Spectra of Rg-water dimers in the region of the D2O ν3 asymmetric stretch (Rg = Ar, Kr, Xe)

Spectra of rare gas (Rg) – D2O dimers (Rg = Ar, Kr, Xe) are studied in the region of the D2O ν3 asymmetric stretch (≈2800 cm−1), using a rapid-scan tunable infrared optical parametric oscillator source to probe a pulsed supersonic slit jet expansion. Three bands are observed in each case, labelled according to the D2O rotational transition with which they correlate as: Σ(101) ← Σ(000), Π(101) ← Σ(000), and Σ(000) ← Σ(101). The Ar-D2O bands exhibit various perturbations and line broadening effects. For Kr-D2O, the Π(101) ← Σ(000) and Σ(000) ← Σ(101) bands are simple and relatively unperturbed with almost no resolved Kr isotope structure, while the Σ(101) ← Σ(000) band is highly perturbed and shows large isotope splittings. This latter perturbation is analyzed in detail with good results. For Xe-D2O, the experimental spectra are unfortunately weaker. Analysis of the Π(101) ← Σ(000) and Σ(000) ← Σ(101) bands is again relatively straightforward, but the Σ(101) ← Σ(000) band is even more perturbed than for Kr-D2O and its analysis proves impossible. Line broadening (for Ar-D2O) and vibrational frequency shift effects are described. GRAPHICAL ABSTRACT


Introduction
Rare gas (Rg) -water dimers are the simplest of the many possible weakly-bound clusters containing the water molecule, but their detailed understanding still poses interesting challenges.Beginning in 1988 with farinfrared spectroscopy of Ar-H 2 O by Cohen et al. [1] there have been over forty Rg-water publications, counting only high-resolution (gas-phase) spectra and closely related theory.Almost half of these have appeared in the last ten years.
Theoretical equilibrium structures for Rg-water, given by the minimum of the potential energy surface, generally locate the Rg atom in the plane of the water molecule with an approximately hydrogen-bonded configuration adjacent to an H (or D) atom [2].But the energy barriers for rotation of the water molecule are relatively low, especially when water's small rotational moments of inertia are taken into consideration, so that it is fairly free to rotate relative to the Rg atom.For this reason, most studies have analyzed Rg-water not in terms of an asymmetric rotor molecule (which it is), but rather in terms of a pseudo-diatomic molecule with different 'vibrational' states, each of which correlates with a particular water monomer rotational state.Thus the ground state of Rg-water corresponds to the J KaKc = 0 00 level of water, and excited states correspond to rotational levels 1 01 , 1 11 , 1 10 , 2 02 , etc.When J > 0, it is necessary to specify its projection on the intermolecular axis, so the Rg-water states have labels like (0 00 ), (1 01 ), (1 01 ), (1 11 ), etc., with , , . . ., denoting projections of 0, 1, 2 . . .Of course we know that H 2 O and D 2 O have distinct nuclear spin species, one with (K a , K c ) = (even, even) or (odd, odd), and the other with (even, odd) or (odd, even), in the ground vibrational state.This carries over into Rg-water, so that if spin relaxation is slow, then even at very low temperatures ( ≈ 2 K in the present work) there are two populated 'ground' states, (0 00 ) and either (1 01 ) or (1 01 ) depending on which is lower in energy.For D 2 O, as studied here, the 0 00 level belongs to the ortho species with a spin weight of 6, and the 1 01 level (at an energy of 12.12 cm −1 ) belongs to the para species with a weight of 3.
Here we describe a few previous studies which are most relevant to the present work.Spectra of Ar-D 2 O were first reported in the early 1990s by three groups: Fraser et al. [3] studied pure rotational microwave transitions within the (0 00 ) and (1 01 ) states, Suzuki et al. [4] studied far infrared transitions from the (0 00 ) state to the (1 11 ) and (1 11 ) states (at about 19.3 and 20.7 cm −1 , respectively), and Zwart and Meerts [5] studied far infrared transitions from the (1 01 ) state to the (1 01 ) and (1 10 ) states (at about 11.0 and 14.0 cm −1 , respectively).More recently, infrared spectra of Ar-D 2 O have been studied for the D 2 O (v 1 , v 2 , v 3 ) = (0,1,0) bending fundamental ( ≈ 1200 cm −1 ) [6][7][8] and the (1,1,1) combination ( ≈ 6550 cm −1 ) [9].A fairly recent theoretical publication [10] on Ar-D 2 O reported a new potential energy surface and focused particularly on the D 2 O ν 2 mode.Results for Kr and Xe are more limited.Detailed microwave studies were reported for Kr-D 2 O by Van Wijngaarden and Jäger [11] and for Xe-D 2 O by Wen and Jäger [12], with the latter also including ab initio potential energy surface calculations.For Kr-D 2 O, infrared spectra have been studied in the (0,1,0) region [6] and a potential surface calculation was reported [13].
In the present paper, we report Rg-D 2 O spectra in the region of the D 2 O ν 3 fundamental ( ≈ 2800 cm −1 ), including three bands in each case: (1 01 ) ← (0 00 ), (1 01 ) ← (0 00 ), and (0 00 ) ← (1 01 ).Analysis of the spectra yields band origins, vibrational shifts, and upper state rotational parameters.Various perturbations and line broadening effects are observed.Especially notable is the (1 01 ) ← (0 00 ) band of Kr-D 2 O, where a local perturbation causes large Kr isotopic splittings which we analyze in detail.For Ar-D 2 O, transitions in this same band are broadened but otherwise relatively unperturbed, while for Xe-D 2 O this band is so perturbed as to resist rotational assignment.Further interesting perturbations are observed in the other two bands.

Results
Spectra were recorded as described previously [14,15] using a pulsed supersonic slit jet expansion probed by a rapid-scan tunable infrared optical parametric oscillator source.The usual supersonic expansion mixtures contained about 0.01% D 2 O plus 0.7% Ar, Kr, or Xe in helium carrier gas with a backing pressure of about 10 atmospheres.Wavenumber calibration was carried out by simultaneously recording signals from a fixed etalon and a room temperature reference gas cell.In all spectra shown here, the vertical axis corresponds to absorption in arbitrary units.Spectral assignment, simulation, and fitting were made with the help of PGOPHER [16].

Ar-D 2 O
Observed spectra of Ar-D 2 O are illustrated in Figure 1 for the bands (1 01 ) ← (0 00 ) and (0 00 ) ← (1 01 ), with two sets of experimental conditions yielding effective rotational temperatures of approximately 4 K (top traces) and 2 K (middle traces).The bottom traces are simulated spectra for 4 K.These simple parallel bands are analyzed as diatomic molecule ← transitions with ground state parameters fixed at previous literature values [4,5] and the resulting parameters are listed in Table 1.A notable difference between the two bands is that all transitions in the (1 01 ) ← (0 00 ) band at 2792 cm −1 show excess broadening due to finite upper state lifetimes (predissociation), while those in the (0 00 ) ← (1 01 ) band at 2781 cm −1 remain sharp (limited by experimental effects) for J < 4 and then broaden somewhat for J = 7-12.These line width effects are discussed in Section 2.4 below.The 2792 band transitions fit very well for J < 9, while the quality of the fit for the 2781 cm −1 band is significantly worse, even though its lines are sharper.Thus the (0 00 ) upper state evidently has small random perturbations for J values up to 10, whereas the (1 01 ) upper state line positions are less perturbed (though broadened) up to J = 8.The (1 01 ) state then experiences large perturbations at J = 8 and 9, after which J = 10 returns to an apparently unperturbed position.We were not able to analyze these perturbations in detail.
The Ar-D 2 O perpendicular band (1 01 ) ← (0 00 ), which is illustrated in the top panel of Figure 2, is more   a Quantities in parentheses are 1σ from the least-squares fit, in units of the last quoted digit.n is the number of observed lines and rmsd is the root mean square average error in the fit.b Ground state parameters are from Suzuki et al. [4] for (0 00 ) and from Zwart and Meerts [5] for (1 01 ).c Two additional lines (R(8) and R( 9)) were given zero weight; their residuals were 0.0033 and 0.0114 cm −1 , respectively.
perturbed than either parallel band.We are only able to assign transitions involving J = 1-5 for the e parity component (i.e. the P -and R-branches) and J = 1-4 for the f parity component (the Q-branch) because of line broadening for higher J .We estimate the band origin to be about 2803.05 cm −1 , but due to limited data and the presence of perturbations, our attempts to fit the (1 01 ) ← AEľ(0 00 ) band were not very meaningful.A simulated spectrum in Figure 2 does not agree very well with the observed spectrum, in which we note strong sharp Q(1) and Q(2) lines, a somewhat weaker Q(3) line, and then a very broad Q(4).Some further broad Q-branch lines seem to be visible in the 4 K spectrum, but their assignment is uncertain.The P -and R-branch lines are considerably weaker than the Q-branch, and quickly lose peak intensity with increasing J , showing large broadening for J = 3.The sudden broadening of the J = 3e and 4f levels must be due to an interaction with a (short lifetime) perturbing state, but there is not enough information for an analysis.Line broadening is discussed further below (Section 2.4).

Kr-D 2 O
The Kr-D 2 O parallel bands are illustrated in Figure 3 and the perpendicular band in Figure 2 (central panel); all three spectra correspond to an effective temperature of about 2 K.The (1 01 ) ← (0 00 ) ( ≈ 2802 cm −1 ) perpendicular band shows almost no resolved isotopic splitting.Its analysis is straightforward and yields parameters, listed in Table 2, which result in a very satisfactory root mean square deviation (rmsd) of 0.0002 cm −1 .This good fit stands in contrast to the perturbed nature of the Ar-D 2 O (1 01 ) ← (0 00 ) band in the previous section.
The widths of the Kr-D 2 O transitions increase steadily with increasing J value, especially in the P -and Rbranches (see Figure 2).This is partly due to unresolved isotopic splitting, but there seems to be additional lifetime (predissociation) broadening as well.The (0 00 ) ← (1 01 ) ( ≈ 2780 cm −1 ) band shows some resolved Kr isotopic splitting at higher J values, but the (1 01 ) ← (0 00 ) ( ≈ 2791 cm −1 ) band shows large isotopic splitting and perturbation effects for all J values.The strongest component in each P -and R-branch line of this band (see Figure 3) is due to 84 Kr, the most Ground state parameters, from our unified fit to the microwave data of Van Wijngaarden and Jäger [11], were held fixed for the infrared fits.
abundant (57%) isotope.Note how the P(3) and R( 1) lines are weaker and slightly lower in frequency than expected.Each has a rather obvious satellite line located 0.066 cm −1 higher, due to a J = 2 perturbing level (indicated by asterisks in Figure 3).The assignment of these satellites (at 2790.596 and 2791.325cm −1 in Figure 3) as real P(3) and R( 1) transitions of 84 Kr-D 2 O is confirmed by the ground state combination difference.Examining the spectrum further, it is clear that the (1 01 ) upper state must be perturbed by another state which starts higher in energy for low J , crosses (1 01 ) just above J = 2 (for 84 Kr-D 2 O), and then moves lower in energy for J = 3 and higher (the crossing point is different for different Kr isotopes).Thus the perturber has a smaller B value and larger isotope splittings than the unperturbed (1 01 ) state, and these splittings are (partially) transferred to (1 01 ) by the interaction.The reason for the small B value and large isotope splittings is that the perturber necessarily involves highly excited intermolecular vibration mode(s), as discussed further below.
In order to treat the Kr isotope effects in a unified manner we use an approach similar to that used previously for CO 2 -Kr [17] and CO 2 -Xe [18].For the isotopic dependence of the rotational constants B and D, we assume: where N represents the Kr atomic mass number, and N 0 = 84, the most abundant isotope.For simplicity, we used atomic mass number rather than the actual atomic mass.F B is the rigid rotor scaling factor, equal to the inverse ratio of the reduced mass of a particular isotopologue relative to 84 Kr-D 2 O. B adj is an empirical correction term to allow for departure from exact rigid rotor scaling.Fortunately, precise Kr-D 2 O microwave pure rotational data are available from Van Wijngaarden and Jäger [11], enabling us to test isotope dependence and determine the B adj parameter.The lower part of Table 2 shows parameters from our analysis of their data, with separate fits and different B adj values for the (0 00 ) and (1 01 ) ground states of ortho and para Kr-D 2 O.The rmsd of our microwave fits are larger than those in the original work [11], but still quite good (0.027 and 0.017 MHz, respectively).Moreover, note that each of our unified fits involves only three adjustable parameters (B, D, B adj ) as compared to eight parameters in Ref. 11 (B and D values for each of 4 isotopes, not counting hyperfine parameters).The main advantage of the unified approach is that the ground state B adj values can now be used for the excited vibrational states in our infrared spectra.Also, the model automatically gives parameters for 83 Kr-D 2 O, which was not included in the microwave results [11].The isotopic dependence of a vibrational band origin is modelled by simply assuming a linear dependence on atomic mass number, ν 0 (N) = ν 0 (N 0 ) + Offset × (N -N 0 ).For the present purposes, the results from this relationship are negligibly different from a more realistic model where, for example, a harmonic stretching frequency scales as the square root of a reduced mass.
There are only a few resolved isotopic splittings in the (0 00 ) ← (1 01 ) ( ≈ 2780 cm −1 ) band (lowest panel of Figure 3), but it is still possible to apply the unified model and the results are listed in the final column of Table 3.For this infrared fit, the ground state parameters are fixed at the values determined in our microwave fit, and the Ground state parameters, from our unified fit to the microwave data of Wen and Jäger [12] were held fixed for the infrared fits.
excited state value of B adj is fixed at the ground state value (note that this is the (0 00 ) value since para and ortho are interchanged in the (001) upper state).This leaves three adjustable parameters (B', D', and Offset) to fit 24 observed transitions with an rmsd of 0.0006 cm −1 .The resulting value of Offset for the (0 00 ) excited state is small and not very well determined.It implies a band origin shift of only -0.0023 cm −1 in going from 80 Kr-D 2 O to 86 Kr-D 2 O. Successful modelling of the highly perturbed (1 01 ) ← AEľ(0 00 ) ( ≈ 2791 cm −1 ) band requires the introduction of a perturbing state with a fairly large Offset value and a relatively small B value, both reasonable outcomes as explained below.The nature of the perturbation is illustrated in Figure 4, which shows how levels of a perturbing state cross those of (1 01 ) from above, with the crossings occurring between J = 1 and 2 for 86 Kr-D 2 O, between J = 2 and 3 for 82,83,84 Kr-D 2 O, and between J = 3 and 4 for 80 Kr-D 2 O (for clarity, 82 Kr and 83 Kr are omitted in Figure 4).The much larger isotopic splittings of the (dark) perturbing state are thus partially transferred to the (bright) (1 01 ) state.The interaction matrix element connecting (1 01 ) and the perturber, assumed to be a state, has the form W × 2 [J(J + 1)/2] 1/2 , where W is a Coriolis coupling term.One expects the isotopic variation of W to be similar to that of B, and scaling W by F B does give a reasonable fit, but better results are obtained by introducing an empirical correction parameter W adj analogous to B adj , so that Final results for the (1 01 ) ← AEľ(0 00 ) band are listed in the left-hand columns of Table 2.For this infrared fit, ground state parameters are again fixed at the values from our microwave fit, and the excited state D and B adj parameters for (1 01 ) are fixed at ground state values.A total of nine parameters are adjusted to fit 51 observed transitions, with a resulting rmsd of about 0.0004 cm −1 .It is important to note that among these transitions are 39 involving Kr isotopes other than the dominant 84 Kr, and also 11 directly involving the perturber state.The parameters varied include a band origin, B value, and Offset parameter for both the (1 01 ) and (perturber) states, plus the Coriolis parameter, W, and its empirical isotopic variation, W adj .Finally, there is a separate B adj parameter for the perturber state, the justification being that this state has a very different nature than (0 00 ) or (1 01 ) since it involves considerable excitation of large amplitude intermolecular modes.As noted, the analysis utilises a state as the perturber.We also tried assuming a state perturber, in which case the interaction matrix element is a constant with no rotational dependence (equal to about 0.03 cm −1 ).However, this perturber analysis results in a significantly worse fit than the original perturber analysis.
The success of the Kr-D 2 O (1 01 ) ← (0 00 ) ( ≈ 2791 cm −1 ) band analysis can be judged from the good agreement of observed and simulated spectra in the upper two panels of Figure 3.The parameters obtained in the fit deserve some comment.The B value of the excited (1 01 ) state is similar to that of the ground (1 01 ) state, as expected.The excited (1 01 ) state Offset parameter is small (though larger than that of (0 00 ) above), and corresponds to a band origin shift of -0.0121 cm

Xe-D 2 O
The (0 00 ) ← (1 01 ) ( ≈ 2779 cm −1 ) and (1 01 ) ← (0 00 ) (≈ 2790 cm −1 ) parallel bands of Xe-D 2 O are illustrated in Figure 5 and the (1 01 ) ← AEľ(0 00 ) ( ≈ 2800 cm −1 ) perpendicular band in Figure 2 (lower panel).The quality of these observed spectra is significantly worse than those of Ar -and Kr-D 2 O, even though we tried to use similar gas mixtures.The Xe-D 2 O spectra have much more interference from transitions due to the D 2 O monomer and dimer (the spectrum of (D 2 O) 2 in this region is reported in Ref. 15).
The 2779 and 2800 cm −1 band structures are clearly evident and have no resolved isotopic splitting or large perturbations.In contrast, the 2790 cm −1 band (upper panel, Figure 5) appears to be fragmented into many weak lines, similar to (but worse than) its Kr-D 2 O counterpart (upper panel, Figure 3).The fragmentation of this band is doubtless due to similar interactions with dark background states involving highly excited intermolecular modes, and we initially hoped to analyze the perturbation in detail, as with Kr-D 2 O.This unfortunately turned out to be impossible, but as a first step in the attempt, we made a unified fit of the ground vibrational state based on the microwave results of Wen and Jäger [12].Details of this fit are entirely analogous to those of Kr-D 2 O, and the results are shown at the bottom of Table 3 (the standard Xe atomic mass number is taken as N 0 = 131).From the microwave fit, we have precise ground state combination differences for each isotopologue of Xe-D 2 O which in principle could allow us to assign transitions in the 2790 cm −1 band even without recognising the band structure.For example, the difference between the R(0) and P(2) lines in the infrared spectrum must equal the difference between the ground state J = 0 and 2 rotational levels, which is 0.3747, 0.3739, 0.3736, 0.3729, and 0.3721 cm −1 for 129 Xe-, 131 Xe-, 132 Xe-, 134 Xe-, and 136 Xe-D 2 O, respectively.Assuming, as we suspect, that the (1 01 ) ← (0 00 ) band origin is around 2789.68 cm −1 , we observe sets of four lines each in the expected R(0) and P(2) regions whose differences equal 0.3743, 0.3727, 0.3739, and 0.3741 cm −1 .This looks promising, and when we examine other line pairs (R(1) and P(3), etc.) we also find possible matches.Many of these could be correct assignments, but putting them all together in a coherent pattern proves impossible!Our conclusion is that the (1 01 ) excited state experiences strong perturbations which are probably due to more than one highly excited intermolecular vibration (at ≈ 116 cm −1 ) within the manifold built on the D 2 O ν 1 intramolecular vibration.The calculated binding energy of Xe-H 2 O is 140 cm −1 , and that of Xe-D 2 O is likely to be around 138 cm −1 (based on the difference between Kr-D 2 O and Kr-H 2 O) [13,20].
Returning to the (0 00 ) ← (1 01 ) ( ≈ 2779 cm −1 ) and (1 01 ) ← (0 00 ) ( ≈ 2800 cm −1 ) bands of Xe-D 2 O, they are analyzed by fixing the ground state parameters at the values from our microwave fits, with results as shown in Table 3.For the (1 01 ) ← (0 00 ) band, five parameters are varied to fit 20 observed transitions with a very good rmsd of 0.0003 cm −1 .For the (0 00 ) ← (1 01 ) band, three parameters are varied to fit 12 observed transitions with an rmsd of 0.0008 cm −1 , and this larger deviation appears to be due to the poor quality .The 2779 cm −1 band is well represented by the simulated spectrum, shown in red, but the 2790 cm −1 band is highly perturbed and is not rotationally assigned, so its exact band origin is uncertain (the simulated spectrum is an approximate guess).
of the spectrum and not due to obvious upper state perturbations.

Line broadening
The observed line broadening in the (0 00 ) ← (1 01 ) and (1 01 ) ← (0 00 ) bands of Kr -and Xe-D 2 O is at least partly due to unresolved isotopic splitting, and this makes it difficult to measure reliably the possible effects due to lifetime broadening (predissociation).No isotopic splitting has to be considered for Ar-D 2 O, for which observed broadening effects are summarised in Table 4 and Figure 6.Precise uncertainties for these broadening parameters are difficult to evaluate, but we estimate that they should be reliable to within about ±10%.The broadening of the rotational levels of the (0 00 ) upper state is smaller than we can measure up to J = 3, reaches a maximum of about 0.0096 cm −1 at J = 8, and then declines somewhat up to the last observed level, J = 12.In contrast, broadening in the (1 01 ) upper state is already present for J = 0, with a value which is roughly constant ( ≈ 0.009 cm −1 ) up to J = 6.It then rises to a peak of 0.02 cm −1 at J = 10, and falls back to about 0.005 cm −1 at J = 11.Finally, the (1 01 ) upper state has highly variable widths, including rather large ones for the J = 3(e) component (0.04 cm −1 , Pand R-branches) and J = 4(f ) component (0.03 cm −1 , Qbranch).Calculated [10] binding energies for Ar-D 2 O are about 95 cm −1 for (0 00 ), 102 cm −1 for (1 01 ), and 91 cm −1 for (1 01 ), and in isolated D 2 O the ν 1 vibrational state lies 116 cm −1 below the ν 3 state.Thus the Ar-D 2 O states associated with ν 1 which could perturb (and  Perturbations and broadening in the analogous ν 3 spectra of Ar-H 2 O were studied by Nesbitt and Lascola [21,22], with further theoretical analysis reported by Bissonette and Clary [23].It was observed that transitions remained sharp in the (1 01 ) ← (0 00 ) and (0 00 ) ← (1 01 ) bands, and in the Q-branch of the (1 01 ) ← (0 00 ) band, but were broadened by predissociation in the Pand R-branches of the (1 01 ) ← (0 00 ) band.The Q-branch accesses the f symmetry components of the (1 01 ) state, while the Pand R-branches access the e components.The fact that the ν 3 (1 01 ) levels with e symmetry are broadened, but not the f levels, was nicely explained as being due to the energies of the respective symmetry-allowed interaction channels being above or below the ν 1 dissociation threshold.In the present case, Ar-D 2 O binding energies are slightly increased ( ≈ 5 cm −1 ) compared to Ar-H 2 O, but, more significantly, the separation between ν 3 and ν 1 is larger for D 2 O (116 cm −1 ) than for H 2 O (99 cm −1 ).The combined effect is that the Ar-D 2 O ν 3 (1 01 ) e and f components both lie above their respective ν 1 dissociation thresholds, as do the ν 3 (0 00 ) and (1 01 ) states.Thus all our observed bands show some broadening, which is almost certainly due to interactions with levels just above the ν 1 threshold.Unfortunately, it is not currently possible to make a detailed analysis of these effects for Ar-D 2 O similar to that of Nesbitt and Lascola [22] for Ar-H 2 O.This is partly because we do not have detailed calculations of high-lying (above dissociation) Ar-D 2 O energy levels, but also because our low rotational temperatures (compared to Nesbitt and Lascola) mean that fewer lines are observed and analysis of the bands is limited, especially for (1 01 ) ← (0 00 ).

Vibrational shifts
Vibrational frequency shifts of simple van der Waals dimers containing Rg atoms are often roughly proportional to the Rg polarizability [24].In Figure 7, we plot the present Rg-D 2 O band origins in this way, showing how they correlate with the respective 0 00 ← 1 01 and 1 01 ← 0 00 transitions in the D 2 O monomer ν 3 band.The fairly large changes indicated by the solid lines connecting

Conclusions
Spectra of Rg-D 2 O dimers (Rg = Ar, Ke, Xe) in the region of the D 2 O ν 3 asymmetric stretch fundamental ( ≈ 2800 cm −1 ) have been studied, using a tunable optical parametric oscillator source to probe a pulsed slit jet supersonic expansion.In spite of considerable recent interest in rare gas -water dimers, this represents the first infrared study involving Xe, and one of only a few involving Kr.Three bands were observed for each dimer, labelled as (1 01 ) ← (0 00 ), (1 01 ) ← (0 00 ), and (0 00 ) ← (1 01 ).For Ar-D 2 O, various effects of line broadening due to predissociation (finite lifetime) were observed, particularly for the (1 01 ) and (1 01 ) upper states.For Kr-D 2 O, the (1 01 ) ← AEľ(0 00 ) band was notable because it showed large Kr isotope dependent splitting effects due to perturbation by a 'dark' background state which could be analyzed in detail.For Xe-D 2 O, the observed spectra were relatively weak and the (1 01 ) ← (0 00 ) band was so perturbed as to defy analysis, but the other bands still gave clear results.

Figure 2 .
Figure 2. Observed and simulated spectra of the (1 01 ) ← (0 00 ) band of Ar-, Kr-, and Xe-D 2 O. Gaps in the observed spectra correspond to regions of D 2 O absorption.

Figure 3 .
Figure 3. Observed and simulated spectra of Kr-D 2 O. Gaps in the observed spectra correspond to regions of D 2 O and (D 2 O) 2 absorption.Weaker lines to the low frequency side of the observed spectrum in the bottom panel are (D 2 O) 2 absorptions.

Figure 4 .
Figure 4. Illustration of the perturbation affecting the excited (1 01 ) state of Kr-D 2 O.For clarity, all rotational energies are reduced by the quantity B eff × J(J + 1), with B eff = 0.071 cm −1 , and the 82 Kr and 83 Kr isotopologues are omitted.Note how the levels of the (1 01 ) state (circles) are shifted by interactions with a perturbing state (squares) which crosses the (1 01 ) state at different points depending on isotope.

Figure 5 .
Figure 5. Observed and simulated spectra of Xe-D 2 O parallel bands.The Xe-D 2 O transitions (Xe/D 2 O/He spectrum shown in blue) are strongly overlapped by (D 2 O) 2 transitions [15] (D 2 O/He spectrum in black).The 2779 cm −1 band is well represented by the simulated spectrum, shown in red, but the 2790 cm −1 band is highly perturbed and is not rotationally assigned, so its exact band origin is uncertain (the simulated spectrum is an approximate guess).

Figure 6 .
Figure 6.Observed line widths (FWHM) in the spectrum of Ar-D 2 O.These are the widths, assumed to be Lorentzian in shape, which are in excess of the normal instrumental width (approximately Gaussian in shape) of about 0.0029 cm −1 .

Figure 7 .
Figure 7. Vibrational frequencies of Rg-D 2 O complexes as a function of Rg polarizability.The D 2 O monomer ν 3 band 0 00 ← 1 01 and 1 01 ← 0 00 rotational transitions (para and ortho spin species, respectively) correlate with the observed Rg-D 2 O bands as indicated (solid lines).The energies of the excited state 0 00 levels (that is, the overall band origins) are shown by the dashed line, where we assume that the ratio of the 1 01 level energies in the ground and excited states for D 2 O-Rg is the same as for D 2 O.

D 2 O
and Ar-D 2 O in this plot demonstrate that the rotation of D 2 O is significantly hindered by the nearby Ar atom.But interestingly the degree of hindering then does not change very much in going to Kr and Xe, possibly because their stronger interactions with D 2 O are compensated by larger intermolecular distances.The dashed line in Figure 7 represents the energy of the J = 0 level in each case, in other words the actual band origin.This line, which better represents the purely vibrational shift effect, is indeed approximately linear as a function of polarizability.

Table 2 .
Molecular parameters for Kr-D 2 O (in cm −1 ). a Quantities in parentheses are 1σ from the least-squares fit, in units of the last quoted digit.n is the number of observed lines in a fit, and rmsd the root mean square average error.Quantities in square brackets were held fixed.Units are in cm −1 except for ground state rmsd (MHz), Offset (cm −1 /Dalton), B adj , W adj ([Dalton] −1 ).Origins and rotational parameters refer specifically to 84 Kr-D 2 O, while B adj , W adj , and Offset describe how these parameters vary with Kr isotope. a

Table 3 .
Molecular parameters for Xe-D 2 O (in cm −1 ). a (1 01 ) ← (0 00 ) (1 01 ) ← (0 00 ) (0 00 ) ← (1 01 ) Quantities in parentheses are 1σ from the least-squares fit, in units of the last quoted digit.n is the number of observed lines in a fit, and rmsd the root mean square average error.Units are in cm −1 except for ground state rmsd (MHz) and B adj ([Dalton] −1 ).Ground state rotational parameters refer specifically to 131 Xe-D 2 O, while B adj describes the variation with Xe isotope. a [19,20]ing from80Kr-D 2 O to 86 Kr-D 2 O.The B value obtained for the (perturber) state is 0.044 cm −1 (for 84 Kr), which at first sight seems impossibly small compared to the usual Kr-D 2 O B value of about 0.072 cm −1 .However, the only reasonable perturbing state involves excitation of the D 2 O ν 1 intramolecular vibration plus considerable excitation of (floppy) intermolecular vibration(s), and the energy of this intermolecular excitation is approximately 116 cm −1 , the amount by which ν 1 lies below ν 3 .Calculated13binding energies of Kr-D 2 O are 121 cm −1 for (0 00 ) or 127 cm −1 for (1 01 ), so the perturbing state lies just below the dissociation threshold.The only available Kr-D 2 O calculation[13]does not include intermolecular vibrational states this high in energy, but in some other water-Rg calculations there are a number of examples of high lying intermolecular states with greatly reduced effective B values[19,20].So the small B value of the perturber state is not unreasonable. The psitive value of B adj for the perturber state is sufficiently large and positive that it causes B to vary from 0.0431 to 0.0445 cm −1 in going from 80 Kr to 86 Kr, a reversal in sign of the expected isotopic dependence.This apparently anomalous variation with reduced mass may not be real, in that it could be a result of the fitting procedure which compensates for imperfections in our model.Or, it could represent a real variation of the effective B value due to isotope dependent mixing of the perturber state with other nearby intermolecular vibrations.The perturber state has a relatively large Offset value, which is just what we would expect for a highly excited intermolecular vibration: intermolecular modes depend much more strongly on Kr mass than do intramolecular (D 2 O) vibrations.The Offset value represents a band origin shift of -0.3244 cm −1 in going from 80 Kr-D 2 O to 86 Kr-D 2 O.The Coriolis interaction parameter, W, has a value of 0.0088 cm −1 for 84 Kr, and the value determined for W adj means that W varies from 0.0074 to 0.0095 cm −1 in going from 80 Kr to 86 Kr.

Table 4 .
Lorentzian widths and excited state lifetimes of Ar-D 2 O in the (001) state of D 2 O.