Femtochemistry Bonding and Dynamics with X-ray Free-Electron Lasers Philippe Wernet Institute for Methods and Instrumentation for Synchrotron Radiation Research Helmholtz-Zentrum Berlin für Materialien und Energie School on Synchrotron and Free-Electron-Laser Methods for Multidisciplinary Applications, ICTP (International Center for Theoretical Physics), Trieste (Italy), May 2018
Outline 1. “I think I need to tell you why…” 2. Setting the stage 3. Some basics 4. Methods 5. One application 6. One of many possible outlooks 2
Ever increasing demand for energy Quantity (world) 2001 2050 2100 Energy consumption rate 13.5 27.6 43.0 TW Population 6.1 9.4 10.4 billion persons Gross domestic product 7470 14850 27320 $/person·year • Electricity • Secure • Make • Heat • Clean • Store, transport • Fuels • Sustainable • Release Lewis, Nocera, PNAS 103 , 15729 (2006) 3 Lubitz, Reijerse, Messinger, Energy Environ. Sci. 1 , 15 (2008)
Energy and chemical bonds Material Energy type Specific energy* (MJ/Kg) Uranium Fission 80620000 Hydrogen (700 bar) Chemical 142 Kerosene Chemical 42.8 Lithium-ion battery Electrochemical 0.5 * Measured as thermal energy (amount of heat energy that can be extracted) Combustion of methane Energy (kJ) C + 4 H + 4 O to CO 2 , water and heat 3000 2000 C + 4 H + 2 O 2 CO 2 + 4 H + 2 O 1000 0 Net energy CH 4 + 2 O 2 -1000 CO 2 + 2 H 2 O 4 https://en.wikipedia.org/wiki/Energy_density#Energy_storage
Photosynthesis ћω CO 2 + H 2 O → (CH 2 O) n + O 2 This process generates carbohydrates and the world supply of oxygen Life Cycle Photosystem II Cytochrome Oxidase How? Aerobic metabolism Oxygen evolution 4 ћω ATP + CO 2 + H 2 O ← (CH 2 O) n + O 2 2 H 2 O → O 2 + 4 H + + 4 e - We consume oxygen to “burn” the energy of carbohydrates The oxygen is derived from water to produce ATP, the biological energy currency 5 Suga et al., Nature 517 , 99 (2015), Young et al., Nature 540 , 453 (2016), Kupitz et al., Nature 513 , 261(2014)
Water splitting – Rearranging bonds 2 H 2 O 2 H 2 + O 2 Energy = 237 kJ/mol, 13 million J/liter Piscina Agonistica Comunale Bruno Bianchi Trieste Water in Piscina Agonistica Comunale Bruno Bianchi Trieste split every second = 19.5 TW World consumption rate in 2001 = 13.5 TW Approx. 50 m x 15 m x 2 m 1.5 million liters of water 6
Recreating the life cycle Artificial Photosynthesis ћω CO 2 + H 2 O → Fuel (H 2 , CH 4 , CH 3 OH,…) + O 2 Fuel + O 2 → CO 2 + H 2 O JCAP*: “Discover new ways to produce hydrogen and carbon-based fuels using only sunlight, water and carbon dioxide as inputs…” Lewis, Nocera, PNAS 103 , 15729 (2006) 7 Lubitz, Reijerse, Messinger, Energy Environ. Sci. 1 , 15 (2008) *www.solarfuelshub.org
Engineering chemical bonds Nocera: „Unexplored basic science issues are immediately confronted when the problem is posed in the simplest chemistry framework.“ Water splitting stategies 8 Lewis, Nocera, PNAS 103 , 15729 (2006)
Learn to rearrange bonds Characterize molecules in weird bonding configurations 9
Outline 1. “I think I need to tell you why…” 2. Setting the stage 3. Some basics 4. Methods 5. One application 6. One of many possible outlooks 10
Pump-probe spectroscopy Ph. Wernet, Electronic structure in real time: Mapping valence electron rearrangements during 11 chemical reactions , Phys. Chem. Chem. Phys. 13 , 16941 (2011).
Outline 1. “I think I need to tell you why…” 2. Setting the stage 3. Some basics 4. Methods 5. One application 6. One of many possible outlooks 12
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 100-1000·10 10 Å/10 15 fs = 0.1-1 Å/100 fs • 13
What time-resolution do I need to resolve molecular motion? 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 H 2 O • T = 1/f, c= λ· f T = λ /c T = 3·10 -6 m/(3·10 8 m/s) = 10 -14 s • • This corresponds to a duration of the vibrational period of ~10 fs 14
What time-resolution do I need to resolve molecular motion? Take the Brownian motion Resolve the mean square displacement 𝑦 2 𝑢 with time 𝑢 : 𝑦 2 𝑢 = 𝑙 𝐶 𝑈 3π𝑆η 𝑢 • With 𝑈 temperature, 𝑆 particle radius, η viscosity • • Albert Einstein (1905), Marian Smoluchowski (1906) and Paul Langevin (1908) Displacement of 1 Å takes 100 fs ( 𝑆 = 1 Å, η = 20·10 -6 kg/(m·s) for O 2 , ideal gas) • 15
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! Thermodynamics Transition state theory 𝑈𝑄𝑆𝑆𝑄𝑈𝑢𝑈𝑄𝑆 𝑄𝑢𝑆𝑢𝑆 𝐿 = [ 𝑄𝑄𝑄𝑄𝑄𝑄𝑢𝑄 ] 𝑙 = υ ∙ 𝑆 −∆𝐻 ‡ [ 𝑆𝑆𝑆𝑄𝑢𝑆𝑆𝑢𝑄 ] = 𝑆 −∆𝐻 ( 𝑆𝑄𝑢𝑈𝑏𝑆𝑢𝑆𝑄 𝑄𝑄𝑑𝑑𝑑𝑆𝑦 ) 𝑆𝑈 𝑆𝑈 ∆𝐻 ‡ Energy Thermodynamic properties of the transition state ( ∆𝐻 ‡ ) • 𝑆𝑆𝑆𝑄𝑢𝑆𝑆𝑢𝑄 ∆𝐻 and the crossing frequency ( 𝜑 ) determine the reaction rate ( 𝑙 ) (the kinetics) of thermal reactions (equilibrium) 𝑄𝑄𝑄𝑄𝑄𝑄𝑢𝑄 • The energy potential landscapes determine the reaction mechanisms (the dynamics) of photochemical reactions Generalized reaction coordinate We talk about the atomic-scale dynamics of chemical interactions See extra slides on the delineation of kinetics and dynamics! 16
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). 17
The Born-Oppenheimer Approximation 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 (10 4 ) that the nuclei appear to be fixed while electrons are moving! Solve the Schrödinger equation for the electrons in the static Ψ molecule = Ψ e · Ψ n potential of the fixed nuclei (“Produktansatz”). Ψ e = Ψ e (r e , R n ) The electronic part of the wavefunction depends on the nuclear Ψ n = Ψ n (R n ) coordinates BUT as a parameter, NOT as a variable! Within the adiabatic approximation (“electrons follow nuclear motions instantaneously”) we can solve the Schrödinger equation for Ψ e at fixed R n repeatedly for many R n : [T e + V e ] Ψ e (r e , R n =const) = E e Ψ e (r e , R n =const) T e /V e = kinetic/potential energy of electrons By plotting the resulting set of solutions E e versus R n we build potential energy curves! (surfaces, landscapes, depending on the number of parameters/reaction coordinates) 18
The Born-Oppenheimer Approximation The potential energy curve E e versus R n corresponds to the “electronic part” of the Rotation al levels total energy of the molecules plus the energy Electronic excited state Electronic excitation arising from repulsion of the nuclei (sum of Vibrational levels kinetic and potential energy of electrons plus Rotation Electronic ground state al levels potential energy of nuclei) Vibrational levels Vibrational and rotational energies of the molecule are missing! 19 Demtröder, Molekülphysik
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 │ < Ψ e A │ d e │ Ψ e X > │ 2 · │ < Ψ n υ │ Ψ n 0 > │ 2 A d e Ψ e X dr e │ 2 · │∫ Ψ n υ Ψ n 0 dR n │ 2 │∫ Ψ e A The QM harmonic oscillator X Haken/Wolf Molecular Physics and Elements of Quantum Chemistry 20 Atkins/Friedman Molecular Quantum Mechanics
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 21
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 │ < Ψ e A │ d e │ Ψ e X > │ 2 · │ < Ψ n υ │ Ψ n 0 > │ 2 A d e Ψ e X dr e │ 2 · │∫ Ψ n υ Ψ n 0 dR n │ 2 │∫ Ψ e A X Those overlap integrals S are the famous Franck-Condon factors Haken/Wolf Molecular Physics and Elements of Quantum Chemistry 22 Atkins/Friedman Molecular Quantum Mechanics
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