Ultrafast electronic spectroscopy

Majed Chergui

Arrhenius formulaTkE BaAeTk /)( in sec-1

A = frequency factorkB = Boltzmann constantT = temperature (in Kelvin)Ea= activation energy

A ~ 1013 !*Kinetics: overall population of reactantsbefore the reaction and of products afterthe reaction

* Note that this corresponds to times of the order of 100 fs

The fundamental time scale in Condensed Matter, Chemistry and Biology

• Speed of sound: 300 m/s-1000m/s => 0.3-1.0 Å in 100 fs

• Time scale of half-oscillations:H2; e= 4155 cm-1 —> 7.6 fsI2; e= 120 cm-1 —> 270 fs

• 1fs / 1s <=> 1s / 32 million years!

Vibrational period of H2 in the X state (e = 4401 cm-1) 7.6 fs

Rotational period of H2 in the X state (EJ = 2BJ, B = 60cm-1):

560 /J fs

Vibrational period of I2 in the B state (e = 125 cm-1) 270 fs

Rotational period of I2 in the B state (EJ = 2BJ, B = 0.029 cm-1): 1.15 /J ns

Vibrational period of a van der Waals molecule Hg-Ar in the Xstate (e = 6 cm-1)

6 ps

Rotational period of Hg-Ar in the B state (EJ = 2BJ, B = 0.02cm-1)

800 /J ps

Number of periods in a 6fs-pulse at 600 nm 3

Length of a 6fs-laser pulse 1.8 m

Spectral width of a 1 ps pulse 15 cm-1

Conventional spectroscopy (energy resolved)also called CW (continuous wave) or steady-state spectroscopy

Time-wavelength relationship

Correspondence between energy and time

• Doppler width 10-3 to 10-1 cm-1

• Rotational energies 10-2 to 10 cm-1

• Phonon energies ≤ 100 cm-1

• Vibrational energies 100 to 4000 cm-1

• Electronic energies ≥ 5000 cm-1

Time-to-width relationships for homogeneous lines

Energy (cm-1 ) Time (seconds)500 10-14

5 10-12

5 10-4 10-8

For a molecular state (e.g. diatomic molecule)

Left: Decay of the autocorrelation function. Right: absorption spectrumT: time to depart from the Franck-Condon regionT: oscillation period of a vibrational quantum in the excited stateT3: electronic lifetime of the state

Decay of H2O, qualitative picture: saddle-shaped potential surface

Bending motion

YX…Y elongation

Photodissociation of H2O

Absorption spectrum

Time evolution of the autocorrelation function

Resonance Raman: time dependent view

Resonance Raman spectrum of CH3I

Exc. 266 nm

mre et al, JPC 84

Some basic quantum mechanics…The time-dependent Schrödinger equation:

has solutions of the form

where (r) is the eigenfunction, which is the solution of the time-independent Schrödinger equation and the exponential term represents the time dependence.

ttritrH

),(),(

/)(),( iEtertr

Superposition of states

n

nn rar )()0,(

)/sin()/cos(/ EtiEte iEt

oscillates from 1 to –i to 1 to i …, at a frequency of /E

e.g., the 2s state has an energy of E= 1.6 10-18 J, i.e. the phase oscillatesat 2.5 1015 Hz (i.e. T= 0.4 fs)

• This is a linear combination of stationary wave functions but is not a solution of the stationary problem. It represents a coherent superposition of states or a wave packet. The an coefficients are given by:

)0( ta nn

/)(),( tiE

nnn

neratr

ˆ t t t

ˆ ˆ,t Hdidt

ˆ ˆ ˆˆ ˆ( )j

A A ATr j j

2

jj jc * jk jki t i tjk j k jkt c c e d e

Density matrix description in Liouville space

Wave packets

Vibrational wave packets

Forms of ultrafast temporal evolution of excited states

• Kinetics: exponential behaviour, evolution of populations

• Dynamics: oscillatory behaviour (wp), evolution of bodies

How to create a wavepacket?

How to create a wavepacket?

(r , t ) an n (r)e iE n t /

n

k

k dktrkgtr ),()(),(

Pump-probe and wavepacket dynamics

0 1 2 3

1

2

3

retard pompe - sonde / picosecondes

t = 300 fs

Pump-probe time delay

3 �m �� 10fs

QuickTime™ and a decompressor

are needed to see this picture.

3 �m �� 10fs

Possible experimental strategies• Transient absorption

Pump-Probe spectroscopy• TR fluorescence

• Non-linear Four WaveMixing spectroscopies– Transient Grating– Photon Echo

• X-rays techniques

• Multidimensionalspectroscopies

• Terahertz spectroscopy...

Revivals: S.I. Vetchinkin et al, Chem. Phys. Letters, 222 (1994) 394

Zewail et al, J. Phys. Chem. 1996, 100, 7832-7848

Transfer of vibrational coherence to products (Zewail et al, J. Chem. Phys. 91 (1989) 7437)

Transfer of coherence to products in a bath(Banin and Ruhman, J. Chem. Phys. 98 (1993) 4391; Pugliano et al, J.

Chem. Phys. 104 (1995) 5062)

IInmhI 23 )308(Solute/pump-fragment/probe experiment:

I2-

Vibrational wave packets (moving structures) in biological systems using transient absorption spectroscopy

From L. Stryer, Biochemistry

Retinal Proteins

11-cis all-trans

13-trans 13-cis

Rhodopsin

Bacteriorhodopsin

Isom. ≈ 70 % in proteinIsom. ≈ 17 % in solution

poche

Heme

Heme pocket

Fe C O

The inset show the absorption band and the pump and probe wavelengths.The figure shows the transient absorption signal of deoxy Mb

The lower figure is a comparison of the power spectrum of the transient in the upper figure with the resonance Raman spectrum of deoxy Mb

Transient absorption spectrum of MbNO. The inset show the absorption bands of Mb and MbNO.

Power spectrum of the trace in The upper figure and resonanceRaman spectrum of MbNO.

Rosca et al, J. Phys. Chem. A104 (2000) 4280)

Summary• Vibrational coherences are observed in a large

class of many-body systems: large molecules, liquids, solids, proteins, etc., even upon product formation.

• Energy can be localised on specific intra- and intermolecular bonds, for eventual control experiments.

• While for chemical and physical systems, the connection between the process and the vibrational coherences is possible, vibrational coherences in proteins do not necessarily imply that the motion that is observed is biologically significant.

Ultrafast emission spectroscopy

• electronic (ps-ns)– TC-SPC – Streak Camera

• purely optical (sub-ps)– Kerr Gating– Up-conversion

Fluorescence Gating

Time delay between pump and gate pulses

I

Fluorescence Up-conversion