Recoil-Induced Ultrafast Molecular Rotation Probed by Dynamical

Home , Recoil

Downloaded by guest on October 3, 2021 www.pnas.org/cgi/doi/10.1073/pnas.1807812116 C Denis effect Doppler rotational by dynamical probed rotation molecular ultrafast Recoil-induced oainlDplreffect Doppler rotational period. which rotational lifetime, the core-hole with the comparable change during is significant orientation a molecular by the explained agreement of is full asymmetry in This shape, theory. line with Auger energy- photon the the a of as changing asymmetry observed is dependent by way a such rotational speed in recoil-induced controlled The rotational dynamics photoelectron. the the the of lifetime change control energy kinetic core-hole cannot and the manipulate we option by and experiment ond time given our delay time in constant delay Since keep time- dynamics. to given conventional or the dynamics in system, the as the use time by and “delay” two spectroscopy point the pump-probe in general vary resolved performed more to be a either can From ways: measurements electron. time-resolved Auger view, the of of natural and ejection rotation the the the initiating from photoionization The originates C1s the emission. experiment between electron delay our Auger in subsequent information time by probed ultrafast recoil-induced is emit- the “pump- we rotation itself: X-ray the nature motion, an by of and offered molecular device effect “kick” probe” Doppler this rotational recoil dynamical visualize the the To use via photoelectron. accompanied molecule monoxide fast the carbon ted up of performed spinning ionization was C1s by this X-ray showcase, a hard angular As by large molecule. a transfer the to to way particular momentum a initi- needs To in one chemistry. rotation, and ultrafast and physics ate in motion topics fundamental molecular are rotation controlling and 2018) Observing 11, May review for (received 2018 18, f December Berlin Eisenberg Helmholtz-Zentrum Wernet, Philippe by Edited Russia Krasnoyarsk, 660041 University, Federal Siberian Chemistry, France; Sweden; Paris, Uppsala, F-75005 20 751 University, Uppsala Astronomy, China; Beijing, 102206 University, a Kushawaha K. Rajesh sntsmercdet h hp fteAgraglrdistri- angular Auger the of shape the to due symmetric shift The not rotation. of is sense of subsequent emission the of and direction photoelectron the the to according shifted” “red or shifted” Doppler rotational the the into (6). dynamics has effect brings core-hole molecule which the of 1), the lifetime (Fig. the state during rotation, orientation As its ultrafast change photoelectron. to the fast time a of ultra- of consequence ejection by photon the caused a the by splitting induced increasing Doppler rotation rotational by fast the increases is that This and energy. spectra to Auger cease lar spectra core-ionization Auger the from the away that far energy threshold. belief photon the common on depend was energy. photon X-ray 5). it the (4, of Still, increase interference an with Cohen–Fano vanish and effects the These 3), postcol- near (2, (1), least interaction resonances at shape lisional by violated to shown is due been threshold statement has photoionization this it that years, studies recent detailed in However, process. ization I asymmetry peak Auger ycrto OEL ’redsMrses 19 i-u-vteCdx France; Cedex, Gif-sur-Yvette 91192 Merisiers, des l’Orme SOLEIL, Synchrotron needn ftepoo nryue o h rcdn ion- are preceding spectra the for Auger used that energy photon statement the textbook of widespread independent a is t na“lsia”pcue h ue lcrneeg s“blue is energy electron Auger the picture, “classical” a In molecu- influences that effect an present we work, this In eolin ´ a,1 iCiLiu Ji-Cai , f aheec hsk ri Universit Freie Physik, Fachbereich | eoleffect recoil e ai oel Piancastelli Novella Maria , b,1 c hoeia hmsr n ilg,RylIsiueo ehooy 09 tchl,Sweden; Stockholm, 10691 Technology, of Institute Royal Biology, and Chemistry Theoretical Vin , | cu a aCruz da Vaz ´ ıcius lrfs rotation ultrafast τ euetesec- the use we , rMtrainudEege eln emn,adacpe yEioilBadMme Richard Member Board Editorial by accepted and Germany, Berlin, Energie, und Materialien ur ¨ tBri,115Bri,Gray and Germany; Berlin, 14195 Berlin, at e ¨ obneUniversit Sorbonne | adX-ray hard c Hans , e,d ap P Ralph , Agren ˚ | ,CR,Lbrtied hmePhysique-Mati Chimie de Laboratoire CNRS, e, ´ uttner ¨ b 1073/pnas.1807812116/-/DCSupplemental. y at online information supporting contains article This avail- are 1 study repository, this laboratory during molecules-excitees-en-couche-interne/downloads LCPMR analyzed the and/or from generated able datasets The deposition: Data the under Published hsatcei NSDrc umsin ..i us dtrivtdb h Editorial the by invited editor guest a is P.W. Submission. Direct PNAS Board. a is article This interest.y of R.P., conflict J.-C.L., no declare D.C., authors research; The H. performed J.-C.L., F.G. D.C., and and data; M.S., analyzed R.P., F.G. M.N.P., and V.V.d.C., R.K.K., J.-C.L., D.C., T.M., research; R.G., designed L.J., M.S. and R.P., M.N.P., D.C., contributions: Author rn adXrypoos led xsigsucso X-ray of sources existing Already deliv- photons. sources of X-ray advent photoelectrons hard the to high-energy ering due of possible become emission recently the has by Auger induced photons. the X-ray effects hard in by observed ionization was core after it also (9) as and Ne energy, doublet of spectra symmetric photon a the in with results grows effect (8). effect general mention recoil very translational should photon the This by one caused above-mentioned context, splitting Doppler this all the In from effects. differs energy-dependent qualitatively effect the physics. of quantum heart and the classical at between funda- is connection which the (7), with of principle consistent limit correspondence the as mental in numbers, coincide rotational wish the descriptions quantum these We to high that Appendix). approach point the (SI quantum stress states to pure rotational a between in interference corresponds wave This rotational the packet. of the parts between “time-delayed” interference and an makes “instantaneous” to publication due asymmetric this profile in Auger used the picture semiclassical The bution. c,d eateto ahmtc n hsc,NrhCiaEeti Power Electric China North Physics, and Mathematics of Department owo orsodnemyb drse.Eal [email protected], [email protected] Email: or addressed. [email protected], be may correspondence whom To hsdnmc ycagn h oainlseduigX-ray using manipulate speed rotational We energies. different the lifetime. of changing photons core-hole by the dynamics this with period rotational comparable the dur- that fact occurs is the orientation exploit We molecular decay. Auger the that ing of show the change we probe since significant to rotation, a molecular opportunity ultrafast unique of a dynamics Auger offers core- time-delayed C1s emission The electron the molecule. of monoxide a spectra carbon of ionized achieved Auger recoil-induced is high-resolution emission dynamics the recording its by monitor by control caused finally to and of recoil motion goal temperature the rotational The to rotational photoelectron. due effective fast K an 10,000 to ultra- about induces up photons rotation X-ray hard fast by molecules of Ionization Significance Lo , ngnrl h bevto fpeoealne orecoil to linked phenomena of observation the general, In 2 (Fig. energy photon with increase its With y f,1 cJournel ¨ ıc acSimon Marc , g nttt fNntcnlg,Setocp n Quantum and Spectroscopy Nanotechnology, of Institute NSlicense.y PNAS e eadGuillemin Renaud , e n ai Gel’mukhanov Faris and , . n ..woetepaper.y the wrote F.G. and A., ˚ https://lcpmr.cnrs.fr/content/relaxation-de- . y r tRyneet(LCPMR) Rayonnement et ere ` e www.pnas.org/lookup/suppl/doi:10. ain Marchenko Tatiana , NSLts Articles Latest PNAS d eateto hsc and Physics of Department B c,a,g and ,this C), | f6 of 1 e ,

PHYSICS a coincidence technique but not with fast-rotating molecules. However, this problem can be overcome by what we would like to define as a natural X-ray “pump-probe” single-molecule device based on the Auger process (Figs. 1 and 3). The Auger electron emitted from the same molecule during the core-hole lifetime τ after fast photoelectron ejection can be used as a probe of the recoil-induced ultrafast rotation, since the rotational Doppler shift is time-dependent on the same “internal” timescale, as we will show below. Contrary to a conventional pump-probe experiment where the real time delay between the pump and the probe pulse is changed, the “time delay” is constant in this experiment. Instead, we change the speed of the process, namely the rotational velocity, by varying the kinetic energy of the photoelectron. In simple words, by increasing the photoelectron energy, we control the recoil-induced rotation of the molecular axis; effectively, we make our core-hole clock “tick” slower by speeding up the recoil- induced rotation. In this context, we should clarify this usage of the term time delay. The actual time delay between the instant of photoelectron ejection and the Auger electron emission is given Fig. 1. Classical picture of the dynamical rotational Doppler effect. In Bot- by a statistical distribution fully governed by the natural lifetime tom, a photoelectron with momentum k is at t = 0 ejected from the carbon τ = 1/2Γ =∼ 7.5 fs. atom (long black arrow) in the direction away from the detector. Induced In this Auger experiment, the recoil-induced ultrafast rota- by the recoil momentum, the molecule translates with a velocity u = k/M tion (Fig. 1) is probed using a time-dependent rotational Dopp- and rotates with an angular velocity wk toward the detector. Therefore, an Auger electron with momentum p emitted at t = τ toward the detector ler shift is blue shifted as indicated in the schematic spectrum displayed in Top. In Middle, the photoelectron is emitted in the opposite direction so that veloc- Drot(t) = wk · jp (t), jp (t) = α[R(t) × p] [1] ity u and angular velocity wk are inverted, resulting in a red-shifted Auger electron in the detector. The shaded gray areas around the carbon atoms of the energy EA of Auger electron. Here, t is the time delay represent an Auger emission with anisotropic angular distribution in the between the photoionization process and the emission of the molecular frame. In Bottom, the preferred direction of the Auger emission Auger electron. As we shall demonstrate, this time delay t, which is rotated from the top toward the detector so that the blue-shifted Auger is in the order of τ, leads to crucial differences of the rotational peak gains intensity as indicated by the long thin black arrow in the gray Doppler shift in photoionization (6, 18–20) and in Auger decay. area. The opposite rotation in Middle lowers the intensity for the red-shifted Auger peak (short thin black arrow). Apparently, after ejection of the fast photoelectron at the instant t = 0, the molecule rotates with the constant angular velocity wk = α[k × R(0)]/I ; note that we assume the angular velocity radiation, such as SOLEIL (France) (10) and SPring-8 (Japan) w = 0 before photoionization (i.e., we neglect thermal rotation). (11), deliver high-brilliance synchrotron radiation up to 10 keV. Here, k and p are the momentums of the photoelectron and X-ray photons with energy of 50–100 keV are available at the Auger electron, respectively, while R(0) and R(t) describe the ESRF (European Synchrotron Radiation Facility) (12, 13) and internuclear radius vector at the time of the photoemission and PETRA III (Positron Electron Tandem Ring Anlage III) (14) the Auger decay, respectively. The quantity jp (t) is the recoil synchrotrons. One should also mention the X-ray free electron angular momentum that the molecule acquires at the instant t laser (XFEL) facility SACLA (SPring-8 Angstrom˚ Compact free by ejection of the Auger electron, I is the momentum of inertia, electron LAser) (Japan) (15), with photons up to 20 keV and intensity 1020W /cm2, as well as the European XFEL (Ham- burg, Germany), with photons up to 25 keV (16); these facilities make it possible to overcome low-ionization cross section in the ABC high-energy region. The experimental procedure (Figs. 1 and 3) consists of the first step of C1s photoionization of the showcase molecule CO with X-rays of energies high above the ionization energy of 296.24(3) eV (17), namely ω = 2.5, 8, and 12 keV. The large momentum of the photoelectron of k ≈ 30 a.u. at a photon energy of ≈ 12 keV gives a recoil “kick” that creates a nonequilibrium distribution over translational and rotational degrees of freedom (6, 8, 9) [W (u) and W (w) in Fig. 3C, respectively] and makes it possible to reach rotational quantum numbers of J ≈ 40 for the core-ionized molecule. In comparison, to force molecules −1 1 + to rotate with the corresponding speed (νk = wk/2π ≈ 4 THz) Fig. 2. Theoretical and experimental C1s → d Σ Auger spectra of CO in thermal equilibrium, a gas temperature above 4,000 K has to given for the X-ray photon energies ω = 2.5 keV (blue dashed line), 8 keV be assumed. These results suggest that highly excited rotational (red dashed–dotted line), and 12 keV (black solid line). (A) The symmetrical states with J in the order of 100 can be created in the future part σ0 of the calculated partial cross section (Eq. 8), where the dynamical by using X-ray photons in the energy range of several tens of contribution to the rotational Doppler shift is neglected. (B) The total theoretical cross section σ of the Auger process displaying the asymmetry of thousands of electronvolts. the Auger profile caused by the dynamical rotational Doppler effect. The The recoil-induced molecular rotation can be detected in prin- simulations are convoluted with a Gaussian instrumental function of 0.1-eV ciple by a probe light pulse. In that case, it would be difficult to width. (C) Experimental data in agreement with the simulations (Fig. 2B) synchronize the probe photon with the molecule as well as with showing that the dynamical asymmetry is growing with increasing photon the ejected photoelectron. This is in principle possible by using energy.

2 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1807812116 Ceolin´ et al. Downloaded by guest on October 3, 2021 Downloaded by guest on October 3, 2021 oei le ntecus fteeetoi ea accompa- decay electronic core the created of The course atom. the carbon the in of filled electron is core hole (2.5 1s photon a X-ray izes high-energy the where abnmnxd molecule monoxide carbon the ultrafast monitoring the for possibility probe dynamics. a molecular to offers recoil-induced resolution” and spectroscopy dynamics “time Auger rotational sufficient femtosecond the a with of implies time clock This duration delay 1). natural (Fig. the decay a since with possible, short, 7. is is rotation process vectors Auger the unit of indicates vation hat the work, (i.e., this throughout that, note dynamics tional of momentum angular well-defined a possesses the shift for Doppler shift Eq. Doppler in described rotational electron Auger time-dependent the of ference respectively. atoms, carbon and α along axis the include that respectively, distributions The photoelectron. W high-energy a of emission the by distribution freedom. of degrees tional C as well as freedom distribution u velocity angular mal and distribution text velocity thermal the core- the in of are of levels distributions details interference rotational (more the different rotational state by through by ionized affected going accompanied strongly channels process Auger is Auger the process the Auger of The picture excitations. the Quantum of direction (B) polarization p. the (A) with photons. radiation setup synchrotron X-ray experimental high-energy the with of Diagram photoionization by initiated process 3. Fig. ¯ C A oi tal. et eolin ´ = 5 = r lnrct hog h ou-addmbl-ie3 distributions, 3D dumbbell-like and torus- the through cuts planar are (u) oilsrt u cee esuyteAgrpoesi the in process Auger the study we scheme, our illustrate To rota- the directly observing allows shift Doppler rotational The dif- qualitative a is there that out point to like would We p -4 -2 sbtente“up oiainadte“rb”Auger “probe” the and ionization “pump” the between fs m 0 2 4 R ˆ 2k O ≡ xeietlstpadpyia itr ftemlclrAuger molecular the of picture physical and setup Experimental BT /(m /2M R/ W W O ω → n h eoiydistribution velocity the and (w) , n nua eoiydistributions velocity angular and (u) D + x + steui etraogtevector the along vector unit the is CO rot = ph R(t m ˆ ˙ CO w ¯ u C = e x = ++ / = ) and ), n h oetmo h eetdAgrelectron Auger detected the of momentum the and (X and u, ¯ p w (d k 2k w 1 · Center 1 Σ W j k BT ph Σ m × + 0 /2I y + (u) ) O o htneiso,sneaphoton a since emission, photon for = R(t ˆ + ) , → W = x and and u 1 y 0 = exp(−u CO ) e / (w) ncmaio ihteangular the with comparison in u k ¯ e. w nue ytephotoelectron; the by induced − Right m x o h rnltoa ere of degrees translational the for = + + / C w ¯ (C exp(−w e 2 e and , B r h asso oxygen of masses the are p / − ipa h nua velocity angular the display u ¯ 1s , 2 W IAppendix SI /( −1 ≤ ,rsetvl,caused respectively, (u), y √ 2 = W / + ) ω π w ¯ | u) ¯ w (w). j ≤ 2 ph 3/2 y /( e .Teobser- The R). / k − 2kV ion- keV) 12 | w √ ¯ n h ther- the and ) Left 1 = .(C ). π τ o h rota- the for w ¯ 1 = hw the shows ) W (21–23). Velocity ) 3/2 and (w) /2Γ with ) e [2] ≈ ek hc sfre anyb he lotpretyoverlap- perfectly of and (v almost spectrum components three vibrational by The mainly ping electron. formed is Auger which the peak, of C1s ejection studied the the by nied rfie e ssatfo eilsia qainfrtecross the for equation semiclassical a from start section us let 30). profile, (29, works previous in system been same has the which that model, to two-step formalism applied used a frequently of the use beyond and the goes interference imply This dynamics in rotational Appendix). states the (SI hence, rotational 28) (27, quantum domain between energy equiv- the interference is domain the time the to in alent here used picture the dynamical with the a that comparison in gives outlined in thermal picture work problem quantum studied this neglect full the in to into used insight possible approach deeper it semiclassical The make rotation. also momentum photo- angular angular large fast a the transfers 1 process, orbital the C1s of the momentum course from the This the ejected describe motion. in electron we rotational since of Instead, possible, picture emerge. is pic- semiclassical to physical a effect clear using a studied process for the used of be to ture cumbersome ( too is experiment language the explains titatively pro- intermediate the an to state of excited is picture molecule state quantum affects the rotational 3B, the molecule Fig. rotating In in shown fast shape. cess to a spectral suited of Auger well dynamics the is the spectrum how the intensi- of illustrate structure, Because the vibrational Appendix). of simple (SI redistribution components this overlapping a these mainly vibrational of the causes ties that (26) notice effect should are One recoil states 25). final (24, dicationic identical and almost core-ionized the of distances rium otetasainlDplrshift Doppler counterpart translational the into to of take dependence to time 6, the ref. account to similar representation, time-dependent the over integration amplitude an scattering denote brackets the where h ifrnebtenteAgrenergy Auger energy the Moreover, between (20). difference state the electronic final the and a erwitna ucino h nl ewe h momen- the between (k angle photoelectron the the of of function tum a as rewritten be can is momentum of analyzer direction a the electron around the with of direction electrons axis polarization Auger the the detail, to parallel In mounted 3A. experiment Fig. the in of setup shown geometrical the on significantly depends ionization. s for expected parameter distribution angular to identical Polynomial, is dre distribution form angular well-known the the that so light synchrotron Here, photoelectron. the trta eed nteoeigangle opening the on depends that eter in ing oudrtn o h oainldnmc fet h Auger the affects dynamics rotational the how understand To sw hl hwi h olwn,teosre ieshape line observed the following, the in show shall we As quantity The j v k |J 00 P ≤ E f σ 2 = k M res αkR + 1 = ftesuidAgrprocess: Auger studied the of f F fteC1s the of σ → ept h atta h unu prahquan- approach quantum the that fact the Despite i. j D k = = ≈ 0 = (0) rot v ζ −1 P −ı hP 0 36 |JM Θ P 2 = (t k 2 k → (e = Z ) 0 steagebetween angle the is Q ( ∞ for α[ k ˆ ,snei hspriua ae h equilib- the case, particular this in since ), eed ntetm,teinzto ie(6), site ionization the time, the on depends hc hndcy otefia rotational final the to decays then which i, p F d P e −1 · |F k 1 ı Here, p). ˆ k · 1 = sn h ie xeietlsetup, experimental given the Using e. ω Σ × 0 R t k) ˆ + 1 = → | 2 D + 12 = R(0)] i, e 2 rot /(∆E d ue rniincnit fol one only of consists transition Auger ,result- (p), electron Auger the and ) ecie h nua itiuinof distribution angular the describes steplrzto ieto fthe of direction polarization the is 1 ( Σ t 1 β e.Teehg ausfrthe for values high These keV. ) + 00 P otemlcl,wihi about is which molecule, the to dt D ζ n hudnotice should One Appendix. SI + 0 = 2 transition. 1 cos = rot (cos e D D ,tequantum the Appendix), SI ı(∆ (t tr tr → p = ) + Here, Θ). E e 1+cos + χ(1 nacn of cone a in NSLts Articles Latest PNAS .Contrary Appendix). (SI v +D k D and 0 E · 2 0 = rot A p/M tr · +ı χ n h resonance the and and k, ∆ + , Γ)t e k ˆ v ftedetector, the of E ıΓ) h rotational the , 00 n a detect can and and dt P χ) = 1 = 2 , switnin written is E β saLegen- a is saparam- a is The R(0). A ˆ χ 2 = → − 22.5 = | v E sthe is 0 f6 of 3 res 1 = [3] P is ◦ k ,

PHYSICS and we shall see further below that it is important for the size AB of the asymmetry in the Auger line shape (SI Appendix has more details). One should notice that the ionization probability Pk can be affected by polar anisotropy caused by the forward scattering effect. However, the forward scattering of a fast photoelectron by the oxygen atom does not bring asymmetry to the Doppler profile; therefore, it is excluded from this analysis (SI Appendix). 2 The probability of the Auger decay Qp = |Ap| depends on the angle between the molecular axis Rˆ(t) and the direction of the Auger electron pˆ. In the simulations, we take into account the first antisymmetric contribution to Ap [i.e., Ap ≈ 1 + η(pˆ · Rˆ(t))/2], where the effective parameter η describes the strength Fig. 4. The dynamical rotational Doppler effect together with the aniso- of this antisymmetrical term (SI Appendix). The term propor- tropy of the Auger decay makes the Auger profile asymmetric. (A) The η tional to is neglected in conventional analyses of Auger spectra, symmetric partial cross section σ0 is responsible for the translational and because the orientational averaging of the related contribution rotational Doppler broadening and the Doppler splitting caused by the in σ is equal to zero as soon as the rotational motion is disre- anisotropy of core ionization. (B) During the Auger process, the molecule garded. However, we show in the following that the dynamical has time to change the orientation. The interference of the instantaneous rotational Doppler shift given by Eq. 1 renders this contribution and time-delayed Auger channels results in an antisymmetric contribu- important, since it explains the observed asymmetry of the Auger tion σint. The results are convoluted with a Gaussian instrumental function profile shown in Fig. 2C. of 0.1-eV width. Inset shows the increase of the asymmetry parameter ω = η ω ω σ We shall now look into the evolution of the time-dependent a( ) a0( ) with the photon energy, where a0( ) is the asymmetry of int at given photon energy as indicated in B for ω = 12 keV. rotational Doppler shift Drot(t). After the ejection of the photoelectron, the initial molecular orientation Rˆ(0) starts to rotate with constant angular velocity wk until the instant t accord- molecular axis is taken into account by the smaller dynamical ˙ F ing to the Newton law Rˆ(t) = wk × Rˆ(t). As a result, the time-delayed term d time-dependent molecular orientation becomes Using Eq. 3 as well as the approximations given for F and Qp , the total cross section becomes σ(∆E) = σ0(∆E) + ησint(∆E), σ (∆E) σ (∆E) Rˆ(t) = Rˆ(0) cos(wk t) + Rˆ ⊥ sin(wk t) ≈ Rˆ(0) + Rˆ ⊥θ(t), [4] where 0 and int are the two first nonvanishing terms. As can be seen in Fig. 4A, the first term due to the 2 where θ(t) = wk t is the angle of rotation of the molecular axis instantaneous scattering channel described by |F0| results in a and Rˆ ⊥ = (wˆk × Rˆ(0)) is a vector orthogonal to Rˆ(0). Through- Doppler broadening and splitting of the symmetric Auger profile out this study, we use for Rˆ(t) an approximation linear in (6, 8, 9): time, because the molecule has no time to perform a full ◦ D 1 + ζP (kˆ · pˆ) E rotation during τ = 1/2Γ, since wk τ ≈ 0.2=11 , even for a pho- 2 b σ0(∆E) = 2 2 . [8] ton energy of ω = 12 keV. The rotation of the molecular axis (∆E + Dtr + Drot,0) + Γ described with Eq. 4 brings dynamics into the rotational Doppler effect and produces in particular a rotational Doppler shift As defined above, the brackets denote an integration over kˆ that depends on the instant t of the Auger electron ejection, and Rˆ(0); note the implicit presence of Rˆ(0) due to Drot,0 = namely wk · jp (0) = wk · α[Rˆ(0) × pˆ]. The splitting refers to the opposite translation and rotational Doppler shifts of two islands ˆ ˆ 2 ˆ Drot(t) = wk · jp (t) ≈ Drot,0 − ρ(R(0) × k) (pˆ · R(0))t. [5] in the velocity distribution W (u) and angular velocity distribution W (w) shown in Fig. 3C. The physical picture of this Here, Drot,0 is the rotational Doppler shift at the instant t = 0. effect is rather similar to what was discussed in refs. 8 and 9. The parameter ρ = α3R3k 2p/I 2 defines the magnitude of the Despite the fact that the rotational motions are treated clas- asymmetric contribution to the line shape, since it is—because sically, there is indeed a pure quantum effect to consider: of k 2—proportional to the kinetic energy of the photoelectron. 2 2 owing to the well-defined phase between the instantaneous and With ρt αjp (w /Drot,0) 1, we can approximate the . k time-delayed parts of the rotational wave packet in the core- scattering amplitude F defined in Eq. 3 to ionized state, there are interferences between these waves. The ∗ Z ∞ interference Re(F0Fd ) of instantaneous (F0) and time-delayed ı[∆E+Dtr+Drot,0+ıΓ]t F ≈ F0 + Fd = −ı dte (Fd ) scattering amplitudes leads to the second antisymmetric 0 contribution ρ × 1 − ı Rˆ(0) × kˆ 2(pˆ · Rˆ(0))t 2 [6] 2 σint(∆E) = −σint(−∆E) [9]

by two qualitatively different contributions, namely D (∆E + Dtr + Drot,0)f E =4ρΓ 2 2 3 , [(∆E + Dtr + Drot,0) + Γ ] Z ∞ 1 F = −ı dt exp(ıφ(0)t) = , 0 ˆ ˆ ˆ 2 ˆ 2 0 ∆E + Dtr + Drot,0 + ıΓ where f = [1 + ζP2(k · pˆ)](R(0) × k) (R(0) · pˆ) (Fig. 4B; details Z ∞ ˆ 2 ˆ ˆ 2 ˆ 2 are SI Appendix, Eq. S15). The quadratic term (R(0) · pˆ) in f is Fd = −ρ(R(0) × k) (R(0) · pˆ) dt exp(ıφ(0)t)t /2 ˆ 0 important, since it does not vanish after averaging over R(0). Re(F F ∗) · Q F ∗ ıρ(Rˆ(0) × kˆ)2(pˆ · Rˆ(0)) It originates from the product 0 d p, where both d ˆ 2 ˆ 2 = 3 , [7] and Qp ≈ 1 + η(R(0) · pˆ) + η (R(0) · pˆ) /4 contribute linearly to [∆E + Dtr + Drot,0 + ıΓ] (Rˆ(0) · pˆ); note that we approximated η(Rˆ(t) · pˆ) by η(Rˆ(0) · pˆ), ◦ where φ(0) = ∆E + Dtr + Drot,0 + ıΓ. The instantaneous term since the molecule typically rotates less then 10 before the F0 describes the Auger process where the molecule has no time Auger decay. This shows that the term η(Rˆ(0) · pˆ) in Qp, which to change the orientation. The recoil-induced rotation of the describes the polar anisotropy of the Auger electron emission

4 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1807812116 Ceolin´ et al. Downloaded by guest on October 3, 2021 Downloaded by guest on October 3, 2021 ino h yaia oainlDplrsit oethat observa- note shift; the Doppler p) for rotational important dynamical is the of axis, tion molecular the to respect with vr loncsayt aetednmclterm dynamical the how- take is, Eq. to it by necessary asymmetry, peak also observed ever, experimentally have the that velocities duce “two-island” photon [W angular the shifts the and to Doppler velocities opposite refers of the 9) increase for (8, distributions splitting the Doppler with This energy. pronounced more becomes 2A Figs. resolution. by experimental the More- simulate 4A to experiment. and eV 0.1 the of in tion parameters as 0.043 the = model energies Γ used given photon cal- above we the We same over, width on energy. based the the photon shapes that for the line shows Auger with clearly the increase culated figure asymmetry This the 2C. and Fig. in of displayed energies photon with toionization C1s exchanged). are atoms O and C the C which transitions, main Auger the the in pres- that states the vibrational out is isolated form point of pure in ence to recoil wish rotational observe dur- We to rotations requirement lifetime. full perform regime core-hole to a the time reach the ing to polyatomic has molecule and study the inertia to which of in possible moment it higher make with molecules will (10–15) radiation ray core-hole the with comparable recoil- period of a lifetime. phenomenon with molecular rotation general induced very showcase this ideal this illustrate an is of to orientation monoxide molecular heart Carbon the lifetime. The core-hole of during change asymmetric. significant profile the is Auger asymmetry: asymmetry whole line which antisymmetry, a the intrinsic as makes an has well contribution as dynamical rotational splitting the the and are electron broadening features Auger Doppler spectral This time-delayed Auger by rotation. Distinctive unique probed emission. molecular a is recoil-induced offers dynamics range rotational study energy to excitation wide opportunity a over carbon core-ionized monoxide of spectra core-hole Auger high-resolution the Recording during rotation Conclusions full molecule perform the to when time energies lifetime photon the higher has much at range decrease energy studied the with together leads, it that so antisymmetric is oqatf h pcrlaymty eitoueaparameter a σ introduce 2C. we Fig. asymmetry, in a shown spectral 2 ones the experimental Fig. quantify the To in with well shown agree as results profiles, Auger metric ˆ .SnYP agCK e’uhnvF(00 oainlDplrefc nx-ray in effect (1976) Doppler eds J, Rotational Nielsen (2010) Rud L, F Rosenfeld Gel’mukhanov 7. C-K, Wang Y-P, Sun 6. P molecules. of photo-ionization 5. the in Interference (1966) U Fano HD, multiple Cohen after interaction 4. postcollision in dynamics Ultrafast (2012) al. et R, Guillemin processes. atomic 3. in interaction Post-collision (1989) SA Sheinerman the MY, Kuchiev of influence 2. The (2008) al. et SL, Sorensen 1. oi tal. et eolin ´ int (ω o oprsnwt hoy h xeietlsetao the of spectra experimental the theory, with comparison For h eetaalblt fnwsucso nes adX- hard intense of sources new of availability recent The ec rnil (1918–1923) Principle dence photoionization. 150:30–33. 1s argon in decays Auger Usp Phys nitrogen. molecular core-ionized ue pcrmo N of spectrum Auger hne inwhen sign changes tnrR ta.(08 tt-eedn eaeugrd nest aisi the in ratios intensity gerade/ungerade State-dependent (2008) al. et R, uttner σ ¨ −1 hc steapiueo h niymti contribution antisymmetric the of amplitude the is which ), .Ti smer aaee nrae with increases parameter asymmetry This 4B). (Fig. 0 tlast ymti obepa tutr,which structure, double-peak symmetric a to leads It . → hwteisatnoscnrbto,wihi described is which contribution, instantaneous the show 9 τ 32:569–587. . d hsterm this 4B, Fig. in seen be can As account. into Vadcnoue h eut ihaGusa func- Gaussian a with results the convoluted and eV 1 Σ + hsRvA Rev Phys ue rniinmaue usqett pho- to subsequent measured transition Auger 2 . hsBMlOtPhys Opt Mol B Phys J photoionization. R(0) NrhHlad mtra) o 3. Vol Amsterdam), (North-Holland, 82:052506. ω hmPy Lett Phys Chem −R(0) → (u) ≤ 12 il or olce ok,TeCorrespon- The Works, Collected Bohr, Niels and ζ 1 = hsRvLett Rev Phys e.Hwvr eepc its expect we However, keV. 41:141001. W . ie,we h oiin of positions the when (i.e., σ ω 78 456:1–6. (w) = eoac nteAgrdcyof decay Auger the on resonance and .,8 n 2kVare keV 12 and 8, 2.5, .T repro- To 3C]. Fig. in hs theoretical These B. 109:013001. η 0 = σ .6 σ 0 int oasym- to , swl as well as η defined ( hsRev Phys R(0) ˆ ω Sov in · 1 aaaY ta.(05 eeomn fhr -a hteeto spec- photoelectron https://www.esrf.eu/UsersAndScience/Experiments/StructMaterials/ID31. X-ray at Available hard Jan- 13. of Accessed https://www.esrf.eu/UsersAndScience/Experiments/EMD. Development at Available (2005) 12. al. et Y, Takata X- Inelastic 11. synchrotron: SOLEIL the at beamline GALAXIES The (2015) al. et JP, Rueff 10. inlyrsle ue pcr a lob xetdfrother for expected C be also (e.g., molecules can polyatomic spectra [e.g., Auger molecules resolved triatomic tionally several in exist CO to known already are 8/- o udn h oki eln ..akolde h support the acknowledges F.G. 16-12-10109. Berlin. Project Foundation in (Vetenskapsr Science Council Russian work Research the Swedish for Pu of funding KAW-2013.0020 Project Grant for Forschungsgemeinschaft Deutsche Foundation 180/6-1 thanks Wallenberg R.P. support. Alice financial and H. 2018MS050. Knut Grant Fundamental Universities edges and Central 11574082 the Grant for supported China Funds was Research of J.-C.L. Foundation 99120122). Science National and Syn- by at 20120642 beamline (Proposals GALAXIES SOLEIL the on chrotron performed were Experiments facility. the ACKNOWLEDGMENTS. Radia- and excitees-en-couche-interne/downloads. Chemistry-Matter Physical repository, of (CNRS) Laboratory tion the from available are the on Availability. Data based are and approaches in quantum outlined method strict kinetic theoretical using a and performed providing were semiclassical eV, calculations 100 The both meV. of 100 the about energy of in pass resolution a pressure energy 1 at the around operated and constant was used, spectrometer kept was was Liquide chamber Air vacuum 45 from of angle (99.997%) the acceptance to monoxide an parallel to set corresponds measurements is 3A the that Fig. axis in Si(111) shown lens EW4000 as exit a vector an with fixed by analyzer nitrogen-cooled analyzed hemispherical are liquid Scienta electrons the a and of by pho- monochromator, energy 12-keV selected double-crystal The to is polarization. 2.3- horizontal X-rays station the provides incoming covers end and which range Spectroscopy) (10), energy beamline PhotoElectron ton GALAXIES X-ray the of (Hard (38) HAXPES the using Experiment. Methods and Materials between transitions the worlds. exploring classical and for quantum quantum prerequisite high very a free- with is of cations degrees numbers molecular the excited of highly all of over dom available, control became full Moreover, molecular recently ultrafast dynamics. monitor which to possibilities resolution, unprecedented offers high at troscopy region. X-ray the hard the (i.e., in dissocia- widespread valid this 30) before not that shows is rotate clearly (29, approximation study not this approximation context, does this recoil In molecule tion). approach axial the This that the fragments. assumption detect- on dissociation by based the determined of is direction frequently orientation the is the ing molecules studies, core-ionized dissociating gas-phase of of in spectra Furthermore, Auger by or molecules. probed fluorescence be can X-ray the which analyzing packets, with wave nuclear states ro-vibrational ro-vibrational ent High-energy reaching vibrational systems. temperature for complex effective simple allow in emission its also the even to after photons photoelectrons, spectra due Auger fast CO, any of influence in will transition it structure, specific a for .SmnM ta.(04 tmcAgrDplrefcsuo msino fast of emission upon effects Doppler Auger Atomic (2014) al. et M, Simon 9. S, Levin Y-P, Sun S, Gavrilyuk 8. 6 hseprmn lutae hthr -a lcrnspec- electron X-ray hard that illustrates experiment This cesdJnay2,2019. 24, January Accessed 2019. 24, uary SPring-8. in BL29XU 50–55. at troscopy range. X-ray hard the Rad in spectroscopy photoelectron and scattering ray photoelectrons. fluorescence. optical ray-induced H 2 6 3–7.Atog hsefc a ige u nti work this in out singled was effect this Although (34–37). ) (31), 22:175–179. h xeietwspromda h ycrto SOLEIL Synchrotron the at performed was experiment The H 2 3) n C 3).I diin uhvibra- such addition, In (33)]. OCS and (32), S a Commun Nat h aaesgnrtdado nlzddrn hsstudy this during analyzed and/or generated datasets The https://lcpmr.cnrs.fr/content/relaxation-de-molecules- etaktesafo OELfrsotl running smoothly for SOLEIL of staff the thank We 10 n e.3.Tesetoee esmd sdfor used mode lens spectrometer The 38. ref. and ge ,Glmkao 21)Rci pitn fX- of splitting Recoil (2010) F Gel’mukhanov H, Agren 5:4069. 5 ˚ − IAppendix SI hsRvA Rev Phys 10 CS ulIsrmMtosPy e A Res Phys Methods Instrum Nucl 6 2 n o raighgl coher- highly creating for and K , N 81:035401. 2 dt R rn 05071and 2015-03781 Grant VR) adet, ˚ . O, NSLts Articles Latest PNAS SO × 10 2 −5 , C br h electron The mbar. 2 H 2 ◦ , uecarbon Pure . C .acknowl- A. Synchrotron J ˚ 2 N | 2 and , f6 of 5 547: e

PHYSICS 14. Franz H, et al. (2006) Technical report. PETRA III: DESY’s new high brilliance third 26. Sałek P, Gel’mukhanov F, Agren˚ H, Bjorneholm¨ O, Svensson S (1999) Generalized generation synchrotron radiation source. Synchrotron Radiat News 19:25–29. Franck-Condon principle for resonant photoemission. Phys Rev A 60:2786–2791. 15. Yabashi M, Tanaka H, Ishikawa T (2015) Overview of the SACLA facility. J Synchrotron 27. Gel’mukhanov FK, Mazalov LN, Kondratenko AV (1977) A theory of vibrational Rad 22:477–484. structure in the X-ray spectra of molecules. Chem Phys Lett 46:133–137. 16. Tschentscher T, Feidenhans’l R (2017) On behalf of the staff at European XFEL and in 28. Gel’mukhanov F, Agren˚ H (1999) Resonant X-ray Raman scattering. Phys Rep 312: the institutes collaborating on the construction of the accelerator and photon beam 87–330. systems, Starting User Operation at the European XFEL. Synchrotron Rad News 30: 29. Prumper¨ G, et al. (2008) Is CO carbon KVV Auger electron emission affected by the 21–28. photoelectron? Phys Rev Lett 101:233202. 17. Fink RF, Piancastelli MN, Grum-Grzhimailo AN, Ueda K (2009) Angular distribution 30. Rolles D, et al. (2010) Molecular-frame angular distribution of normal and resonant of Auger electrons from ﬁxed-in-space, and rotating C 1s → 2π photoexcited CO: Auger electrons. J Phys Conf Ser 212:012009. −1 Theory. J Chem Phys 30:014306. 31. Puttner¨ R (2008) A vibrationally resolved C 1s Auger spectrum of CO2. J Phys B 18. Thomas TD, et al. (2011) Experimental observation of rotational Doppler broadening 41:045103. in a molecular system. Phys Rev Lett 106:193009. −1 → 1 −2 32. Poygin M (2006) Detailed study of the S2p X A1(2b1 ) normal Auger spectra 19. Miron C, et al. (2014) Site-selective photoemission from delocalized valence shells of H2S. Phys Rev A 74:012711. induced by molecular rotation. Nat Commun 5:3816. 33. V Sekushin, et al. (2012) A comprehensive study of the vibrationally resolved S2p−1 20. Miao Q, et al. (2015) Rotational Doppler effect: A probe for molecular orbital Auger electron spectrum of carbonyl sulﬁde. J Chem Phys 137:044310. anisotropy. J Phys Chem Lett 6:1568–1572. 34. Eland JHD (2003) Complete double photoionisation spectra of small molecules from 21. Garetz BA (1981) Angular Doppler effect. J Opt Soc Am 71:609–611. TOF-PEPECO measurements. Chem Phys 294:171–186. 22. Bialynicki-Birula I, Bialynicka-Birula Z (1997) Rotational frequency shift. Phys Rev Lett 35. Furuhashi O, Kinugawa T, Masuda S, Yamada C, Ohtani S (2001) Double charge trans- 78:2539–2542. 2+ fer spectroscopy of acetylene dication C2H2 at vibrational resolution. Chem Phys 23. Arita Y, Mazilu M, Dholakia K (2013) Laser-induced rotation and cooling of a trapped Lett 342:625–630. microgyroscope in vacuum. Nat Commun 4:2374. 36. Hochlaf M, Eland JHD (2008) Structure, spectrum and decomposition of the doubly 24. Correia N, et al. (1985) Theory of Band shape formation in Auger and autoionization ++ charged ion C2N2 Phys Chem Phys 10:5394. spectra of molecules. Numerical applications and new high-resolution spectra of CO. 37. Eland JHD (2008) Spectra of the dications of benzene, naphthalene and azulene. J Chem Phys 83:2035–2052. Chem Phys 345:82–86. 25. Puttner¨ R (2007) Potential energy curves of the quasi-stable states of CO2+ 38. Ceolin´ D, et al. (2013) Hard X-ray photoelectron spectroscopy on the GALAXIES determined using Auger spectroscopy. Chem Phys Lett 445:6–11. beamline at the SOLEIL synchrotron, J Electron Spectrosc Relat Phenom 190:188–192.

6 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1807812116 Ceolin´ et al. Downloaded by guest on October 3, 2021