1. Remeasurement* of the Microwave Spectrum of
2-Methylmalonaldehyde and Analysis of the Hydrogen Transfer and Internal Rotation Motions
Vadim V. Ilyushin,1 Eugene A. Alekseev,1
Yung-Ching Chou,2,3 Yen-Chu Hsu,2
Jon T. Hougen,4 Frank J. Lovas,4 and Laura B. Picraux5
1Institute of Radio Astronomy of NASU, Chervonopraporna 4, Kharkov, Ukraine
2Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 107, Taiwan
3Department of Natural Science, Taipei Municipal Univ. of Education, Taipei, Taiwan
4Optical Technology Division, NIST, Gaithersburg, MD , USA
5Chemical Sciences and Technology Laboratory, NIST, Gaithersburg, MD 20899, USA
*Previously presented at Columbus 2005

2. Two large-amplitude motions : Intramolecular hydrogen transfer
Internal rotation of a methyl rotor
(123)(45)(78)(9,10)
H11
H11 O8 O7 O8 O7 C5 C4 C5 C4
H10 C6 H9
H10 C6 H9 H2
C12
C12 H1 H1 H2 H3 H3
Intramolecular hydrogen transfer induces a tautomerization in the ring, which then triggers a 60 degree internal rotation of the methyl rotor.

3. N. G. Sanders, J. Mol. Spectrosc. 86, 27-42 (1981)
Part of Columbus 2005 Slide
Refit of Sanders’ data
(0  J 10, 0  K  6, 14    40 GHz)
N. G. Sanders, J. Mol. Spectrosc. 86, (1981)
We used G12m group-theoretical formalism developed for
the wagging-torsional-rotational problem in methylamine
to refit Sanders’ spectra (2-MMA-d0 and -d1)
Today: 30  more data,  more precision

4. Overview of 2-MMA measurements used in the present work
Lab Year Apparatus Range Unc #lines d0 rms #lines d1 rms
[GHz] [kHz] [kHz] [kHz]
NIST FTMW ,
Harvard Stark
Kharkov 2006 sub-mm
Kharkov 2006 sub-mm
Overall rms of 2578 d0 lines to 37 parameters = 15.1 kHz
Overall rms of 2552 d1 lines to 32 parameters = 15.3 kHz
Overall weighted rms (dimensionless) = 0.98 and 1.08.

5. So what is the problem? = Today’s Talk
Spectral fit to tunneling Hamiltonian is excellent.
So what is the problem? = Today’s Talk
Interpretation: Fitting Parameters → Barrier Heights
This is a long-standing problem (last 20 years)
for the multi-dimensional tunneling formalism.
Assumption: To determine the barrier height from
tunneling splittings for a 1-D tunneling path we need:
1. tunneling splitting (from the fitting)
2. path length a between the two minima 0  x  a
3. potential function along this path V(x)
4. effective mass moving along this path m(x)

6. For this molecule there are two tunneling frequencies
h2v = H-transfer + 60º int. rot. tunneling frequency
(→ NH2 inversion frequency for CH3NH2)
h3v = pure 120º internal rotation tunneling frequency
So we want two barriers.
The calculation of both barriers leads to troubles:
The internal rotation barrier has a small trouble.
The H-transfer barrier has a big trouble.

7. Consider first the pure internal rotation problem
Use formalism in the literature (Lin and Swalen)
H = F p2 + ½ V3(1-cos3)
Calculate F from structure and fix it
Determine V3 from A-E tunneling splitting
for both –OH and –OD isotopologs of 2-MMA
Check for consistency: V3(OH) = 399 cm-1
V3(OD) = 311 cm-1

8. d1 anomaly: 3-fold increase in torsional splitting (h3v)
1. Not an assignment or fitting problem (this work)
2. Path1-Path2 information leakage in model ?
3. O-H stretch zero-point effect on V3 ? (ab initio?)

9. 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 V6(1-cos6)
Determine F() = (constant)/I() classically
T = ½ i mi vi2 = ½ i mi (dri/dt)2 =
= ½ i mi (dri/d)2 (d/dt)2
= ½ i I() (d/dt)2

10. Two large-amplitude motions : Intramolecular hydrogen transfer
Internal rotation of a methyl rotor
(123)(45)(78)(9,10)
H11
H11 O8 O7 O8 O7 C5 C4 C5 C4
H10 C6 H9
H10 C6 H9 H2
C12
C12 H1 H1 H2 H3 H3
Intramolecular hydrogen transfer induces a tautomerization in the ring, which then triggers a 60 degree internal rotation of the methyl rotor.

11. Barrier results Move hydroxyl and methyl H’s = 4 H’s V3(OH) = 413 cm-1
V3(OD) = 730 cm-1
Move only hydroxyl H = 1 H
V3(OH) = 4056 cm-1
V3(OD) = 4064 cm-1
Mass of the 3 methyl H’s is “hidden”
during the tunneling process.
What does this mean ???

12. 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 CH3 group
Which implies no time reversal symmetry

13. The six equivalent local minima in the “hydrogen transfer-methyl torsion” potential surface
Ground vibrational level  A1, B1, E1, E2 sublevels

15. 2-MMA 2h2v h2v +h2v +2h2v 0 H-transfer -0.5 h2v  -1.0
 h3v internal rotation 0
h3v
+2h3v A1 B1
Energy E1 E2
-OD -OH
CH3NH CH3NH2
vt= vt=0

16. Related molecules: Ref. 15 5-methyltropolone Ref. 16
5-methyl-9-hydroxyphenalenone
acetic acid–benzoic acid mixed dimer
Ref. 17
15. Nishi, Sekiya, Kawakami, Mori, Nishimura, JCP 111, 3961 (1999)
16. Nishi, Sekiya, Mochida, Sugawara, Nishimura, JCP 112, 5002 (2000)
17. Nandi, Hazra, Chakraborty, JCP 121, 7562 (2004)