Concerted electron and proton transfer in ionic crystals mapped by ...

THE JOURNAL OF CHEMICAL PHYSICS 133, 064509 共2010兲

Concerted electron and proton transfer in ionic crystals mapped by femtosecond x-ray powder diffraction Michael Woerner,a兲 Flavio Zamponi, Zunaira Ansari, Jens Dreyer, Benjamin Freyer, Mirabelle Prémont-Schwarz, and Thomas Elsaesser Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie, 12489 Berlin, Germany

共Received 3 June 2010; accepted 7 July 2010; published online 13 August 2010兲 X-ray powder diffraction, a fundamental technique of structure research in physics, chemistry, and biology, is extended into the femtosecond time domain of atomic motions. This allows for mapping 共macro兲molecular structure generated by basic chemical and biological processes and for deriving transient electronic charge density maps. In the experiments, the transient intensity and angular positions of up to 20 Debye Scherrer reflections from a polycrystalline powder are measured and atomic positions and charge density maps are determined with a combined spatial and temporal resolutions of 30 pm and 100 fs. We present evidence for the so far unknown concerted transfer of electrons and protons in a prototype material, the hydrogen-bonded ionic ammonium sulfate 关共NH4兲2SO4兴. Photoexcitation of ammonium sulfate induces a sub-100 fs electron transfer from the sulfate groups into a highly confined electron channel along the c-axis of the unit cell. The latter geometry is stabilized by transferring protons from the adjacent ammonium groups into the channel. Time-dependent charge density maps derived from the diffraction data display a periodic modulation of the channel’s charge density by low-frequency lattice motions with a concerted electron and proton motion between the channel and the initial proton binding site. Our results set the stage for femtosecond structure studies in a wide class of 共bio兲molecular materials. © 2010 American Institute of Physics. 关doi:10.1063/1.3469779兴 I. INTRODUCTION

Electron and proton transfers belong to the most basic reactions occurring in chemistry and biology.1–3 They play a key role in photosynthesis and many other processes of energy conversion. An important class of molecular materials, in which electron and proton transfers are expected to determine basic electronic properties, are hydrogen-bonded ionic crystals. Prototype materials such as 共NH4兲2SO4 共ammonium sulfate兲 and KH2PO4 exist in different ferroelectric and paraelectric phases and show pronounced changes of the dielectric function with temperature. At the microscopic level, the interplay of electronic and ionic charges in defining the electronic properties and the character of charge transport is understood only in part. Elementary steps of electron and proton transfer frequently occur in the femtosecond time domain, governed by the interplay of electronic and nuclear degrees of freedom. While ultrafast spectroscopy has provided substantial insight into the reaction kinetics and the underlying interactions, the determination of transient electronic structure and atomic positions occurring during and after the reactions requires novel structure sensitive methods with femtosecond time resolution.4–12 X-ray diffraction from polycrystalline powder samples, the Debye–Scherrer diffraction technique, is a standard method for determining equilibrium structures.13,14 The different crystallite orientations with respect to the incoming a兲

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monochromatic x-ray beam result in a distribution of the angles of incidence ␪ and a cone of diffracted x-rays with an opening angle 2␪. On a planar detector, x-rays diffracted from different lattice planes give rise to ringlike patterns with a diameter reflecting the different diffraction angles. The intensity of the rings is determined by the respective x-ray structure factor which represents the Fourier transform of the spatial electron density for a particular reciprocal lattice vector, i.e., set of lattice planes. Thus, charge density maps of the material can be derived from the diffraction pattern. Mapping nonequilibrium structural changes15 on the time scale of atomic motions requires an extension of x-ray powder diffraction into the femtosecond time domain. In this article, we report the results of such experiments in which a femtosecond pump pulse initiates a structure change and changes of intensity and/or diameter of many diffraction rings were measured with a 100 fs time resolution by scattering hard x-ray pulses from the excited sample.16 From such data, transient atomic positions and charge density maps on the femtosecond time scale are derived. As a prototype material, we study ammonium sulfate 共AS兲 forming a hydrogen-bonded ionic orthorhombic structure with four 共NH4兲2SO4 entities per unit cell 关Fig. 1共a兲兴.17–20 Our experiments allow for deriving transient charge density maps, revealing a so-far unknown ultrafast relocation of electrons and protons, which leads to the formation of conducting channels in the material. A short summary of such results has been presented in a recent review article.21 Here, we report an in-depth quantitative analysis of the femtosecond x-ray dif-

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atoms within the unit cell. However, the microscopic nature of both phase transitions and the lattice motions involved are not fully understood. B. Femtosecond x-ray powder diffraction

FIG. 1. 共a兲 Left: Unit cell of ammonium sulfate containing sulfate SO2− 4 and ammonium NH+4 groups 共yellow: sulfur atoms; red: oxygen; blue: nitrogen; gray: hydrogen兲. The dimensions are a = 0.778 nm, b = 1.064 nm, and c = 0.599 nm. The shaded area marks a plane defined by the c-axis and the line connecting two hydrogens of the NH4共I兲 groups 共see text兲. Right: View of the lattice along the c-axis. 共b兲 Femtosecond powder diffraction setup showing the path of the x-ray probe through the multilayer focusing optic, the optical pump 共blue兲 at 400 nm incident onto the powder sample and the Debye–Scherrer rings captured onto a CCD detector. The powder sample is mounted vertically in the focus of the x-ray beam. A typical diffraction pattern obtained after a 7 min exposure is shown. 共c兲 Top: Measured 共black line兲 and calculated 共red dots兲 intensity profile of the Debye–Scherrer ring pattern as a function of 2␪ 共␪: diffraction angle兲. The intensities are normalized to that of the 共111兲 peak. Bottom: Intensity change of the rings observed 260 fs after excitation of the sample.

fraction data, complemented by optical pump-midinfrared probe experiments and quantum chemical calculations. In this way, the different steps and mechanisms of the structure change are identified. II. EXPERIMENTAL TECHNIQUES AND DATA ANALYSIS A. Ammonium sulfate

At room temperature 共T = 300 K兲, AS is in a paraelectric phase affiliated with the space group Pnam 关Fig. 1共a兲兴. Under equilibrium conditions, AS transforms to a ferroelectric phase at T = 223 K having a lower symmetry and the space group Pna21. A second phase transition occurs at a much higher temperature of T = 423 K retaining the space group Pnam. Here, a contraction of the unit cell19 and pronounced changes of the dielectric function,22,23 in particular, of the material’s electric conductivity,24 have been found. Stationary x-ray and neutron diffraction experiments show that both phase transitions are connected with a rearrangement of the

The ground dry polycrystalline AS powder sample 共Alfa Aesar, purity of 99.999%兲, squeezed tightly into a 1 mm diameter, 250 ␮m deep hole in an aluminum holder, is sealed at the front and the back with a 20 ␮m thick diamond window and a thin mylar film, respectively 关Fig. 1共b兲兴. The sample is held at a temperature of T = 300 K and mounted vertically in the focus of the x-ray beam 共focal spot size of ⬇200 ␮m兲. In the x-ray experiments 关cf. Fig. 1共b兲兴, the sample is electronically excited25,26 via three-photon absorption of a 50 fs pump pulse at 400 nm and the resulting structural dynamics is probed by diffracting a 100 fs hard x-ray pulse 共Cu K␣, photon energy of 8.05 keV兲 from the excited sample. Changes of the pattern of diffraction rings recorded with a large-area charge coupled device 共CCD兲 detector 共sensitive area of 60⫻ 60 mm2兲 are measured as a function of pump-probe delay. Both visible pump and hard x-ray probe pulses are generated using an amplified Ti:sapphire laser system working at a 1 kHz repetition rate in combination with a laser-driven Cu K␣ 共photon energy of 8.05 keV兲 plasma source.27,28 The experimental setup has been discussed in detail in Ref. 16. The 400 nm pump pulses have an energy of 70 ␮J and a spot size of ⬇400 ␮m, resulting in an intensity of 5 ⫻ 1011 W / cm2 at the sample entrance. Due to the strong elastic scattering of 400 nm light off AS crystallites, the penetration depth of the pump light is limited to approximately dex ⬍ 30 ␮m and there is no residual 400 nm beam at the exit of the sample. From the intensity of the diffusively scattered 400 nm light and of the beam reflected from the front window, we estimate an energy of up to ⬇50 ␮J per pulse absorbed in the sample. The group velocity mismatch between the 400 nm pump and the hard x-ray probe on the short interaction length is less than 60 fs, allowing for the very high time resolution of our experiments of 100 fs. The x-ray probe pulses are focused onto the sample using a multilayer optics.29 The x-ray flux on the sample is up to 5 ⫻ 106 photons/ s. In the spectral range below ប␻ ⬍ 6.2 eV 共␭ ⬎ 200 nm兲, the optical absorption coefficient of AS is below 30 cm−1 共Ref. 25兲. Recent experiments26 indicate that the fundamental direct gap lies between 6.2 and 8 eV. Thus, at least three photons of the 400 nm pump light 共3 ⫻ ប␻ = 9 eV兲 are required to electronically excite the AS crystallites. Nonlinear absorption measurements on AS single crystals demonstrate a significant nonlinear absorption of 400 nm light at intensities of 5 ⫻ 1011 W / cm2. Intensity dependent measurements point to a predominant three-photon absorption, but higher order processes cannot be fully excluded. Excitation of the AS powder with the pulse train of a 1 kHz repetition rate results in a temperature increase which is highest close to the diamond entrance window of the sample. A maximum temperature of T = 350 K at the entrance window was derived from measurements with an in-


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Concerted electron and proton transfer

frared camera detecting the thermal radiation from the excited sample. This value is well below the temperature of TC = 423 K at which the second phase transition of AS occurs under equilibrium conditions. C. Reconstructing the transient three-dimensional electron density from the measured femtosecond powder pattern

␩⌬␳e共x,y,z,t兲 =

The structure of AS at T = 300 K, i.e., in the paraelectric phase, is known from neutron diffraction data.17 Using the atomic positions from such measurements and the atomic form factors for x-ray diffraction with Cu K␣ radiation, we gr of calculated the initial 共ground state兲 structure factors Fhkl the unit cell before optical excitation. The amplitudes of the diffraction peaks were calculated with help of Eq. 4.10 of Ref. 14, whereas their width was chosen according to the finite angular resolution of our femtosecond diffraction experiment. We find an excellent agreement of the calculated intensity I共2␪兲关red dots in Fig. 1共c兲兴 with the measured stationary powder pattern 关black solid line in Fig. 1共c兲兴. To derive the complex structure factor Fhkl = 兩Fhkl兩exp共i␾hkl兲 and the spatially resolved charge density from the diffraction data, one needs to solve the “phase problem,” i.e., determine ␾hkl. In general, recursive methods of data analysis are applied to address this issue.14 In our timeresolved diffraction experiments, however, we can exploit the interference of x-rays diffracted from the small fraction of excited 共modified兲 unit cells and from the majority of unexcited ones within a single crystallite. The unexcited AS powder at T = 300 K represents a simple case because of the inversion symmetry of the orthorhombic crystal structure. In other words, each crystallite is a racemate of AS molecules, i.e., it contains for each molecule also its mirror image. Since our photoexcitation does not select one type of enantiomers, there is, for each unit cell which contains a photoexcited AS molecule of arbitrary shape, a corresponding inverted unit cell containing the mirror image of the photoexcited species. Thus, when averaging over the crystallite inversion symmetry is preserved even after an arbitrary photoinduced structure change. As a result, 具Fhkl典 averaged over a single crystallite is and remains real-valued with ␾hkl = 0 or ␲. The change of diffracted intensity is given by mod modⴱ gr 2 ⌬I共␪hkl,t兲 = Chkl关兩␩共Fhkl + Fhkl 兲/2 + 共1 − ␩兲Fhkl 兩 gr 2 − 兩Fhkl 兩兴,

共1兲

where ␩ is the fraction of modified unit cells in the sample mod modⴱ gr and Fhkl , Fhkl , and Fhkl are the structure factors of the modified unit cells, their mirror image, and the unexcited unit cells, respectively. Chkl contains all reflection dependent factors for powder diffraction except 兩Fhkl兩2 共cf. Eq. 4.10 in Ref. 14兲. For weak excitation as in our experiments, i.e., ␩ Ⰶ 1, this expression can be simplified by keeping only terms linear in ␩, mod gr ␩⌬Fhkl = ␩ Re共Fhkl − Fhkl 兲=

⌬I共␪hkl,t兲 gr 2ChklFhkl

.

in the denominator on the right hand side of the equation are known, i.e., a measurement of ⌬I共␪hkl , t兲 gives the transient mod 兲 if the value of ␩ is known. From structure factor Re共Fhkl Eq. 共2兲 the change ⌬␳ of the three-dimensional charge density is calculated,

共2兲

This equation directly connects the observed changes in the intensity to the change of the structure factor. All quantities

␩

冋冉

兺 ⌬Fhkl共t兲cos abc hkl

2␲

hx ky lz + + a b c

冊册

. 共3兲

We determine the real part of the structure factor change Re共⌬Fhkl兲共a possible imaginary part remains unknown兲 and, thus, the calculated difference map ⌬␳e = 共␳mod共x , y , z , t兲 + ␳mod共−x , −y , −z , t兲兲 / 2 − ␳gr共x , y , z , t兲 contains the average of the modified charge density and the spatially inverted modified charge density. The obtained charge density map of the modified unit cells 共␳mod共x , y , z , t兲 + ␳mod共−x , −y , −z , t兲兲 / 2 represents an average over one crystallite and, thus, does not tell us how many molecules per excited unit cell and which particular molecule in an excited unit cell are structurally modified. Since ␳mod共x , y , z , t兲 ⬎ 0 and ␳gr共x , y , z , t兲 ⬎ 0, however, a negative ⌬␳共x , y , z , t兲 can exclusively occur at spatial positions where initially atoms 共electrons兲 are present and positive peaks in the difference map ⌬␳e共x , y , z , t兲 prove definitely the occurrence of atoms 共electrons兲 at the respective spatial positions in one of the excited unit cells and provide a spatially resolved image of the structurally modified AS molecules after photoexcitation. The course of action for reconstructing ⌬␳e共x , y , z , t兲 from our time-resolved experiment was the following. First, we calibrated Chkl in Eq. 共1兲 by means of a comparison of the measured stationary pattern with the theoretical one 关cf. Fig. 1共c兲兴. We then calculated the temporal change of the threedimensional electron density ␩⌬␳e共x , y , z , t兲 with the help of Eqs. 共2兲 and 共3兲. It is important to note that the change of diffracted intensity allows for deriving the product ␩⌬␳e共x , y , z , t兲, while the ratio ␩ = Nmod / Ntot is not known yet. For estimating ␩, one has to consider the possible changes of charge density in more detail. A spatial broadening of the electron density will result in a decrease of ␳e共x , y , z , t兲 on the atom and a compensating increase of electron density in the vicinity with the charge integral around the atom remaining constant. If an atom moves a small distance, e.g., in a molecular vibration or phonon, one observes a sign change of ⌬␳e共x , y , z , t兲 centered on the atom. A transfer of electrons over a distance larger than the atomic radius results in a decrease of charge density at the original site and an increase at the new position. The charge integral at the new site has a value identical to the elementary charge e or a multiple of it. This additional constraint allows to derive ␩ in such a case. D. Femtosecond vibrational spectroscopy

To complement our x-ray experiments, we studied transient vibrational spectra of photoexcited AS powder. A thin 共d ⬇ 1 ␮m兲 polycrystalline AS sample held in-between two thin diamond windows was excited by 400 nm pump pulses and the resulting change of the vibrational spectrum was measured with midinfrared probe pulses. The intensity of the


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FIG. 2. Changes in intensity 共circles兲 of particular Debye–Scherrer rings as a function of time delay between the optical pump and x-ray probe. The solid lines are guides to the eye. Bottom panel: transient bleach of the bending mode ␯4 of the ammonium ion NH+4 共pump energy E = 12 ␮J兲. Please note the logarithmic time scale after the break.

pump pulses was chosen to get a deposited energy density of ⬇10 meV/unit cell similar to the x-ray experiments. The time resolution was 100 fs. The details of the experimental setup have been reported in Ref. 30. III. RESULTS AND DISCUSSION A. Femtosecond powder diffraction

The ring pattern recorded with the unexcited AS sample in our setup displays approximately 20 different reflections 关Fig. 1共c兲兴. Upon femtosecond excitation, the intensities undergo pronounced changes as shown for a pump-probe delay of 260 fs in the lower panel of Fig. 1共c兲. In Fig. 2, the time evolution of intensity changes for a number of diffraction rings is presented for the first 2 ps after excitation and for

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longer time delays up to 12 ps. Most transients exhibit an intensity change rising around delay zero, superimposed by oscillations at later time delays. Such results give direct evidence of the ultrafast nature of the induced structural changes. The oscillations with a period of Tosc = 650 fs 共˜␯osc = 50 cm−1兲 match the low-frequency Ag-phonon of AS,31,32 involving librational motions of sulfate ions, an angular reorientation of the ammonium units, and a concomitant modulation of the distance between the oxygen atoms 1 and 2 of opposite sulfate groups 关cf. Fig. 4共a兲兴. The onset of the oscillations with femtosecond photoexcitation points to an impulsive excitation of this lattice mode, resulting in a modulation of atomic positions in the lattice and, thus, of diffracted x-ray intensity. The angular positions of the different diffraction rings remain unchanged on the time scale shown in Fig. 2, pointing to essentially unchanged lattice vectors and, thus, a negligible expansion and/or volume change of the material. From the data in Figs. 1 and 2, we derived transient charge density maps, i.e., the spatially resolved change of electron density ⌬␳e共x , y , z , t兲 with femtosecond time resolution, applying the procedure described in Sec. II C. In Fig. 3, electron density maps are shown for the x-y plane of the unit cell at z / c = 0.25 关Fig. 3共a兲兴 and for a plane containing the z-axis and the oxygen atoms 1 and 2 of opposite sulfate groups 关Fig. 3共b兲兴. Transient charge density maps for other sectional views and at additional delay times are shown in Refs. 16 and 21. The different lattice atoms are clearly identified in the steady-state maps ␳e共x , y , z , t = −⬁兲共center of Fig. 3兲 with the highest electron densities on the sulfur atoms. Femtosecond photoexcitation induces pronounced changes ⌬␳e共x , y , z , t兲 with the strongest decrease ⌬␳e ⬍ 0 on the sulfur atoms and a less pronounced decrease on the oxygen and the nitrogen共II兲 atoms. The strongest increase ⌬␳e ⬎ 0 is found at the initially unoccupied spatial positions rជH = 共0 , 0 , 0兲, 共0 , 0 , 0.5c兲, 共0.5a , 0.5b , 0兲, and 共0.5a , 0.5b , 0.5c兲 within the unit cell. Such increase of electron density is equivalent to the formation of “electron channels” at 共0 , 0 , z兲 and 共0.5a , 0.5b , z兲, parallel to the z axis in-between the oxygen atoms 1 and 2. The areas of enhanced electron density in the channel display a very small diameter in the x-y plane of

FIG. 3. Contour plots 共right hand side兲 showing the electron density as a function of delay time, and the corresponding planes 关共a兲 upper row and 共b兲 bottom row兴 through the unit cell of AS 共left hand side兲 for easy visualization. 共a兲 The blue dashed line indicates a plane perpendicular to the Z direction, cutting the unit cell at z / c = 0.25. 共b兲 The blue dashed line marks a plane parallel to the Z direction through the unit cell corresponding to the “zigzag” orientation of the oxygen atoms that belong to two different sulfate ions. An electron channel appears between these oxygens 共last contour plot兲 along the position marked in red.


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FIG. 4. 共a兲 Distance between the O1 and O2 atoms of adjacent SO2− 4 groups 共arrow in the left inset兲 as a function of delay time as derived from the x-ray data. Insets: Crystal structure of AS before 共left hand side兲 and after 共right hand side兲 the concerted electron and proton transfer into the conducting channel along the z-direction. 共b兲 Transient change of electron density ⌬␳e共x , y , z , t兲 at the initial proton position within the ammonium ion 共open symbols兲 and at the transitional channel position, i.e., x = a / 2, y = b / 2, z = c / 2 共solid circles兲. 共c兲 Time-dependent change of total charge in the electron channel calculated by integrating over a cylindrical volume along the z-axis with a Gaussian lateral envelope of 0.1 nm width.

approximately 0.1 nm 关rightmost panel of Fig. 3共b兲兴 which corresponds roughly to 2aB 共aB = 0.05 nm, Bohr radius of the hydrogen atom兲. This strong charge localization points to attractive Coulomb centers, i.e., nuclei which have moved to such positions and to which the electron charge is attached. The maps for a delay time of 260 fs clearly exhibit a charge transfer from the sulfur atoms to a well-separated position in the electron channel. This behavior allows for estimating a fraction of excited unit cells of ␩ = 0.06. The x-ray results suggest the following scenario of structural change 关Fig. 4共a兲兴: Photoexcitation induces a shift of electronic charge predominantly from the SO2− 4 units and a concomitant translocation of a proton from the adjacent NH+4 共I兲 group into a position in-between the oxygens 1 and 2 of opposite SO2− 4 groups. From a chemical point of view, the − following process occurs: NH+4 + SO2− 4 → NH3 + SO4 + H. The structural change mediates a hydrogen bond between the two oxygen atoms shown as green dashed lines in Fig. 4共a兲. In this way, hydrogen atoms along the axes 共0 , 0 , z兲 and 共0.5a , 0.5b , z兲 stabilize the transferred electronic charge in the channel region. After its ultrafast creation, the spatial charge distribution undergoes ultrafast changes as shown in Fig. 4. Panel 4b shows the time-dependent change of electron density ⌬␳e共x , y , z , t兲 at rជ = 共0.5a , 0.5b , 0.5c兲 in the channel 共solid circles兲 and at the initial proton position on the NH+4 共I兲 ion 共open circles兲; panel 4c the time-dependent total charge in

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the channel, given by the integral of ⌬␳e共x , y , z , t兲 over a cylindrical volume of 0.1 nm diameter and the length c = 0.599 nm of the unit cell. The electronic charge in the channel displays pronounced oscillations, i.e., charge flows periodically into and out of the channel region. The maximum charge in the channel is of the order of 2e, twice the elementary electron charge e. The oscillation period is close to that of the 50 cm−1 Ag phonon modulating the distance between the oxygen atoms 1 and 2 关Fig. 4共a兲兴. Maxima in the channel’s electronic charge occur at maxima of the O1 – O2 distance, a geometry in which the proton stabilizing the charge position in the channel can easily be accommodated. The pathways of electron flow into and out of the channel region are derived from the data in Fig. 4共b兲 and from integrals of electron density over particular volumes of the crystal structure. Figure 4共b兲 shows that minima in the channel’s electron density correspond to maxima on the original positions of the protons on the NH+4 共I兲 groups. As has been discussed earlier 共cf. Fig. 10 in Ref. 21兲, the transient increase of charge in the plane ZX⬘ defined by the z 共channel兲 axis and the axis X⬘ linking the original proton positions on two neighboring NH+4 共I兲 groups originates fully from a concomitant decrease of charge in the volume of the two opposite SO2− 4 groups. For all delay times, such two transients show a one-to-one correspondence of electron density, demonstrating that the SO2− 4 groups are the primary source of electron density transferred into the ZX⬘ plane. The change of electron density in the plane ZX⬘ is constant between 0.2 and 1 ps, while the charge in the channel undergoes pronounced oscillations 关Figs. 4共b兲 and 4共c兲兴. We conclude that the oscillations are connected with a concerted electron and proton transfer, i.e., the motion of a H atom, between the channel and the newly formed NH3 group, leaving the total electron density in the ZX⬘ plane constant. The transfer rate is controlled by the period of the 50 cm−1 Ag phonon, modulating the angular orientation of the NH3 groups and the oxygen-oxygen distance between opposite SO−4 groups. B. Ultrafast vibrational spectroscopy

The femtosecond x-ray studies were complemented by measurements of transient vibrational spectra of AS powder. The linear infrared absorption spectrum of such a sample is shown in Fig. 5共a兲共solid lines兲. The measured spectrum agrees well with that calculated from the reflectivity data of Refs. 33 and 34 共dashed line兲. The vibrational assignments in Fig. 5共a兲 are based on density functional theory 共DFT兲 calculations of vibrational spectra. The calculated oscillator strengths of the relevant vibrations of the initial AS structure and the product structure generated after photoexcitation are summarized in Table I. In the femtosecond experiments, we studied changes of the NH+4 ion bending absorption ␯4 centered at 1420 cm−1. The strength of this band is proportional to the number of NH+4 groups in the initial crystal structure. Upon photoexcitation, this band displays a pronounced absorption decrease. The time evolution of the absorption decrease 共bottom panel of Fig. 2兲 with a maximum amplitude ⌬A / A0 ⯝ 0.1 builds up within the 100 fs time resolution and decays on a slow time


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FIG. 6. Calculated electronic ground state energy along the reaction coordinate of the proton NH+4 + 共SO4兲2− ↔ NH3 + HSO−4 . Solid line: transfer of one proton in the unit cell of AS; dashed line: same curve for an ion pair in free space.

C. Mechanisms of structural change FIG. 5. 共a兲 Linear absorption of a ⬇1 ␮m thick AS layer 共black solid line兲 in the midinfrared spectral range 共red solid line: measured with femtosecond probe pulses兲. Dashed line: absorption spectrum calculated from reflectivity data of Refs. 33 and 34. 共b兲 The amplitude of the bleach of the NH+4 -ion bending mode corresponds exactly to the expected excitation intensity dependence for the three-photon absorption process. 共c兲 Loss function −␻I关1 / ⑀共␻兲兴共solid line兲 and spectrally integrated energy loss rate 共dashed line兲 as a function of the frequency of polar excitations of AS.

scale within 1 ns. The strong absorption decrease gives direct evidence for the reduction of the NH+4 concentration due to the induced structure changes. Experiments with different energies E of the pump pulses show that the absorption decrease scales with E3, in agreement with a three-photon excitation process 关Fig. 5共b兲兴. For the highest pump energy in Fig. 5共b兲, one estimates an excitation density of approximately 0.1, very similar to that in the x-ray experiments 共␩ = 0.06兲. It is important to note that the resulting infrared absorption change ⌬A / A0 = 0.1 is in good agreement with the expected fraction of NH+4 groups releasing a proton. Thus, the infrared data strongly support the picture of structural change derived from the x-ray study. A comment should be made on the vibrational bands of the product species generated by ultrafast electron and proton transfer 共cf. Table I兲. The NH3 bending absorption, the 1− SO stretch of SO1− 4 , and the OH stretch of HSO4 are too weak to be detected in an ultrafast infrared experiment. The SO stretch of the product HSO1− 4 displays a frequency and oscillator strength very similar to the SO stretch of the educt SO2− 4 . This band cannot serve as a probe of the structure change as the decrease of SO2− 4 absorption is compensated by the concomitant increase of HSO1− 4 absorption.

In order to get a deeper insight into the microscopic mechanisms underlying the concerted electron and proton transfer, we performed quantum chemical calculations of the AS electronic ground state for different proton arrangements. Such DFT calculations use three-dimensional periodic boundary conditions and include the long-range Coulomb interaction between different unit cells, i.e., the Madelung energy.35 They were performed as implemented in GAUSSIAN 36 03. The pure functional PBEPBE was applied together with the density fitting basis set 3–21G/auto. We focus on the potential energy along the reaction trajectory of the proton − NH+4 + SO2− 4 → NH3 + HSO4 . In the hydrogen sulfate group the proton is oriented along the connecting line between the oxygens of two opposing sulfate ions 关cf. Fig. 3共b兲兴. In Fig. 6, the potential energy is plotted along the reaction trajectory for a free molecular ion pair 共dashed line兲 and the same reaction in the crystalline environment 共solid line兲. Both potential curves show an almost barrierless trajectory between the two extremal proton positions with reaction energies of ⌬E = 1 and 0.67 eV,24 respectively. In the crystal the Madelung energy modifies the free ion scenario in a way that the potential minimum shifts from the NH3 + HSO−4 geometry to the NH+4 + SO2− 4 configuration, representing the ground state of the crystal. The ground state of the NH3 + HSO−4 geometry lies ⌬E = 0.67 eV higher. In our experiments, three-photon absorption of the 400 nm pump pulse generates approximately 0.001 electronhole pairs per unit cell. This number is distinctly smaller than the experimentally observed fraction of modified unit cells of ␩ = 0.06 共x-ray兲 and the related infrared absorption change ⌬A / A0 = 0.1. Thus, the excess energy of one photoexcited

TABLE I. Calculated oscillator strengths of all relevant educt and product vibrations.

Ion vibration

NH+4 共educt兲 bending

NH3 共product兲 bending

SO2− 4 共educt兲 SO stretch

SO1− 4 共product兲 SO stretch

HSO1− 4 共product兲 SO stretch

HSO1− 4 共product兲 OH stretch

km/mol

743

25

649

15

645

1


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electron drives the decomposition of a large number of NH+4 groups. This behavior is described appropriately by a solid state picture using the electronic bandstructure and the phonon modes of the AS crystal, rather than by using a model considering individual molecular entities. In the ionic AS, a high-energy electron loses its energy by exciting many vibrational quanta of strongly polar modes, including dissociation processes of protons from NH+4 ions. The energy loss rate of high-energy electrons can be calculated from the dielectric function of AS,33,34 using a standard approach.37 The loss function −␻I关1 / ⑀共␻兲兴关solid line in Fig. 5共c兲兴 determines the relative contribution of various polar lattice vibrations to the energy loss of an energetic electron. The dashed line shows the spectrally integrated energy loss rate as a function of frequency. The total rate is of the order of ⬇10 eV/100 fs, i.e., a photoexcited electron can lose its excess energy within 100 fs, the time resolution of our experiment. The dashed line in Fig. 5共c兲 shows that this energy is preferentially 共⬇70%兲 transferred to polar modes involving proton motions. Theoretical calculations based on a polaron model38,39 suggest that the excess energy is deposited in a volume given by the stopping length ᐉ ⬇ 100 nm times the typical wave packet size ⌬x2 ⬇ 10−20 m2 of the photoexcited electron 关cf. Fig. 1共f兲 of Ref. 38兴. Details of this model will be published elsewhere. The high-energy density of proton motions in such a small volume corresponds to a “hot” proton distribution in the local potential landscape around the formerly photoexcited electron. The extremely rapid deposition of excess energy into vibrations involving proton motions leads to an ultrafast elongation of the reaction coordinate and the formation of the NH3 + HSO−4 geometry with the hydrogen atom in the channel. During this process, the moving proton pulls electron density from the inner part of the sulfate group into its new position, resulting in the observed reduction of electron density on the sulfur atoms. In addition to the formation of the channel geometry, a coherent wavepacket motion of the 50 cm−1 Ag phonon of AS occurs after photoexcitation. This phonon motion modulates the distance between the SO4 oxygen atoms being part of the newly formed hydrogen bonds. The modulation of hydrogen bond length leads to a modulation of the barrier between the two potential minima in Fig. 6 and, thus, enables the coherent motion of electron and proton between the channel and the NH3 group 关cf. Fig. 4共b兲兴. Eventually, this motion is damped by vibrational dephasing of the Ag phonon wavepacket on a time scale of a few picoseconds. It should be noted that a full quantitative theoretical description of the reaction scenario would require highly accurate time-dependent electronic structure calculations including many-body effects. Such treatment is definitely beyond the semiquantitative description presented here. Nevertheless, our estimations based on standard quantum chemical tools enable us to draw a qualitative picture which is in agreement with the full set of x-ray diffraction and vibrational spectroscopy data. IV. CONCLUSIONS

In conclusion, we have introduced ultrafast x-ray powder diffraction to observe atomic rearrangements in molecular

crystals in real-time and derive transient charge density maps. Relocations of a small fraction of an elementary charge are resolved with high accuracy. Our pump-probe scheme with hard x-ray probe pulses from a laser-driven plasma source provides a spatial resolution of 30 pm and a time resolution of 100 fs. In ammonium sulfate, photoexcitation induces a concerted electron and proton transfer. The quantitative measurement of transient maps of electronic charge density reveals transient positions of both the heavier atoms and of hydrogen atoms, the latter switching periodically between their new and their original positions. Such high sensitivity makes our approach very promising for a broad range of future applications of femtosecond powder diffraction, including inorganic, organic, and biomolecular materials. ACKNOWLEDGMENTS

We thank Klaus Reimann 共Max Born Institute兲 for Madelung energy calculations and Uli Schade 共HelmholtzZentrum Berlin兲 and Erik Nibbering 共MBI兲 for help in taking 共transient兲 vibrational spectra. This work was supported in part by the Deutsche Forschungsgemeinschaft 共Grant No. SPP 1134兲. J. Jortner and M. Bixon, Adv. Chem. Phys. 106 共1999兲. D. Gust, T. A. Moore, and A. L. Moore, Acc. Chem. Res. 34, 40 共2001兲. Hydrogen Transfer Reactions, edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen 共Wiley VCH, Weinheim, 2007兲, Vols. 1–4. 4 C. Rischel, A. Rousse, I. Uschmann, P. A. Albouy, J. P. Geindre, P. Audebert, J. C. Gauthier, E. Förster, J. L. Martin, and A. Antonetti, Nature 共London兲 390, 490 共1997兲. 5 K. Sokolowski-Tinten, C. Blome, J. Blums, A. Cavalleri, C. Dietrich, A. Tarasevitch, I. Uschmann, E. Förster, M. Kammler, M. Horn-vonHoegen, and D. von der Linde, Nature 共London兲 422, 287 共2003兲. 6 M. Bargheer, N. Zhavoronkov, Y. Gritsai, J. C. Woo, D. S. Kim, M. Woerner, and T. Elsaesser, Science 306, 1771 共2004兲. 7 A. M. Lindenberg, J. Larsson, K. Sokolowski-Tinten, K. J. Gaffney, C. Blome, O. Synnergren, J. Sheppard, C. Caleman, A. G. MacPhee, D. Weinstein, D. P. Lowney, T. K. Allison, T. Matthews, R. W. Falcone, A. L. Cavalieri, D. M. Fritz, S. H. Lee, P. H. Bucksbaum, D. A. Reis, J. Rudati, P. H. Fuoss, C. C. Kao, D. P. Siddons, R. Pahl, J. Als-Nielsen, S. Duesterer, R. Ischebeck, H. Schlarb, H. Schulte-Schrepping, Th. Tschentscher, J. Schneider, D. von der Linde, O. Hignette, F. Sette, H. N. Chapman, R. W. Lee, T. N. Hansen, S. Techert, J. S. Wark, M. Bergh, G. Huldt, D. van der Spoel, N. Timneanu, J. Hajdu, R. A. Akre, E. Bong, P. Krejcik, J. Arthur, S. Brennan, K. Luening, and J. B. Hastings, Science 308, 392 共2005兲. 8 A. Cavalleri, S. Wall, C. Simpson, E. Statz, D. W. Ward, K. A. Nelson, M. Rini, and R. W. Schoenlein, Nature 共London兲 442, 664 共2006兲. 9 C. von Korff Schmising, M. Bargheer, M. Kiel, N. Zhavoronkov, M. Woerner, T. Elsaesser, I. Vrejoiu, D. Hesse, and M. Alexe, Phys. Rev. Lett. 98, 257601 共2007兲. 10 M. Braun, C. von Korff-Schmising, M. Kiel, N. Zhavoronkov, J. Dreyer, M. Bargheer, T. Elsaesser, C. Root, T. E. Schrader, P. Gilch, W. Zinth, and M. Woerner, Phys. Rev. Lett. 98, 248301 共2007兲. 11 C. von Korff Schmising, A. Harpoeth, N. Zhavoronkov, Z. Ansari, C. Aku-Leh, M. Woerner, T. Elsaesser, M. Bargheer, M. Schmidbauer, I. Vrejoiu, D. Hesse, and M. Alexe, Phys. Rev. B 78, 060404 共2008兲. 12 S. L. Johnson, P. Beaud, E. Vorobeva, C. J. Milne, E. D. Murray, S. Fahy, G. Ingold, and L. Johnson, Phys. Rev. Lett. 102, 175503 共2009兲. 13 P. Debye and P. Scherrer, Phys. Z. 17, 277 共1916兲. 14 B. E. Warren, X-ray Diffraction 共Dover, New York, 1968兲. 15 P. Coppens, I. I. Vorontsov, T. Graber, M. Gembicky, and A. Y. Kovalevsky, Acta Crystallogr., Sect. A: Found. Crystallogr. 61, 162 共2005兲. 16 F. Zamponi, Z. Ansari, M. Woerner, and T. Elsaesser, Opt. Express 18, 947 共2010兲. 17 E. O. Schlemper and W. C. Hamilton, J. Chem. Phys. 44, 4498 共1966兲. 18 S. Ahmed, A.M. Shamah, R. Kamel, and Y. Badr, Phys. Status Solidi A 1 2 3


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