Mapping chemical interactions and dynamics with x-ray ...

Mapping chemical interactions and dynamics with x-ray spectroscopy Philippe Wernet Institute for Methods and Instrumentation for Synchrotron Radiation Research Helmholtz-Zentrum Berlin für Materialien und Energie Ultrafast X-ray Summer School (UXSS) 2016, SLAC National Accelerator Laboratory (Stanford, USA), June 2016

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LCLS on Sunday, 12 June 2016

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Outline Part I What are we talking about? Some fundamentals…

Part II

Part III

Only x-ray spectroscopy!

See the other talks and extra slides for other x-ay methods and methods without x-rays.

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See the atoms move

http://www.molecularmovies.com/


Michael Odelius, Stockholm University , Sweden

Molecular motors

Photochemistry Organic chemistry

Water

Lars Ojamäe, Linköping University , Sweden

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A. Zewail, Nobel price in Chemistry (1999) „… for his studies of the transition states of chemical reactions using femtosecond spectroscopy.“

Nobel Lecture http://nobelprize.org/nobel_prizes/chemistry/laureates/1999/zewail-lecture.html# „Femtochemistry: Atomic-Scale Dynamics of the Chemical Bond Using Ultrafast Lasers“

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Wait a second: What do we actually talk about? Chemical dynamics deals with the atomic-scale view of the elementary steps of a chemical reaction (pico- to femtoseconds and Ångstrom).

This could be a triggered reaction (pump-probe) or a non triggered reaction (e.g. thermally activated). Most often, photoreactions (triggered) are studied!

We talk about the atomic-scale dynamics of chemical interactions See extra slides on the delineation of kinetics and dynamics!

Ener

gy

Generalized reaction coordinate

𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃

𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑃𝑃

∆𝐺‡

𝑇𝑃𝑅𝑅𝑃𝑇𝑃𝑇𝑃𝑅 𝑃𝑃𝑅𝑃𝑅 (𝑅𝑃𝑃𝑇𝑎𝑅𝑃𝑅𝑃 𝑃𝑃𝑐𝑐𝑐𝑅𝑐)

∆𝐺

𝐾 =[𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃][𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑃𝑃] = 𝑅−

∆𝐺𝑅𝑅 𝑘 = υ ∙ 𝑅−

∆𝐺‡

𝑅𝑅

Thermodynamics Transition state theory

• Thermodynamic properties of the transition state (∆𝐺‡) and the crossing frequency (𝜐) determine the reaction rate (𝑘) (the kinetics) of thermal reactions

• The energy potential landscapes determine the reaction mechanisms (the dynamics) of photochemical reactions

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A textbook example for molecular dynamcis A. Zewail

Real-time tracking of nuclear dynamics (1000 m/s = 1 Å/100 fs)

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But wait, why bother?

Fundamental questions in solar energy conversion

Book chapter in „X-Ray Free Electron Lasers“ by J. Yano, V. Yachandra, U. Bergmann (Eds.), Royal Society of Chemistry Energy and Environment Series, Ph. Wernet (2016).

9

But wait, why bother?

Fundamental questions in solar energy conversion


• Electronic excitation • (Ultrafast) relaxation

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Electronic excitation

Demtröder, Molekülphysik

Energy


Svanberg Atomic and Molecular Spectroscopy

Electronic ground state

Electronic excited state

Vibrational levels

Vibrational levels

Rotational levels

Rotational levels

Distance

Schematic representation of the energy levels of a diatomic molecule

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The Born-Oppenheimer Approximation

• When we describe chemical interactions

• By forming molecular from atomic orbitals

• We often assume the nuclei to be at rest

• We need to drop this approximation!

• Nuclear movements are now part of the problem!

• This problem is not analytically solvable…

• We need the Born-Oppenheimer approximation!

Max Born and Robert Oppenheimer: Zur Quantentheorie der Molekeln, Annalen der Physik, 389 (20), p. 457–484 (1927).

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Solve the Schrödinger equation for the electrons in the static potential of the fixed nuclei (“Produktansatz”). The electronic part of the wavefunction depends on the nuclear coordinates BUT as a parameter, NOT as a variable!

Ψmolecule = Ψe · Ψn

Ψe = Ψe(re, Rn)

Ψn = Ψn(Rn)

By neglecting the coupling of nuclear and electron motions we can treat the motion of nuclei and electrons independently. Masses of electrons and nuclei are so different (104) that the nuclei appear to be fixed while electrons are moving!

Within the adiabatic approximation (“electrons follow nuclear motions instantaneously”) we can solve the Schrödinger equation for Ψe at fixed Rn repeatedly for many Rn:

[Te + Ve] Ψe(re, Rn=const) = Ee Ψe(re , Rn=const) Te/Ve = kinetic/potential energy of electrons

By plotting the resulting set of solutions Ee versus Rn we build potential energy curves!

(surfaces, landscapes, depending on the number of parameters/reaction coordinates)

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Demtröder, Molekülphysik

The potential energy curve Ee versus Rn

corresponds to the “electronic part” of the

total energy of the molecules plus the energy

arising from repulsion of the nuclei (sum of

kinetic and potential energy of electrons plus

potential energy of nuclei)

Vibrational and rotational energies of the

molecule are missing!


Electronic ground state

Electronic excited state

Vibrational levels

Vibrational levels

Rotational levels

Rotational levels

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The Franck-Condon Principle For the transition between state X and A with vibrational levels υ the transition probability

(electronic dipole transition) is proportional to:

The electronic dipole moment times the Franck-Condon factors

│< ΨeA │ de │ Ψe

X > │2 · │< Ψnυ │ Ψn

0 > │2

│∫ ΨeA de Ψe

X dre│2 · │∫ Ψnυ Ψn

0 dRn│2

Haken/Wolf Molecular Physics and Elements of Quantum Chemistry Atkins/Friedman Molecular Quantum Mechanics

The QM harmonic oszillator

X

A

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The Franck-Condon Principle For the transition between state X and A with vibrational levels υ the transition probability

(electronic dipole transition) is proportional to:

The electronic dipole moment times the Franck-Condon factors

│< ΨeA │ de │ Ψe

X > │2 · │< Ψnυ │ Ψn

0 > │2

│∫ ΨeA de Ψe

X dre│2 · │∫ Ψnυ Ψn

0 dRn│2

Haken/Wolf Molecular Physics and Elements of Quantum Chemistry Atkins/Friedman Molecular Quantum Mechanics

X

A

Those overlap integrals S are the famous Franck-Condon factors

X

A

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Electronic excitation and (ultrafast) relaxation

Haken/Wolf Molecular Physics and Elements of Quantum Chemistry

Red-shift of fluorescence!

Sequence of radiationless transitions

• Internal conversion

• Intramolecular vibrational redistribution

• Intersystem crossing

• Thermalization

(see extra slides for details)

Fluorescence Absorption

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Electronic excitation and (ultrafast) relaxation


Typical energy level diagram of a molecule

Singlet states

Triplet states

Intersystem crossing

Abso

rptio

n

Fluo

resc

ence

Abso

rptio

n

Phos

phor

esce

nce

Internal conversion

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Femtosecond Absorption Spectroscopy of Transition Metal Charge-Transfer Complexes, James K. McCusker, Acc. Chem. Res. 36, 876-887 (2003).

Absorption

Fluorescence (Emission)

Electronic excitation and (ultrafast) relaxation A famous example

Wai-Yeung Wong (Ed.) Organometallics and Related Molecules for Energy Conversion

19 Femtosecond Absorption Spectroscopy of Transition Metal Charge-Transfer Complexes, James K. McCusker, Acc. Chem. Res. 36, 876-887 (2003).

If we can make this state live long, we can efficiently make use of the electron-hole pair!

Electronic excitation and (ultrafast) relaxation A famous example

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(Nuclear) Wavepackets

A. Zewail

Superposing plane waves

For dissociative states

• Coherent superposition of vibrational states • Formation of a nuclear wavepacket • The wavepacket is evolving in time (nuclei are

moving)! • Wavepackets to describe particles confined in space

t1

t2 t3

For free particles

Atkins, Friedman, Molecular quantum mechanics

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Reaction coordinate

Pote

ntia

l ene

rgy

Pump

Ground state X

Excited state A

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Reaction coordinate

Pote

ntia

l ene

rgy

kT

Intermediate state

Transition state („activated complex“)

Transient configurations


Pump

Probe

…and phenomena that happen on their way (IVR, IC, ISC, …)

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Quiz part I

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How many drawings in one?

1. Shape of the harmonic potential V(x)

2. Energy levels E of the harmonic oscillator

3. Nuclear wavefunctions plotted vs. x

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Reaction coordinate

Pote

ntia

l ene

rgy

Pump

Ground state X

Excited state A

What is “wrong” here (within the BOA)?

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Spot the different pictures/concepts/approximations!


Singlet states

Triplet states

Intersystem crossing

Abso

rptio

n

Fluo

resc

ence

Abso

rptio

n

Phos

phor

esce

nce

Internal conversion

• One-electron orbital picture • Many-electron total energy picture

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What time-resolution do I need to resolve molecular motion?

Take the speed of sound • Resolve corresponding displacements • “Speed of atoms” several 100-1000 m/s • This corresponds to resolving 100-1000·1010 Å/1015 fs = 0.1-1 Å/100 fs Take the oscillation period of a molecule • Resolve the oscillatory motion • E.g. 3500 cm-1 (wavelength of ~3 µm) for the O-H stretch vibration in H2O • T = 1/f, c=λ·f T = λ/c T = 3·10-6m/(3·108m/s) = 10-14 s • This corresponds to a duration of the vibrational period of ~10 fs Take the Brownian motion • Resolve the mean square displacement 𝑐2 𝑃 with time 𝑃: 𝑐2 𝑃 = 𝑘𝐵𝑅

3π𝑅η𝑃

• With 𝑇 temperature, 𝑅 particle radius, η viscosity • Albert Einstein (1905), Marian Smoluchowski (1906) and Paul Langevin (1908) • Displacement of 1 Å takes 100 fs (𝑅 = 1 Å, η = 20·10-6 kg/(m·s) for O2, ideal gas)

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How fast do electrons move?

• Ask yourself: Why do I care? • Do I want to observe electron motion?

– Classically, the electron takes 150 as to circulate the proton (and there are other ways to

estimate those time scales…)

– I need as time resolution!

• Do I want to follow the rearrangements of electrons as nuclei are moving? – I need fs time resolution!

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How big is the “mistake” we make in calculating the energy of a state within the Born-

Oppenheimer approximation? • That’s not an easy question! • Think about it (slide 11): “Masses of electrons and nuclei are so different (104)…”

Within the adiabatic approximation (“electrons follow nuclear motions instantaneously”) we can solve the Schrödinger equation for Ψe at fixed Rn repeatedly for many Rn:

[Te + Ve] Ψe(re, Rn=const) = Ee Ψe(re , Rn=const) Te/Ve = kinetic/potential energy of electrons


Electrons

Nuclei

Neglect within BOA

Schrödinger equation with „Produktansatz“:

Masses of nuclei mn

Mass of elctron me

The neglected part of the energy is smaller by m0/m1, 2 = me/mn = 10-4

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What do you see?

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Molecular dynamics simulation Michael Odelius (Stockholm University)

Fe(CO)5 dissociation in ethanol

Where are the electrons?

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Part II

Part III

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Gilles Bachelet My Cat, The Silliest Cat in the World

How did that happen?

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Resolving transient and intermediate states Why short pulses and what is „short“?

Palo Alto, CA 1872

Leland Stanford Eadweard Muybridge

The birthday of ultrafast technology (?)

Bet: Does a galloping horse have all 4 hooves in the air at any instant?

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Why short pulses and what is „short“?

Théodore Géricault - Derby in Epsom (Wikipedia)

Resolving transient and intermediate states

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Palo Alto, CA 1872

Leland Stanford Eadweard Muybridge

Temporal resolution: 1/60 s (17 ms)


The birthday of ultrafast technology (?)

Bet: Does a galloping horse have all 4 hooves in the air at any instant?

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Animations based on photos from E. Muybridge, Wikipedia


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Gilles Bachelet My Cat, The Silliest Cat in the World

How did that happen?

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So let’s first have a look at how we can resolve transient states

41 Ph. Wernet, Electronic structure in real time: Mapping valence electron rearrangements during chemical reactions, Phys. Chem. Chem. Phys. 13, 16941 (2011).

Mapping valence electron rearrangements

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Experiment

• Valence photoelectron spectroscopy

• Femtosecond VUV/XUV (23 eV) pulses from HHG

Wernet, Odelius, Godehusen, Gaudin,Schwarzkopf, Eberhardt, PRL 103, 013001 (2009).

43 Wernet, Odelius, Godehusen, Gaudin,Schwarzkopf, Eberhardt, PRL 103, 013001 (2009).

Experiment Theory

A‘ and B‘ of excited molecule

3P of free atom


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Experiment

Theory

Wernet et al. PRL 103, 013001 (2009).


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Quiz part II

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Which one applies? Detect the differences…

Ph. Wernet, Electronic structure in real time: Mapping valence electron rearrangements during chemical reactions, Phys. Chem. Chem. Phys. 13, 16941 (2011).

Binding energy O

rbita

l ene

rgy

Koopmans' theorem: The first ionization energy of

a molecular system is equal to the negative of the

orbital energy of the highest occupied molecular

orbital (HOMO).

Nuclear distance

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What time-resolution do we need?

Fourier-transform limited pulses

ΔtFWHM · ΔEFWHM = 1.85 eV fs

e.g. 20 fs, 0.1 eV

Svanberg Atomic and Molecular Spectroscopy

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Now let’s see how we resolve intermediate states and why that is important

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Part II

Part III

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Richard Avedon – Photographs 1946-2004

51 Shibuya Hachiko crossing, Tokio – Photographed from Starbucks (2009)

52 Shibuya Hachiko crossing, Tokio – Photographed from Starbucks (2009)

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How can we pick out a specific signal from a soup of molecules?

How can we be selective?

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Why x-rays? Spectroscopy

Element-, site- and orbital-specific

• Coordination • Charge density • Spin density

Tuneable, short and intense soft x-ray pulses

55 Reaction coordinate

Ener

gy

Ground state

Valence excited states

Core-excited state 2


Chemical species 1

Chemical species 2

This is what we are interested in! This where the

chemistry happens!

Femtosecond x-ray spectroscopy with FELs


Ener

gy

Ground state




Chemical species 1

Chemical species 2

This „just“ the probing!



Ener

gy

Ground state




Chemical species 1

Chemical species 2


5-10 eV

5-10 eV

Our probe needs to be sensitive to the ev-sub eV scale!

58

Fe C O

In

Out

1 mol/l in EtOH

K. Kunnus et al. Rev. Sci. Instrum. 83, 123109 (2012). Ph. Wernet et al. Nature 520, 78-81 (2015).

<100 fs

„16-electron catalyst“

Time-resolved RIXS at LCLS

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Resonant inelastic (x-ray) scattering

Demtröder, Laser Spectroscopy (Fig. 8.1)

X-rays (RIXS) UV/Vis

Selecting elements and sites by tuning to their core-electron resonances!

Molecule


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Selecting elements and sites by tuning to their core-electron

resonances!

Core electron binding energy Chemical shift (ESCA, K. Siegbahn)

61

Resonant inelastic x-ray scattering


62

Resonant inelastic x-ray scattering


63

Selecting orbitals by tuning to the respective resonances!

64

Bonding in Fe(CO)5

65

RIXS of Fe(CO)5


66

RIXS of Fe(CO)5


2π*

5σ

dσ*

67

5σ*

2π*

dσ*

dπ dπ

ΔE

Fe(CO)5 CO Fe(CO)4

2π*

5σ

dσ*

68

5σ*

2π*

dσ*

dπ dπ

ΔE

Fe(CO)5 CO Fe(CO)4

2π*

5σ

dσ*

69

5σ*

2π*

dσ*

dπ dπ

ΔE

Fe(CO)5 CO Fe(CO)4

2π*

5σ

dσ*

70

5σ*

2π*

dσ*

dπ dπ

ΔE

Fe(CO)5 CO Fe(CO)4

71

Fe(CO)5 Fe(CO)4 fragments

Ph. Wernet, K. Kunnus, I. Josefsson, I. Rajkovic, W. Quevedo, M. Beye, S. Schreck, S. Grübel, M. Scholz, D. Nordlund, W. Zhang, R. W. Hartsock, W. F. Schlotter, J. J. Turner, B. Kennedy, F. Hennies, F. M. F. de Groot, K. J. Gaffney, S. Techert, M. Odelius, A. Föhlisch, Nature 520, 78-81 (2015).

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Fe(CO)5 Fe(CO)4 fragments Early Late

Ph. Wernet, K. Kunnus, I. Josefsson, I. Rajkovic, W. Quevedo, M. Beye, S. Schreck, S. Grübel, M. Scholz, D. Nordlund, W. Zhang, R. W. Hartsock, W. F. Schlotter, J. J. Turner, B. Kennedy, F. Hennies, F. M. F. de Groot, K. J. Gaffney, S. Techert, M. Odelius, A. Föhlisch, Nature 520, 78-81 (2015).

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RIXS from an excited state (Anti-Stokes)

RIXS from a triplet species (intersystem crossing)

RIXS from ligated species (solvent ligation)

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Solvent ligation

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Temporal evolution

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Simple, conceptual conclusions


78 Book chapter in „X-Ray Free Electron Lasers“ by J. Yano, V. Yachandra, U. Bergmann (Eds.), Royal Society of Chemistry Energy and Environment Series, Ph. Wernet (2016).

79 Book chapter in „X-Ray Free Electron Lasers“ by J. Yano, V. Yachandra, U. Bergmann (Eds.), Royal Society of Chemistry Energy and Environment Series, Ph. Wernet (2016).

Radial probability distributions in H

a0 = Bohr radius (~0.5 Å)

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Quiz part III

81

What is shown here?

Ene

rgy

Inversion

3 2

1

4

Stimulated emission

1 2 3 4

82

What is the difference?


Ener

gy

Ground state




Where are the arrows for XAS and RIXS?

Delay Δt XAS

RIXS

Core-hole lifetime

84

See the atoms move



Michael Odelius, Stockholm University , Sweden

Molecular motors

Photochemistry Organic chemistry

Water

Lars Ojamäe, Linköping University , Sweden

But don‘t forget the electrons!

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Further reading

„X-Ray Free Electron Lasers“, Royal Society of Chemistry Energy and Environment Series, J. Yano, V. Yachandra, U. Bergmann (Eds.) (2016).


Demtröder Laser Spectroscopy

Atkins/Friedman Molecular Quantum Mechanics

86

Some extra slides

87

Chemical and thermodynamic equilibrium 1

Chemical equilibrium:

𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑃𝑃 ⇄ 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 e.g.: 𝐴 + 𝐵 ⇄ 𝐶 + 𝐷

𝑅𝑅𝑃𝑅 =𝑃[𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃]

𝑃𝑃 α [𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑃𝑃]

α: Proportional to

[…]: Concentration of …

e.g. 𝑅𝑅𝑃𝑅 = 𝑑[𝐶]𝑑𝑑

α 𝐴 ∙ [𝐵] (neglecting stochiometry and reaction order)

Proportionality constant 𝒌 (rate konstant):

𝑅𝑅𝑃𝑅 = 𝑘 ∙ [𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑃𝑃]

The rate (the rate konkstant) quantifies the speed/the efficiency of the reaction.

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𝑅𝑅𝑃𝑅 𝑓𝑃𝑃𝑓𝑅𝑃𝑃 = 𝑅𝑅𝑃𝑅 𝑏𝑅𝑃𝑘𝑓𝑅𝑃𝑃

𝑘𝑓𝑓𝑓𝑓𝑓𝑓𝑑 ∙ 𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑃𝑃 = 𝑘𝑏𝑓𝑏𝑘𝑓𝑓𝑓𝑑 ∙ [𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃]

⇒ 𝑘𝑓𝑓𝑓𝑓𝑓𝑓𝑑𝑘𝑏𝑓𝑏𝑘𝑓𝑓𝑓𝑑

= [𝑃𝑓𝑓𝑑𝑃𝑏𝑑𝑃][𝑅𝑅𝑓𝑏𝑑𝑓𝑅𝑑𝑃]

≡ 𝐾 Equilibrium constant

Thermodynamic equilibrium:

∆𝐺 = −𝑅𝑇 ∙ 𝑐𝑅𝐾

⇒ 𝐾 =[𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃][𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑃𝑃]

= 𝑅−∆𝐺𝑅𝑅

with ∆𝐺 = 𝐺 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 − 𝐺(𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑃𝑃)

Ener

gy



𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑃𝑃 ∆𝐺

89


Ener

gy



𝐾 = 𝑅−∆𝐺𝑅𝑅 with ∆𝐺 = 𝐺 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 − 𝐺(𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑃𝑃)

∆𝐺 < 0 𝐾 ≫ 1

∆𝐺 > 0 𝐾 ≫ 1

∆𝐺 = 0 𝐾 = 1

Energy is released Energy is consumed

90

Transition state theory 1 En

ergy




∆𝐺‡

𝑇𝑃𝑅𝑅𝑃𝑇𝑃𝑇𝑃𝑅 𝑃𝑃𝑅𝑃𝑅 (𝑅𝑃𝑃𝑇𝑎𝑅𝑃𝑅𝑃 𝑃𝑃𝑐𝑐𝑐𝑅𝑐)

∆𝐺‡ = 𝐺 𝑃𝑃𝑅𝑅𝑃𝑇𝑃𝑇𝑃𝑅 𝑃𝑃𝑅𝑃𝑅 − 𝐺(𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑃𝑃)

𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑃𝑃 ⇄ 𝑇𝑃𝑅𝑅𝑃𝑇𝑃𝑇𝑃𝑅 𝑃𝑃𝑅𝑃𝑅 → 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃

𝑅𝑅𝑃𝑅 = υ ∙ [𝑇𝑃𝑅𝑅𝑃𝑇𝑃𝑇𝑃𝑅 𝑃𝑃𝑅𝑃𝑅]

υ: Crossing frequency (frequency of crossing the barrier)

Collision frequency (for treatment within collision theory)

Neglecting molecular orientation (steric effects)

91

Transition state theory 2

With 𝑅𝑅𝑃𝑅 = 𝑘 ∙ 𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑃𝑃 it follows:

υ ∙ 𝑇𝑃𝑅𝑅𝑃𝑇𝑃𝑇𝑃𝑅 𝑃𝑃𝑅𝑃𝑅 = 𝑘 ∙ 𝑅𝑅𝑅𝑃𝑃𝑅𝑅𝑃𝑃

Or

𝑘 = υ ∙ 𝐾 = υ ∙ [𝑅𝑓𝑓𝑅𝑃𝑇𝑑𝑇𝑓𝑅 𝑃𝑑𝑓𝑑𝑅][𝑅𝑅𝑓𝑏𝑑𝑓𝑅𝑑𝑃]

Sometime called the Eyring equation.

With 𝐾 = 𝑅−∆𝐺‡

𝑅𝑅 we arrive at:

𝑘 = υ ∙ 𝑅−∆𝐺‡

𝑅𝑅 Sometime called the Eyring equation.

92

Transition state theory 3 En

ergy




Connecting with the Arrhenius equation

𝑘 = 𝐴 ∙ 𝑅−𝐸𝑎𝑅𝑅

𝐸𝑓 is the activation energy.

What is 𝐴 (besides an experimental parameter)?

Does 𝐴 have a physical meaning?

Can 𝐸𝑓 be calculated?

𝐸𝑓

Transition state theory gives answers:

• 𝐴 could be the collision frequency: 𝐴 = υ

• 𝐴 could be the collosion frequency including a factor 𝜌 accounting for steric

effects (such as the relative orientation of molecules): 𝐴 = υ ∙ 𝜌

• 𝐸𝑓 = ∆𝐺‡ can be calculated

93

Transition state theory 4 Limitations

• Its original goal was to calculate absolute rate konstants („absolute-rate theory“).

• TST turned out to be more successful in calculating the thermodynamic properties of

the transition state from measured rate constants (calculating the Gibbs energy ∆𝐺‡ as

well as the enthalpy and entropy).

• TST neglects the possibility of tunneling through the barrier (it assumes that the

reaction does not occur unless particles collide with enough energy to form the

transition structure).

• TST can fail for high temperatures when high vibrational modes are populated and

transition states far from the lowest energy saddle point are formed.

• TST assumes that intermediates (reactants and products, see above, of elementary

steps in a multi-step reaction) are long-lived (reaching a Boltzmann distribution of

energies) and thus TST fails for short-lives intermediates.

• TST generally fails for photochemical reactions (that are determined by the energy

potential landscape rather than the thermodynamics properties of TSs).

94

Femtochemistry (A. Zewail)

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Important technical terms (see EXTRA SLIDES for more detailed explanations)

• Reaction intermediate (next slide) • Transition state (next slide) • Transient species (next slide) • Intramolecular vibrational redistribution (IVR)

– Redistribution of vibrational energy within one electronic state of the molecule

• Internal conversion (IC) – Conversion from electronic into vibrational energy within one molecule (vibronic coupling)

• Intersystem crossing (ISC) – Change of multiplicity of the molecule (e.g. change from singlet to triplet)

See the IUPAC (International Union of Pure and Applied Chemistry) Gold Book: http://goldbook.iupac.org/index.html See the review paper by I. Hertel and W. Radloff: Rep. Prog. Phys. 69, 1897 (2006).


Pote

ntia

l ene

rgy

kT

Intermediate state

Transition state („activated complex“)



Pump

Probe

…and phenomena that happen on their way (IVR, IC, ISC, …)

Reaction intermediates, transition states and transient configurations

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Reaction intermediates

Reaction intermediate / intermediate / reactive intermediate:

• Most chemical reactions occur in a step wise fashion with more than one elementary step

• Reaction intermediate = – Molecular entity formed from the reactants or preceding intermediates in each step (except for

the last one)

– With a lifetime appreciably longer than a molecular vibration corresponding to a local potential

energy minimum of depth greater than kT

– Reacts further to give the directly observed products of the reaction (last step)

• Are usually short lived and seldom isolated • Need to be distinguished from transition states (through their lifetime)

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Transition states

Transition states: • The state through which the molecule must pass as it changes from reactants or

intermediates to products or another set of intermediates • The state corresponding to the highest energy along the corresponding reaction

coordinate (nuclear distance e.g.) • The molecules goes through transient states / transient species / transient

configurations as they pass the transition state • This often involves bond breaking and making • See also transition state theory, transition state method, activated complex (slightly

different from the transition state)

See also:

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Intramolecular vibrational redistribution (IVR)

• Redistribution of vibrational energy within one electronic state of the molecule

• IVR leads from the initially populated vibrational states (e.g. a particular stretch vibration) to a broad distribution of vibrational energy equilibrated over all vibrational degrees of freedom (e.g. all stretch and bend vibrations)

• Usually occurs on a time scale of ps to ns

• Can be described by coupled anharmonic oscillators

which exchange energy

• IVR is a sequence of radiationless transitions

• IVR leads to the fact that the fluorescence is

red-shifted compared to the absorption (see figure)

• If the molecule is embedded in a medium (e.g. a liquid),

IVR is faster than in the isolated molecule and leads to

a thermalization with respect to the temperature of the

medium

radiationless

Photon energy

Fluorescence

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Internal conversion (IC)

• Conversion from electronic into vibrational energy within one molecule • Radiationless transition within one molecule • Usually occurs on a time scale of fs to ps • Mediated by vibronic coupling (see figure) between different electronic states of

the same molecule

Model for vibronic coupling

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Intersystem crossing (ISC)

• Change of multiplicity of the molecule (e.g. change from singlet to triplet) • Radiationless transition within one molecule • Usually occurs on a time scale of ps to µs • Mediated by spin-orbit coupling (often/fast when heavy atoms are present) • Often results in phosphorescence (see figures comparing fluorescence and

phosphorescence)

From: Atkins, Friedman, Molecular quantum mechanics

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Environments: Where chemical dynamics occurs • Gas phase

– Low concentrations (1010-1013 molecules/cm3) limits the set of methods

– Elementary reactions, “simple” systems, isolated systems

– Hard to get certain molecules into the gas phase (biomolecules e.g.)

• Liquids – Solutes (note the higher concentrations than in the gas phase: 1 mol/l corresponds to

approximately 1020 molecules/cm3)

– Solvents (hydrogen-bond dynamics, collective phenomena)

– Their interactions

• Bio-molecules – Special case (depending on sample preparation in the gas phase, in solution or in solids)

• Surfaces/interfaces – Often treated in a specialized community due to very different sample preparation in

vacuum

– Very few x-ray methods applied to chemical dynamics on surfaces (W. Wurth/Hamburg, A.

Nilsson/Stanford)

• Rarely: In solids (e.g. crystals, rare gas matrices)

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Other methods (not using x-rays)

• “Laser femtochemistry” Sets the stage! – Pump-probe methods with laser/optical/IR/THz wavelengths

– Detecting ions, fluorescence etc.

• Laser photoelectron spectroscopy Strong overlap with x-ray PES – Special case of “laser femtochemistry”

• Electron scattering Hard to get fs pulses but high spatial resolution! – Gas phase

– Surfaces

• fs-IR spectroscopy Strong overlap with XAS/EXAFS (in terms of insight) – Liquids

– Surfaces

Why x-rays?

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Why x-rays? Why x-rays for studying chemical dynamics?

• X-ray absorption spectroscopy (XAS/XANES/NEXAFS) and Extended X-ray Absorption Fine Structure (EXAFS)

– Element and chemical state selective (“chemical shift”)

– Local (starts from a core level which is well localized in space)

– Symmetry sensitive (dipole selection rule implies sensitivity to orbital symmetry)

– Combines sensitivity to electronic and geometric structures

• X-ray scattering – Structural probe with atomic scale resolution (both in time and space)

– Global view (e.g. solute and solvent)

• Photoelectron spectroscopy (PES) – See XAS/EXAFS

– In contrast to laser PES: Reach all possible ionic final states (complete picture)

• Resonant Inelastic X-ray Scattering (RIXS) – See XAS/EXAFS

Study fundamental aspects of elementary reactions

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X-ray methods: How to probe chemical dynamics

• X-ray absorption spectroscopy (XAS/XANES/NEXAFS) and Extended X-ray Absorption Fine Structure (EXAFS) Mostly hard x-rays

– Liquids

– Bio-molecules

– [Surfaces/interfaces]

• X-ray scattering Exclusively hard x-rays – Liquids

– [Gas phase, future at FELs (holography from within)?]

• Photoelectron spectroscopy (PES) Mostly laser and VUV wavelengths – Gas phase

– Surfaces/interfaces

– [Liquids]

• Resonant Inelastic X-ray Scattering (RIXS) Well suited for liquids – Liquids

– Solids/surfaces/interfaces

– Not yet for gas phase and bio-molecules (target density)

Mapping chemical interactions and dynamics with x-ray ...

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