1. OCS trimer and tetramer: Calculated structures and infrared spectra
Luca Evangelisti, Cristobal Perez, Nathan A. Siefert, Brooks H. Pate
Department of Chemistry, University of Virginia
M. Dehghany, N. Moazzen-Ahmadi
Department of Physics and Astronomy, University of Calgary
A.R.W. McKellar
National Research Council of Canada
In spite of the title, I’ll concentrate on OCS tetramer. This is a collaboration between us and Brooks Pate’s group. And you have just heard about the amazing results from Pate’s group on OCS clusters.

2. The known OCS dimers
Previous to the present work, we had high resolution spectroscopic data on two isomers of OCS dimer. Both are planar. Nonpolar isomer is the lower energy form, and is observable in the infrared, but not the microwave. The higher energy polar isomer was observed in our lab for the first time and is only detected in a supersonic expansion with helium as the carrier gas.
Polar dimer Afshari, Dehghani, Abusara, Moazzen-Ahmadi, McKellar, J. Chem. Phys. 126, (2007)
Nonpolar dimer Randall, Wilkie, Howard, Muenter, Mol. Phys. 69, 839 (1990)

3. (OCS)3 The known OCS trimer
Microwave: Connelly, Bauder, Chisholm, Howard, Mol. Phys. 88, 915 (1996) Peebles, Kuczkowski, J. Phys. Chem. A 103, 6344 (1999)
We also had spectroscopic data on this unsymmetric OCS trimer. The 3 views here are along the inertial axes. The structure is approximately “barrel-shaped”, with two monomers aligned and the third monomer anti-aligned.
Infrared: Afshari, Dehghani, Abusara, Moazzen-Ahmadi, McKellar, J. Chem. Phys. 127, (2007)

4. The present work has three parts
Cluster structure calculations: based on a recent high-level ab initio OCS intermolecular.
Infrared spectra from Calgary: pulsed supersonic slit-jet expansion (very dilute OCS in He), tunable IR laser probe, ν1 region (~2060 cm-1).
Broad-band chirped-pulse microwave spectra from Virginia (3 – 9 GHz).
The present work has three parts. Cluster structure calculations based on a recent high-level ab initio OCS intermolecular PES. Infrared spectra from Calgary using a pulsed supersonic slit-jet expansion of a very dilute OCS in helium and the microwave spectra from Virginia using Brooks Pate’s broad-band Chirped-pulse spectrometer.

5. OCS Cluster Structures from ab initio Pair Potential
Thanks! to Richard Dawes (Missouri-Rolla) for subroutines to evaluate their potential surface [Brown, Wang, Dawes and Carrington, J. Chem. Phys. 136, (2012)].
Simply(!) find global and local minima assuming pair- wise additivity, starting with random structures and going ‘downhill’ (using the Powell method).
Sounds easy, but remember it’s a 14-dimensional space for OCS tetramer.
The number of isomers increases very rapidly with cluster size.
Here is how the cluster calculations is done. The program was written by Bob McKellar. It’s a purely classical problem of finding the minima on a potential energy function. BUT, the dimensionality is high for a large size cluster. The numerical simulations start with N molecules, in this case 4, in random positions and orientations, and adjust the 5N-6 dimensional structure, in nthis case 14, to find the ‘nearest’ energy minimum using the Powell method given in numerical recopies. Repeating this hundreds or thousands of times, we can be confident that the global minimum and most or all low-lying local minima have been located.

6. Rotational constant / MHz Dipole (monomer units)
There are (at least!) 20 local minima for the tetramer within 100 cm-1 of the global minimum at cm-1
Isomer
Energy / cm-1
Symmetry
Rotational constant / MHz
Dipole (monomer units) A B C a b c
P4-1
-2773 C1
635
316
309
1.7
0.9
0.1
P4-2
-2771 S2
714
341
291
0.0
P4-3
-2762 Cs
673
352
296
1.6
1.1
P4-4
684
342
283
P4-5
-2757
666
356
290
1.0
P4-6
-2756
668
334
319
0.3
0.5
0.2
P4-7
-2753
608
314
306
0.8
P4-8
-2745
725
325
301
0.4
P4-9
-2738
490
434
336
P4-10
-2717
471
464
1.9
P4-11
-2713
C2v
638
358
331
P4-12
-2711
654
349
P4-13
-2699
569
351
322
0.6
P4-14
-2698
469
448
1.3
P4-15
-2697
533
382
340
P4-16
-2683
552
377
308
1.5
P4-17
-2682
508
373
338
P4-18
-2680
570
335
328
P4-19
-2676
645
348
277
P4-20
-2674
391
302
1.2
The number of isomers increases very rapidly with cluster size. There are at least 20 local minima within 100 cm-1 of the global minimum. Binding energies, rotational constants and the dipole moment components in monomer unit are listed here.

7. Here are the first four calculated minima
Here are the first four calculated minima. Most isomers have no symmetry.
0 cm-1
2 cm-1
11 cm-1
11 cm-1
relative to the global minimum at cm-1

8. And the next four calculated minima
Here are the next four and in particular the seventh isomer which also has no symmetry.
16 cm-1
17 cm-1
20 cm-1
28 cm-1
relative to the global minimum

9. OCS Cluster Structures from ab initio Pair Potential
Note that pair-wise additivity ignores possible many- body non-additive effects.
There are also recent direct ab initio OCS trimer and tetramer calculations which automatically include non- additive effects, but of course they at a lower level of theory [Sahu, Singh, Gadre, J. Phys. Chem. A 117, (2013)].
In both cases, the structures are classical potential minima. This ignores quantum effects (zero-point motion), which can be significant for weakly-bound clusters.
The pair potential we are using is very good, but even if it were perfect, there are two significant approximations here!! The pair-wise additivity ignores possible many-body non-additive effects. There are also recent direct ab initio OCS trimer and tetramer calculations which automatically include non-additive effects, at a lower level of theory. In both cases, however, the structures are classical potential minima and quantum effects (zero-point motion), which can be significant for weakly-bound clusters, are ignored.
The question is what’s better for a large size van der Waals cluster: a very high-level ab initio pair potential, or a not-so-high-level direct ab initio calculation?

10. (OCS)4 Infrared Spectra
For a number of years, we observed possible IR bands of (OCS)4, but the situation was confused. Finally, one such band was briefly mentioned in our 2013 review paper.
For a number of years, we have had unpublished spectra showing infrared bands of OCS tetramer. But some of these bands seemed to have slightly different ground state rotational constants. This would, of course, tie in with the calculations showing many low-lying isomers with similar structures. One such band was briefly mentioned in our 2013 review paper.

11. This was the clearest of our OCS “tetramer” bands
Here is the band from the same review paper.
The simulation is for a symmetric rotor, but it would also work for a slightly asymmetric rotor.

12. with one 34S substitution (in natural abundance)
(OCS)4
with one 34S substitution (in natural abundance)
Like many microwavers, Pate’s lab often uses OCS as a test molecule (many isotopes, simple spectrum, …).
He wondered whether our suspected infrared OCS tetramer might also appear in their ‘deep’ scans of jet-expanded OCS/He mixtures.
Yes, it does!!
Well, actually, it’s not quite that simple…
(OCS)4
normal isotopologue
Like many microwavers, Pate’s lab often uses OCS as a test molecule (many isotopes, simple spectrum, large dipole moment, …).
He wondered whether our suspected infrared OCS tetramer might also appear in their OCS/He mixture spectra.
It turns out, it does!! Here is the simulation for R(7) line and its K-structure for the normal isotopolougue. K=1 doublet falls outside the region shown.
Well, actually, it’s not quite that simple…and even after assigning some of the lines to OCS trimer and tetramer, there are still thousands of unassigned lines (impurities, new OCS clusters, isotopes, …)!

13. It’s not that simple … because the microwave tetramer is not responsible for the published cm-1 band, but rather for two unpublished infrared bands, at 2048 and 2061 cm-1 (one shown here, the B-values agree to <0.1 MHz).
Interestingly, there is a twist in the story. The microwave tetramer is not responsible for the published cm-1 band, but rather for two unpublished infrared bands, at 2048 and 2061 cm-1 (one shown here, the B-values agree to <0.1 MHz).

14. (OCS)4
As seen in the previous talk, the microwave tetramer is an asymmetric rotor with no symmetry.
The experimental structure agrees well (but not perfectly) with our most stable calculated tetramer, P4-1, shown here.
Obs Calc
A MHz B C
As seen in the previous talk, the microwave tetramer is an asymmetric rotor with no symmetry.
The experimental structure agrees well (but not perfectly) with our most stable calculated tetramer, the lowest energy isomer, shown here.
The structure is similar to the barrel-shaped trimer, with an OCS monomer stuck on the “top” end, close to two S atoms.

15. But what about the other infrared band, which does not quite agree??
It corresponds to the 7th most stable isomer, with a relative energy of 20 cm-1. It does not appear in the MW spectrum (its calculated dipole moment is much smaller).
Looks a bit like the other tetramer, right??
Main difference: the “top” monomer is now at the other end of the trimer barrel.
Obs Calc
A  MHz
(B+C)/
(B-C) <
But what about the published infrared band, which does not quite agree??
It corresponds to the 7th most stable isomer, with a relative energy of 20 cm-1. It does not appear in the MW spectrum (perhaps because its calculated dipole moment is much smaller).

16. P4-1
The lowest energy form is shown on top and two views of isomer 7 is shown at the bottom. This isomer looks a bit like the lowest energy tetramer, the main difference being that the “top” monomer is now at the other end of the trimer barrel.
P4-7

17. (CS2)4 (OCS)4 (N2O)4 [S4] CPL 570, 12 (2013) JCP 134, 074310 (2010)
Unlike its N2O and CS2 ‘cousins’, the OCS tetramer is nonsymmetric. CO2 tetramer is not spectroscopically known. CS2 tetramer has D2d symmetry with four equivalent monomers. For N2O we have observed two isomers, the one which is a sort of a sandwich structure with one nonpolar dimer stacked on the top of another rotated by 90 degrees. This is shown here.
(N2O)4 [S4]
JCP 134, (2010)

18. (N2O)4 Prolate (D2d symmetry) Oblate (S4 symmetry)
Here is the second isomer which is an oblate symmetric top with D2d symmetry and four equivalent monomers with alternating orientations. we do not know for sure which of the two isomers is the more stable form.
Prolate
(D2d symmetry)
Oblate
(S4 symmetry)

19. Conclusions
First spectroscopic observation of OCS tetramers. One isomer is well-characterized from MW spectrum, and also observed by two IR bands. Another isomer observed by one IR band may correspond to calculated isomer P4-7..
Amazing broad-band microwave spectra, has many! lines still unassigned.
The ‘direct’ ab initio calculations of the Gadre group (Kanpur) are in good general agreement with our pairwise calculations. But, significantly, they missed 16 of the 20 lowest energy tetramers, including the lowest 3.