Infrared spectra of Ne–C_{2}D_{2} are observed in the region of the ν_{3} fundamental band (asymmetric C–D stretch, ≈2440 cm^{−1}) using a tunable optical parametric oscillator to probe a pulsed supersonic slit jet expansion from a cooled nozzle. Like helium-acetylene, this system lies close to the free rotor limit, making analysis tricky because stronger transitions tend to pile up close to monomer (C_{2}D_{2}) rotation-vibration transitions. Assignments are aided by predicted rotational energies calculated from a published *ab initio* intermolecular potential energy surface. The analysis extends up to the *j* = 3←2 band, where *j* labels C_{2}D_{2} rotation within the dimer, and is much more complete than the limited infrared assignments previously reported for Ne–C_{2}H_{2} and Ne–C_{2}HD. Two previous microwave transitions within the *j* = 1 state of Ne–C_{2}D_{2} are reassigned. Coriolis model fits to the theoretical levels and to the spectrum are compared. Since the variations observed as a function of C_{2}D_{2} vibrational excitation are comparable to those noted between theory and experiment, it is evident that more detailed testing of theory will require vibrational averaging over the acetylene intramolecular modes.

## I. INTRODUCTION

There have been two previous experimental studies of spectra of the weakly bound neon–acetylene van der Waals complex. The first, in 1998, examined infrared transitions of Ne–C_{2}H_{2} and Ne–C_{2}HD in the C–H stretching region (≈3300 cm^{−1}).^{1} Rotational assignments were made for Ne–C_{2}HD with the help of accompanying theoretical calculations, but it turned out that the Ne–C_{2}H_{2} spectrum is broadened by predissociation effects so that detailed assignments were not possible, though the observations were still generally compatible with theory. The second neon-acetylene paper, in 2003, was a comprehensive study of microwave transitions (5–23 GHz) which included eight different isotopologues.^{2} Neon-acetylene is close to the free rotation limit (as discussed further below) which makes rotational assignments somewhat tricky and means that the quantum number for acetylene rotation, which we label as *j*, is significant. All the assignments in the two previous papers involved only levels correlating with *j* = 0 and 1. The present paper is a study of the infrared spectrum of Ne–C_{2}D_{2} in the C–D stretching region (≈2450 cm^{−1}). To help overcome the tricky assignment problem just mentioned, we make use of detailed energy level predictions from a high-level *ab initio* potential energy surface^{3} and of a Coriolis interaction model. Compared to the previous work,^{1,2} our rotational assignments are considerably extended, reaching up to levels correlating with *j* = 2 and 3. As well, the analysis reveals that two microwave transitions were previously mis-assigned.

Spectra of neon-acetylene, and the problems of analysing them, resemble in many ways those of helium-acetylene,^{4–12} and the present work is particularly related to our recent study of He–C_{2}D_{2}.^{5} Of course, the Ne complexes are more strongly bound, but by some measures they seem just as close to the free rotation limit. In contrast, complexes of C_{2}H_{2} with Ar^{13–22} and Kr^{23,24} behave much more like “normal” semi-rigid molecules.

## II. THEORETICAL *AB INITIO* ENERGY LEVELS

The rotational level labelling scheme is the same as used previously for He–C_{2}D_{2}.^{5} In addition to quantum number *j* for C_{2}D_{2} internal rotation, we have *J* for the total angular momentum, σ, π, δ, φ, or γ for the projection of *J* on the intermolecular axis (i.e., *K* = 0, 1, 2, 3, 4), and *e* or *f* for parity.^{25} For *j* = 0, there is a single rotational “stack” (*J* = 0, 1, 2, etc.) with *e* parity. For *j* = 1, there are three stacks: σ*e*, starting with *J* = 0, plus π*e* and π*f* starting with *J* = 1. For *j* = 2, there are five stacks: the same three as for *j* = 1, plus a pair (*e* and *f*) of δ stacks which start with *J* = 2. And for *j* = 3, there are seven stacks: the same five as for *j* = 2, plus a pair of φ stacks which start with *J* = 3. Within a given value of *j* > 0, stacks with the same parity (*e* or *f*) become increasingly mixed with increasing *J* by a Coriolis interaction, so their labelling (as σ, π, etc.) becomes increasingly ambiguous.

A potential energy surface for neon–acetylene obtained at the coupled-cluster single double (triple) [CCSD(T)] level by Fernández and Munteanu^{3} is used in our calculations. It has a global energy minimum at −50.20 cm^{−1} for an intermolecular distance of *R* = 3.95 Å and a Ne–H–C angle of 43.3°. This skewed global minimum is different from the linear geometry of helium-acetylene, but there is also a linear local minimum only 0.46 cm^{−1} higher in energy. Energy levels for Ne–C_{2}D_{2} calculated using the BOUND program^{26} are illustrated graphically in Fig. 1, and listed in Table A-I of the supplementary material.^{27} For greater clarity, Fig. 1 is a *reduced* energy diagram in which, for a given *J* value, the energy of the lowest (*j* = 0) state level is subtracted. Thus, the lowest *j* = 0 σ state appears as a horizontal line at the bottom of Fig. 1, with the other levels are expressed relative to it. Figure 1 includes levels with *J* = 0–8 and *j* = 0–4. Near the top of the diagram, a new set of levels with *j* = 0 and 1 appears, which we assign to the first excited van der Waals stretch mode of the dimer. These *j* = 0 levels cross the upper *j* = 4 levels of the ground state, causing some perturbations. Note, however, that even- and odd-*j* levels cannot interact due to symmetry, so the excited *j* = 1 levels do not perturb *j* = 4. As *J* increases, each *j*-value in Fig. 1 fans out to form a series of roughly evenly spaced levels. This even spacing is characteristic of, and can be labelled by, a rotational quantum number *L* which characterizes the end-over-end rotation of the dimer. Generally speaking, labelling with (*j*, *J*, *L*) works better for higher *J*, while labelling with (*j*, *J*, *K*, *e*, or *f*) works better for low *J*.

## III. THE CORIOLIS MODEL FOR ROTATIONAL ENERGIES

The Coriolis model^{28,29} we used for He–C_{2}D_{2} is also employed here, and the reader is referred to Ref. 5 for details. Rotational energies for the *j* = 0 σ*e* and *j* = 1 *πf* stacks (not affected by Coriolis interactions) are given by simple linear molecule expressions,

The *j* = 1 σ*e* and 1 π*e* energies are obtained by diagonalizing a 2 × 2 matrix with diagonal elements,

and

and off-diagonal elements given by [*β*(1) *J*(*J* + 1) + *β*(1)_{D} (*J*(*J* + 1))^{2}]^{1/2}, where *β* characterizes the strength of the Coriolis interaction.

The *j* = 2 levels are represented similarly, with diagonal energies,

and off-diagonal elements [*β*(2) *J*(*J* + 1) + *β*(2)_{D} (*J*(*J* + 1))^{2}]^{1/2} connecting the (2σ) and (2π) levels, or [*γ*(2) (*J*(*J* + 1) − 2) + *γ*(2)_{D} (*J*(*J* + 1) − 2)^{2}]^{1/2} connecting the (2π) and (2δ) levels. The expressions for *j* = 3 and 4 are entirely analogous, with added parameters *E _{v}*,

*B*, and

*D*for the φ (

*K*= 3) and γ (

*K*= 4) stacks and added Coriolis parameters

*δ*(connecting δ and φ levels) and ε (connecting φ and γ levels). (The

*δ*(3) or

*δ*(4) Coriolis parameters are not to be confused with the δ (

*K*= 2) stack labels.)

The results of fitting this Coriolis model to the theoretical levels (Table A-I of the supplementary material)^{27} are shown in the first column of Table I for *j* = 0–3, and in Table A-II for *j* = 4.^{27} The fit included all levels up to *J* = 8, and the quality of the fit was very good, with average errors of 0.000 05, 0.000 15, 0.000 93, 0.000 36, and 0.000 45 cm^{−1} for *j* = 0, 1, 2, 3, and 4, respectively. Note that three levels for *j* = 4 were given reduced weight due to the perturbation mentioned above. The values of the resulting parameters in Table I and Table A-II^{27} are generally reasonable and self-consistent.

. | v = 0 . | v = 1 . | |
---|---|---|---|

. | Theory^{a}
. | Experiment^{b}
. | Experiment^{b}
. |

E(0) _{v} | 0.0 | 0.0 | [2439.35] |

B(0) | 0.089 051 2(35) | 0.089 067 52(32) | 0.089 499(20) |

D(0) | 0.000 020 95(15) | 0.000 024 861(36) | 0.000 023 89(32) |

H(0) | −8.50(15) × 10^{−8} | −7.32(11) × 10^{−8} | [−7.30 × 10^{−8}] |

E(1σ) _{v} | 1.446 00(13) | 1.433 77(29) | 1.446 08(35)^{c} |

B(1σ) | 0.081 966(13) | 0.081 754(12) | 0.081 531(32) |

D(1σ) | 0.000 011 57(19) | 0.000 013 34(29) | 0.000 012 53(58) |

E(1π) _{v} | 1.807 79(12) | 1.896 46(27) | 1.693 60(28)^{c} |

B(1π) | 0.093 621 2(90) | 0.094 095(20) | 0.094 117(17) |

D(1π) | 0.000 013 34(13) | 0.000 013 23(33) | 0.000 012 19(21) |

β(1)^{1/2} | 0.081 725(14) | 0.081 517(18) | 0.081 283(32) |

β(1)_{D}^{1/2} | −0.000 029 66(27) | −0.000 034 5(6) | −0.000 034 8(10) |

E(2σ) _{v} | 5.190 64(92) | 5.031 19(40) | 5.054 77(47)^{c} |

B(2σ) | 0.083 226(102) | 0.083 419(50) | 0.082 418(55) |

D(2σ) | −0.000 011 2(16) | −0.000 018 2(10) | −0.000 018 9(12) |

E(2π) _{v} | 4.820 33(86) | 4.848 35(37) | 4.840 38(43)^{c} |

B(2π) | 0.087 191(75) | 0.087 143(40) | 0.087 061(33) |

D(2π) | 0.000 007 7(11) | 0.000 005 0(9) | 0.000 006 95(65) |

E(2δ) _{v} | 5.158 7(12) | 5.191 67(54) | 5.036 94(56)^{c} |

B(2δ) | 0.096 122(90) | 0.096 760(49) | 0.096 895(47) |

D(2δ) | 0.000 012 6(12) | 0.000 013 7(9) | 0.000 015 42(93) |

β(2)^{1/2} | 0.133 367(92) | 0.132 003(43) | 0.131 146(57) |

β(2)_{D}^{1/2} | −0.000 079 8(18) | −0.000 079 2(13) | −0.000 067 2(20) |

γ(2)^{1/2} | 0.124 77(11) | 0.124 772(52) | 0.124 834(74) |

γ(2)_{D}^{1/2} | −0.000 035 4(21) | −0.000 036 0(17) | −0.000 042 8(24) |

Ev(3σ) | 9.421 38(34) | 9.166 11(57)^{c} | |

B(3σ) | 0.082 880(45) | 0.082 643(87) | |

D(3σ) | 0.000 003 66(71) | 0.000 002 4(28) | |

Ev(3π) | 10.405 13(34) | 10.237 92(62)^{c} | |

B(3π) | 0.084 973(37) | 0.084 431(88) | |

D(3π) | 0.000 005 94(55) | −0.000 001 7(23) | |

Ev(3δ) | 9.843 98(54) | 9.737 41(71)^{c} | |

B(3δ) | 0.090 172(43) | 0.090 541(82) | |

D(3δ) | 0.000 009 88(58) | 0.000 022 6(18) | |

Ev(3φ) | 10.004 92(84) | 9.774 32(151)^{c} | |

B(3φ) | 0.097 930(52) | 0.098 71(13) | |

D(3φ) | 0.000 008 06(64) | 0.000 010 8(27) | |

β(3)^{1/2} | 0.180 671(46) | 0.177 944(120) | |

β(3)_{D}^{1/2} | −0.000 049 85(85) | −0.000 038 7(54) | |

γ(3)^{1/2} | 0.180 496(56) | 0.178 634(119) | |

γ(3)_{D}^{1/2} | −0.000 073 8(11) | −0.000 090 8(55) | |

δ(3)^{1/2} | 0.159 030(59) | 0.159 108(83) | |

δ(3)_{D}^{1/2} | −0.000 052 0(11) | [−0.000 035] |

. | v = 0 . | v = 1 . | |
---|---|---|---|

. | Theory^{a}
. | Experiment^{b}
. | Experiment^{b}
. |

E(0) _{v} | 0.0 | 0.0 | [2439.35] |

B(0) | 0.089 051 2(35) | 0.089 067 52(32) | 0.089 499(20) |

D(0) | 0.000 020 95(15) | 0.000 024 861(36) | 0.000 023 89(32) |

H(0) | −8.50(15) × 10^{−8} | −7.32(11) × 10^{−8} | [−7.30 × 10^{−8}] |

E(1σ) _{v} | 1.446 00(13) | 1.433 77(29) | 1.446 08(35)^{c} |

B(1σ) | 0.081 966(13) | 0.081 754(12) | 0.081 531(32) |

D(1σ) | 0.000 011 57(19) | 0.000 013 34(29) | 0.000 012 53(58) |

E(1π) _{v} | 1.807 79(12) | 1.896 46(27) | 1.693 60(28)^{c} |

B(1π) | 0.093 621 2(90) | 0.094 095(20) | 0.094 117(17) |

D(1π) | 0.000 013 34(13) | 0.000 013 23(33) | 0.000 012 19(21) |

β(1)^{1/2} | 0.081 725(14) | 0.081 517(18) | 0.081 283(32) |

β(1)_{D}^{1/2} | −0.000 029 66(27) | −0.000 034 5(6) | −0.000 034 8(10) |

E(2σ) _{v} | 5.190 64(92) | 5.031 19(40) | 5.054 77(47)^{c} |

B(2σ) | 0.083 226(102) | 0.083 419(50) | 0.082 418(55) |

D(2σ) | −0.000 011 2(16) | −0.000 018 2(10) | −0.000 018 9(12) |

E(2π) _{v} | 4.820 33(86) | 4.848 35(37) | 4.840 38(43)^{c} |

B(2π) | 0.087 191(75) | 0.087 143(40) | 0.087 061(33) |

D(2π) | 0.000 007 7(11) | 0.000 005 0(9) | 0.000 006 95(65) |

E(2δ) _{v} | 5.158 7(12) | 5.191 67(54) | 5.036 94(56)^{c} |

B(2δ) | 0.096 122(90) | 0.096 760(49) | 0.096 895(47) |

D(2δ) | 0.000 012 6(12) | 0.000 013 7(9) | 0.000 015 42(93) |

β(2)^{1/2} | 0.133 367(92) | 0.132 003(43) | 0.131 146(57) |

β(2)_{D}^{1/2} | −0.000 079 8(18) | −0.000 079 2(13) | −0.000 067 2(20) |

γ(2)^{1/2} | 0.124 77(11) | 0.124 772(52) | 0.124 834(74) |

γ(2)_{D}^{1/2} | −0.000 035 4(21) | −0.000 036 0(17) | −0.000 042 8(24) |

Ev(3σ) | 9.421 38(34) | 9.166 11(57)^{c} | |

B(3σ) | 0.082 880(45) | 0.082 643(87) | |

D(3σ) | 0.000 003 66(71) | 0.000 002 4(28) | |

Ev(3π) | 10.405 13(34) | 10.237 92(62)^{c} | |

B(3π) | 0.084 973(37) | 0.084 431(88) | |

D(3π) | 0.000 005 94(55) | −0.000 001 7(23) | |

Ev(3δ) | 9.843 98(54) | 9.737 41(71)^{c} | |

B(3δ) | 0.090 172(43) | 0.090 541(82) | |

D(3δ) | 0.000 009 88(58) | 0.000 022 6(18) | |

Ev(3φ) | 10.004 92(84) | 9.774 32(151)^{c} | |

B(3φ) | 0.097 930(52) | 0.098 71(13) | |

D(3φ) | 0.000 008 06(64) | 0.000 010 8(27) | |

β(3)^{1/2} | 0.180 671(46) | 0.177 944(120) | |

β(3)_{D}^{1/2} | −0.000 049 85(85) | −0.000 038 7(54) | |

γ(3)^{1/2} | 0.180 496(56) | 0.178 634(119) | |

γ(3)_{D}^{1/2} | −0.000 073 8(11) | −0.000 090 8(55) | |

δ(3)^{1/2} | 0.159 030(59) | 0.159 108(83) | |

δ(3)_{D}^{1/2} | −0.000 052 0(11) | [−0.000 035] |

^{a}

Fitted to the levels calculated from the *ab initio* potential energy surface of Munteanu and Fernández.^{3}

^{b}

Fitted to the observed spectrum.

^{c}

Expressed relative to the estimated band origin of 2439.350 cm^{−1}.

## IV. THE OBSERVED SPECTRUM OF NE–C_{2}D_{2}

The spectra were recorded using a previously described pulsed supersonic slit jet apparatus at the University of Calgary,^{30} with a Lockheed Martin Aculight Argos optical parametric oscillator (OPO) as probe. The expansion gas mixture was about 0.1% C_{2}D_{2} in neon and the backing pressure was about 6.5 atmospheres. Wavenumber calibration utilized signals from a fixed etalon and from a reference gas cell containing room temperature N_{2}O.^{31} The PGOPHER computer package was used for spectral simulation and fitting.^{32}

The central regions of the Ne–C_{2}D_{2} *j* = 1←0 and 0←1 subbands are illustrated in Fig. 2. The figure is arranged to show the expected “mirror image” nature of these two subbands (the x-axis in the upper panel runs backward), but the mirror image is evidently not exact. This is due to the fact that the intermolecular potential, and hence energy levels, are not exactly the same in the excited state (that is, the C_{2}D_{2} asymmetric C–D stretch) as in the ground state (and also to the fact that the monomer *B*-value is slightly different). The present spectrum in these two regions is qualitatively similar to that of He–C_{2}D_{2},^{5} with the obvious difference that there are more lines here since Ne–C_{2}D_{2} has smaller rotational constants and more bound states. In both cases, there is a strong and rather chaotic “clump” of lines located just below the C_{2}D_{2} monomer *R*(0) transition (and above monomer *P*(1)), plus a more regular *Q*-branch series located on the other side of the monomer line. In addition to these strong features, there are also much weaker and widely spaced series extending to higher and lower frequencies, out of the range of Fig. 2. As with He–C_{2}D_{2}, the rotational assignments were a bit tricky for the chaotic clump regions, and easier for the regular *Q*-branches and the weak widely spaced series.

The central regions of the *j* = 2←1 and 1←2 subbands are shown in Fig. 3. Most of the intensity is again concentrated close to the C_{2}D_{2} monomer transitions, a reflection of relatively free internal rotation in the dimer. And again, the mirror image nature of the subbands is far from perfect. In the *j* = 2←1 subband (lower panel of Fig. 3), a number of the different rotational branches are somewhat separated and visible, whereas in the 1←2 subband (upper panel), some of these branches are less recognizable because they tend to fall on top of each other.

The *j* = 3←2 subband is shown in Fig. 4. We also observed some fragments of the 2←3 subband around 2434.6 cm^{−1}, but they were too weak for a detailed analysis. The 2←3 subband is disadvantaged compared to 3←2 not only by a Boltzmann population factor but also by the 2:1 nuclear spin statistics of C_{2}D_{2} which favor subbands with even values of *j*″. In addition, there is more interference from the C_{2}D_{2} dimer^{33,34} in the *j* = 2←3 region. As well, we observed fragments of the *j* = 4←3 subband in the 2445.2–2446.8 cm^{−1} range which we were not able to analyse. In this case, the problem was not only the weakness of the spectrum but also its complexity, which was compounded by the fact that we do not have data for the ground state *j*″ = 3 levels (but only for the excited state *j*′ = 3 levels).

## V. ASSIGNMENT AND FITTING OF THE SPECTRUM

The structure of the *j* = 1←0 or 0←1 subband is relatively simple, with a total of just 5 possible rotational branches, of which 3 are strong and 2 are weak. The difficulties in assignment can then arise for the very weak transitions, and in regions of overlapping lines (e.g., ≈2440.82 cm^{−1} in Fig. 2). As *j* increases, the subband structures become rapidly more complicated. For *j* = 2←1 or 1←2, there are 23 possible branches of which 9 tend to be strong, and for *j* = 3←2 the numbers are 53 possible and 15 strong branches. In all cases, the strong transitions are those where the end-over-end quantum number *L* does not change, Δ*L* = 0, and the weak transitions have Δ*L* = 2. This is because the infrared dipole transition moment is attached to the C_{2}D_{2} (and thus to *j*) and not to *L*. In contrast, the Ne–C_{2}D_{2} microwave transitions^{2} depend on a weak induced dipole which is attached to *L* and have the selection rule Δ*L* = 1.

In the face of the various assignment difficulties, our analysis was guided by the *ab initio* theoretical levels discussed in Sec. II, by the need for self-consistency (e.g., between the *j* = 2←1 and 1←2 subbands, or between 2←1 and 0←1 which share a common lower state), and by the line position and intensity predictions of the Coriolis model. The resulting assignments are listed in Tables A-III to A-V of the supplementary material.^{27} There are a total of 35 lines for the *j* = 1←0 subband, 37 for 0←1, 78 for 2←1, 65 for 1←2, and 71 for 3←2. Tables A-III and A-IV^{27} are arranged so that analogous (mirror image) transitions in the two subbands (*j* = 1←0 and 0←1, or 2←1 and 1←2) appear on the same row.

In our recent analysis of He–C_{2}D_{2}, we used a term value approach in which the spectrum was first analysed in terms of “experimental” energy levels which were then fitted in terms of the Coriolis model. But since Ne–C_{2}D_{2} has many more levels and transitions, with well-developed series, it was more effective to directly fit the spectrum itself using the Coriolis model, simultaneously including all the data from Tables of the supplementary material.^{27} Note that the analysis actually comprises two parts which are separate due to symmetry, with the *j* = 1←0, 1←2, and 3←2 subbands forming one part, and the *j* = 0←1 and 2←1 subbands forming the other unconnected part.

In addition to the present infrared data, there are also very precise microwave pure rotational data for Ne–C_{2}D_{2} within the *j*″ = 0 and 1 states from the results of Liu and Jäger.^{2} The *j*″ = 0 transitions accurately fix the energies of the ground state 0 σ*e* stack for *J* = 0–4. This high precision is then partly carried over to the excited state *j* = 1 levels in our analysis of the *j* = 1←0 subband. Interestingly, our analysis indicates that the *j*″ = 1 transitions reported in Ref. 2 were mis-assigned. Rather than being the *R*(1) and *R*(2) transitions within the 1 π*f* stack as assigned,^{2} we are confident that they are instead due to the *R*(2) and *R*(3) transitions within the 1 σ*e* stack. As shown in Table II, we predict the real 1 π*f R*(1) and *R*(2) transitions to lie about 272 and 867 MHz higher in frequency, respectively.

j Kp J L
. | j Kp J L
. | Observed^{a}
. | Present fit^{b}
. |
---|---|---|---|

1 σe 1 0 | 1 σe 0 1 | 2 152.57 | |

1 σe 2 1 | 1 σe 1 0 | 6 185.00 | |

1 σe 3 2 | 1 σe 2 1 | 10 999.1518 | 10 999.15 |

1 σe 4 3 | 1 σe 3 2 | 16 015.7988 | 16 015.80 |

1 πf 2 2 | 1 πf 1 1 | 11 270.95 | |

1 πf 3 3 | 1 πf 2 2 | 16 882.63 |

j Kp J L
. | j Kp J L
. | Observed^{a}
. | Present fit^{b}
. |
---|---|---|---|

1 σe 1 0 | 1 σe 0 1 | 2 152.57 | |

1 σe 2 1 | 1 σe 1 0 | 6 185.00 | |

1 σe 3 2 | 1 σe 2 1 | 10 999.1518 | 10 999.15 |

1 σe 4 3 | 1 σe 3 2 | 16 015.7988 | 16 015.80 |

1 πf 2 2 | 1 πf 1 1 | 11 270.95 | |

1 πf 3 3 | 1 πf 2 2 | 16 882.63 |

Our analysis included 288 infrared transitions from Tables A-III to A-V of the supplementary material,^{27} plus 6 microwave transitions,^{2} which were given a relative weight of 10^{6} to reflect their higher precision. These were fitted in terms of 64 parameters whose final values are reported in Table I. The quality of the fit was excellent, with average errors of 0.000 63 cm^{−1} for the infrared data, and about 0.005 MHz for the microwave data. The numbers in parentheses following each observed line position in Tables A-III to A-V^{27} show the individual residuals (observed minus calculated) in units of 0.0001 cm^{−1}.

The Ne–C_{2}D_{2} band origin cannot be directly determined from experiment because Δ*j* = 0 infrared transitions are forbidden, but we estimate its value to be about 2439.350 cm^{−1}. This represents a vibrational blue shift of +0.106 cm^{−1} relative to the C_{2}D_{2} monomer band origin.^{35} To facilitate comparison of v = 0 and 1 levels, this band origin has been subtracted from the experimental v = 1 energies in Table A-I,^{27} and from the v = 1 origins (*E _{v}*(1σ), etc.) in Table I. For comparison, the vibrational shift observed

^{5}for He–C

_{2}D

_{2}was +0.036 cm

^{−1}.

## VI. DISCUSSION AND CONCLUSIONS

### A. Comparison of Coriolis model parameters

Examining the Coriolis parameters in Table I, we note generally good agreement between theory (fitted to the *ab initio* levels) and experiment (fitted to the spectrum). But there are still a number of interesting points and surprises. The theoretical values for *B*(0), *D*(0), and *H*(0) are quite close to the experimental ones for v = 0, though of course even small differences can accumulate to have larger effects on the levels themselves (Table A-I of the supplementary material).^{27} Interestingly, the experimental *B*(0) value for v = 1 is significantly larger than for v = 0, implying a shrinkage of the effective intermolecular separation with excitation of the C_{2}D_{2} asymmetric C–D stretch (specifically, *R*_{eff} = 4.027 Å for v = 0 and 4.018 Å for v = 1). This was not the case for He–C_{2}D_{2},^{5} and it shows that Ne–C_{2}D_{2} is somehow more tightly bound in the excited state, even though the potential well is slightly shallower (as shown by the blue-shifted vibrational frequency).

For the *j* = 1, 2, and 3 states in Table I, the various *B* and *D* values for theory and experiment track each other fairly well, as do the Coriolis parameters *β* and *γ*. In contrast, the origin values, *E _{v}*(1σ),

*E*(1π),

_{v}*E*(2σ), etc., show significant differences between theory and experiment, and between v = 0 and 1. These state origins have a direct effect on the energy levels, particularly for low

_{v}*J*. But their precise meaning is not so obvious, in terms of how they depend on the shape of the intermolecular potential.

There are some fairly significant differences in the experimental parameters between v = 0 and 1, which of course is why the analogous subbands like *j* = 1←0 and 0←1 are not perfect mirror images. Therefore, we should not expect the current theoretical levels and parameters to match the experimental ones, even for v = 0, and even if the theoretical potential is perfect, because the theory is for a fixed (equilibrium) acetylene geometry and does not include dependence of the potential on the acetylene vibrations. The spectrum tells us that the potential certainly does depend on the acetylene C–D asymmetric stretch, and of course there could also be dependence on the other intramolecular modes. In view of the overall agreement between theory and experiment in Table I, we conclude that the neon–acetylene potential of Ref. 3 is already very good and that further refinement and testing against experiment will require accounting for vibrational averaging.

### B. Conclusions

We have assigned in detail a large part of the observed infrared spectrum of the Ne–C_{2}D_{2} dimer in the region of the C–D asymmetric stretch fundamental (≈2440 cm^{−1}). These spectra were obtained in a pulsed supersonic slit jet with an effective temperature of about 2.5 K, using a tunable OPO probe. Like He–C_{2}D_{2}, the Ne–C_{2}D_{2} energy level pattern is close to that of a free internal rotor, so the spectrum consists of subbands with *j* = 1←0, 0←1, 2←1, etc., where *j* labels the C_{2}D_{2} rotation. Compared to previous spectra reported^{1} for Ne–C_{2}H_{2} and Ne–C_{2}HD, which were only assigned for *j* = 1←0, the present analysis extends up to the more complicated *j* = 3←2 subband. The results indicate that two transitions in the previously reported^{2} microwave spectrum of Ne–C_{2}D_{2} should be reassigned as *R*(2) and *R*(3) in the 1 σ*e* stack, rather than *R*(1) and *R*(2) in the 1 π*f* stack. Theoretical predictions based on the *ab initio* intermolecular potential of Munteanu and Fernández^{3} were an invaluable aid in the current analysis. The theoretical and experimental results are already sufficiently close that further progress will probably require explicit averaging over the intramolecular vibrational modes of acetylene.

## Acknowledgments

We gratefully acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada and the Canadian Space Agency. This work has been supported by the Ministerio de Ciencia e Innovación (Project No. CTQ2011-29311-C02-01) and by the U.S. National Science Foundation through Grant No. CHE-1300504.

## REFERENCES

*j*= 0 to 4, Coriolis parameters for j = 4, and the observed infrared line positions and assignments.