Infrared spectra of (CO$_2$)$_2$-Rg trimers, Rg = Ne, Ar, Kr, and Xe

High resolution spectra of (CO$_2$)$_2$-Rg trimers (Rg = Ne, Ar, Kr, and Xe) in the region of the CO2 nu3 fundamental (~2350 cm$^{-1}$) are reported, using a tunable OPO laser source to probe a pulsed supersonic slit jet expansion. These (CO$_2$)$_2$-Rg transitions tend to be hidden among stronger spectra due to other species, such as CO$_2$-Rg and (CO$_2$)$_2$. Each trimer consists of a (CO$_2$)$_2$ unit which is similar to the free carbon dioxide dimer (planar parallel staggered) plus an Rg atom located out-of-plane on the dimer C$_2$ symmetry axis, but the (CO$_2$)$_2$ unit may not remain exactly planar in the dimer. Experimental structures show that the C-Rg bond lengths in the trimers are similar to those in the corresponding CO$_2$-Rg dimers. As well, the vibrational band origin shifts, relative to (CO$_2$)$_2$ itself, are similar to those of CO$_2$-Rg relative to CO$_2$.


Introduction
Weakly bound dimers composed of a carbon dioxide molecule and a rare gas atom have been extensively studied by high resolution spectroscopy. In addition, the trimer CO2-Ar2 is known, and other CO2-(Rg)n clusters are being studied in our lab. Here, we report on another family of trimers, namely those containing two CO2 molecules and one rare gas atom. The present work was inspired by our recent studies of the related trimers (CO2)2-CO and (CO2)2-N2, 1,2 whose structures can be described as resembling a CO2 dimer (near planar, staggered) with the CO or N2 aligned along the CO2 dimer C2 symmetry axis. Not surprisingly, it turns out that (CO2)2-Rg trimers have similar structures with the Rg atom located on the symmetry axis, as shown in Fig. 1.

Results
The spectra were recorded as described previously, 9,27 using a pulsed supersonic slit jet expansion probed by a rapid-scan optical parametric oscillator source. A typical gas expansion mixture contained about 0.04% CO2 plus 0.5 to 1.0% Ne, Ar, Kr, or Xe in helium carrier gas with a backing pressure of about 13 atmospheres. Wavenumber calibration was carried out by simultaneously recording signals from a fixed etalon and a reference gas cell containing room temperature CO2. Spectral simulation and fitting were made using the PGOPHER software. 28 It turns out that the C2 symmetry axis which runs through the Rg atom in (CO2)2-Rg trimers (see Fig. 1) coincides with the b-inertial axis for Ne and Ar, but the a-axis for Kr and Xe. This has consequences for the rotational selection rules in our observed spectra, as well as nuclear spin statistics (arising from equivalent CO2 molecules and zero nuclear spins for 12 C and and c-type transitions and allowed ground state levels with (Ka, Kc) = (even, even) and (even, odd). Here the c-type transitions are somewhat stronger, with the a-or b-type ones being roughly 20% weaker, as in the case of (CO2)2.
The (CO2)2-Rg spectra are difficult to observe because they tend to be obscured among stronger transitions due to CO2-Rg dimers (including CO2-He, from the He carrier gas), CO2 monomers, (CO2)2 dimers, and other larger clusters. This probably explains why they have not been reported previously. But we were encouraged by our previous detection 1 of the analogous (CO2)2-CO trimer, and by the fact that it was straightforward to estimate the (CO2)2-Rg structures (and hence rotational parameters) with reasonable accuracy. The strongest and most obvious feature in the (CO2)2-Rg spectra is a central Q-branch peak. Figure 2 shows the example of (CO2)2-Xe, for which this Q-branch appears at 2349.24 cm -1 in a relatively uncrowded region of the spectrum. It is evident that all the other spectral peaks of (CO2)2-Xe, in the P-and Rbranch regions, are much weaker than the Q-branch.  15 The strongest feature in the (CO2)2-Xe spectrum is the Q-branch at 2349.24 cm -1 . Lines marked with an asterisk are due to CO2-He.
The pattern of the present (CO2)2-Rg spectra is illustrated in Fig. 3 by simulated spectra, and the parameters resulting from fits to the spectra are listed in Table 1. The most difficult case was that of (CO2)2-Kr, in part because its Q-branch happens to be obscured by CO2 monomer absorption (R(0) of the fundamental band). This is reflected in larger standard deviations for the (CO2)2-Kr parameters in Table 1. A notable feature of these parameters is that the B-values of (CO2)2-Ne and -Ar and the A-values of (CO2)2-Kr and -Xe are nearly equal to each other (0.0463 cm -1 ) and in turn very similar to the C-value of (CO2)2 itself (0.0453 cm -1 ). This is just what we expect from the fact that the (CO2)2-Rg trimers resemble (CO2)2 with an Rg atom added on the symmetry axis.
In the case of both (CO2)2-CO and -N2, we observed two fundamental bands in the CO2 3 region, a stronger (a,c)-type band corresponding to the (CO2)2-Rg bands reported here, and a weak b-type band. 2 Detection of the weak band confirmed that the (CO2)2 dimer subunits in (CO2)2-CO and -N2 are not planar, and calculations indicated that each CO2 unit departs from planarity by about 19°. We searched for the analogous second fundamentals for (CO2)2-Rg, but were not able to observe them. This does not prove exact planarity, but it probably indicates that the (CO2)2 dimer subunits are more nearly planar for (CO2)2-Rg than for (CO2)2-CO and -N2.

Structures
Assuming C2 symmetry, four structural parameters are required to specify the structure of a (CO2)2-Rg trimer. These can be specified as: R1 (center of mass (c.m.) separation of Rg and (CO2)2 subunits); R2 (c.m. separation of CO2 subunits, that is, C-C distance);  (angle between a line connecting the C atoms of the CO2 units and an OCO axis); and  (departure from planarity of (CO2)2 subunit). But we only have three rotational constants for each trimer, and so cannot determine unique experimental structures. In order to obtain structures here, we assume  = 0 (planar (CO2)2 subunit) and this yields the structural parameters listed in Table   a  is angle between the C-C and OCO axes; R2 is the C-C distance; R1 is the Rg to (CO2)2 center of mass distance; and R(C-Rg) is the Rg to C atom distance for the trimer and (for comparison) the corresponding dimer.

Vibrational shifts
The shifts of the (CO2)2-Rg band origins with respect to that of (CO2)2 are listed in Table 3.
There is a systematic trend from a small blue shift for (CO2)2-Ne to a much larger red shift for (CO2)2-Xe. Interestingly, this trend is remarkably similar to that determined previously for CO2-Rg dimers, 25 as illustrated in two ways in Fig. 4. The lower panel in Fig. 4 also shows how both the dimer and trimer shifts have an almost linear dependence on the polarizability of the rare gas atom. The relatively small differences between the dimer and trimer shifts may be of theoretical interest for future modeling of potential surfaces and nonadditive three body effects.  Another avenue for future investigation involves combination bands of the present trimers involving excitation of the CO2 3 mode plus a low frequency intermolecular mode. Such bands have already been observed 2 for both (CO2)2-CO and -N2. They are relatively weak, but have the advantage of being more likely to appear in spectral regions with less interference from other species.
In conclusion, weakly-bound trimers of the form (CO2)2-Rg (Rg = Ne, Ar, Kr, Xe) have been observed by high-resolution infrared spectroscopy in the region of the CO2 3 fundamental band (2350 cm -1 ). Their structures resemble the carbon dioxide dimer, (CO2)2 (near planar, side-by-side staggered) with an Rg atom located on its out-of-plane C2 symmetry axis.
Experimental structures derived from the observed rotational constants (assuming planarity for the (CO2)2), confirm the similarity of the (CO2)2 unit in the trimers to the carbon dioxide dimer and give C-Rg distances similar to those in the corresponding CO2-Rg dimers. Vibrational shifts of the (CO2)2-Rg trimer band origins relative to (CO2)2 are found to be remarkably similar to those of CO2-Rg dimers relative to CO2.