Transition states Calculus trick or reality?

CHEM 761 Basic ideas of femtosecond chemistry LASER spectroscopy basics again LIF, MPI fs chemistry definition making short pulses fs-photo dissociation (pump-&-probe) fs bimolecular reactions LASER bla basics fs chemistry examples, 2017 Uwe Burghaus, Fargo, ND, USA

Definition *) Characterizing the molecular motion in the vicinity of the transition state in physical, chemical, and biological systems. Transition states Calculus trick or reality? *) A.H. Zewail, Nobel lecture 1999, J.Phys.Chem. A104 (2000) 5660. (1fs = 1x10-15 s)

Ahmed Hassan Zewail (born 1946) American / Egyptian scientist "father of femtochemistry won the 1999 Nobel Prize in Chemistry first Arab scientist winning a Nobel Prize in a scientific field working at the California Institute of Technology George Hornidge Porter (1920 2002) British chemist 1967 Nobel Prize in Chemistry together with M. Eigen (German) and R.G.W. Norrish (UK) developed flash photolysis There are some more which should be mentioned, I guess.

energy E kin energy energy pre-dissociation ν ex distance direct dissociation Excitation above dissociation level distance direct dissociation Excitation to purely repulsive potential distance indirect dissociation Excitation to bound level but affected by level crossing

These are the two main detection techniques used in (photo-dissociation) fs chemistry Remember? Some more details today

energy v=3 v=2 tunable cw LASER ν ex excites molecules AB AB * fluorescence relaxation of these excited molecules v=1 v=0 ν ex v=0 v=2 ν LIF v=3 v=2 fluorescence v i v f line spectra reflecting rot/vib population of ground state v=1 wavelength v=0 j fluorescence intensity ~ ground state population

Photo-dissociation dynamics of acetone (CH 3 ) 2 CO pulsed acetone/he molecular beam photolysis at 193 nm methyl 2 CH 3 + CO MPI LIF 140-170 nm Fluorescence intensity measured vib/rot excited CO is produced Excitation wavelength varied RESULT: high j values for all v Reproduced with permission, copyright AIP J. Chem. Phys. 91, 7498 (1989)

Photo-dissociation dynamics of acetone (CH 3 ) 2 CO < 200 nm 2 CH 3 + CO Vib/rot excited CO is produced High j values for all v Unequal forces act on CO (generates high j values) Consistent with sequential dissociation CH 3 COCH 3 CH 3 CO + CH 3 CH 3 CO CO + CH 3 acetyl CH 3 CH 3 methyl CH 3 J. Chem. Phys. 91, 7498 (1989)

energy ν ex v=3 tunable LASER ν ex excites molecules AB AB * v=1 v=2 E.g. same LASER ν ex ionizes the molecule AB * AB + + e - ionization has large cross-section v=0 # of ions, AB +, ~ vib/rot population of ground state ν ex v=0 v=2 v=3 v=2 both LIF & MPI probe ground state population ions easier to detect than photons greater sensitivity often multi-photon processes are used for excitation & ionization v=1 v=0

N 2 O photolysis at 204 nm N 2 + ½ O 2 molecular beam MPI TOFMS measuring geometry N 2 (ν,j) Reproduced with permission, copyright AIP JCP 97 (1993) 7242

That was mostly old stuff old classes but directly related to our topic today

What is that?

e.g. Femtosecond Chemistry, VCH-Verlag (1995), Ed.: J. Manz, L. Wöste A.H. Zewail, Femtochemistry, World Scientific publications (2000) C.V. Shank, Generation of Ultrashort Laser pulses, in Topics in Applied Physics Vol. 60 (Ed.: W. Kaiser) Femtosecond LASER pulses, C. Rullier (Ed.), Publisher springer, Chapter 8 http://www.nobelprize.org/nobel_prizes/chemistry/laureates/1999/zewail-lecture.pdf Review, Femtochemistry: Atomic-Scale Dynamics of the Chemical Bond Using Ultrafast Lasers (Nobel Lecture), Ahmed H. Zewail, Angewandte, Volume 39, Issue 15, Pages 2586 2631 Tutorials in Molecular Reaction Dynamics, RSC Publishing, 2010, chapter 11 ISBN 9780854041589

A.H. Zewail, Nobel lecture 1999, J.Phys.Chem. A104 (2000) 5660 A.H. Zewail, Science 242 (1988) 1645. Zewail, Ahmed H. (2000). "Femtochemistry: Atomic-Scale Dynamics of the Chemical Bond ". The Journal of Physical Chemistry A 104 (24): 5660 5694. Bersohn, Zewail, Ber.Bunsenges.Phys.Chem. 92 (1988) 373. M. Dantus, M.J. Rosker, A.H. Zewail, J. Phys. Chem. 89, 1988, 6128

FTS = femtosecond transition-state spectroscopy Definition *) Characterizing the molecular motion in the vicinity of the transition state in physical, chemical, and biological systems. *) A.H. Zewail, Nobel lecture 1999, J.Phys.Chem. A104 (2000) 5660. (1fs = 1x10-15 s)

FTS = femtosecond transition-state spectroscopy Chemists in the future will be as art directors making movies of molecules on a femtosecond time scale with sub-nanometre resolution with the final goal of atomic engineering. M. Bonn, A.W. Kleyn, G.J. Kroes, Surf.Sci. xx (2002) xx.

Time integrated techniques Crossed molecular beam experiment state-to-state molecular beam scattering techniques after before and after Time resolved techniques Ultra-fast LASER techniques Molecular beam scattering but during? } during

Decomposition reaction hν ABC ----> [A...BC] # ----> A + BC Bimolecular reaction collision A+BC ----> [ABC] # ----> AB + C Bond breaking / bond making: But how (mechanism)? How fast is that? How does the transition state look like? How does the potential energy surface look like? Calculus trick or is that real?

matter wavelength = Planck constant particle momentum λ = h p Nobel price for physics in 1929 Diffraction requires a wavelength of the order of the lattice constants (= interatomic spacing of crystals 4-5Å) Electron kinetic energy (20-200) ev de Broglie wavelength (3-0.8) Å λ 151/ E X-rays (0.001 10 nm) E in ev λ in Å

We need him. For a velocity of one kilometer per second and a distance of one angstrom, the time scale is about 100 fs. A.H. Zewail, Femtochemistry, vol. II, page xv, world scientific publishing, 1994 10 fs is the vibrational period of a covalent bond (Tutorials in Molecular Reaction Dynamics, ISBN 9780854041589)

k = kbt h # Q Q Q A B Is that fast? Or not? E0 exp( ) k T 0.1 s blinck of an eye B 0.1 ms Responds time of the humen ear ms flash photography k = stopped-flow method 10 ns Kerr cell switch 33 ps travling time of a photon for 1 cm kbt 12 10 1 s 170 fs h 10 fs vibrational period of a covalent bond fs atomic/thermal motions (~0.01Å) Or, consider: Typical velocity of atoms/molecules 1 km/s Typical distances 1Å fs ( 300 K ) k preexponential coefficient k B Boltzmann constant h Plank`s constant Q partition function

Short lifetime of the transition states Small concentration of intermediates Limitations impost by uncertainty principle

F + Na 2 --> [NaNaF] # * --> Na * + NaF τ(na * ) ~ 10-8 s τ([nanaf] #* ) ~ 10-12 s Therefore, fluorescence intensity of the [NaNaF] # intermediate is only ~ 10 4 compared with Na * reaction product Would be difficult to detect with time integrated techniques But, detecting a signal while a pulse interacts with a sample is difficult. Thus, the pulse can burry processes with short timescale. A.H. Zewail, Science 242 (1988) 1645. τ = lifetime

Key words cw light/waves vs. pulsed light/waves why using pulsed LASER quantum beam spectroscopy LASER operating principle making LASER pulses cavity damping Q switching mode locking pulse compression self phase modulation CPM: colliding-pulse mode locked ring dye laser Femtosecond LASER pulses, C. Rullier (Ed.), Publisher Springer, Chapter 2 The generation of ultrashort laser pulses, P M W French, Rep. Prog. Phys. 58 (1995) 169-267. Tutorials in Molecular Reaction Dynamics, RSC Publishing, 2010, chapter 11, ISBN 9780854041589 The question always is: should we start with Adam & Eve? If we do, where do we arrive after 2x50 min

1 amplitude 0 + 1 i = ω ω t E( ) e dω 2π iωt ε ( t) E( ω ) = ε ( t) e dt 1.0 amplitude -1 0.5 0.0-0.5-1.0 plane wave 0 100 200 300 400 500 time pulse -200 0 200 time A plane wave is the opposite of a LASER pulse. + example ω ω 10 fs pulse covers nearly the visible spectral range < t >= + + tε ( t) ε ( t) 2 2 dt dt t ω 1 2 2 < ω >= + 2 ω E( ω) + E( ω) 2 2 dt dt

If not: look it up again. PChem Quantum mechanics population inversion mirror LASER medium (gain medium) mirror Resonator optical cavity https://en.wikipedia.org/wiki/laser

1) Cavity dumping 2) Q-Switching 3) Mode locking 4) Puls compression ns ps - fs gain saturation absorber saturation self phase modulation group velocity dispersion

Need a break?

mirror mirror LASER pulse mirror probe dt pump sample Detector

pump probe delay time The pump pulse transitions the sample from an initial state to another (excited) state. Excited state decays. The probe pulse transfers the exited state into another state. That state generates a signal proportional to its population (see examples).

Even in 2017 the fastest electronics cannot measure femtosecond transients directly. Correct: Yes Therefore, pump-probe techniques are used. I am confused: how can one now make fs delays? Does the delay require any fast electronics? Nope. Use optical delay line. t = 10fs x = 3 µm path length

dt mirror LASER pulse probe pump sample x Detector

two-color pump pulse dt sample probe pulse x

Problems & Concepts used to study photo-dissociation reactions reactant transition states products ABC + hν ABC* [A BC] #* A + BC pump pulse starts reaction defines t 0 = 0 probe pulse determines product concentration at t 0 + t via fluorescence of reaction product reaction coordinate ABC A.BC A..BC A..BC A + BC R A, BC distance basic concept idea pump-&-probe allows for measuring the different transition states depending on R A, BC

Problems & Concepts reactant transition states products ABC + hν pump ABC* [A BC] #* A + BC probe pulse starts reaction defines t 0 = 0 t λ probe probe pulse determines product concentration at t 0 + t via fluorescence of reaction product To map the transition state in time t and λ probe are varied. The story is complicated. A simplified PES is shown next.

Problems & Concepts ABC [A BC] #* A + BC hν pump hν probe potential energy 0 V 0 V 1 Pump at t 0 excites ABC from V 0 to dissociative V 1 forming finally A + BC V 2 with increased t also R A, BC increases transition state is formed somewhere hν pump ν probe [A BC]# ABC A + BC R A, BC ν probe A+BC along V 1 potential Probe at a given ν probe the probe pulse is in resonance with V 1 V 2 transition at a given distance R A, BC every ν probe corresponds to a certain R A, BC one ν probe will correspond to the transition state(s) bond length another ν probe corresponds to A + BC equilibrium distance measured is fluorescence that corresponds to concentration of species at given R A, BC

Problems & Concepts ABC [A BC] #* A + BC hν pump hν probe potential energy 0 V 1 V 2 ν probe [A BC]# A + BC ν probe A+BC If the story is correct, the absorption or fluorescence for different ν probe should look very different. V 0 hν pump ABC R A, BC

Problems & Concepts ABC [A BC] #* A + BC hν pump hν probe potential energy 0 V 1 V 2 ν probe [A BC]# A + BC ν probe A+BC absorption t 0 pump ν probe A+BC R A, BC = large dissociation rate of ABC t V 0 hν pump ABC absorption ν probe [A BC]# t 0 R A, BC = R # transition state lifetime pump R A, BC t

hν ICN ----> [I...CN] #* τ ----> I + CN 389.7 Here is the real deal. 389.8 Absorption 390.4 391.4 λ (nm) pump - probe Verzögerung (fs) Bersohn, Zewail, Ber.Bunsenges.Phys.Chem. 92 (1988) 373. M. Dantus, M.J. Rosker, A.H. Zewail, J. Phys. Chem. 89, 1988, 6128 Reproduced with permission, copyright AIP

Femtosecond LASER pulses, C. Rullier (Ed.), Publisher springer, Chapter 8

I.N. Levine, 5 th ed. pump & probe

van der Waals clusters

Homework assignment, read: I.N. Levine, 5 th ed., page 893- Femtosecond LASER pulses, C. Rullier (Ed.), Publisher springer, Chapter 8.2.4

Let s have a short break if you like. Take 5.

Basic ideas of femtosecond chemistry LASER spectroscopy basics again LIF, MPI fs chemistry definition making short pulses fs-photo dissociation (pump-&-probe) fs bimolecular reactions

2. Beispiel A + B --> AB Problem: Determine t 0? When does the reaction start? Trick: Use van der Waals precursor molecules In a crossed beam experiments the reactant pairs (A+B) form at random and do not form at the same time. Prepare weakly bound reactant pairs as van der Waals clusters (A B) ahead of starting the reaction with a LASER pulse. A+B A.B (cluster) LASER trigger AB Standard example: OH-formation H + CO 2 IH...OCO(cluster) [HOCO] # OH + CO N.F. Scherer, L.R. Khundkar, R.B. Bernstein, A.H. Zewail, JCP 87 (1987) 1451.

ICH dissoziation H addition complex formation product formation form van der Waals custers in molecular beam gas expansion ps pump -pulse starts the reaction Result Lifetime of transition state ~ 5 ps t H + CO 2 IH...OCO(cluster) [HOCO] # OH + CO ps probe -pulse detecting OH formation

H + CO 2 IH...OCO(cluster) [HOCO] # OH + CO...The rise time of the OH signal after deconvolution is found to be - 5-15 ps. This first direct observation of the time evolution of the nascent product of a bimolecular reaction N.F. Scherer, L.R. Khundkar, R.B. Bernstein, A.H. Zewail, JCP 87 (1987) 1451. Reproduced with permission, copyright AIP

Surface melting C.V. Shank, R.T. Yen, C. Hirlimann, PRL 51 (1983) 900. fs-radar (LIDAR) Structural information Combine electron and light pulses C. Day, Physics Today 8 (2001) 17. J.C. Williamson, et al. Nature 386 (1997) 159. Fusion reactor (use great intensity of short LASER pulses) Optical communication

fs chemistry definition Characterizing the molecular motion in the vicinity of the transition state in physical, chemical, and biological systems. absorption What is LID? What is MPI? t 0 What is the most common experimental technique? What is the lifetime of a TS? How long does IVR take? Why are pulsed LASER used? pump t Explain the different curve shapes obtained in this pump & probe experiment.

What is the object of fs-chemistry? Why is fs time resolution required? What is coherent and non-coherent LASER spectroscopy? What are quantum beats? How are short LASER pulses made? What is a chirped pulse? How does a pump and probe experiment work? Illustrate a fs photo dissociation experiment. How can bimolecular reactions be studies with fs time resolution? Even in 2017 the fastest electronics cannot measure femtosecond transients. Yes/No? What is the most common experimental technique? What is the lifetime of a TS? How long does IVR take? Why are pulsed LASER used?

https://en.wikipedia.org/wiki/spectroscopy https://en.wikipedia.org/wiki/ultrafast_laser_spectroscopy https://en.wikipedia.org/wiki/franck%e2%80%93condon_principle https://en.wikipedia.org/wiki/transition_dipole_moment https://en.wikipedia.org/wiki/femtochemistry#pump.e2.80.93probe_spectroscopy https://en.wikipedia.org/wiki/spectral_line_shape https://en.wikipedia.org/wiki/flash_photolysis https://en.wikipedia.org/wiki/laser-induced_fluorescence http://www.nobelprize.org/nobel_prizes/chemistry/laureates/1999/zewail-lecture.pdf https://en.wikipedia.org/wiki/time-resolved_spectroscopy

Figure acknowledgement All images shown in this power point presentation were made by the author except the following with are excluded for the copyright of the author: See notes section for each slide. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means except as permitted by the United States Copyright Act, without prior written permission of the author. Trademarks and copyrights are property of their respective owners., 2016, 2017 Publisher and author: Uwe Burghaus, Fargo, ND, USA