Application of the hybrid program
for fitting microwave and farinfrared 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
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
2
Last year: Two large-amplitude motions in methyl malonaldehyde:
Intramolecular hydrogen transfer
Internal rotation of a methyl rotor
O8
H10
C5
H2
H3
H11
C6
C12
O7
C4
H1
O8
(123)(45)(78)(9,10)
H9
H10
C5
H2
H11
C6
C12
O7
C4
H9
H1
H3
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
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
Pure tunneling formalism: V3 = 399 cm-1
Hybrid formalism:
V3 = 302 cm-1
.
2-MMA-OD
Diff.
V3 = 311 cm-1
88 cm-1
V3 = 315.5 cm-1 15 cm-1
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) 474-501.
5
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.
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 torsionrotation corrections.
7
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
P2, cos6, Jx2, Jy2, Jz2
cos3, (JxJz+JzJx)
PJy
Occur in blocks
LL, RR, LR, RL
LL, RR
LR, RL
8
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]
360
1.44
0.0007 cm-1
GSCD from FIR
99
1.36
0.0010 cm-1
MW lines [1,2]
1254 8.3
______________________________________________________
[1] Ohashi et al JMS 1987 and references herein
[2] Motyenko et al A&A 2014 and references herein
Fitting vt= 0 and 1 together ….still a problem!
_ _________________________________________________
Lines wrms
MW A-species
542 13.8
MW E-species
656 23.0
________________________________________________
Lines rms
Weight
Pure rot vt = 0-0 FIR lines [1]
351 2.54
0.0007 cm-1
GSCD from FIR
99
0.94
0.0010 cm-1
Vt = 1-0 FIR [1]
411 50.7
0.0006 cm-1
MW lines [1,2]
1198 19.4
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
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
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
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 energylevel program using a one-step diagonalization
procedure (easy to program and easy to check).
Conclusions
1)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
Additional slides
hydrogen transfer
Diagram of Frameworks for the Pure Tunneling Formalism
n=2
n=6
n=4
n=6

-120
-60
0
60
120
180
240
300
 (degree)
360

n=1
n=3
n=5
methyl torsion
Diagram of Frameworks for the Hybrid Formalism
+


17
Theoretical Model: the global approach
RAM = Rho Axis Method (axis system) for a Cs (plane) frame
HRAM = Hrot + Htor + Hint + Hd.c.
Rotational Operators
Torsional operators and potential function V()
Constant
s
1
1
1-cos3 p2 Jap
1-cos6 p4
Jap3
V3/2
F

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
ab
dab
dab6
ab
ddab
Kirtman et al 1962
Lees and Baker, 1968
Herbst et al 1986
 = angle of torsion,  = couples internal rotation and global rotation, ratio
of the moment of inertia of the top and the moment of inertia of the whole
molecule
Hougen, Kleiner, Godefroid JMS 1994
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 = 0.00115 cm-1 for far-infrared pure rotational data vt = 1-1
S = 0.00100 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
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 …
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 0.005 cm-1
- 526 lines pure rotational spectrum vt = 0 – 0 (precision : 0.0007 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 : 0.0010 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= 0.00063 cm-1