1. THE MILLIMETER-WAVE SPECTRUM OF METHACROLEIN
THE MILLIMETER-WAVE SPECTRUM OF METHACROLEIN. TORSION-ROTATION-VIBRATION EFFECTS IN THE EXCITED STATES
OLENA ZAKHARENKO, JUAN-RAMON AVILES MORENO, ROMAN A. MOTIYENKO, THERESE R. HUET Laboratoire PhLAM, UMR8523 CNRS - Université Lille 1, Villeneuve d’Ascq, France.

2. Volatile organic compounds (VOCs) sources
lifetime is short  oxidation and degradation products
formation of SOAs  influence on the global climate and human health
Antropogenic
 100 TgC/yr
Natural
 1170 TgC/yr
Others VOCs
Monoterpenes
Isoprene
Biomass burning
Energy use and transfer

3. Isoprene oxydation products
Isoprene C5H8
Methacrolein (MAC)
Trans
Cis
Methyl vinyl ketone (MVK)
Reaction with OH /NOx/ O3
Objectives:
Analysis of ground state and low lying excited states
Study of large amplitude motion (internal rotation of methyl group)
Providing required information for analysis of high resolution IR spectra
can also originate from primary emissions such as fuel evaporation or combustion (vehicular emissions)

4. Quantum chemical calculations
C3v symmetry group
the internal rotation potential function:
V α = V −cos3α + V −cos6α
V3(CH3)
Trans most stable
Cis cm-1
244,20-234,19 E A
J.-R. Alives Moreno et al., 69th ISMS, 2014, TI01

5. Rho-Axis Method (RAM) B > A θRAM Ir (a, b, c→ z, x, y)
a= z Ir
IIl
PAM (MHz)
RAM (MHz) A B C
θRAM
80.8°
-9.2° μx
2.67 D
2.77 D μz
0.84 D
0.40 D
θRAM ρ
Ir (a, b, c→ z, x, y)
B > A
b = x
IIl (a, b, c→ x, z, y) OK
PAM to RAM:
𝐴 𝑅𝐴𝑀 = 𝐴 𝑃𝐴𝑀 cos 2 𝜃 𝑅𝐴𝑀 + 𝐵 𝑃𝐴𝑀 sin 2 𝜃 𝑅𝐴𝑀
𝐵 𝑅𝐴𝑀 = 𝐴 𝑃𝐴𝑀 𝑠𝑖𝑛 2 𝜃 𝑅𝐴𝑀 + 𝐵 𝑃𝐴𝑀 𝑐𝑜𝑠 2 𝜃 𝑅𝐴𝑀
𝐶 𝑅𝐴𝑀 = 𝐶 𝑃𝐴𝑀
𝐷 𝑎𝑏 =− 𝐴 𝑃𝐴𝑀 − 𝐵 𝑃𝐴𝑀 cos 𝜃 𝑅𝐴𝑀 sin 𝜃 𝑅𝐴𝑀
𝜇 𝑎 𝜇 𝑏 𝑅𝐴𝑀 = 𝑐𝑜𝑠 𝜃 𝑅𝐴𝑀 𝑠𝑖𝑛 𝜃 𝑅𝐴𝑀 −𝑠𝑖𝑛 𝜃 𝑅𝐴𝑀 𝑐𝑜𝑠 𝜃 𝑅𝐴𝑀 𝜇 𝑎 𝜇 𝑏 𝑃𝐴𝑀
RAM Hamiltonian:
𝑯 𝑹𝑨𝑴 = 𝑯 𝑹 + 𝑯 𝒄𝒅 +𝑯 𝑻 + 𝑯 𝒊𝒏𝒕 ,
where HR is the rotational Hamiltonian,
Hcd the centrifugal distortion Hamiltonian,
HT the torsional Hamiltonian,
Hint contains higher-order torsional-
rotational interaction terms.

6. Rho-Axis Method (RAM) B > A θRAM Ir (a, b, c→ z, x, y)Ir
IIl
PAM (MHz)
RAM (MHz) A B C
θRAM
80.8°
9.2° μx
2.67 D
2.77 D μz
0.84 D
0.40 D ρ
θRAM
Ir (a, b, c→ z, x, y)
B > A
b = z
IIl (a, b, c→ x, z, y) OK
PAM to RAM:
𝐴 𝑅𝐴𝑀 = 𝐴 𝑃𝐴𝑀 cos 2 𝜃 𝑅𝐴𝑀 + 𝐵 𝑃𝐴𝑀 sin 2 𝜃 𝑅𝐴𝑀
𝐵 𝑅𝐴𝑀 = 𝐴 𝑃𝐴𝑀 𝑠𝑖𝑛 2 𝜃 𝑅𝐴𝑀 + 𝐵 𝑃𝐴𝑀 𝑐𝑜𝑠 2 𝜃 𝑅𝐴𝑀
𝐶 𝑅𝐴𝑀 = 𝐶 𝑃𝐴𝑀
𝐷 𝑎𝑏 =− 𝐴 𝑃𝐴𝑀 − 𝐵 𝑃𝐴𝑀 cos 𝜃 𝑅𝐴𝑀 sin 𝜃 𝑅𝐴𝑀
𝜇 𝑎 𝜇 𝑏 𝑅𝐴𝑀 = 𝑐𝑜𝑠 𝜃 𝑅𝐴𝑀 𝑠𝑖𝑛 𝜃 𝑅𝐴𝑀 −𝑠𝑖𝑛 𝜃 𝑅𝐴𝑀 𝑐𝑜𝑠 𝜃 𝑅𝐴𝑀 𝜇 𝑎 𝜇 𝑏 𝑃𝐴𝑀
RAM Hamiltonian:
𝑯 𝑹𝑨𝑴 = 𝑯 𝑹 + 𝑯 𝒄𝒅 +𝑯 𝑻 + 𝑯 𝒊𝒏𝒕 ,
where HR is the rotational Hamiltonian,
Hcd the centrifugal distortion Hamiltonian,
HT the torsional Hamiltonian,
Hint contains higher-order torsional-
rotational interaction terms.

7. THz Spectrometer in Lille
Previous study :
GHz
up to J = 10
only ground state
Present study :
150 – 465 GHz
up to J = 76 and Ka = 17
ground state + low lying excited energy states
J.R. Durig et al. Spectrochimica Acta A 42, (1986).
M. Suzuki, K. Kozima, J. Mol. Spectrosc. 38, (1971).
Spectrometer performance:
150 – 990 GHz (was recently extended up to 1.5 THz)
frequency multiplication chain output power: 5 µW - 5 mW
sensitivity: cm-1
Doppler limited resolution
measurement accuracy: 30 kHz, 50 kHz, 100 kHz depending on the observed S/N ratio and the frequency range
Spectrometer based on solid state sources Pathway m Frequency modulation technique

8. Spectrum of MAC
Examples of the spectrum in frequency range from 150 to 210 GHz.
H2O
150 – 465 GHz
up to J = 76 and Ka = 17
ground state + low lying excited energy states
Dipole moments PAM: μa = 2.67 D and μb = 0.84 D

9. CH3 torsion
Analysis of g.s.
Prediction of v27=1
Assignment of v27=1
Global fit of g.s.+ v27=1
Prediction of v27=2
Parameter
(v=0 and v27=1 ) cm-1 F
fixeda Ρ
(41) V3
(24) V6
(22) A
(23) B
(25) C
(45) ∙10-1
2Dab
(17) ∙10-1
θRAM
-8.737° n
3411
rms(MHz)
0.0319
wrms
0.776
+ 19 parameters
CH3 barrier (cm-1)
Method
Trans
Cis
B3LYP/ G(2df,p)
468
451
M062X/ G(2df,p)
493
516
MP2/AVTZ 
501
509
Experimental
This work
494  -
[1] v=0
[2] IR
444
441
Global fit of the ground state and the first excited torsional state:
Up to J, Ka = 76, 17
> 3000 transitions
rms = MHz
wrms = 0.776
[1] M. Suzuki, K. Kozima, J. Mol. Spectrosc. 38, (1971).
[2] J.R. Durig et al. Spectrochimica Acta A 42, (1986).
a the MP2 aug-cc-pVTZ calculations
v27 = 2: assignments only for rotational transitions with Ka<5
E: 275,23 – 265,22
E: 274,23 – 264,22

10. Rotation- vibration interactions
Scheme of the lowest vibrational states in s-trans methacrolein.[3]
Fermi and c-type Coriolis interactions between v27=2 and v25 = 1
shift of approx. 9.5 cm-1 between observed and predicted v27 = 2-1
cis
1←0 (A,E)
trans
1←0 (A,E)
~9.5 cm-1
2←1(E)
2←1(A)
1←0 (A,E)
Spectral resolution: 0.1 cm-1
[3] J.R. Durig et al. Spectrochimica Acta A 42, (1986).

11. Scheme of the lowest vibrational states in s-trans methacrolein.
Vibrational modes
v27
v26
Scheme of the lowest vibrational states in s-trans methacrolein.
v27 – methyl torsion
v26 – antisymmetric CCC out-of-plane bending vibration (skeletal torsion)
v25 – symmetric CCC in-plane bending vibration

12. Skeletal torsion v26
The anomalous A-E splittings: the splittings of v26 mode are much bigger than these ones of ground state
A and E tunneling sublevels are inversed compared to the typical order of transitions in the ground state
The anomalous A-E splittings and unusual sequence of A-E transitions in the v26=1 state were explained by kinetic coupling between methyl and skeletal torsional modes

13. Scheme of the lowest vibrational states in s-trans methacrolein.
Kinetic coupling
The relative displacements of the atoms for the ν27 and ν26 modes obtained with the MP2 aug-cc-pVTZ calculations
Methyl torsion v27=1
Skeletal torsion v26=1
Atom X Y Z C1
0.00
0.04
0.13 H2 H3
0.15
0.32 C4
-0.05
-0.08 C5
-0.03 H6
0.50
-0.45 H7
0.46
-0.31
-0.38
0.06
0.22 H8
-0.46
0.03
0.38
-0.06 C9
-0.09
-0.17
H10
-0.29
-0.48
O11
0.11
0.12
Scheme of the lowest vibrational states in s-trans methacrolein.
Hydrogen atoms of CH3
v27
v26
both normal modes may be represented as a mixture of pure methyl top torsion, and out-of-plane motion of others atoms

14. Skeletal torsion v26 By reason of inverted sequence of AE splittings
⟹The v26=1 state is assigned as a virtually first excited state of the methyl torsional mode
⟹ Separated fit of the v26 state using RAM Hamiltonian
Parameter
(v=0 and v27=1 ) cm-1
(v26=1) cm-1 F
fixed ρ
(41)
(45) ∙10-1 V3
(24)
626.46(28) A
(23)
(14) B
(25)
(43) C
(45) ∙10-1
(17) ∙10-1
2Dab
(17) ∙10-1
(55) ∙10-1
θRAM
-8.737°
-11.81° n
3411
1054
rms(MHz)
0.0319
0.0376
wrms
0.776
0.844
+ 19 parameters
+ 8 parameters
Fit of the skeletal torsion state:
up to J, Ka = 44, 17
1054 transitions
rms = MHz
wrms = 0.844
fit is purely effective
v26

15. Conclusions analysis of the rotational spectrum of s-trans MAC
significant advance in the knowledge on the molecular structure and dynamics, and on the low-lying excited vibrational states
determined value of the barrier to internal rotation
analyzed the first excited vibrational state of the skeletal torsional mode ν26
Provided information for analysis of high resolution infrared spectrum

16. THANK YOU FOR YOUR ATTENTION
Support from the CaPPA project (Chemical and Physical Properties of the Atmosphere) is acknowledged. CaPPA is funded by the French National Research Agency (ANR) through the PIA (Programme d'Investissement d'Avenir) under contract "ANR-11-LABX " and by the Regional Council “ Nord-Pas de Calais » and the  "European Funds for Regional Economic Development (FEDER)