1. Microwave Study of a Hydrogen-Transfer-Triggered Methyl-Group Internal Rotation in 5-Methyltropolone Vadim V. Ilyushin a, Emily A. Cloessner b, Yung-Ching Chou c, Laura B. Picraux d, Jon T. Hougen e, Richard Lavrich b a RIAN, Kharkov, Ukraine, b College of Charleston, VA, c Taipei University of Education, Taiwan, d Sun Chemical, Cincinnati, OH, e NIST, Gaithersburg, MD (Chemical synthesis, FTMW measurements, LAM least-squares fits, Quantum chemistry calculations)

2. O. Vendrell, M. Moreno, J. M. Lluch

3. C4C4 C6C6 C5C5 O7O7 O8O8 H9H9 H 11 H 10 C 12 C4C4 C6C6 C5C5 O7O7 O8O8 H9H9 H 11 H 10 H1H1 C 12 H3H3 H3H3 H2H2 H2H2 H1H1 Another example: 2-methylmalonaldehyde: LAM 1 = Intramolecular hydrogen transfer LAM 2 = Internal rotation of a methyl rotor Intramolecular hydrogen transfer induces a tautomerization in the ring, which then triggers a 60 degree internal rotation of the methyl rotor.

4. There are two tunneling motions (LAMs) H-transfer + 60º corrective internal rotation tunneling frequency Pure CH 3 120º internal rotation tunneling frequency So we want two tunneling frequencies and also a good spectral fit from some effective Hamiltonian = high-barrier 2-D tunneling Hamiltonian

5. Various tunneling frequencies H-transfer CH 3 internal rotation 5-MT-d 0 655 MHz 295 MHz 5-MT-d 1 not studied not studied 2-MMA-d 0 21 013 MHz 112 MHz 2-MMA-d 1 2 696 MHz 348 MHz Summary from a spectral-fitting point of view The high-barrier 2-D tunneling theory works well It fits FTMW lines to exp. error = 1.5 kHz (5-MT) (Lines)/(Parameters) = 1015/20  50 (for 5-MT)

6. There are two LAMs and two tunneling frequencies So we now want two barrier heights. But for barrier determinations, the high-barrier 2-D tunneling Hamiltonian approach does not work well In 2-methylmalonaldehyde, calculation of both barriers leads to troubles we do not fully understand. 1. The H-transfer barrier has a big problem. 2. The internal rotation barrier has a small problem.

7. Tunneling Splittings → Barrier Heights For the Multi-Dimensional Tunneling Formalism this is a long-standing problem (last 20 years) Review the 1-D Tunneling Path problem. We need: 1. tunneling splitting (from the fitting) 2. path length a between the two minima 0  x  a 3. functional form of V along this path V(x) 4. effective mass moving along this path m(x) (Ex. of 1-D = K. Tanaka et al. MI-03 vinyl radical)

8. The six equivalent local minima in the “hydrogen transfer-methyl torsion” potential surface hydrogen transfer methyl torsion There are two main tunneling frequencies: H-transfer + 60º int. rot. tunneling frequency pure 120º internal rotation tunneling frequency

9. 2-MMA H-transfer barrier results Move hydroxyl and methyl H’s = 4 H’s V 3 (OH) = 413 cm -1 V 3 (OD) = 730 cm -1 Move only hydroxyl H = 1 H V 3 (OH) = 4056 cm -1 V 3 (OD) = 4064 cm -1 Mass of the 3 methyl H’s is “hidden” during the tunneling process. What does this mean ???

10. The six equivalent local minima in the “hydrogen transfer-methyl torsion” potential surface hydrogen transfer methyl torsion There are two main tunneling frequencies H-transfer + 60º int. rot. tunneling frequency pure 120º internal rotation tunneling frequency

11. Difference between 1-D and 2-D For 1-Dimensional Treatment All of T and all of V are always in the same coordinate. Energy flow = T ↔ V For 2-Dimensional Treatment We have T = T 1 +T 2 and V = V 1 +V 2 put large E 1 = T 1 + V 1 into coordinate 1 put small E 2 = T 2 + V 2 into coordinate 2 Energy flow = T ↔ V and 1 ↔ 2

12. Consider the pure internal rotation problem Use formalism in the literature (Lin and Swalen) H = F p  2 + ½ V 3 (1-cos3  ) Calculate F from structure and fix it Determine V 3 from A-E tunneling splitting for both –OH and –OD isotopologs of 2-MMA Consistency check V 3 (OH) = 399 cm -1 is not good:V 3 (OD) = 311 cm -1

13. Various tunneling splittings H-transfer CH 3 internal rotation 2-MMA-d 0 21 013 MHz 112 MHz 2-MMA-d 1 2 696 MHz 348 MHz 5-MT-d 0 655 MHz 295 MHz 5-MT-d 1 not studied not studied 112 MHz ≠ 348 MHz Pictorial explanation = “leakage” Experimental test of leakage = 5-MT-d 1 Quantum mechanical explanation (N. Ohashi) may be non-orthogonality of basis set

14. Conclusions from this talk Present 2-D tunneling formalism is very successful for “engineering“ applications: Making spectral assignments and fits Making spectral atlases Present 2-D tunneling formalism needs a much deeper quantum mechanical understanding of some of its 2-D aspects

16. In some sense, the H-transfer splitting and the internal rotation splitting for a given molecule are in competition with each other. A general unifying idea: If two energy parameters A ≥ 0 and B ≥ 0 compete, it can be useful to plot the energy pattern against A/B. But, to avoid the infinity at B = 0, it is more useful to plot the pattern against  1 ≤ (A  B)/(A+B) ≤ +1 We will now do that for A = h 2v = H-transfer splitting (C 6 H 6  -orbitals) B = h 3v = internal rotation splitting (A-E splitting)

17. 2 2 1 1 +1+1 +2+2 -1.0 internal rotation 0 H-transfer +1.0 (h 2v  h 3v )/(h 2v + h 3v )  1 +2 A1A1 B1B1 0 E1E1 A1A1 E2E2 B1B1 E1E1 E2E2 -OD -OH CH 3 NH 2 CH 3 NH 2 v t =1 v t =0 0 2-MMA Energy/ ( h 2v + h 3v ) 5-MT

18. Related molecules 5-methyl-9-hydroxyphenalenone acetic acid–benzoic acid mixed dimer Nishi, Sekiya, Mochida, Sugawara, Nishimura JCP 112, 5002 (2000) Electronic Spectrum Nandi, Hazra, Chakraborty, JCP 121, 7562 (2004) Electronic Spectrum

19. Synthesis at College of Charleston (Lavrich, Cloessner) 1.tropolone + Br 2 → 2,6-dibromotropolone to block 2,6 sites (+ 2-bromo + 2,4,6-tribromotropolone) 2. heat with formalin and morpholine Mannich reaction → -CH 2 -N O at 5 3. H 2 + Pd:C → removes Br and –N O following unsuccessful attempts at NIST (Hougen, Picraux) Br O N-CH 2

20. Microwave measurements: College of Charleston & NIST (Lavrich, Cloessner, Ilyushin) Fourier transform microwave spectrometers Heated nozzle with Ar backing pressure Supersonic jet cooling of beam to 1-2 K Lines measured from 7 to 26 GHz

21. 606 ← 505 616 ← 515 A1/A2 E2 B1/B2E1 E2 B1/B2 A1/A2 E1

22. 5-methyltropolone H. Ushiyama and K. Takatsuka Angew. Chem. Int. Ed. 44 (2009) 1237-1240 Full dimensional ab initio molecular dynamics at the RHF level (6-31G) Run many fixed-energy trajectories 0 fs H transfer (to middle) occurs 10 fs single-double bond rearrangement begins 30 fs 60º CH 3 rotation begins 100 fs 60º CH 3 rotation ends

23. Next look at barrier to H transfer motion from a 1-Dimensional point of view: Tunneling path is a 1-D line in (3N-6)-D space Use a 1-D tunneling coordinate  with a 6-fold periodic potential and path dependent F H = F(  ) p  2 + ½ V 6 (1-cos6  ) Determine F(  ) = (constant)/I(  ) classically T = ½  i m i v i 2 = ½  i m i (dr i /dt) 2 = = ½  i m i (dr i /d  ) 2 (d  /dt) 2 = ½  i I(  ) (d  /dt) 2

24. Maybe the H-transfer dynamics are really a “2-D problem” H. Ushiyama & K. Takatsuka (ab initio), Angew. Chem. Int. Ed. 44 (2005) 1237 say First comes the H transfer Then comes the electron rearrangement = single double bond rearrangement Then comes corrective internal rotation of the CH 3 group Implies: no single-valued mapping onto 1-D