ROTATIONAL SPECTRUM AND LARGE AMPLITUDE MOTIONS OF 3,4-, 2,5- and 3,5-DIMETHYLBENZALDEHYDE

I. KLEINERLaboratoire Interuniversitaire des Systèmes Atmosphériques (LISA),

CNRS, Universités Paris Est et Paris Diderot, Créteil, FranceM. TUDORIE

Service de Chimie Quantique et Photophysique, Université Libre de BruxellesM. JAHN, J-U. GRABOW

Gottfried-Wilhelm-Leibniz-Universitat, Hannover, GermanyM. GOUBET

Laboratoire PhLAM, Université de Lille, France

Objectives:1) Follows up a study on para-tolualdehyde:

Information Transfer Through Conjugated bonds?

V6 vs. V3 barrier to internal rotationWalther 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

C1

3

2

aldehyde group introduces asymmetry:

Toluène – 6-fold (V6 = 4.84 cm-1)V. Ilyushin, Z. Kisiel, L. Pszczolkowski, H.Mader, J.T. Hougen, JMS 259 (2010) 26-38

Para-tolualdehyde (pT) –

(V3 = 28 cm-1, V6 = -5.328 cm-1)W. Caminati, H. Saal, A.R. Hight Walker, Kleiner, J.T. Hougen, J.-U. Grabow, in préparation

Meta-tolualdehyde (mT) –

(V3 = 36 cm-1 cis

(V3 = 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-mT Trans-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)

V3 = 503 cm-1

Cis 3,4-DMBA Trans 3,4-DMBA

Cis 2,5-DMBA

3,5 DMBA

V3 = 52.26 cm-1

V3 = 25.44 cm-1

V3 = 528.3 cm-1

V3 = 6.10 cm-1

V3 = 514 cm-1

V3 = 456 cm-1

V3 = 487 cm-1

High-HighBarriers

Low-Low barriers

High-Low Barriers

BELGI-2Tops: 2 internal inequivalent rotorsapplied to METHYL ACETATE Tudorie et al JMS 2010

JKaKc

3 sets of internal rotation splittings :

(AA,EA). V3 = 100 cm-1

1 = a few GHz

(AA,AE). V3 = 425 cm-1

2 = a few MHz (AA,EE). Interaction

between the 2 tops a = 1.64 D, b = 0.06 D

0 0

0 ±1

± 1 0

± 1 1±1 ±1

1 2

Permutation-inversion group G18

Without torsion

Top 1 Top 2 Interaction

Global approach for two tops : Ohashi’s modelN. Ohashi, J. T. Hougen, R. D. Suenram, F. J. Lovas, Y. Kawashima, M. Fujitake, and J. Pyka, JMS 2004

. Htor = F1 p1

2 + F2 p22 + F12 p1p2 + (1/2) V31 (1-cos31) + (1/2) V32 (1-

cos32) +V12c (1-cos31) ( 1-cos32) +V12s sin31sin32

Hrot = AJz2 + BJx

2 + CJy2 + cent.distorsion

Hint = r1 Jxp1 + r2 Jx p2 + q1 Jzp1 + q2 Jzp2

+B1 p12Jx

2 + B2p22Jx

2 +B12 p1p2Jx2 + C1 p1

2Jy2 + C2 p2

2Jy2 + C12 p1p2Jy

2

+q12p p1p2 (p1+p2) Jz +q12m p1p2 (p1-p2) Jz + ...

“coaxially oriented beam resonator arrangement“(COBRA) FTMW-Spectrometer at Hannover

Accuracy : 1 kHz

2-26.5 GHz

Low-Low barriers

High Barrier

Low barrier

High-HighBarrier

Overview of the data and quality of the fit 3,5 DMB 2,5 DMB 3,4 cis 3,4 trans Low-low barrier High-low High-high

c N. lines rms N. lines rms N. lines rms N. lines rms kHz kHz kHz kHzA 39 3.5 94 2.4 72 1.7 56 1.1E1 40 4.6 80 3.0 81 0.7 53 1.0E2 39 5.4 87 2.5 84 1.0 54 0.9E3 32 4.0 73 2.8 81 1.4 53 1.1E4 26 4.9 76 2.8 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 kHz

Results 3,5 DMB (cm-1): « quasi PAM »

Low barrier top: Higher barrier top: V32= 25.44 (12) V31 = 52.261 (20) F2= 5.539 F1 = 5.479 Q2 = -0.085895 (34) Q1 = -0.0279796 (47) R2 = -0.050705 (16) R1 = 0.0703861(33) C2 = 0. 2986 (28) x 10-6 C1 = -0. 1475(27) x 10-6

B2 = 0. 620 (14) x 10-5

Top-Top interaction

F12 = -0.02865(42)

V12C = -8.8553 (99)

V12S = 1.282(37)

B12 = -0. 6966321 (25) x10-4

C12 = -0. 244212 (78) x 10-4

R12m = -0.0000467 (18) x 10-4

3,5 DMB- comparison with ab initio results

2,5 – DMBA : XX/cc-pVTZ

conf. E /kJ.mol-1 Ae / MHz Be / MHz Ce /

MHz a / D b / D c / D

methode B3LYP MP2 cis 0.00 0.00 2498.874 992.855 716.746 3.45 0.80 0.00

trans 3.79 4.18 1833.086 1177.635 723.392 3.30 1.32 0.00

cis-2,5-DMBA trans-2,5-DMBA

F1 = 5.343 cm-1

V3,1 = 528.3 cm-1

F2 = 5.345 cm-1

V3,2 = 6.098 cm-1

f12 = 0.1527 cm-1

This conformer was not observed in the jet

12

34

5

6

Observed

3,4 DMB

3,4 – DMBA ; B3LYP/cc-pVTZ

conf. E / kJ.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

Cis 3-4 DMBA Trans 3-4 DMBA

F1 = 5.359 cm-1

V3,1 = 502.8 cm-1

F2 = 5.315 cm-1

V3,2 = 514.2 cm-1

f12 = 2*F12 =

0.0946 cm-1

F1 = 5.333 cm-1

V3,1 = 456.3 cm-1

F2 = 5.362 cm-1

V3,2 = 487.2 cm-1

f12 = 2*F12 =

0.1268 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 (V12c (1-cos31) ( 1-cos32)

+V12s sin31sin32)?

Some hints from the dimethylether study by

Senent and Carvajal (2012).

Calculated harmonic frequencies (MP2/cc-pVTZ) level and observed frequencies (RS Soleil) of the low frequency modes (< 300 cm-1) of the 3,4-DMBA and 2,5-DMBA isomers.

isomer mode ab initio exp.

aldehyde torsion 88.5 (1.8) 85.5 gear methyl torsions 104.6 (0.0) n.o aldehyde + anti-gear

methyl torsions 161.3 (6.2) 155.5

aldehyde in-plane bend 177.5 (6.4) 174.5 aldehyde + methyl C4

torsions 182.8 (1.9) 178.5

cis 3,4-DMBA

aldehyde + methyl C3 torsions

203.5 (2.9) 196.5

aldehyde torsion 89.9 (1.6) 87.5 gear methyl torsions 100.5 (0.0) n.o

aldehyde + methyl C4 torsions

148.8 (3.3) 142.0

anti-gear methyl torsions 167.0 (1.3) 163.0 aldehyde bend 185.0 (5.5) 182.0

trans 3,4-DMBA

aldehyde + methyl C3 torsions

236.0 (9.0) 231.5

methyl C5 torsion 50.2 (0.2) n.o aldehyde + methyl C2

torsions (anti-gear) 89.3 (4.0) 86.0

ring puckering 128.2 (0.3) n.o methyl C2 torsion 181.2 (0.0) n.o

aldehyde in-plane bend 216.3 (4.2) n.o*

cis 2,5-DMBA

aldehyde + methyl C2 torsions (gear)

236.3 (9.7) 226.5

values are in cm-1 In parentheses: calculated intensities in km/mol * blended into the hot bands sequence of the 226.5 cm-1

SynchrotonSOLEIL

0

5

10

15

20

25

20 40 60 80 100 120 140

dihedral angle of the C5 methyl group torsion / °

E /

cm-1

eq.

clockwise TS: staggered

eq.(mirror)

eq.(mirror)

anti-clockwise TS: eclipsed

E /cm-1

2,5 DMBA C2 methyl group at eq.: 1) we first fix the

2

And we turn the C5steering wheel …

E /cm-1

0

5

10

15

20

25

30

35

20 40 60 80 100 120 140

dihedral angle of the C5 methyl group torsion / °

E /

cm-1

~ +10 cm-1

~ -5 cm-1

C2 methyl group @ eq.

C2 methyl group @ TS

2,5 DMBA2) Then we fix the C2 at the staggered position (max of its one –dimensional potential)

H

HAfter 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

resonatortuning

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-C3v-top program was written in 2009:

1. For low, medium or high barriers2. 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

HRAM = Hrot + Htor + Hint + Hc.d.

RAM = Rho Axis Method (axis system) for a Cs (plane) frame : get rid of Jxp

Constants 1 1-cos3 p2 Jap 1-cos6 p4

Jap3

1 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 - Jc

2 (B-C)/2* c2 c1 c4 c11 c3 c12

JaJb+JbJa Dab or Eab dab ab ab dab6 ab ab

Torsional operators and potential function V()

Ro

tati

on

al O

per

ato

rs

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 1962Lees and Baker, 1968 Herbst et al 1986

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 = AJa2 + BRJb

2 +CRJc2 + q1Jap1 + q2Jap2 + r1Jbp1 + r2Jbp2

Hc.d usual centrifugal distorsion termsHint higher order torsional-rotational interactions terms : cos3 cos32 , p1, p and global rotational operators like Ja, Jb , Jc

Htor = F1 p12 + F2 p2

2 + F12 p1p2 + (1/2) V31 (1-cos31) + (1/2) V32 (1-cos32)

+V12c (1-cos31) ( 1-cos32) +V12s sin31sin32

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 1MHz Obs-Calcsnucleus Ar-acetone, (CH3)2SiF2

_____________________________________________________________________ERHAM Groner one or two Effective vt states fit

internal rotors Fourier series for Torsionalof sym. C3v or C2v Tunneling SplittingsJ up to 120. High Barrier

acetone, diMEether_____________________________________________________________________SPFIT/ Pickett one or two internal Potential Function fitSPCAT rotors, sym or asym. propane

_____________________________________________________________________OHASHI Ohashi two C3v internal rotors Potential Function fit Hougen Cs or C2h Frame A and E species fit together

1 kHz accuracy, but very slow N-methylacetamide, biacetyl