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

QQ

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