Progress in Understanding the Infrared Spectra of He- and Ne-C 2 D 2 Nasser Moazzen-Ahmadi Department of Physics and Astronomy University of Calgary A.R.W. McKellar National Research Council of Canada Berta Fernández University of Santiago de Compostela David Farrelly Utah State University

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 pulsed supersonic jet / tunable laser apparatus at The University of Calgary Etalon Laser Controller TDL, QCL, or OPO

Evidently He-C 2 H 2 was observed in Roger Miller’s lab around 1990, but exact rotational assignments were not possible at that time There were no published experimental spectra of helium – acetylene prior to 2012

Our 2012 paper only covered the region of the C 2 D 2 R(0) transition, shown here Now, our analysis is extended to the P(1) and R(1) regions

These spectra are difficult to assign because He-acetylene dimers are close to the free rotation limit, so lines tend to pile up on top of each other! In such cases, a simple Coriolis model is useful. Used by Brian Howard for Rg – SiH 4 and by the Köln group for Rg – CH 4 One stack of rotational levels for j = 0, denoted 0 σe Three stacks for j = 1, denoted 1 σe, 1  e, 1  f Five stacks for j = 2, denoted 2 σe, 2  e, 2  f, 2  e, and 2  f j is the DCCD rotation, J is the overall rotation E(0 σe) = B(0) J(J + 1) – D(0) [J(J + 1)] 2 E(1  f) = E v (1  ) + B(1  ) J(J + 1) – D(1  ) [J(J + 1)] 2 E(1 σe) = E v (1  ) + B(1σ) J(J + 1) – D(1  ) [J(J + 1)] 2  2x2 matrix with off-diagonal Coriolis coupling: [  (1) J(J +1)] 1/2  E(1  e) = E v (1  ) + B(1  ) J(J + 1) – D(1  ) [J(J + 1)] 2

E(2 σe) = E v (2  ) + B(2σ) J(J + 1)  3x3 matrix with off-diagonal Coriolis coupling: [  (2) J(J +1)] 1/2  E(2  e) = E v (2  ) + B(2  ) J(J + 1)  3x3 matrix with off-diagonal Coriolis coupling: [  (2) (J(J +1) - 2)] 1/2  E(2  e) = E v (2  ) + B(2  ) J(J + 1) E(2  f) = E v (2  ) + B(2  ) J(J + 1)  2x2 matrix with off-diagonal Coriolis coupling: [  (2) (J(J +1) - 2)] 1/2  E(2  f) = E v (2  ) + B(2  ) J(J + 1) Extension of Coriolis model to j = 2 now all stacks are affected by Coriolis coupling Here centrifugal distortion is omitted since there are already 8 parameters and not many j = 2 levels to fit!

This is the best He-HCCH potential currently available, so we asked Berta Fernández to calculate energy levels for He-HCCH and He-DCCD.

He – C 2 D 2 energy levels calculated by Fernández & Farrelly from the Munteneau & Fernández CCSD(T) ab initio potential

j = 1 – 0 sub band (R(0) region) previously assigned j = 0 – 1 sub band (P(1) region) newly assigned weaker due to Boltzmann and spin should be mirror-image of R(0)

Knowing the j = 0 – 1 assignments, made it (somewhat!) easier to analyze the j = 2 – 1 sub band (C 2 D 2 R(1) region) * indicates j = 1 – 0 sub band transition j Kp J L 2  f 1 21  f (–3) 2  e 1 11  f (–1) 2  e 0 21  e (0) 2  f 1 21  e (–9) 2  f 3 21  f (–1) 2  e 2 21  f (+3) 2  f 2 11  f (–3) 2  f 2 31  e (0) 2  e 2 01  e (0) 2  e 3 11  e (0) 2  e 4 21  e (0) 2  e 5 31  e (0) 2  e 1 11  e (+1) 2  f 3 21  e (+1) 2  f 2 11  e (+3) 2  f 4 31  e (0) 2  e 2 21  e (–7) 2  e 2 21  e (+4) 2  f 1 21  e (+12) 2  e 1 31  f (0)

After figuring out assignments with help from theory and the Coriolis model, we use a term value approach to determine “experimental” energy levels

v = 0v = 1 TheoryExp E v (0) B(0) D(0) E v (1σ) E v (1  ) B(1σ) B(1  )  (1) 1/ D(1σ) D(1  ) E v (2σ) E v (2  ) E v (2  ) B(2σ) B(2  ) B(2  )  (2) 1/  (2) 1/ Then we fit the ‘experimental’ and theoretical levels using the Coriolis model Results for j = 0 and 1are similar to what we reported earlier. For j = 2, they are new. Nice that the ratio  (2) 1/2 /  (1) 1/2 = 1.61 is fairly close to the expected value of 3 1/2 = 1.73, and that  (2) 1/2   (2) 1/2. Note: 1  > 1σ 2σ > 2  > 2 

Acetylene is isoelectronic with carbon monoxide Interesting to compare He – C 2 D 2 with He – CO Symmetry makes a difference, also the fact that He – C 2 D 2 is basically linear, while He – CO is T-shaped

Ne – C 2 D 2 free rotor Coriolis model works here, too j = 1  0 spectrum, near C 2 D 2 R(0)

Ne – C 2 D 2 j = 2  1 spectrum, near C 2 D 2 R(1) – good progress! j = 3  2 spectrum, near C 2 D 2 R(2)

Ar – C 2 D 2 here a more conventional model is appropriate K = 1  0 subband