Experiments to resolve structure and structural dynamics C O H O Structural methods: (1) NMR spectroscopy (µs, native environment, atomic resolution) (2) X-ray diffraction (fs, crystals, atomic resolution, destructive) (3) Vibrational spectroscopy (fs, native environment, atomic resolution) (4) Nonlinear vibrational Spectroscopy: information about couplings (5) Visible (electronic) spectroscopy (6) EPR spectroscopy (7) Microscopy Local vibrational modes are local probes of chemical bonds
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Experiments to resolve structure and structural dynamics
pure thioacetic acid 13.9 M 3.98 M 2.32 M 0.34 M 0.14 M
Abso
rban
ce /
OD
Frequency / cm-1
Thioacetic acid in CCl4
1000 2000
0
5
10
pure 13.9 M 3.98 M 2.32 M 0.34 M 0.14 M
Abso
rban
ce /
OD
Frequency / cm-1
Thioacetic acid in CCl4
3000 35000,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
pure 13.9 M 3.98 M 2.32 M 0.34 M 0.14 M
Abso
rban
ce /
OD
Frequency / cm-1
Thioacetic acid in CCl4
Infrared transitions
In the Born-Oppenheimer approximation the total initial wavefunction is given by:
)(),(),( QQrQr knki ΧΦ=Ψ
k : quantum number of electronic state
n : Quantum number of nuclear state
Q : normal mode coordinates
drdQerQeZM ij l
ljjfif Ψ
−Ψ= ∑ ∑∫ *
dQQQMQM kn
knif )()()( 0
* ΧΧ= ∫ ′
Transition dipole moment Mif for a transition from state i to state f
For a vibrational transition in the same electronic state, k does not change and the integration over dr leads to the permanent dipole moment M0(Q) in the electronic state k. The transition dipole moment vanishes if M0(Q) is constant zero.
Infrared transitions
Vibrational transitions are infrared inactive if the permanent dipole moment M0(Q) does not depend on any change of Q, which can occur on symmetry reasons.
If we expand M0(Q) in a Taylor series around the equilibrium position:
dQQQQQMM nin
i equiif )()( ΧΧ
∂∂
= ∫∑ ′
For harmomic oscillator wavefunction : ∆n = ±1 for vibrational quanta
transition from v=0 (Boltzmann distribution); Overtones (∆v = ±2) are weak
)()0())exp(1(32)( tMMdte
TknVcti
B∫∞
∞−
−−−= ωωπωωα
Absorption coefficient α(ω) is given by the ensemble average of the two-time dipole correlation function:
Polyatomic molecules
Transformation to 3N-6 normal mode coordinates Qi
3657 cm-1
not IR active
1595 cm-1
IR active
3756 cm-1
IR active
H2O vibrations (gas phase)
∑∑
+==
iiiii
ii QkQQHH 22
21
21)( µ
21
=≈′
=′ D
H
mm
µµ
ωω
Isotope shift for a harmonic oscillator:
same force constant
Fermi resonance
In special cases the strength of overtones or combination bands is enhanced if their energy matches a fundamental transition:
+−±+=± 2
22 4)2(2
21
hV ab
baba ννννν
Theoretical unperturbed bands are shaded and observed bands are
unshaded
Estimation:
Infrared absorption spectra
Contributions to IR band properties
electronic effect: change in the distribution of electrons
cis-trans isomers: higher symmetry in trans isomers -> smaller dipole moments
steric effect: can change force constants e. g. ring strain
solvent effect: shift frequencies
temperature effect: higher T leads normally to lower frequencies and broader bands
polar solvent-solute interaction: can cause dramatically shifts of group frequencies and alterations in band shapes for example: hydrogen bonds
1650 1700 1750 1800 0
1
Abso
rban
ce (a
rb. u
nits
)
0 mM 3 mM 5 mM 10 mM 15 mM 20 mM 30 mM 35 mM 50 mM
C102 in C2Cl4 with different phenol concentrations
hydrogen bonded v(C=O) Not hydrogen bonded v(C=O)
Properties of hydrogen bonds: acceptor modes
~ 30 cm-1 shift of the v(C=O ) upon formation of a hydrogen
bond to lower energies. Reduction of the C=O force
constant due to the hydrogen bond.
Allows a detection of hydrogen bond acceptor modes
E. T. J. Nibbering et al., Israel J. Chem., 39, 1999, 333-346
N O O
C102
Properties of hydrogen bonds: donor modes
Acetic acid dimer in CCl4
Phenol in C2Cl4
Frequency (cm-1) 3500 2000
OH
The infrared band of the donor group (OH) is dramatically and entirely unusual changed upon
formation of a hydrogen bond:
Halfwidth increases
with temperature ~T½.
• Red-shift of ν(O-H) reduced force constant
• Very strong broadening - distribution of bond lengths - anharmonic coupling to low- frequency modes - Fermi resonances - homogeneous broadening
Peculiar bandshape
X H Y -
Q(t)
q(t)
Q(t) X....Y H-bond vibration low frequency ~ 50-350 cm-1 period ~ 100-500 fs
X H Y -
q(t) X-H stretching vibration high frequency ~ 3200 cm-1 period ~10 fs
X H Y -
( )H q Q, = m p 2 ω eff
2 (Q)q 2
m 2 1 2 + P
MM Qlow
22 2
212
+ ω+ , ωeff(Q) = ωhigh + bQ + ...
X H X Y
= + bm q Q mb q Qhighω 2 2 2 212
+pm
m qhigh
22 2
212
+ ω PM
M Qlow
22 2
212
+ ω
anharm. coupl.
+
Anharmonicity of hydrogen bonds: donor modes
Bond length of hydrogen bonds
The spectral position of the hydrogen bonded v(OH) vibration indicates the hydrogen bond length and its strength
strong weak free medium
distribution
Types hydrogen bonds
2000-2500 ; > 3 ; 200 ;
1500-2000 ; > 30 ; 2000 ;
1000-1500 ; ~ 30 ; 1000-1500 ; 1.1
300-1000 ; 10-15 ; 500 ; 1.3
100-300 ; 5-10 ; 100-300 ; 1.4
0 ; 1 ; 10 ; 1.41
∆-freq. Width rel. Intensity ∆-isotop
Ultrafast nonlinear infrared spectroscopy
How can we distinguish between Fermi resonances and low-frequency modes? How strong and relevant are the influences of each coupling?
Infrared Pump/Probe Setup:
Folding of two functions
Ultrafast infrared pump-probe measurements
• No spectral diffusion
• Spectral width of holes: T2OH ≥ 180 fs
(CH3COOD)2
2 1’
0’
1
0
~ 0.6 ps
~ 15 ps
(CD3COOH)2
hot molecule cold molecule
red shifted
blue shifted
Excited state of the O-H stretching vibration
Excited state lifetime (ν=1): 200 fs oscillation frequency ~ 160 cm-1
Where does the energy go? What is the relaxation channel?
(CH3COOD)2 : Total signal Oscillatory component
• Pronounced beating pattern indicate two different oscillation frequencies
• Damping of the oscillations: Dephasing times of about 1 ps
Time - resolved pump-probe signals
(CH3COOD)2 :
K. Heyne et al., Chem. Phys. Lett. 369 (2003) 591-596
Polarization interference; anharmonic and Davydov coupling
Frequency
A
ω0
2V0
Ω
No oscillations due to excitonic coupling:
∆AP P
EvQ vQ
pr
( ) Im[( ) ( )
( )]
( ) ( )
ω ωω ω
ω∝ −
+= =03
13
Oscillatory signals from mixed dimers
No excitonic coupling.
Single O-H
Single O-D
CDO
O H O
OC CHH C3 3
CDO
O H O
OC CHH C3 3
Identical oscillations.
Dephasing of Coherent O-H Stretching Excitations
CHO
O H O
OC CHH C3 3
2-pulse photon echoes: T=0.
CDO
O H O
OC CHH C3 3
No excitonic coupling
Excitonic coupling
Recurrencies
Dephasing of Coherent O-H Stretching Excitations
CDO
O H O
OC CHH C3 3
Simulations with one (dash-dotted line) and two (solid line) low-frequency modes and measured data (dots)
Dephasing of Coherent O-H Stretching Excitations
CDO
O H O
OC CHH C3 3
Multi-level character of O-H stretch-ing excitation results in multi-level coherences:
• Quantum beats due to anharmonic coupling to low-frequency modes
• Less relevant: Polarization interfe- rences due to excitonic coupling.
Simulations: density matrix approach (sum over states)
O-H stretching mode + 1 low-frequency mode at 50 cm-1
O-H stretching mode
(CH3COOD)2 : Total signal Oscillatory component
• Pronounced beating pattern indicate two different oscillation frequencies
• Damping of the oscillations: Dephasing times of about 1 ps
Time - resolved pump-probe signals
(CH3COOD)2 :
K. Heyne et al., Chem. Phys. Lett. 369 (2003) 591-596
Raman-active low-frequency modes
τbg methyl torsion γbg dimer oop wagging
δag dimer ip bending νag dimer ip stretching
Origin of the coherent oscillations
(CD3-COOH)2 (CH3-COOD)2
τbg γbg
δag νag
Fermi resonance
δ(OH) ν(OH)
ν(OH) δ (OH) ν =0
ν =1 δ = 2
δ = 1
δ = 0 ν(OH) δ (OH)
ν = 0
(ν,δ) =(1,2)
δ = 1
δ = 0
What is the role of the OH bending mode for intra- and intermolecular vibrational energy redistribution? Is there an impact of Fermi resonances on the dynamics? 2xδ
Coupling to O-H bending and C-O stretching modes
Excite O-H stretch (νex=2980 cm-1)
Probe δ(OH) and ν(C-O).
• Perturbed free induction decay on δ(OH) and ν(C-O) fundamen- tals.
• Similar rise of bleaching and enhanced absorption.
Coupling to O-H stretching mode.
C H O
O H O
O C CD D C 3 3
Perturbed free induct- ion decay: T2'≈ 500 fs
Lifetime v=1 state T1=250 fs
Vibrational cooling Tr ≈ 15 ps
Direct O-H bending excitation
No indication of transient v≥1 populations of OH bending mode.
Our picture:
Red-shift of OH bend by excitation of other anharmonically coupled modes. Early times: O-H stretch. Late times: other (low-frequency) modes.
v=0 v=0
v=1
v=1
v=2
OH stretch OH bend
pump probe
Coupling to O-H bending and C-O stretching modes
Fermi resonance coupling
νbuC−O
νbuC=O
δbuO-H
δbuCH3
IR
νagC−O
νagC=O
δagO-H
δagCH3
Raman
Intramolecular H-bond in PMME
3000 2500 2000 1500
0,0
0,5
1,0
0,0
0,5
νO-D
Abso
rban
ce (O
D)
δO-H
νC=O
Wavenumber (cm-1)
νO-H
Abso
rban
ce (O
D)
δO-H
Abso
rban
ce (O
D)PMME: Phthalic acid monomethyl ester
γHB
O-H stretch dynamics of a medium strong H-bond
0 1000 2000 3000
-3
-2
-1
0
1 3200 cm-1
2800 cm-1
Chan
ge o
f Abs
orba
nce
(mO
D)
Delay times (fs)
2600 cm-1
3600 3200 2800 2400 20000,0
0,1
0,2
0,3
Abso
rban
ce (O
D) PMME in C2Cl4
v = 0
v = 1
v = 2
v‘ = 0
v‘ = 1
cold molecule hot molecule
vibrational population
decay
νOH vibrational cooling
< 250 fs
~ 10 ps
Madsen et al., Bull. Chem. Soc. Jpn., 75, 909 (2002)
Low-frequency vibration
Excited state O-H stretching vibration dynamics
0 1000 2000
0,0
0,5
1,0
150 100 500,0
0,5
1,0
Delay Time (fs)
Wavenumbers (cm-1)
A F (no
rm.)
Chan
ge o
f Abs
orba
nce
(mO
D)
3500 3000 2500 20000,0
0,1
0,2
Abso
rban
ce (O
D)
Frequency (cm-1)
Pmme-H in CCl4 pump pulse probe pulse
νOH V = 0
V = 1
V = 2
v = 1 state of the νOH decays with 200 ± 80 fs
coherent oscillations modulate the excited state dynamics with 100 cm-1
200 fs
Pump-probe experiments on PMME
I. excite νOH ; probe δOH
II. excite δOH ; probe δOH
3000 2500 2000 1500 10000,0
0,5
1,0
Abso
rban
ce (O
D)Frequency (cm-1)
Pmme-H in CCl4
δOH νOH νCO
I. excite νOH ; probe δOH
I. excite νOH ; probe δOH
II. excite δOH ; probe δOH
III. excite νCO ; probe δOH
Transient difference spectra
1440 1420 1400 1380 1360 1340 1320-1,2
-0,8
-0,4
0,0
0,4
0,8
Excitation at 1390 cm-1
02 09 03
Abso
rban
ce C
hang
e (m
OD)
Delay times (fs): 140 200 400 800 1600 10000
1440 1420 1400 1380 1360 1340 1320-4
-3
-2
-1
0
1
2
3
4
Excitation at 2900 cm-1
28.08.03
Chan
ge o
f Abs
orba
nce
(mO
D)
Frequency (cm-1)
Delay times (fs): 140 200 400 800 1600 10000
Spectral region of the δOH and δCH3 absorption bands after excitation of the νOH (I), δOH (II) and νC=O (III) vibrations
(I)
(II)
(III)
Similar dynamics for excitation (I) and (II)
Fast component around 1415 cm-1 and 1390 cm-1 in (III) is missing
1440 1420 1400 1380 1360 1340 1320
-1
0
1
15.10.03
Excitation at 1740 cm-1
Abso
rban
ce C
hang
e (m
OD)
Frequency (cm-1)
Delay times (fs): 140 200 400 800 1600 10000
δOH δCH3
Dynamics at selected frequency positions
0 1000 2000
-1,4
-0,7
0,0
0,7
1415 cm-1
Abso
rban
ce C
hang
e (m
OD)
Delay Time (fs)
1390 cm-1
0 10000 20000
-0,7
0,0
0,7
1415 cm-1
Abso
rban
ce C
hang
e (m
OD)
Delay Time (fs)
1390 cm-1
νOH (I)
Ο δOH (II)
νCO (III)
negative and positive signals exhibit exhibit similar dynamics cooling of the δOH with about 7± 1 ps
v = 1 decay of the δOH with 800 ± 100fs
Perturbed free induction decay PFID with 550 fs ~ 19 cm-1 (18 cm-1 linewidth) upon νCO excitation only cooling after δOH and νOH excitation population of the v = 1 of the δOH vibration More than 30% of the δOH v = 1 level is populated after νOH excitation
Efficient energy relaxation channel PFID
7 ps 800 fs
Energy relaxation in PMME
δOH νOH
200..300 fs
δ‘OH
800 fs
7 ps
Energy is redistributed from the OH stretching vibration over the OH bending vibration into lower energy modes
Energy relaxation channel from νOH involving the δOH v = 1 state is very efficient