ROTATIONAL SPECTRUM AND LARGE AMPLITUDE MOTIONS OF 3,4-, 2,5- and 3,5- DIMETHYLBENZALDEHYDE I. KLEINER Laboratoire Interuniversitaire des Systèmes Atmosphériques (LISA), CNRS, Universités Paris Est et Paris Diderot, Créteil, France M. TUDORIE Service de Chimie Quantique et Photophysique, Université Libre de Bruxelles M. JAHN, J-U. GRABOW Gottfried-Wilhelm-Leibniz-Universitat, Hannover, Germany M. GOUBET Laboratoire PhLAM, Université de Lille, France

Objectives: 1) Follows up a study on para-tolualdehyde: Information Transfer Through Conjugated bonds? V 6 vs. V 3 barrier to internal rotation Walther Caminati, Angela R. Hight-Walker, Jon T. Hougen, Isabelle Kleiner, Hilkka Saal, Jens-Uwe Grabow, to be published. Will the methyl group know about the asymmetry? H O C aldehyde group introduces asymmetry:

Toluène – 6-fold (V 6 = 4.84 cm -1 ) V. Ilyushin, Z. Kisiel, L. Pszczolkowski, H.Mader, J.T. Hougen, JMS 259 (2010) Para-tolualdehyde (pT) – (V 3 = 28 cm-1, V 6 = cm -1 ) W. Caminati, H. Saal, A.R. Hight Walker, Kleiner, J.T. Hougen, J.-U. Grabow, in préparation Meta-tolualdehyde (mT) – (V 3 = 36 cm -1 cis (V 3 = 5 cm -1 trans ) J. Shirar, D S. Wilcox, K M. Hotopp, G L. Storck, I Kleiner, B C. Dian, JCP 2010 pT Toluène Cis-mTTrans-mT

Objectives 1) This study follows up the para- tolualdehyde work by Grabow et al 2) The DMB are good tests of the two-top BELGI code, applied so far to methyl acetate (Tudorie et al JMS 2010) and methyl propionate (Mol. Phys. 2012)

V 3 = 503 cm -1 Cis 3,4-DMBATrans 3,4-DMBA Cis 2,5-DMBA 3,5 DMBA V 3 = cm -1 V 3 = cm -1 V 3 = cm -1 V 3 = 6.10 cm -1 V 3 = 514 cm -1 V 3 = 456 cm -1 V 3 = 487 cm -1 High- High Barriers Low-Low barriers High-Low Barriers

BELGI-2Tops: 2 internal inequivalent rotors applied to METHYL ACETATE Tudorie et al JMS 2010 JK a K c 3 sets of internal rotation splittings : (AA,EA). V 3 = 100 cm -1  1 = a few GHz (AA,AE). V 3 = 425 cm -1  2 = a few MHz (AA,EE). Interaction between the 2 tops  a = 1.64 D,  b = 0.06 D 0 0 ±1 ± 1 0 ± 1 1 ±1  1  2 Permutation-inversion group G 18 Without torsion Top 1 Top 2 Interaction

Global approach for two tops : Ohashi’s model N. Ohashi, J. T. Hougen, R. D. Suenram, F. J. Lovas, Y. Kawashima, M. Fujitake, and J. Pyka, JMS H tor = F 1 p F 2 p F 12 p 1 p 2 + (1/2) V 31 (1-cos3  1 ) + (1/2) V 32 (1-cos3  2 ) +V 12c (1-cos3  1 ) ( 1-cos3  2 ) +V 12s sin3  1 sin3  2 H rot = AJ z 2 + BJ x 2 + CJ y 2 + cent.distorsion H int = r 1 J x p 1 + r 2 J x p 2 + q 1 J z p 1 + q 2 J z p 2 +B 1 p 1 2 J x 2 + B 2 p 2 2 J x 2 +B 12 p 1 p 2 J x 2 + C 1 p 1 2 J y 2 + C 2 p 2 2 J y 2 + C 12 p 1 p 2 J y 2 +q 12p p 1 p 2 (p 1 +p 2 ) J z +q 12m p 1 p 2 (p 1 -p 2 ) J z +...

“coaxially oriented beam resonator arrangement“ (COBRA) FTMW-Spectrometer at Hannover Accuracy : 1 kHz GHz

Low-Low barriers High Barrier Low barrier High- High Barrier

Overview of the data and quality of the fit 3,5 DMB2,5 DMB3,4 cis3,4 trans Low-low barrierHigh-lowHigh-high  c N. lines rms N. lines rms N. lines rms N. lines rms kHzkHz kHzkHz A E E E E Total Mesurements performed in Hanover : 2 – 26.5 GHz, J  15, Ka  4 accuracy: 1 kHz

Results 3,5 DMB (cm -1 ): « quasi PAM » Low barrier top: Higher barrier top: V 32 = (12) V 31 = (20) F 2 = F 1 = Q 2 = (34) Q 1 = (47) R 2 = (16) R 1 = (33) C 2 = (28) x C 1 = (27) x B 2 = (14) x Top-Top interaction F 12 = (42) V 12C = (99) V 12S = 1.282(37) B 12 = (25) x10 -4 C 12 = (78) x R 12m = (18) x 10 -4

3,5 DMB- comparison with ab initio results

cis-2,5-DMBA trans-2,5-DMBA F 1 = cm -1 V 3,1 = cm -1 F 2 = cm -1 V 3,2 = cm -1 f 12 = cm -1 This conformer was not observed in the jet Observed

3,4 DMB 3,4 – DMBA ; B3LYP/cc-pVTZ conf.  E / kJ.mol -1 A e / MHzB e / MHzC e / MHz  a / D  b / D  c / D cis trans Cis 3-4 DMBATrans 3-4 DMBA F 1 = cm -1 V 3,1 = cm -1 F 2 = cm -1 V 3,2 = cm -1 f 12 = 2*F 12 = cm -1 F 1 = cm -1 V 3,1 = cm -1 F 2 = cm -1 V 3,2 = cm -1 f 12 = 2*F 12 = cm -1

Conclusions When the two barriers are low, the splittings are large and the fit converges rather quickly When the two barriers (or one of them) is high, splittings are small and some internal rotation parameters are not well determined Use of ab initio values as initial guesses are crucial.

To solve How to compare top-top interaction terms from ab initio calculations to the values of BELGI-2tops (V 12c (1-cos3  1 ) ( 1-cos3  2 ) +V 12s sin3  1 sin3  2 )? Some hints from the dimethylether study by Senent and Carvajal (2012).

Synchroton SOLEIL

eq. clockwise TS: staggered eq. (mirror) eq. (mirror) anti-clockwise TS: eclipsed  E /cm -1 2,5 DMBAC2 methyl group at eq. : 1) we first fix the 2 And we turn the C5 steering wheel …

 E /cm -1 ~ +10 cm -1 ~ -5 cm -1 C2 methyl eq. C2 methyl TS 2,5 DMBA 2) Then we fix the C2 at the staggered position (max of its one –dimensional potential) H H After 60° 

Thank you ! M. TUDORIE and I. KLEINER acknowledge the ANR for the financial support from the contract ANR-08-BLAN-0054 TopModel

Coaxial oriented Beam-Resonator Arrangement (COBRA) Fabry-Perot resonator resonator tuning FT FID Impulse polarization pulse: coherence between rotating molecular dipoles oscillating macroscopic dipole moment: electromagnetic field at frequencies of molecular transitions

The new code: BELGI-2tops a new two-C 3v -top program was written in 2009: 1. For low, medium or high barriers 2. With high accuracy (obs-calcs < 1 kHz) 3. With high computational speed Begin with Ohashi’s two-top program, but use: 1. Two-step diagonalization (Herbst, BELGI) 2. Banded matrix computational methods suggested in 2009 ?

Theoretical Model: the global approach for one top H RAM = H rot + H tor + H int + H c.d. RAM = Rho Axis Method (axis system) for a C s (plane) frame : get rid of J x p  Constants1 1-cos3  p2p2 JapJap 1-cos6  p4p4 Jap3Jap3 1V 3 /2F  V 6 /2k4k4 k3k3 J2J2 (B+C)/2*FvFv GvGv LvLv NvNv MvMv k 3J Ja2Ja2 A-(B+C)/2*k5k5 k2k2 k1k1 K2K2 K1K1 k 3K J b 2 - J c 2 (B-C)/2*c2c2 c1c1 c4c4 c 11 c3c3 c 12 JaJb+JbJaJaJb+JbJa D ab or E ab d ab  ab  ab d ab6  ab  ab Torsional operators and potential function V(  ) Rotational Operators Hougen, Kleiner, Godefroid JMS 1994  = 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 Kirtman et al 1962 Lees and Baker, 1968 Herbst et al 1986

Two-step diagonalization for the two-top problem H RAM = H tor + H rot + H c.d + H int 1) Diagonalization of the torsional part of the Hamiltonian : Eigenvalues = torsional energies 2) A low set of torsional Eigenvectors x rotational wavefunctions are then used to set up the matrix of the rest of the Hamiltonian: H rot = AJ a 2 + B R J b 2 +C R J c 2 + q 1 J a p 1 + q 2 J a p 2 + r 1 J b p 1 + r 2 J b p 2 H c.d usual centrifugal distorsion terms H int higher order torsional-rotational interactions terms : cos3    cos3  2, p 1, p  and global rotational operators like J a, J b, J c

Overview of Existing Two-Top Programs Name Authors What it does? Method programs for rotational spectroscopy (Z. Kisiel) _____________________________________________________________________ XIAM Hartwig up to 3 sym tops « IAM » Potential Function fit Maederup to one quad Often 1MHz Obs-Calcs nucleusAr-acetone, (CH 3 ) 2 SiF 2 _____________________________________________________________________ ERHAM Gronerone or two Effective v t states fit internal rotors Fourier series for Torsional of sym. C 3v or C 2v Tunneling Splittings J up to 120. High Barrier acetone, diMEether _____________________________________________________________________ SPFIT/ Pickettone or two internalPotential Function fit SPCATrotors, sym or asym.propane _____________________________________________________________________ OHASHI Ohashitwo C 3v internal rotorsPotential Function fit Hougen C s or C 2h Frame A and E species fit together 1 kHz accuracy, but very slow N-methylacetamide, biacetyl