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Rotational Spectroscopic Study of Quantum Solvation in Isotopologic (pH) -CO Clusters 2
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Paul L Raston, and Wolfgang Jaeger J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 01 May 2017 Downloaded from http://pubs.acs.org on May 6, 2017
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The Journal of Physical Chemistry
Rotational Spectroscopic Study of Quantum Solvation in Isotopologic (pH2)N-CO Clusters Paul L. Raston1* and Wolfgang Jäger2 1
Department of Chemistry and Biochemistry, James Madison University, Harrisonburg, Virginia 22807, USA
2
Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
*
Author to whom correspondence should be addressed. Electronic mail:
[email protected].
Abstract: We report the Fourier transform microwave spectra of (pH2)N-13C16O, (pH2)N12 18
C O, and (pH2)N-13C18O (N≤8) clusters. We find that the frequencies of the a-type J=1-0
transitions decrease to a minimum at N=6, then rapidly increase up to at least N=8; this is similar to what was previously reported for (pH2)N-12C16O, for which the turnaround was found to correlate with an increase in the superfluid fraction of the pH2 component of the clusters [Raston et al., Phys. Rev. Lett., 2012, 108, 253402]. The data suggest that the turnaround in the transition frequency marks an abrupt decrease in the anisotropy of the potential (i.e. in going from N=6→7→8), as evidenced from the isotopologic differences rapidly evolving from end-over-end to free-rotor character. Structurally, a more quantitative analysis of the anisotropy was hindered by the lack of accurate frequencies in the b-type series, and a simple Kraitchman analysis yielded unphysical results. In addition to comparing the transition frequencies of the different isotopologic clusters, we provide here more comprehensive details and further discussion of the initial measurements made on (pH2)N12 16
C O.
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1. Introduction Studies of molecules and clusters embedded in helium nanodroplets (N>1000) have provided convincing evidence that these finite sized systems are superfluid.1-3 Solid evidence came from the electronic spectrum of glyoxal embedded in helium nanodroplets, where a phonon gap, characteristic of superfluid helium, was observed.4 Indications of a Landau critical velocity were gained from the laser induced ejection of NO molecules and Ag atoms from helium nanodroplets, where a peak in the speed distribution of ~50 m/s was determined.5 Direct evidence that helium nanodroplets are superfluid came from the identification of quantum vortices by imaging xenon clusters pinned to them.6 In analogy to the classic Andronikashvili experiment where the superfluid fraction was established as a function of temperature,7 the "microscopic Andronikashvili experiment" focused on determining the number of 4He atoms required for superfluidity around an OCS molecule in 3He nanodroplets to occur.8 Size resolved rotational studies of relatively small helium clusters (N1) clusters. Interestingly, it was suggested over a decade ago43 that CO would be a better probe for perpendicular superfluid response44 than OCS because of its weaker interactions with pH2 (the H2-CO well depth is 109.27 cm-145). While a perpendicular response has not been observed in (pH2)N-OCS clusters (for N≤746), evidence for a parallel response has been gained from anomalies in the infrared spectra of (pH2)N-OCS in helium nanodroplets;47 the Q-branch disappeared from the infrared spectrum for certain cluster sizes, and this was theoretically connected with superfluidity in the dimension parallel to the OCS axis.48 Subsequent simulations for (pH2)N-OCS clusters predict partial decoupling of (pH2)N density from cluster rotation for N≥14, and associate this with an increase in the perpendicular superfluid pH2 fraction.49 This non-classical response is predicted to occur significantly later than in the case of the corresponding HeN-OCS clusters (N=9→10) as a result of the stronger interactions between pH2 and OCS.12 Microwave50 and infrared46 studies of (H2)N-OCS clusters with N up to 7 did not reveal a non-classical behavior of the rotational constants. Molecular superfluid responses have since been observed for both CO2 and CO probes, where the turnaround is delayed from N=5→6 for HeN-CO211 to N≈11→12 for (pH2)N–CO239, and from N=3→4 for HeN-CO14 to N=6→7 for (pH2)N–CO51. The turnaround occurs at lower N for CO containing clusters because of the more isotropic effective interaction potential with HeN or (pH2)N, which facilitates solvent delocalization. The first spectroscopic investigation of (pH2)N-12C16O clusters was by Moroni et al. in the infrared spectral region.52 In that study, the a- and b-type R1(0) transitions (υ=1←0, J=1←0) of clusters with N≤17 were detected and assigned with the aid of simulations. For the most part, only transitions from the ground rotational state were observed for each cluster size, and so separation of the rotational and vibrational contributions to the line positions was not possible. In a more recent study, the a-type R0(0) microwave transitions (υ=0←0, J=1←0) of clusters with N≤8 were reported, thus allowing for reasonably accurate determination of the rotational and vibrational contributions to the infrared line positions.51 Here, we report the analogous transition frequencies (R0(0)) for three minor isotopologues of CO (13C16O, 12C18O, and 13C18O). -3-
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2. Experimental The details of the experimental apparatus used to measure rotational spectra of (pH2)NCO clusters have been presented elsewhere.53-54 Briefly, the clusters are produced using a pulsed nozzle with conical exit channel and then expanded into an evacuated Fabry-Pérot resonator consisting of two spherical aluminum mirrors. The a-type J=1-0 rotational transition of clusters with a specific N value are then excited with a π/2 microwave excitation pulse, and the subsequent coherent emission signal at the resonance frequency is detected in the time domain and Fourier transformed to give the power spectrum. Typical sample gas mixtures consisted of 0.01% CO and 5% pH2 in He, at pressures of up to 150 bar (2200 psi). para-enriched hydrogen was produced by liquefying normal-hydrogen for approximately one hour in the presence of chromium oxide. The apparatus previously used36, 50
was improved upon for the (pH2)N-CO studies by enclosing the stainless steel converter in a
copper sleeve which extends into liquid helium, as inspired by Ref. 55. This allows for better control over the temperature, without which the conversion efficiency is poor. The converter was conditioned before each use by heating it to over one hundred degrees Celsius under vacuum, followed by flushing with hydrogen gas before cooling.
3. Results and discussion 3.1 Normal isotopologue The transitions of the normal isotopologue were measured and assigned before those of the minor isotopologues, and so we discuss them first. Two sets of predicted rotational frequencies for (pH2)N-12C16O clusters were available from the joint infrared-computational study to aid the search for microwave transitions.52 The first was obtained from the experimental data, under the assumption that the vibrational band shift decreases linearly from N=1 to 8, utilizing the known shift for (pH2)1-CO.56 The second was from rotational dynamics simulations which employed the reptation quantum Monte Carlo algorithm57 using Bose statistics52. As previously reported,51 we found seven lines in the 10-26 GHz range, corresponding to the a-type J=1-0 transitions of (pH2)N=2-8-12C16O. The assignment was primarily made from the intensity variations in the line intensities with the concentration of pH2 in the gas mixture, as shown in Fig. 1. We also relied on the smoothness in evolution of the isotopologic data (see next section) and vibrational shift (see below), the proximity and similarity in trend of the measured and predicted transition frequencies (see Fig. 2), and the pressure dependence of the line intensities (see Fig. S1) to establish firm assignments. Despite -4-
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The Journal of Physical Chemistry
considerable efforts, we were unable to detect the warmer a-type J=2-1 line of (pH2)6-CO, which is predicted to lie just at the edge of the operating range of our spectrometer. The low rotational temperature at the high backing pressure of the expansion, together with the suboptimal spectrometer performance in this frequency range, may be to blame. Note that the CO unit undergoes quasi-free internal rotation within these clusters and that it is most appropriate to use (J, j, l) notation to label energy levels.58 Here, the quantum numbers l, j, J correspond to the end-over-end rotation of the cluster, to the CO internal rotation, and to their vector sum, respectively. The a-type J=1-0 (i.e. J,j,l = 101←000) transition frequencies are listed in Table 1. The transition frequencies for N=1-8 are plotted in Fig. 2 for the normal isotopologue, and are shown together with the values from theory.52 The comparison reveals the calculated values to be in reasonable agreement with the measured ones, although, as with HeN-CO, the calculated values (both using reptation quantum Monte Carlo) are somewhat overestimated;14, 59
note that the calculated rotational energies of HeN-CO from Ref. 60 (using diffusion Monte
Carlo) are much closer to the experimental values. This may be due to the quality of the (pH2)-CO potential energy surface used in the quantum Monte Carlo simulations. The basis for this assumption lies in two previous quantum Monte Carlo simulations of HeN-OCS,17-18 where the discrepancies between the calculated rotational energies can be traced back to the different He-OCS surfaces used.61 It will be interesting to see how theory and experiment compare using the recently reported potential that was used to assign the notoriously complicated infrared spectrum of ortho-H2-CO.62-63 The turnaround in rotational frequency of (pH2)N-CO in going from N=6→7 coincides with an increase in the superfluid fraction, and this was explained by the shift in the differential hydrogen density (∆ρN = ρN - ρN-1) from the oxygen end of CO towards the carbon end.51 Unlike the case of (pH2)N-CO2 clusters, where the pronounced turnaround in going from N=11→12 is transitory,39, 64 it seems to persist in (pH2)N-CO clusters for N>6.51-52 The vibrational band shift of CO as a function of the number of attached pH2 molecules is shown in Fig. 3. It was obtained by subtracting the R0(0) microwave frequencies from the a-type R1(0) infrared transition frequencies,52 thus assuming that the rotational frequencies are the same in the ground and first excited vibrational states; this is approximately valid considering the υ=0 and υ=1 B constants differ by only 0.2% for pH2CO.56, 65 It was pointed out in the infrared study that the assignments of the a-type transitions for N=6 and 7 may be interchanged.52 As discussed previously,51 not only doing this, but also reassigning the "N=7" peak to N=6 & 8 results in a much smoother vibrational shift with -5-
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respect to N, thus supporting this assignment. The binding energy of pH2-CO is 3.5 times larger than that of He-CO,45, 66 which results in an increasingly nonlinear vibrational shift of pH2-CO relative to He-CO with increasing N.14, 67 In Fig. 4 we show the "measured" (N=1-8) and extrapolated (N=9-12) experimental B values for (pH2)N-12C16O clusters using the microwave and infrared data, under the assumption of a linear vibrational shift (see figure caption for details). Here we assume that the rotational transition frequencies are approximately given by 2B, thus neglecting the centrifugal distortion term, DJ, which only contributes 0.3% to the J=1-0 rotational frequency for pH2-CO.56 For doped helium clusters, where sufficient data are available, DJ is less than 0.6% of B for N
