institut für physikalische chemie & elektrochemie, lehrgebiet a structure of the benzene dimer...
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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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