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Unravelling the Pathways of UltrafastVibrational Energy Flow in Hydrogen
Bonds
Oliver KühnMilena Petkovic, Gireesh Krishnan
Physical and Theoretical ChemistryFree University Berlin
AGENDA
Huggins (1936) H+ in H2OHuggins (1936) H+ in H2O
O OH
Ene
rgy
multidimensional quantumdynamics
potential energy surfacesequations of motion
correlation
H-atom ↔ H-bond
O OH
M. L. Huggins, JPC 40, 723 (1936)
MULTIDIMENSIONALITY & IR SPECTRUM
0 3000
strong H-Bond [1]
red-shiftbroadeningsubstructure
wavenumber (cm-1)
H3O
+S
igna
l
1000 1500 wavenumber (cm-1)
3000
abso
rban
ce
medium-strong H-Bonds
abso
rban
ce
gas-phase [2]
C2Cl4 [3]
2000
200wavenumber (cm-1)
[1] K. Asmis et al., Science 299, 1375 (2003), [2] NIST, [3] J. Stenger et al. �
A SIMPLE ADIABATIC MODEL
A BH
Q
q
A .... B
νq=1
νq=0
Q?
ω
absorption
Franck-Condon-like transition
VIBRATIONAL RELAXATION MODELS
via H-bond motion via Fermi-resonance
νOH=1δOH=2
δOH=1νOH=0
νOH=1
Q
A .... B
PMME-H: 2-COLOR IR SPECTROSCOPY
wavenumber (cm-1)
abso
rptio
n
3000 2000
pum
p-pr
obe-
sign
al
-1 0 1 2 3τ (ps)
T1(νOH)=200fs, T1(δOH)=800fsrelaxation via δOH=1 (>30%)Tcool ~ 20 psνosc ~ 100 cm-1
probe pump
νOHδOH δOH νCO
K. Heyne et al. JPCA 108, 6083 (2004)
SYSTEM-BAD APPROACH
H = HSYS (s;t) + HBATH (q,Z ) + HSB (s,q,Z )
qqssV (s,q)
ZZV (s,Z ) V (q,Z )
POTENTIAL ENERGY SURFACES
E(c
m-1
)
Qν[a0(a.m.u.)1/2]
• Reaction Surface Hamiltonian
no proton transferno bond dissociation
• normal mode representation
...),,,(),,(),()(
)()()(
)4()3()2(
)1(
+++=
+=
∑∑∑
∑
≠≠≠≠≠≠lkji
lkjikji
kjiji
jicorr
corrii
QQQQVQQQVQQVV
VQVV
Q
choice of relevant coordinatescalculation of correlation potential
PMME: 5D DISSIPATIVE MODEL
11
1
1
221+1
2 +11+1+12+1
2
νOH = 3036 cm-1 δOH = 1455 cm-1
γ1 = 792 cm-1 γ2 = 690 cm-1 νHB = 63 cm-1
PMME-H: IR SPECTRUM
Abs
orpt
ion
diabatic states3
QHB [a0(a.m.u.)1/2]
E/h
c (1
03cm
-1) )v,v,v,v(
21 γγδν
-6 -4 -2 0 2 4 60
1
2
2000 3000E/hc (cm-1)
DISSIPATIVE QUANTUM DYNAMICS
( ))(ˆ)(ˆtr),( tsOtsO SYS ρ=
ρ̂(t) = trBATH ρ̂total (t)( )
Quantum-Master Equation
ss
ZZ
observables
reduced density operator
∑∑ −−+−=∂
∂
cdcdcdab
caccbcbacabab
ab RddtiEit
ρρρρωρ,)()(
relaxation/dissipationcoherent dynamics
PMME: SYSTEM-BATH MODEL
V (s = Q,q,Z )
1
221+1
2 +11+1+12+1
2intramolecular+ solvent
solvent
relevant interactions
1
11
QHB
PMME: RELAXATION OF HB-MODE
bilinear coupling spectral density
υHB = 2
υHB = 1
υHB = 0
J(ohmic)(ω)
J(eff)(ω)
∑=λ
λλ ZgQH IHBHB
ISB
)(,
)( classical MD PMME/CCl4 at T=300K
T1~1.6ps
H. Naundorf, O.K. PCCP 5, 79 (2003)
OH-STRETCH RELAXATION
)v,v,v,v(21 γγδν
-6 -4 -2 0 2 4 6
diabatic states
T1 times νOH ~ 200fs δOH ~ 800-900fs
3
QHB [a0(a.m.u.)1/2]
E/h
c (1
0-3cm
-1)
2
1
0
RELAXATION MODELS
relaxation via bending modes
relaxation via HB-mode
SUMMARY
vibrational relaxation pathways in H-bonds
classical MD
quantum chemistryQuantum Master
Equation
nonlinear IR spectroscopy OH-relaxation via in- and out-of-plane bendings
T1 relaxation times νOH ~ 200fs δOH ~ 800-900fs νHB ~ 1.6ps
COHERENT WAVE PACKET MOTIONE
(cm
-1)
Qν[a0(a.m.u.)1/2]
HTropolone: reactivestrong anharmonicity
PMME: nonreactivemoderate anharmonicity
H-TRANSFER AND ENERGY FLOW
quasi-coherentwave packet dynamics
str
bsy
as
K. Giese et al. JTCC 3, 567 (2004)
total harmonic energy
THANKS TO
FU Berlin: H. NaundorfK. GieseJ. Manz
MBI Berlin: T. ElsaesserJ. DreyerE. NibberingK. Heyne
Financial support: DFG (Sfb450), FCI