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
Electronic mail: [email protected].
0021-9606/2010/133共6兲/064509/8/$30.00
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-
133, 064509-1
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Woerner et al.
J. Chem. Phys. 133, 064509 共2010兲
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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064509-3
J. Chem. Phys. 133, 064509 共2010兲
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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064509-4
Woerner et al.
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
J. Chem. Phys. 133, 064509 共2010兲
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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064509-5
Concerted electron and proton transfer
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
J. Chem. Phys. 133, 064509 共2010兲
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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064509-6
J. Chem. Phys. 133, 064509 共2010兲
Woerner et al.
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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064509-7
J. Chem. Phys. 133, 064509 共2010兲
Concerted electron and proton transfer
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
Downloaded 05 Nov 2010 to 141.16.91.19. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions
064509-8
99, 131 共1987兲.
S. Ahmed, A. M. Shamah, A. Ibrahim, and F. Hanna, Phys. Status Solidi
A 115, K149 共1989兲.
20
D. Swain and T. N. Guru Row, Inorg. Chem. 46, 4411 共2007兲.
21
T. Elsaesser and M. Woerner, Acta Crystallogr., Sect. A: Found. Crystallogr. 66, 168 共2010兲.
22
A. V. Desyatnichenko, A. P. Shamshin, and E. V. Matyushkin, Ferrolelectrics 307, 213 共2004兲.
23
J.-L. Kim and K. S. Lee, J. Phys. Soc. Jpn. 65, 2664 共1996兲.
24
U. Syamaprasad and C. P. G. Vallabhan, Solid State Commun. 38, 555
共1981兲.
25
A. Abu El-Fadl and S. Bin Anooz, Cryst. Res. Technol. 41, 487 共2006兲.
26
B. Andriyevsky, C. Cobet, A. Patryn, and N. Esser, J. Synchrotron Radiat. 16, 260 共2009兲.
27
N. Zhavoronkov, Y. Gritsai, M. Bargheer, M. Woerner, T. Elsaesser, F.
Zamponi, I. Uschmann, and E. Foerster, Opt. Lett. 30, 1737 共2005兲.
28
F. Zamponi, Z. Ansari, C. von Korff Schmising, P. Rothhardt, N. Zhavoronkov, M. Woerner, T. Elsaesser, M. Bargheer, T. Trobitzsch-Ryll, and
M. Haschke, Appl. Phys. A: Mater. Sci. Process. 96, 51 共2009兲.
29
M. Bargheer, N. Zhavoronkov, R. Bruch, H. Legall, H. Stiel, M.
19
J. Chem. Phys. 133, 064509 共2010兲
Woerner et al.
Woerner, and T. Elsaesser, Appl. Phys. B: Lasers Opt. 80, 715 共2005兲.
K. Adamczyk, M. Prémont-Schwarz, D. Pines, E. Pines, and E. T. J.
Nibbering, Science 326, 1690 共2009兲.
31
H. G. Unruh, J. Krüger, and E. Sailer, Ferroelectrics 20, 3 共1978兲.
32
H. G. Unruh, E. Sailer, H. Hussinger, and O. Ayere, Solid State Commun.
25, 871 共1978兲.
33
G. V. Kozlov, S. P. Lebedev, A. A. Volkov, J. Petzelt, B. Wyncke, and F.
Brehat, J. Phys. C 21, 4883 共1988兲.
34
D. De Sousa Meneses, G. Hauret, P. Simon, F. Brhat, and B. Wyncke,
Phys. Rev. B 51, 2669 共1995兲.
35
K. N. Kudin and G. E. Scuseria, Chem. Phys. Lett. 289, 611 共1998兲.
36
M. J. Frisch, G. W. Trucks, H. B. Schegel, et al., GAUSSIAN 03, Revision
C.02.
37
B. K. Ridley, Quantum Processes in Semiconductors, 3rd ed. 共Clarendon,
Oxford, 1993兲.
38
P. Gaal, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey,
Nature 共London兲 450, 1210 共2007兲.
39
W. Kuehn, P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey,
Phys. Rev. Lett. 104, 146602 共2010兲.
30
Downloaded 05 Nov 2010 to 141.16.91.19. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions