1. Unusual Internal Rotation Coupling in the Microwave Spectrum of Pinacolone Yueyue Zhao 1, Ha Vinh Lam Nguyen 2, Wolfgang Stahl 1, Jon T. Hougen 3 1 Institute of Physical Chemistry, RWTH Aachen University, Landoltweg 2, D-52074 Aachen, Germany. 2 Laboratoire Interuniversitaire des Systèmes Atmosphériques (LISA), CNRS/Universités Paris Est & Paris Diderot, 61 avenue du Général de Gaulle, F-94010, Créteil cedex, France. 3 Sensor Science Division, NIST, Gaithersburg, MD 20899-8441, USA. 1

2. H 3 C – C(=O) – C(CH 3 ) 3 Pinacolone 2

3. 4 methyl tops 1 tert-butyl top 1 methyl top problem  3

4. Pinacolone MW Measurements and Fits Lab = RWTH Aachen University (3 authors + 1 visitor) Apparatus = Two FTMWs Data Ranges = 2.6 – 26.5 GHz & 26.5 – 39.4 GHz Measurement error ~ 2 kHz Measurement years = 2010 to 2013 Assignments ~ 400 stronger lines assigned ~ 800 lines present in spectrum Fits are not good  not a normal talk ! We tried 5 well-known programs: XIAM, ERHAM, BELGI-Cs, RAM36, BELGI-C1. Best standard deviations are only ~20 kHz  2 4

5. Scientific Problems: 1. The best fits are only to ~10  measurement error, whereas we often achieve  ~1  measurement error. 2. The lines/parameters ratio is ~10, whereas we often achieve ratios of 40 or higher. (e.g., I. Kleiners talk 2552 lines/31 parameters  80)  Something is wrong = subject of todays talk Four possible places to look for trouble. 1. Bad Measurements (test combination differences) 2. Bad Assignments (test combination differences) 3. Bad Model (design new model) 4. Operator Error (we hope not !!!) 5

6. A species transitions E species transitions Diagrams of assigned lines to show the many combination differences that can be checked. 6

7. Possible Explanations for Fitting Difficulties 1. Bad Measurements NO ! 2. Bad Assignments NO ! 3. Bad Model (Think about new model = present stage of work) What physics are we missing in the old model ??? 4. Operator Error (Authors of this talk do not like this explanation.) 7

8. 4 methyl tops 1 tert-butyl top 1 methyl top + 1 tert-butyl top problem  8

9. 2-dimensional cut of the MP2/6-311++G(d,p) potential surface for pinacolone = V(  1,  2 ). Horizontal axis = 360  of methyl torsion   1. Vertical axis = 360  of tert-butyl torsion   2. What do we see on this potential surface? Minima, maxima, and saddle points. 9 H 3 C- torsion angle (CH 3 ) 3 C- torsion angle V (  1,  2 )

10. 10 The methyl torsion sees 6 wells in a 360  interval, with 6 small barriers, when tert-butyl torsion ~0 , ~120 , or ~240 . The tert-butyl group also sees 6 wells in a 360  interval, when the methyl torsion angle is ~0 , ~120 , or ~240 , but the barriers are much higher, so that tunneling is impossible (unfeasible in the Longuet-Higgins’s sense). H 3 C- torsion angle (CH 3 ) 3 C- torsion angle V (  1,  2 )

11. What model(s) should we use to calculate energy levels and wavefunctions  for this potential V? One choice = 2-inequivalent-top model. Wolfgang Stahl expanded V(  1,  2 ) as a double Fourier series in  1,  2, and used a 2-D free-rotor product basis set of the form e +im  1 e +in  2. He got  the v 1 =v 2 =0 A-species  function shown at left 11 H 3 C- torsion angle (CH 3 ) 3 C- torsion angle  V(  1,  2 )

12. 8 lowest energy levels calculated from a 2-D surface (  1,  2 ) using a 2-top Hamiltonian and e +im  1 e +in  2 basis set. Energies are plotted against  1, but the real tunneling path is a 1-D  zig-zag line lying within one horizontal strip of the V surface. 12 The 1:2:1 energy level spacings resemble those for a cos6  well. Can we devise some 1-D model for top #1 ??? (since top #2 only oscillates ~  20  about 120  = equilibrium) 2 1 1

13. Future Measurement Plans Get high resolution coverage of 0A, 0E and 1E, 1A in the 2.6 to 40 GHz region. Confirm assignments by combination differences. 1E & 1A survey is done. High Res. is not finished. 0A & 0A high resolution and global fits are done. 13

14. Future Theoretical Plans 1.Two-top internal rotation formalism How far can we go with this formalism??? Maybe not very far. Why? 2-top model may not be useful for spectral fitting because tert-butyl torsion samples only ~1/9 of 360 . Many Hamiltonian parameters will not be determined. 2-top program will be slow, because it needs a large free-rotor basis set for computational accuracy in high- barrier case. 14

15. Future Theoretical Plans 2. Two-dimensional pure tunneling model What about the 2-D tunneling model used for CH 3 NH 2 etc.? Biggest change from CH 3 NH 2 is the “unequal” well spacing.  New symmetry treatment & new group theory & significantly modified tunneling matrix elements. 15

16. Future Theoretical Plans 3. New thinking Try to develop a 1-D quantum mechanical model Periodic barrier problem is usually easy. BUT velocity vector of the system point on V changes direction nearly discontinuously at 6 “corners” along the 1-D curve that defines the path of system point. If p changes nearly discontinuously, then p 2  T = kinetic energy becomes infinite. How do we deal with this ??? 16

17. 17 H 3 C- torsion angle (CH 3 ) 3 C- torsion angle  Use the full  1,  2 square for the 2-D 2-top model in pinacolone. Try to adapt the 2-D CH 3 NH 2 tunneling model to one horizontal strip of the   1,  2 square. Change = unequal well spacing. Try to develop a 1-D quantum mechanical model for periodic motion along a  zig-zag path within one horizontal strip.