X-ray Free-Electron Lasers: Challenges for Theory, Cambridge, Massachusetts, USA, June 19, 2006 Infrared X-ray pump-probe spectroscopy Hans Ågren Department of Theoretical Chemistry Royal Institute of Technology, S Stockholm, Sweden

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X-ray spectroscopies of molecules driven by strong IR fields Principles of IR - X-ray pump-probe spectroscopy Coherent laser induced electronic and nuclear wave packets The phase dependence of the wave packets and the X-ray spectra Role of molecular alignment Recoil effect in the field of IR laser Applications Diatomic Molecules Application on proton transfer in core ionized water dimer Role of vibronic coupling in pump-probe spectroscopy of Glyoxalmonoxime Contents

Principles of X-ray pump probe spectroscopy Pump (optical or IR) laser orients/aligns molecules: Structure determination. Coherent laser radiation creates nuclear or electronic wave packets. X-ray pulse probes the dynamics of wave packet Laser excitation strongly modifies X-ray spectra. Many-electron transitions are enhanced

Optical or UV laser creates the electronic wave packet: This electronic wave packet moves in molecule X-ray pump probe spectroscopy with electronic degrees of freedom gerade MO ungerade MO core hole X-ray absorption Optical laser mixes gerade HOMO and ungerade LUMO and creates electronic wave packet Optical or UV field

OK X-ray absorption spectra of NO excited in ground state vibrational levels: 0, 1, 2 (incoherent IR pump or heating) Incoherent population by IR light of ground state vibrational levels results in strong change of X-ray absorption spectrum One can use continuum wave IR laser with rather small intensity: W/cm2 NO*(1s  2  X-ray IR

Coherent IR pulse induces wave packet dynamics IR field creates coherent superposition of vibrational quantum states Square of WP (and WP dynamics) depends on the IR phase Ehrenfest’s theorem (for the force) Dynamics and phase effect disappear when IR field is incoherent

Principle of X-ray + IR pump-probe spectroscopy (coherent IR field) Formation of OK X-ray spectrum of NO driven by IR field

Origin of the phase dependence of X-ray spectra interference of one- and two-photon channels under core electron excitation: X-ray photon IR photon 2-photon channel depends on the phase of IR field

Some Theory General case of overlapping pump and probe pulses: Coupled Schrödinger equations for nuclear WPs of ground and core excited states IR field interacts with molecules in both states The interactions with IR (L) and x-ray (X) pulses Schrödinger equation has to be solved for each frequency of x-ray field

1.IR field interacts only with molecules in the ground state 2.Back propagation of the WP in the core excited potential 3.The spectrum is the norm of the WP in the frequency domain Now  c (t) does not depend on the x-ray frequency Probe pulse is delayed (probe and pump pulses do not overlap) The solution consists of three steps:

QUANTUM CONTROL OF THE SYSTEM Fast switching off of the IR field compared with the Rabi period: Slow switching off of IR field compared with the Rabi period: Populations IR field Dynamics of the wave packet after the pump pulse leaves the system and effect of the phase memory Short IR pulse Long IR pulse Molecule remains vibrationally excited after IR pulse Nuclear dynamics after IR pulse Phase memory Adiabatic depopultion of vibrational states No nuclear dynamics after IR pulse No phase memory

Preparation of localized nuclear wave packet with higher mean energy CO Rabi period:

Time resolved x-ray probe spectra Evolution of the wave packet in potential well ( as well as its phase dependence) can be probed by short x-ray pulses The trajectories in the coordinate and frequency domains coincide with high accuracy. Revival period Wave packet X-ray spectrum

Wave packet revival }{ Wave packet squeezing Wave packet broadening } { Coupled oscillators with different frequencies experience beatings or revivals Revival period is inversely proportional to the anharmonicity constant of the system:

Role of the duration of x-ray pulse Short x-ray pulses Long x-ray pulses Long x-ray pulse can not probe fast nuclear dynamics Neither ultra-short nor long x-ray pulses can ”see” nuclear dynamics and phase effect Broadening of the spectrum does not allow to see dynamics 

Role of molecular orientation We discussed before pump-probe spectroscopy of oriented molecules Spectra of oriented or fixed-in-space molecules can be measured in the ion yield mode Ion detector X-ray

Larger intensity of IR field: Smaller intensity of IR field: Larger phase effectSmall phase effect X-ray spectra averaged over molecular orientations The phase effect for randomly oriented molecules is small for small IR intensity and it increases for higher IR intensity. The reason for this is: The multi-photon absorption of the IR field grows with the increase of the laser intensity. NO Role of molecular orientation I L = 1.5 x W/cm 2 I L = 2.3 x W/cm 2

Role of the molecular orientation versus pump level Small IR intensity: 1+2 absorption (no interference-no phase effect) Higher IR intensity: 1+3 absorption (interference remains after orient. averag.)

X-Ray pump probe spectroscopy of water dimer Ground state equilibrium structure of water dimer

Propagation of the wave packet in donor core ionized potential surface of water dimer (no IR field !) Tunneling and over barrier propagation classical pathway Proton transfer well Proton transfer region can be studied using x-ray fluorescent or Auger specroscopies

Potential curves of ground state and core ionized states in donor and acceptor oxygens in water dimer Ordinary XPS spectroscopy is able to map the potentials Only near equilibrium XPS driven by IR allows to study the proton transfer region (far away from equilibrium) IR field

Formation of O1s X-ray photoelectron spectrum of water dimer in a strong IR field

Phase dependence of the trajectory of the wave packet in the ground state potential of water dimer created by a strong IR field

IR - X-ray pump-probe spectrum of water dimer for different phases (  L ) and time delays (  t )  L = 3.8 rad  L =  /2. I L = 5.4 x W/cm 2 Proton transfer band

Role of vibronic coupling on proton transfer in core ionized glyoxalmonoxime driven by field of strong IR pulses

Role of vibronic coupling (VC) on proton transfer in core ionized glyoxalmonoxime (GM) Hydrogen donor Hydrogen acceptor q Core ionization of O2 results in the formation of the tautomer 2-nitrosoethenol (NE) VC

Trajectory of nuclear wave packet in the ground state X-ray photoionization

Populations by IR pulse of the ground state vibrational levels of GM

X-ray +IR pump-probe maping of proton transfer dynamics Strength of vibronic coupling VC mixes core-ionized states localized in different oxygens and creates dark and bright state IR field IR induced bands

Pump-probe spectroscopy of molecules driven by IR field both in ground and excited states Overlapping x-ray and IR pulses

Photoelectron spectra of CO (ionization of 2b MO: I=15.6 eV) hot band Without IR IR in both states IR only in ES IR only in GS

Role of interaction with IR field in core excited state Interaction with IR field is forbidden in the ground state due to symmetry (d=0) X-ray IR 0 1

Scheme of X-ray IR pump-probe measurements Orthogonal orientation of X-ray and IR beams which allows to reduce the dephasing caused by the phase factor k L z sample Role of spatial phase of the IR field:

XPS: Recoil effect : Excitation of vibrations due to ejection of photoelectron Formal origin of the recoil effect is generalized FC amplitude To increase the recoil effect we need large size of nuclear wave packet CO molecule k-momentum of photoelectron

Enhancement of the recoil effect When fast photoelectron is ejected the molecule experiences recoil. The transfer of the momentum to nuclei The recoil becomes to be important when the phase factor starts to deviate from 1 High photoelectron momentum p (high x-ray frequency). Broad wave packet (IR field). It can occur due to:

Enhancement of the recoil effect experienced by molecule due to ejection of photoelectron Recoil energy increases internal kinetic energy of molecule in core ionized state. But core ionization takes maximum in turning point where kinetic energy is equal to zero This happens only if the transition is not vertical and it is shifted by: Recoil shifts XPS band: Shift is large when gradients approach each other

Relative difference between the gradients of the core ionized and ground state potentials versus internuclear distance Left turning point Right turning point CO molecule

Oxygen K XPS spectrum of CO driven by strong IR pulse

We have studied X-ray pump-probe spectra with coherent and incoherent pump radiation as well as with CW and pulsed light sources. Phase of coherent pump radiation is transferred to nuclear or electronic wave packet. This makes trajectory of the wave packet and X-ray pump-probe spectra sensitive to the phase of the pump field. The phase sensitivity of the IR + X-ray pump-probe spectra depends strongly on the duration of the X-ray pulse, delay time, shape of IR pulse, molecular orientation. X-ray pump-probe spectroscopy is a proper tool to study the dynamics of proton transfer in liquids. Revival effect allows to study dynamics of different relaxation processes in liquids and to measure hyperfine structure like anharmonicity. Conclusions

Royal Institute of Technology: Freddy Fernandes Guimarães Viktor Kimberg Viviane Felicissimo Ivo Minkov Amary Cesar Faris Gel’mukhanov Acknowledgments