1. Application of the hybrid program for fitting microwave and far-infrared spectrum of methyl amine
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)
Last year: In 2-methyl malonaldehyde (see next slide):
Internal rotation = methyl-group rotation
Back-and-forth motion = hydrogen-atom transfer
This year: 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
Last year: 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. Successful solution of the specific 2-methylmalonaldehyde problem
-With the hybrid formalism we fit the 2-MMA-d0 and -d1 fits from Ilyushin et al. JMS (2008) with the same quality
-the -OH vs -OD discrepancy has been greatly reduced:
V3 values from the old pure tunneling and the new hybrid formalism
2-MMA-OH MMA-OD Diff.
Pure tunneling formalism: V3 = 399 cm V3 = 311 cm cm-1
Hybrid formalism: V3 = 302 cm V3 = cm cm-1 .

5. 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 pure tunneling Hamiltonian formalism*.
Its two main deficiencies (which the hybrid program is supposed to fix) are:
-It cannot treat vibrational states near or above the top of the barrier to any tunneling motion.
-It cannot treat the tunneling components of two different vibrational states at the same time.
*N. Ohashi, J. T. Hougen, J. Mol. Spectrosc. 121 (1987)

6. 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.

7. 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

8. 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

9. Present status of the fit
Relatively good fit of vt=0 levels =
MW + GS combination differences
Lines wrms Weight
______________________________________________________
Pure rot vt = 0-0 FIR lines [1] cm-1
GSCD from FIR cm-1
MW lines [1,2]
[1] Ohashi et al JMS 1987 and references herein
[2] Motyenko et al A&A 2014 and references herein

10. Fitting vt= 0 and 1 together ….still a problem!
_ _________________________________________________
Lines wrms
MW A-species
MW E-species ________________________________________________
Lines rms Weight
Pure rot vt = 0-0 FIR lines [1] cm-1
GSCD from FIR cm-1
Vt = 1-0 FIR [1] cm-1
MW lines [1,2]

11. Possible reasons for this fitting problem
1) is the hybrid model correct , can it handle this problem???
2) Missing high order terms in the BELGI type term and/or in the
interaction tunneling-internal rotation necessary to fit vt=1-0
3) assignments errors or uncompatibility between vt =0 and 1 in the literature dataset, labeling problems going from the tunneling formalism to the hybrid formalism
4) truncation error due to two step diagonalisation or
programming errors

12. Possible reasons for this fitting problem
2) Simplest possible explanation = not enough terms in H
This hybrid program is a new approach, so we lack experience in what to do.
We will continue to add terms, but there are some questions:
(i) Determinable parameters for this approach have not been investigated.
We have been assuming that it is essentially like in Tsunekawa et al paper, where terms with odd n in their nlm scheme can be neglected. Maybe this is not the case.
(ii) Higher-order terms involving  and P terms may be more important than we think

13. Possible reasons for this fitting problem (suite)
3) There could be some unsuspected assignment inconsistency across vt=1, since in the tunneling formalism, the splitting parameters for vt=0 and vt=1 are not connected by a potential energy surface.
We are not sure how to begin looking for such a possible inconsistency, since we are not quite sure what it even means.
(i) But we will try fitting A,B 1, B2 levels without E1, E2 levels (similar to 1 top fits).
(ii) We will try fitting vt=0 and vt=1 separately like the successful pure tunneling fits did and see which parameters change by a suspicious amount

14. Possible reasons for this fitting problem (suite)
4) There could be some errors in the code. We are constantly checking for these, using a J=6 energy-level program using a one-step diagonalization procedure (easy to program and easy to check).

15. Conclusions This problem is more difficult than expected
We went too fast. Return back to the vt = 0 problem
2) we hope to report if ithe trouble is in
the model or in the code in a later meeting

16. Additional slides

17. Diagram of Frameworks for the Pure Tunneling Formalism
Diagram of Frameworks for the Hybrid Formalism 17

18. Theoretical Model: the global approach
RAM = Rho Axis Method (axis system) for a Cs (plane) frame
HRAM = Hrot + Htor + Hint + Hd.c.
Torsional operators and potential function V(a)
Constants 1
1-cos3a
p2a
Japa
1-cos6a
p4a
Jap3a
V3/2 F r
V6/2 k4 k3 J2
(B+C)/2* Fv Gv Lv Nv Mv
k3J
Ja2
A-(B+C)/2* k5 k2 k1 K2 K1
k3K
Jb2 - Jc2
(B-C)/2* c2 c1 c4
c11 c3
c12
JaJb+JbJa
Dab or Eab
dab
Dab
dab6
DDab
ddab
Rotational Operators
Rotational constants give the structure.
Using the diagonalization of the inertial tensor, one can get the orientation angles of the CH3 group relative to the PAS
= angle of torsion, r = couples internal rotation and global rotation, ratio of the moment of inertia of the top and the moment of inertia of the whole molecule
Kirtman et al 1962
Lees and Baker, 1968
Herbst et al 1986
Hougen, Kleiner, Godefroid JMS 1994 18

19. Methylamine microwave and FIR literature (suite)
1) Microwave Spectrum of Methyl Amine: Assignment and Analysis
of the First Torsional State
Ohashi, Tsunekawa, Takagi and Hougen, JMS 1989
-add 30 new microwave vt = 1- 1 to the previously assigned
-Fit 714 lines with 38 parameters for vt = 1
S = 0.75 MHz for the 216 MW data
S = cm-1 for far-infrared pure rotational data vt = 1-1
S = cm-1 for upper state (vt = 1) combination
differences from the far-infrared torsional band data
2) Far-Infrared Spectrum of Methyl Amine: Assignment of the Second Torsional State
Oda and ohashi, JMS 1989
35 pure rotational transitions in vt = 2- 2
87 transitions vt = 2 -1

20. Methylamine data set from literature: tunneling formalism
- Rotational spectroscopy of methylamine up to 2.6 THz
Motiyenko, Ilyushin, Drouin, Yu, and Margulès, A&A 2014
vt = 0, 76 parameters,
weighted rms deviation = 0.87,
J ≤ 50 and Ka ≤ 20.
2563 MW lines, 96 vt=0 GSCD and 416 pure rotational lines from and FIR spectrum (Ohashi et al 1987)
Previous works : Lide 1954; Shimoda et al. 1954; Hirakawa et al. 1956; Nishikawa 1957, Takagi & Kojima 1971, 1973, Kreglewski&Wlodarczak 1992; Ilyushin et al. 2005, Ilyushin & Lovas 2007, Ohashi 1987 …

21. Methylamine microwave and FIR literature (suite)
Far-Infrared Spectrum and Ground State Constants of Methyl Amine, Ohashi, Takagi, Hougen Olson and Lafferty, JMS 1987
40 to 350 cm-1 by BOMEM Fourier transform spectroscopy with an apodized resolution of cm-1
526 lines pure rotational spectrum vt = 0 – 0 (precision : cm-1)
- 496 lines in fundamental torsional band vt = 1 – 0: cannot treat vt=0 and 1 together so they fit 96 ground state combination differences (precision : cm-1)
1000 energy differences for the ground state vt = 0 with 0 < K < 19 and
J < 30 were fit to 30 molecular parameters S= cm-1