Signal Jet Controller (Iota One) Jet Controller IR Detectors TDL Controller (L5830) Etalon Monochromator pulsed supersonic jet / tunable diode laser apparatus at The University of Calgary

3. CO 2 dimer C 2h cyclic CO 2 trimer C 3h barrel-shaped CO 2 trimer C 2

4. Carbon dioxide clusters, (CO 2 ) N Last year at Columbus we described assignments of specific IR bands to clusters with N = 6 to 13. Since then, we have published preliminary results, made further assignments, and made new calculations of structures and vibrational shifts.

5. Cluster structure calculations: SAPT-s potential Original assignments were based on structures calculated by Takeuchi using the empirical M-O-M potential. We have now made calculations using the SAPT-s potential, a simplified function based on high level ab initio results. The results are generally similar, and give us extra confidence in our cluster assignments. For N = 10, a different isomer has the lowest energy. Cluster shift calculations: resonant dipole model The resonant dipole-dipole interaction model is widely used to calculate vibrational shifts for CO 2 and other molecules in clusters or condensed phases. Given the structure of cluster (CO 2 ) N and a value for the CO 2 3 transition dipole, we predict band origins and intensities for all its bands by diagonalizing an N x N matrix. Quantitatively, the results are not so great, but this still provides a useful qualitative tool. Takeuchi, JPC A 107, 5703 (2008). Murthy, O’Shea, McDonald, Mol. Phys. 50, 531 (1988) – [M-O-M potential]. Bukowski, Sadlej, Jeziorski, Jankowski, Szalewicz, Kucharski, Williams, Rice, JCP 110, 3785 (1999) – [SAPT-s potential].

6. M-O-M potential SAPT-s potential Note the extra stability of N = 6, 9, and 13

7. We assign these two bands to (CO 2 ) 6. It is formed by stacking two cyclic trimers and has S 6 point-group symmetry – all 6 CO 2 are equivalent. ( 12 C 18 O 2 ) 6 also observed and fitted. CO 2 hexamer (S 6 isomer) ObsSAPT-sM-O-M B / MHz 360.1369.2371.1 C / MHz 297.5298.7295.9 Simply stacking two trimers predicts C = 298.4 MHz for the hexamer! Parallel band (combination) Perpendicular band (fundamental)

8. Now we have assigned the spectrum of a second hexamer! E = -4664 -4646 cm -1 M-O-M potential E = -4886 -4849 cm -1 SAPT-s potential All six CO 2 monomers are equivalent One pair (“top” and “bottom”) are equivalent. The remaining four (“ring”) are equivalent.

9. The parallel band has intensity because the four monomers in the ring are not co-planar – they have a projection on the c-axis. The stronger perpendicular band is overlapped by CO 2 dimer and trimer absorption. The parallel band for ( 12 C 18 O 2 ) 6 is also observed and fitted. ObsSAPT-sM-O-M B / MHz 352.9359.1359.6 C / MHz 308.7312.0309.7 Parallel band Perpendicular band new CO 2 hexamer (S 4 isomer)

10. This band is assigned to (CO 2 ) 7, an asymmetric rotor. ( 12 C 18 O 2 ) 7 is also observed and fitted. ObsSAPT-sM-O-M A / MHz 314.8322.6325.8 B / MHz 270.7273.9272.9 C / MHz 210.9215.1216.8 looking along the a-axisb-axisc-axis CO 2 heptamer (or septamer)

11. We think this band is due to (CO 2 ) 9, which is calculated to be a (very) asymmetric rotor. Simulation is a c-type band. CO 2 nonamer ObsSAPT-sM-O-M A / MHz 207210.5211.4 B / MHz 161163.9163.7 C / MHz 125126.9126.8

12. This band is assigned to (CO 2 ) 10, which is calculated to be an asymmetric rotor. Now, we have assigned another band at 2344.08 cm -1 to (CO 2 ) 10. Simulation is a mostly c-type band. CO 2 decamer ObsSAPT-sM-O-M A / MHz 155.4158.6164.5 B / MHz 144.0146.4145.8 C / MHz 111111.1111.3 SAPT-s gives a distinct isomer as the lowest energy form. Its rotational constants are very similar, but agree better with experiment. (Note: the experimental C is not well determined).

13. We think that this band is due to (CO 2 ) 11, another asymmetric rotor. CO 2 hendecamer ObsSAPT-sM-O-M A / MHz 136137.9138.6 B / MHz 114116.7116.1 C / MHz 10699.899.2

14. This prominent band is assigned to (CO 2 ) 12. It has an interesting central Q-branch. The simulation uses  a :  b :  c  1:1.7:1 CO 2 dodecamer * (known (CO 2 ) 3 lines ObsSAPT-sM-O-M A / MHz 109111.0111.4 B / MHz 106108.1107.7 C / MHz 9395.895.2

15. We observe three bands with the same line spacing which we assign to (CO 2 ) 13. It has a remarkable symmetric top structure. CO 2 tridecamer (or triskaidecamer) J.-B. Maillet, A. Boutin, S. Buttefay, F. Calvo, and A.H. Fuchs, J. Chem. Phys. 109, 329 (1998) Two nearby symmetric top parallel bands with a common ground state. The third band is at 2345.01 cm -1. S 6 point group ObsSAPT-sM-O-M B / MHz 92.694.894.5 C / MHz 9093.192.8

16. Summary of observed cluster band origins

17. Summary of observed cluster band origins with resonant dipole predictions in red

18. Summary two highly symmetric isomers (S 4 and S 6 ) observed for CO 2 hexamer resonant dipole model predicts the observed blue shifts, but not quantitatively (as already known for cyclic (CO 2 ) 3 ) structures from the M-O-M and SAPT-s potentials are consistent with each other and with experimental rotational constants most bands have strong, sharp Q-branches – maybe these can be used to pump energy into select-sized clusters Thanks to Colin Western for PGOPHER!!