1. Isabelle Kleinera and Jon T. Hougenb
COMPETITION BETWEEN TWO LARGE-AMPLITUDE MOTION MODELS: NEW HYBRID HAMILTONIAN VERSUS OLD PURE-TUNNELING HAMILTONIAN
Isabelle Kleinera and Jon T. Hougenb
aLISA, Université de Paris Est and CNRS, Créteil, F-94010, France
bSensor Science Division, NIST, Gaithersburg, MD 20899, USA

2. Hybrid program for methylamine-type molecules.
What is a “methylamine-like molecule”?
= A molecule with 2 Large Amplitude Motions:
1 internal rotation motion (rotatory)
1 back-and-forth motion (oscillatory)
2015: In 2-methyl malonaldehyde:
Internal rotation = methyl-group rotation
Back-and-forth motion = hydrogen-atom transfer
Kleiner and Hougen JPC 2015
2016: In CH3-NH2:
Internal rotation = methyl-group rotation
Back-and-forth motion = amino-group inversion

3. Intramolecular hydrogen transfer Internal rotation of a methyl rotor
2015: Two large-amplitude motions in methyl malonaldehyde:
Intramolecular hydrogen transfer
Internal rotation of a methyl rotor C4 C6 C5 O7 H9
H11
H10
C12 H3 H2 H1 O8
(123)(45)(78)(9,10)
Intramolecular hydrogen transfer induces a tautomerization in the ring, which then triggers a 60 degree internal rotation of the methyl rotor.
Kleiner and Hougen, JPC 2015

4. Why do we need a hybrid program ?
Up to now, the rotational levels of methylamine-like molecules have been fit nearly to measurement error by a traditional tunneling Hamiltonian formalism*.
Its two main deficiencies (which the hybrid program is supposed to fix) are:
-It cannot treat torsional states near or above the top of the barrier.
-It cannot treat the tunneling components of two different torsional states with one set of parameters.
*N. Ohashi, J. T. Hougen, J. Mol. Spectrosc. 121 (1987)

5. Fit more than one vibrational state simultaneously
This year :
Fit more than one vibrational state simultaneously
Try to get a global fit of CH3NH2 rotational levels in the vtorsion = 0 and 1 states with vinversion = 0. Much of this MW and FIR data is already in the literature. Ohashi et al, Ilyushin et al …
BREAKTHROUGH: NEW DATASET
Accurate rovibrational energies for the first excited torsional state of methylamine
I. Gulaczyk, M. Kreglewski, V.-M. Horneman, JMS 2016
high resolution IR spectrum : cm-1. Over 11,700 transitions with a resolution of cm-1 for 0 ≤ K ≤ 17 and K ≤ J ≤ 40, 143 parameters (88 for vt = 1, 55 parameters for the GS vt = 0).
Standard deviation vt = 1-0 : cm-1 (0.31 MHz for the MW)

6. Theoretical approach of the “hybrid” program
For internal rotation RAM
Hamiltonian of Herbst et al (1984):
F(PJz)2 + ½V3(1 cos3),
+ higher order torsion-rotation
terms as found in the
BELGI code.
For the motion in a double-well
potential (-NH2 inversion or H
transfer motion),
a tunneling formalism,
where H = T + V is replaced
with one tunneling splitting
parameter +
higher-order torsion-
rotation corrections.
‘s BELGI

7. Different ordering scheme for the parameters
Theoretical approach of the “hybrid” program
Interaction terms include all G12 group-theoretically allowed products of powers of the basic operators:
Torsional motion: Pk, cos3m, sin3n,
Back-and-forth motion: P, 
Rotational motion: Jxp, Jyq, Jzr
e.g., Operators Occur in blocks
P2, cos6, Jx2, Jy2, Jz LL, RR, LR, RL
cos3, (JxJz+JzJx) LL, RR
PJy LR, RL
‘s BELGI
Different ordering scheme for the parameters
n = t + r + w
Diagonal g terms: w = 0 cos3, (JxJz+JzJx), cos6a
Off-diagonal W terms : w = 2 cos6a
Off-diagonal Pg terms : w = 2 PgJy

8. ntrw Operator & Coefficient Block in H Par. Value (cm-1) RAM system
2200 P2 * F LL, RR (49)
½(1  cos3) * V3 LL, RR (18)
2110 PJz * (-2F)* r LL, RR (14) unitless
PJx * AXG LL, RR (11)
2020 Jx2 * B LL, RR (81)
Jy2 * C LL, RR (21) !
Jz2 * A LL, RR (4)
{Jx Jz }* DAB LL, RR (47)  
* WAG2. LR, RL (21)
_________________________________________________________  
PJy * WCPG LR, RL 0.
________________________________________________________

9. Fitting vt= 0 and 1 together ….progress from last year!
_ _________________________________________________
Last year (J ≤20) This year (J ≤40, 69 parameters)
Lines wrms Lines wrms
MW A-species
MW E-species ___________________________________________
Lines wrms Lines wrms Weight
Pure rot vt = 0-0
FIR lines vt=0-0 [1] cm-1
vt=1-1 [1]
GSCD from FIR cm-1
Vt = 1-0 FIR [3] cm-1
MW lines vt =0-0 [1,2]
MW lines vt =1-1 [1,2] not fitted
[1] Ohashi et al JMS 1988, 1989
[2] Ilyushin et al JMS 2005,[3] Gulaczyk et al JMS 2016

10. Comparing our fit with Gulaczyk et al 2016
_ _________________________________________________
Gulaczyk et al Our fit (69 parameters)
Nber parameters 55 vt=0 69
88 vt=1 ___________________________________________
Lines rms Lines rms
vt = 0-0 FIR [1] cm-1
vt = 1-1 FIR [1] cm-1
vt = 1-0 FIR [3] cm-1
MW lines vt = MHz
MW lines vt = MHz MHz
[1] Ohashi et al JMS 1988, 1989
[2] Ilyushin et al JMS 2005,[3] Gulaczyk et al JMS 2016

11. Future work and conclusions
The hybrid model seems to be useful to treat
two torsional states simultaneously in a two-dimensional large amplitude problem, but about three ?
After cleaning up the dataset:
Add higher order terms
(reduction of the Hamiltonian like Tsunekawa et al did on methanol would be useful)
- Convergence problems related to the non-linearity
(statistical and mathematical research would be useful)
- Predict and fit vt=1, 2 states of methylamine (FIR and MW data)