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STRUCTURE OF THE BENZENE DIMER

-

GOVERNED BY DYNAMICS.

MELANIE SCHNELL, Center for Free-Electron Laser Science, Hamburg, Germany

UNDINE ERLEKAM, GERT V. HELDEN, GERARD MEIJER, Fritz-Haber-Institut, Berlin, Germany

PHILIP R. BUNKER, National Research Council of Canada, Ottawa, Canada

JENS-UWE GRABOW, Gottfried-Wilhelm-Leibniz-Universtät, Hannover, Germany

AD VAN DER AVOIRD, Radboud University, Nijmegen, The Netherlands

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tilted T-shaped parallel displaced

cap

stem

very floppy system - internal dynamics is not understood

The benzene dimer•study of intermolecular forces as benchmark for ab initio studies

dispersion interaction: intermolecular (non-local) electron correlation

two competing structures:

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aromatic stacking interactions in supermolecular chemistry; edge-to-face stacking (T-stacking)

Interests of benzene dimer

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What is known so far...J. Chem. Phys. 63 (1975) 1419

J. Chem. Phys. 97 (1992) 2189

J. Chem. Phys. 98 (1993) 4294

symmetric-top spectrum with complex internal rotation

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Coaxially oriented Beam-Resonator Arrangement (COBRA):molecular excitation

)()(

)()(

tt

tt

bbba

abaa

0 baab

tMW pulse

1μs

before excitation pulse: dipole moments cancel

Eb

Ea

many two-level systems

single particle, Schrödinger equation:

iH

iH ,ensemble properties, von Neumann equation

wavefunction

density matrix

density matrix:

(no) coherence:

population: 0 bbaa

J.-U. Grabow, W. Stahl, Z. Naturforsch. 45a, 1043 (1990).

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Coaxially oriented Beam-Resonator Arrangement (COBRA):molecular response

E

t

T = 100μs

MW signal

after excitation pulse: oscillating macroscopic dipole moment

density matrix:

)()(

)()(

tt

tt

bbba

abaa

0, baab

coherence:

population: 0bbaa

Fourier Transform

Frequency Domain, Spectrum

Time Domain, FID

U. Andresen, H. Dreizler, J.-U. Grabow, W. Stahl, Rev.Sci.Instrum. 61, 3694 (1990).J.-U. Grabow, W. Stahl, H. Dreizler, Rev.Sci.Instrum. 67, 4072 (1996).

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Production of Non-volatile Species:(Heated) Reservoire Source

Resistive wire

Ceramic ring

Teflon ring

Liquid/Solid reservoir

solenoid valve / reservoir nozzle

efficient benzene dimer production external reservior can be used:not heating, but cooling (~0°C) was required!

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Hyperfine structure;Quadrupole coupling

constants

Internal fields: quadrupole coupling

Field gradientsBonding characters

Internal dynamics:Tunneling processes

Fine structure;Torsion-tilting-rotation

interaction

(Some) Aspects Rotational spectroscopy

BarriersStructural information

Trajectories

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Hyperfine structure;Quadrupole coupling

constants

Internal fields: quadrupole coupling

Field gradientsBonding characters

Internal dynamics:Tunneling processes

Fine structure;Torsion-tilting-rotation

interaction

BarriersStructural information

Trajectories

Molecular dynamicstheory

Stark effect measurements

(Some) Aspects Rotational spectroscopy

Permutation-inversiongroup theory

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First FT-Microwave study:22 ‘quartets’ of lines in the 2.5 to 6 GHz regionE. Arunan and H. S. Gutowsky, J. Chem. Phys. 98, 4294(1993).

All 22 have aquartet structure

with a “1-3-1” energysplitting

observed spectral features:

Spectroscopic fingerprint

22 lines fit symmetric toppattern J,K → J+1,K

~180 kHz

~60 kHz~60 kHz

Lines viewed as doubly-split(by a smaller splitting on topof a larger splitting) suggestingtwo motions as origin

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COBRA FT-MW transitions

1 12•why do we observe a symmetric-top spectrum?

how can we explain exact -2:-1:1:2 quartet pattern?

-125 kHz

-63 kHz 62 kHz

125 kHz

28 kHzDoppler-Doublets

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Deuterated Benzene Dimers

different reduced masses of the internally rotating moieties

spacing between the 4 tunneling components depends on site of deuteration

cap

stem

(C6D6)c(C6H6)s

(C6H6)c(C6D6)s

vs.

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Mixed Dimer: Collisional interconversion

Erlekam, Frankowski, von Helden, Meijer, Phys. Chem. Chem. Phys. 9 (2007) 3786

Collisional coformational conversion driven by rare gas atoms

c c

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t A tunneling splitting changes upon isotopic labeling

8 J+1 J transitions detectedmore complicated due to quadrupole coupling (I(D)=1)again symmetric top spectrum;again -2:-1:1:2 pattern (reduced to about 70 %)

The Mixed dimer (C6D6)C(C6H6)S

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Tunneling splittings: Experiment and TheoryV6 potential

“perfect” -2:-1:1:2 splitting:

fingerprint of high-barrier

V6 tunneling (of the stem)

strong J and K

dependence needed

+2+1

-1-2

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Symmetric-top character

6D calculations show: cap is nearly freely rotating about its C6 axis

group theory (G576): all motions, but insignificant cap turnover and cap/stem exchange: accidental degeneracy for Kcap=3n1

K++K-, G7++G7

-, G1++G1

- states behave as symmetric top

similar findings for other benzene complexes with low barriers, such as benzene-CO

Reduced-dimensionality approach and group theory:M. Schnell, U. Erlekam, P.R. Bunker, G. von Helden, J.-U. Grabow, G Meijer, A. van der Avoird,Phys. Chem. Chem. Phys. 15 (2013) 10207.

6D calculations:A. van der Avoird, R. Podeszwa, K. Szalewicz, C. Leforestier, R. van Harrevelt, P.R. Bunker, M. Schnell, G. von Helden, G. Meijer, Phys. Chem. Chem. Phys. 12 (2010) 8219.

Benzene-CO:T. Brupbacher, A. Bauder, J. Chem. Phys. 99 (1993) 9394

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Reduced-dimensionality approach

concerted motion of cap tilt tunneling and stem internal rotation required to describe observed splitting pattern

M. Schnell, U. Erlekam, P.R. Bunker, G. von Helden, J.-U. Grabow, G Meijer, A. van der Avoird, Phys. Chem. Chem. Phys. 15 (2013) 10207.

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Resonator Reflectors as Stark Electrodes

- +15 kV max

MWE

StarkE

coaxially oriented beam-resonator arrangement (COBRA)

63 cm

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Circular Electrodes for Field Homogenization

ground HV

decreasing potential

M = 1

MWE

StarkE

coaxially aligned electrodes for Stark-effect applied in resonators (CAESAR)

M-selection rule:

M. Schnell, D. Banser, J.-U. Grabow, Rev. Sci. Instrum. 75, 2111(2004).

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Stark-effect measurementsfirst order behavior

µexp=0.580(51) D based on 6 transitions, 30 componentsµcalc=0.51 D for tilted T-shape Hobza, Selzle, Schlag, J. Chem. Phys. 93 (1990) 5893

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Condition for linear Stark effect:

antisymf J 2

The anti-symmetric square [2]antisym of the torsional symmetry species needs to contain the symmetry species (f)of the space fixed components of the dipole moment operator f

Stark effect of torsional species

J. K. G. Watson, J. Mol. Spectr. 50, 281 (1974).

Experimental results show:Cap torsion, cap tilting, and stem torsion are feasible:MS group G144 = Gcap Gstem = C6v(M) D6(M)(G144): cap stem

Symmetry of Kcap=3n1 levels in C6v(M) is: (Kcap=3n1) = E1or E2

Symmetry of Kcap=1,2,.. levels in C6v(M) is: (Kcap=1,2,..) = A1+A2 or B1+B2

[2(E1)]antisym = [2(E2)]antisym = [2(A1+A2)]antisym =[2(B1+B2)]antisym = A2

Symmetry of f in G144 is: (f) = A2 A1

first order Stark effect in levels having symmetry: E1 stem or E2 stem

levels with Kcap=3n1 but not Kcap=0 will have a first order Stark effectM. Schnell, P.R. Bunker, G. von Helden, J.-U. Grabow, G Meijer, A. van der Avoird, to be published.

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Summarygroup theory: dynamics leads to symmetric-top spectrum (with cap internal rotation) and linear Stark effect

concerted motion of cap tilt tunneling and stem internal rotation required to describe observed splitting pattern

important as benchmark system

transferable to other molecular systems involving C-H -- -bonding

M. Schnell, U. Erlekam, P.R. Bunker, G. von Helden, J.-U. Grabow, G Meijer, A. van der Avoird, Phys. Chem. Chem.Phys. 2013, DOI: 10.1039/C3CP51181B, in print. Benzene-CO: T. Brupbacher, A. Bauder, J. Chem. Phys. 99 (1993) 9394

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Intramolecular dynamics

The benzene dimer: Structure governed by dynamics

Angew. Chem. Int. Ed. 52 (2013) 5180-5183.

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Thanks!

Wolfgang Rogge, electronic shop of the PCI

Mechanical shop of the PCI

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