ROTATIONAL SPECTRUM AND LARGE AMPLITUDE MOTIONS OF 3

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 Ph. LAM, Université de Lille, France

Objectives: 1) Follows up a study on para-tolualdehyde: Information Transfer Through Conjugated bonds? aldehyde group introduces asymmetry: 2 1 3 H C O Will the methyl group know about the asymmetry? 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.

Toluène – 6 -fold (V 6 = 4. 84 cm-1) V. Ilyushin, Z. Kisiel, L. Pszczolkowski, H. Mader, J. T. Hougen, JMS 259 (2010) 26 -38 Para-tolualdehyde (p. T) – (V 3 = 28 cm-1, V 6 = -5. 328 cm-1) Toluène W. Caminati, H. Saal, A. R. Hight Walker, Kleiner, J. T. Hougen, J. -U. Grabow, in préparation Meta-tolualdehyde (m. T) – (V 3 = 36 cm-1 cis (V 3 = 5 cm-1 trans ) p. T J. Shirar, D S. Wilcox, K M. Hotopp, G L. Storck, I Kleiner, B C. Dian, JCP 2010 Cis-m. T Trans-m. T

Objectives n 1) This study follows up the para-tolualdehyde work by Grabow et al n 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 = 514 cm-1 Cis 3, 4 -DMBA Trans 3, 4 -DMBA High Barriers V 3 = 487 cm-1 = 503 cm-1 V 3 = 52. 26 cm-1 Cis 2, 5 -DMBA High-Low Barriers V 3 = 528. 3 cm-1 V 3 = 456 cm- 3, 5 DMBA Low-Low barriers V 3 = 6. 10 cm-1 V 3 = 25. 44 cm-1

BELGI-2 Tops: 2 internal inequivalent rotors applied to METHYL ACETATE Tudorie et al JMS 2010 ± 1 ± 1 1 JKa. Kc ± 1 0 n 3 sets of internal rotation splittings : n 0 ± 1 0 0 Without torsion Top 1 Top 2 Interaction Permutation-inversion group G 18 s 1 s 2 (AA, EA). V 3 = 100 cm-1 D 1 = a few GHz -1 n (AA, AE). V 3 = 425 cm 2 = a few MHz n (AA, EE). Interaction between the 2 tops n a = 1. 64 D, b = 0. 06 D

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 2004 . n Htor = F 1 p 12 + F 2 p 22 + F 12 p 1 p 2 + (1/2) V 31 (1 -cos 3 a 1) + (1/2) V 32 (1 -cos 3 a 2) +V 12 c (1 -cos 3 a 1) ( 1 -cos 3 a 2) +V 12 s sin 3 a 1 sin 3 a 2 n Hrot = AJz 2 + BJx 2 + CJy 2 + cent. distorsion n Hint = r 1 Jxp 1 + r 2 Jx p 2 + q 1 Jzp 1 + q 2 Jzp 2 +B 1 p 12 Jx 2 + B 2 p 22 Jx 2 +B 12 p 1 p 2 Jx 2 + C 1 p 12 Jy 2 + C 2 p 22 Jy 2 + C 12 p 1 p 2 Jy 2 +q 12 p p 1 p 2 (p 1+p 2) Jz +q 12 m p 1 p 2 (p 1 -p 2) Jz +. . .

“coaxially oriented beam resonator arrangement“ (COBRA) FTMW-Spectrometer at Hannover Accuracy : 1 k. Hz 2 -26. 5 GHz

Low-Low barriers High Barrier Low barrier High Barrier

Overview of the data and quality of the fit 3, 5 DMB Low-low barrier 2, 5 DMB 3, 4 cis High-low c N. lines rms N. lines k. Hz A 39 3. 5 94 E 1 40 4. 6 80 E 2 39 5. 4 87 E 3 32 4. 0 73 E 4 26 4. 9 76 rms k. Hz 2. 4 3. 0 2. 5 2. 8 3, 4 trans High-high N. lines rms k. Hz 72 1. 7 56 1. 1 81 0. 7 53 1. 0 84 1. 0 54 0. 9 81 1. 4 53 1. 1 81 0. 8 54 1. 3 Total 176 4. 3 410 2. 7 399 1. 1 270 1. 1 Mesurements performed in Hanover : 2 – 26. 5 GHz, J 15, Ka 4 accuracy: 1 k. Hz

Results 3, 5 DMB (cm-1): « quasi PAM » n n n n Low barrier top: Higher barrier top: V 32= 25. 44 (12) V 31 = 52. 261 (20) F 2= 5. 539 F 1 = 5. 479 Q 2 = -0. 085895 (34) Q 1 = -0. 0279796 (47) R 2 = -0. 050705 (16) R 1 = 0. 0703861(33) C 2 = 0. 2986 (28) x 10 -6 C 1 = -0. 1475(27) x 10 -6 B 2 = 0. 620 (14) x 10 -5 n Top-Top interaction F 12 = -0. 02865(42) V 12 C = -8. 8553 (99) V 12 S = 1. 282(37) B 12 = -0. 6966321 (25) x 10 -4 C 12 = -0. 244212 (78) x 10 -4 R 12 m = -0. 0000467 (18) x 10 -4

3, 5 DMB- comparison with ab initio results

F 1 = 5. 343 cm-1 V 3, 1 = 528. 3 cm-1 F 2 = 5. 345 V 3, 2 = 6. 098 cm-1 6 5 1 4 2 3 cis-2, 5 -DMBA trans-2, 5 -DMBA f 12 = 0. 1527 cm-1 Observed This conformer was not observed in the jet

3, 4 DMB 3, 4 – DMBA ; B 3 LYP/cc-p. VTZ conf. E / k. J. mol-1 Ae / MHz Be / MHz Ce / MHz a / D b / D c / D cis 0. 00 2698. 822 910. 701 686. 655 3. 69 -1. 53 0. 00 trans 0. 57 2948. 310 860. 427 671. 529 4. 22 0. 94 0. 00 F 1 = 5. 359 cm-1 V 3, 1 = 502. 8 cm-1 F 1 = 5. 333 cm-1 V 3, 1 = 456. 3 cm-1 F 2 = 5. 315 cm-1 V 3, 2 = 514. 2 cm-1 F 2 = 5. 362 cm-1 V 3, 2 = 487. 2 cm-1 f 12 = 2*F 12 = 0. 0946 cm-1 f 12 = 2*F 12 = 0. 1268 cm-1 Cis 3 -4 DMBA Trans 3 -4 DMBA

Conclusions n When the two barriers are low, the splittings are large and the fit converges rather quickly n When the two barriers (or one of them) is high, splittings are small and some internal rotation parameters are not well determined n 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-2 tops (V 12 c (1 -cos 3 a 1) ( 1 -cos 3 a 2) +V 12 s sin 3 a 1 sin 3 a 2)? Some hints from the dimethylether study by Senent and Carvajal (2012).

Synchroton SOLEIL

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

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

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

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

The new code: BELGI-2 tops a new two-C 3 v-top program was written in 2009: 1. For low, medium or high barriers 2. With high accuracy (obs-calcs < 1 k. Hz) 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 RAM = Rho Axis Method (axis system) for a Cs (plane) frame : get rid of Jxpa HRAM = Hrot + Htor + Hint + Hc. d. Torsional operators and potential function V(a) Rotational Operators Constants 1 1 -cos 3 a p 2 a Ja p a 1 -cos 6 a p 4 a Ja p 3 a V 3/2 F r V 6/2 k 4 k 3 J 2 (B+C)/2* Fv Gv Lv Nv Mv k 3 J Ja 2 A-(B+C)/2* k 5 k 2 k 1 K 2 K 1 k 3 K (B-C)/2* c 2 c 1 c 4 c 11 c 3 c 12 Ja. Jb+Jb. Ja Dab or Eab dab 6 ab ddab 1 Jb 2 - Jc 2 a = angle of torsion, r = couples internal rotation and global rotation, ratio Kirtman et al 1962 Lees and Baker, 1968 of the moment of inertia of the top and the moment of inertia of the whole molecule Herbst et al 1986 Hougen, Kleiner, Godefroid JMS 1994

Two-step diagonalization for the two-top problem HRAM = Htor + Hrot + Hc. d + Hint 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: Hrot = AJa 2 + BRJb 2 +CRJc 2 + q 1 Jap 1 + q 2 Jap 2 + r 1 Jbp 1 + r 2 Jbp 2 Hc. d usual centrifugal distorsion terms Hint higher order torsional-rotational interactions terms : cos 3 a 1, cos 3 a 2 , p 1, p 2 and global rotational operators like Ja, Jb , Jc

Overview of Existing Two-Top Programs Name Authors What it does? Method http: //info. ifpan. edu. pl/~kisiel/prospe. htm: programs for rotational spectroscopy (Z. Kisiel) ___________________________________ XIAM Hartwig up to 3 sym tops « IAM » Potential Function fit Maeder up to one quad Often 1 MHz Obs-Calcs nucleus Ar-acetone, (CH 3)2 Si. F 2 ___________________________________ ERHAM Groner one or two Effective vt states fit internal rotors Fourier series for Torsional of sym. C 3 v or C 2 v Tunneling Splittings J up to 120. High Barrier acetone, di. MEether ___________________________________ SPFIT/ Pickett one or two internal Potential Function fit SPCAT rotors, sym or asym. propane ___________________________________ OHASHI Ohashi two C 3 v internal rotors Potential Function fit Hougen Cs or C 2 h Frame A and E species fit together 1 k. Hz accuracy, but very slow N-methylacetamide, biacetyl