Femtosecond Diffraction with Ultrabright Electrons: Shooting Atomic Movies on Location
Femtosecond Electron Diffraction (FED) has availed atomic resolution of structural changes as they occur, essentially watching atoms move in real time. It combines temporal resolution on the hundred femtosecond (fs) time scale – a time scale typically only accessible by time-resolved optical spectroscopy – with real-space structural information on the atomic scale.
The visualization of atomic motions has long been used as a gedanken experiment to develop a conceptual basis for various phenomena. One can look to the typical transition states or proposals of reactive intermediates in organic chemistry as classic examples of this thought experiment. Similar examples can be found in biology in pondering how protein structure affects transition states at active sites, unwinding of DNA etc. Within physics, there are numerous examples from Coulomb explosions to atomic displacements involved in phase transitions and phonon propagation. This classic thought experiment has long been considered out of the realm of experiment. With the recent development of femtosecond electron pulse sources with sufficient number density to execute nearly single-shot structure determinations, this experiment was first realized (see Siwick et al., Science 2003, in particular Figure 1). These first grainy frames are very similar to the first Daguerreotypes in photography. It was the first time to capture sufficient diffraction orders to fully resolve the structural changes at the atomic level of detail (see Siwick et al., Science 2003, in particular Figure 2B for the real space transform). One could literally watch the onset of the liquid state with the key motions involving shear or transverse motions. One of the definitions for the onset of the liquid state is the inability to support shear motions, with the rms motions exceeding the transverse barrier and here we see these motions directly.
The First Atomic Movies – A Personal Account (RJDM). This first atomically resolved depiction of a structural transition (or “molecular movie”) was even more interesting that it may seem at first glance. Melting was driven under rather special boundary conditions involved with strongly driven phase transitions. The particular question being addressed by this work dates back to a long standing debate in the 1930’s concerning the onset of the liquid state under extreme pressures and temperatures (see Miller, Science 2014 for a historical account). This issue also has ramifications for understanding the state of matter in other extreme conditions such as the interior of planets or stars. To put this question in proper context, consider the melting of a block of ice. We all know ice melts from the surface in a process referred to as heterogeneous nucleation. We also know that if we direct a blow torch to the ice it will melt faster. What if you could heat up the ice so fast that based on extrapolations of heating rates and melt velocities, you would predict the system should melt faster than the atoms could move (or more correctly faster than the speed of sound)? Now, that is an interesting question.
The answer can be gleaned from this data directly without a high level of analysis (see Siwick et al., Science 2003, in particular Figure 1). The experiment used a special “blow torch”, in this case a femtosecond laser system, to achieve heating rates approaching 1015 K/s. At 500 fs, you can see high order diffraction rings illustrating that the Al is still in its nascent face centered cubic (FCC) lattice. At 1.5 ps, you can see these rings become dimmer as the initially photoexcited electrons lose energy to lattice phonons. The increase in rms motion of the atoms reduces the lattice coherence and corresponding diffraction as described by temperature dependent Debye-Waller factors. The most astonishing event happens between 2.5 ps and 3.5 ps. There is an incredibly fast lattice collapse in which covalent bonds are broken and the face centered cubic coordination number goes from 12 to an ensemble average of 10 for the unstructured shell like structure of a liquid. Once reaching the critical point for this degree of superheating, the whole melting process occurred within 1 ps. This time scale has to be fully appreciated. This is 10 times faster than this process could occur through normal heterogeneous nucleation. The melting process was literally occurring faster than the speed of sound for heterogeneous nucleation. Rather than melting from the surface in an “outside-in” fashion (heterogeneous nucleation), the system was melting from the “inside-out”. This was the first atomic view of the long predicted process of homogeneous nucleation. From the real space transform, it was possible to discern that the largest changes involve shear atomic motions with the collapse of the transverse barrier as part of forming the liquid state. As a physical chemist, this was a very gratifying observation as the importance of shear type motions in formation of the liquid state is a key concept taught to understand nucleation growth and phase transitions. Now we can see this process directly at the atomic level.
Most important, these observations showed how to control nucleation growth to as few as 10 atoms and avoid cavitation induced shock waves and thermal damage in laser driven ablation. Based on this new insight, a picosecond IR laser tuned to the OH stretch of water in tissue was developed for laser surgery with the correct temporal profile to restrict nucleation growth. This method has now been shown to be capable of cutting tissue without scar tissue formation, or ionizing radiation effects, and as an added bonus to give fully intact protein signatures of tissue. The big surprise was the lack of excessive fibroblast formation that leads to scar tissue formation (see Amini-Nik et al PLoS 2010). The importance of this development is readily appreciated. In this respect, the promise of the laser for achieving the fundamental (cellular) limit to minimally invasive surgery has now been achieved with a number of promising applications identified. Generally it is difficult to trace the thread from basic science to societal benefits. Here the connection is clear.
Subsequent work in the area has primarily focused on photoinduced phase transitions (see Ernstorfer et al., Science 2009, Harb et al., Phys. Rev. Lett. 2008, Sciaini et al., Nature 2009, Eichberger et al., Nature 2010 etc.). One has to appreciate that on the femtosecond time scale of the photoexcitation process, the lattice is effectively frozen. The optical transition to a higher lying electronic state instantaneously changes the electron distribution relative to the time scale of nuclear motions. We now have a unique opportunity to directly observe the effects of changes in electron distribution and electron correlation energies on bonding, or the many body potential defining the bound state, by observing the atomic motions in response to these changes. The observation of structural transitions at this fundamental space-time limit in terms of following the nuclear coordinate have led to new insights and in many cases surprises. These studies include strongly driven phase transitions involved in nonthermal melting or electronically driven nucleation effects, to creating states of warm dense matter with a counterintuitive apparent increase in bond strengths (so called bond hardening) at high excitation levels, to the direct observation of highly cooperative many body physics ¾ to the extent of providing coherent responses to weak perturbations of strongly correlated electron-lattice systems. With respect to the latter case, the highest quality atomic movies of structural transitions have in fact been observed in layered compounds that exhibit interesting 2D effects on electron correlation energies and bonding (see Eichberger et al., Nature 2010). Charge Density Waves (CDW) are examples in which small modulation in plane leads larger wavefunction overlap in the plane and to higher overall lattice stability. By photoinducing a change in charge distribution, this delicate balance in forces between intra and interplane coupling is modified and the lattice relaxes to a higher symmetry state. The best example of this is the movie of the photoinduced suppression of the CDW modulation in TaS2 where one can observe a very dramatic effect in which both the suppression and reformation of the CDW occur at the fundamentally fastest possible speeds. This work has been extended to other related systems such as TaSe2 where one observes similar effects however with very interesting differences due to different inter-plane couplings (see Miller Science 2014 for full references to important related work and to put the above into proper historical context). When one observes such a collective effect at the atomic level, there is an immediate appreciation of the highly cooperative nature of strongly correlated electron-lattice systems. The visual connection to the many body effects helps to drive home the operating physics in a single measurement. Effectively, it is a direct observation of the electron-lattice coupling. These observations should then provide rigorous benchmarks for high level theory that together will help advance our understanding and control of the novel properties of strongly correlated electron-lattice materials.
From a chemistry perspective, the real power of high bunch charge (brightness) electron sources has been recently demonstrated using femtosecond crystallography to follow the photoinduced reaction dynamics of organic systems, the mainstay of chemistry. This class of materials invariably has low thermal conductivities and involves large amplitude motions as part of the reaction dynamics. Both effects conspire to greatly limit the sampling rate and number of photocyles. In addition, organic systems have much more complex structures than the solid state systems with simple unit cells discussed above. Further improvements in source brightness were essential to open up the study of organic systems. In what could be considered to be the first truly molecular movie, an extension of rf pulse compression methods enabled the capture of the photoinduced structural changes in the interesting organic system EDO-TTF (see Gao et al., Nature 2013).
This system can be photoswitched from insulating to metallic properties involving formally a charge transfer process strongly coupled to nuclear modes stabilizing the change in charge distribution. Inspection of the differences between the insulating and metallic structures shows that the formation of the metallic state involves the flattening of the EDO-TTF rings. The displacement of a bending mode toward this planar configuration would lead to an increase the π-π wavefunction overlap and electronic delocalization as part of increasing the electronic coupling between molecules towards the formation of a conduction band. Within a conventional transition state picture, one would naturally expect the bending coordinate to be the dominant mode in stabilizing the charge displacement and directing the structural transition towards the onset of metallic properties. If this was a thermally propagated structural transition, the saddle point or transition state would be expected to be defined by the halfway displacement along this mode. However, this simplified line of thinking only works for few atom systems. Considering just the molecules within a single unit cell, this problem involves over 280 different degrees of freedom or dimensions. The motion along any one could in principle contribute to stabilizing the photoinduced charge separated state. However, there was a major surprise in store in the direct observation of the photoinduced structural changes leading to the onset of metallic behavior. Through a correlation analysis of the different modes connecting the initial and final structure, it was found that all of diffraction orders, using multiple crystal orientations, could be fit by the displacement of just 3 reduced modes. One of which was in fact the bending mode but the dominant mode involved motion of the heavy PF6- counterion. In hind sight, this observation is understandable as the photoinduced change in electron distribution will lead to a change in the local field that will exert a force on the counterion. An even bigger surprise to a certain extent was that the 3 different modes needed to map the reaction trajectory could have had been completely be independent. The displacement along any of these reduced dimensions could have had any sign or magnitude, however, it is clear that there are strongly correlated motions involved. The projections along the 3 reaction coordinates (see Miller, Science 2014 Figure 4) look like shadow projections of one another. This observation means that the slowest, most strongly coupled mode, is the dominant mode directing the system to the product surface. If higher frequency modes were dominating the slowest mode could not track the changes in potential and the modes would not seem as strongly correlated as they clearly are. The slowest mode is expected to be the PF6- counterion. This is a large counterion that will encounter significant steric effects as it moves in response to the charge separation. As it moves in response to the reaction field, other atoms will likewise be displaced by these steric forces. As the strongest coupled mode to the charge displacement, it would be this same motion, thermally excited, that would direct the system to the new structure for a thermally propagated structural transition. In this respect, the empirical connection of material properties for this class of compounds to the counterion can now be explained. Its motion constitutes a strongly coupled mode that clearly mixes with the EDO-TTF moieties in defining the potential energy surfaces of the system.
To me, these observations were eye-opening. One typically uses an approximate frozen slice of a many body potential to discuss reaction coordinates and get a feel for the forces and types of motion involved in directing the process. This line of thinking is out. The modes are dynamically coupled and it is clear that one cannot intuitively guess which modes are involved or the relative degree of coupling. In principle, time dependent ab initio theory can provide the information on the relative degree of coupling between the different possible motions. However, even with advances in computation power, even the highest level of time dependent ab initio theoretical methods have to use truncated model systems with fewer than 30 atoms to approximate the problem. In this respect, theoretical calculations of reaction coordinates are generally projected along the modes most strongly coupled to the reaction coordinate. Given the level of approximations required in treating electron correlation energies and highly simplified model structures, the observed reduction in dimensionality even within full modal calculations might be considered to be an artifact of the basis used to model the reaction coordinate. From these experiments, we see that for even very complex systems there is in fact an enormous reduction in dimensionality that again is the key to how chemistry reduces to transferrable concepts in the form of reaction mechanisms.
The first study of a strictly chemical reaction with the necessary space-time resolution to directly observe the correlated atomic motions through barrier crossing regions is that of the photoinduced cyclization-ring opening reaction of diarylethene (see Jean-Ruel et al., J. Phys. Chem. B 2013). This study really highlights the importance of using ultrabright electron sources. This system was specifically designed by Erie and co-workers to serve as a photochromic material, capable of undergoing over 10,000 photon cycling processes and would appear to be an ideal candidate for even single electron pulse probes. However, this degree of photocycling is only for low fractional excitation. At the excitation levels needed to observe the structural changes above background, even this system is only capable of approximately 100 photocycles before irreversible changes occur. There is only a finite quantum yield for any given process before a side reaction occurs. These experiments were simply not possible without the development of ultrabright electron sources.
This system provides a classic example of a cyclization reaction with conserved stereochemistry. As in the case of EDO-TTF, there is an enormous reduction in the nuclear degrees of freedom coupled to the reaction coordinate. A detailed correlation analysis of the femtosecond time resolved diffraction patterns for the ring closing reaction found that there is an initial motion occurring around the central bond that involves the whole molecule and brings the labile carbon atoms involved in the bond formation into close proximity for increased wavefunction overlap. The observed time scale from optical measurements hinted at the prospect. It was only possible to connect the dynamics to the actual atomic displacements based on the femtosecond time resolved diffraction data. The initial motion is best approximated by the lowest frequency 55 cm-1 found in a vibrational mode analysis using density function theory. This is the key mode that directs the system to the seam in the reaction coordinate. The question is how does such a spatially delocalized mode lead to the highly localized motions needed to close the ring? Again there is a surprise. These latter displacements leading to bond formation and ring closing occur on a picosecond time scale. From a time dependent ab initio calculation using a truncated model system, these relaxation processes involve additional seams connecting the product and ground state from the excited state. In this case, the time scale for the relaxation along the reaction coordinate is convolved to this transition probability such that the degree of correlation or mode coupling as observed in EDO-TTF is not so apparent. Experimentally, it was still possible to cast out from the fs diffraction data a series of localized rotational motions that mix to produce the ring closed form. The ultrafast nature of this process still clearly separates the possible modes that are involved and highlights the importance of sufficient space-time resolution to connect the initial low frequency mode to the localized rotational coordinates. This atomic level view of the cyclization process gives remarkable insight into the highly reduced dimensionality of the problem and the key modes involved in terms of directing this process and conserving stereochemistry.
We now have had our first look at the enormous reduction in dimensionality that occurs in molecular systems during structural transitions. Each reaction mechanism undoubtedly has a well defined power spectrum as part of this reduction in dimensionality at saddle points along the reaction coordinate. It is the mixing of modes under the highly anharmonic conditions at these positions in nuclear configuration space that leads to the localized motions and concepts of breaking the weakest bond that chemists have empirically learned to control. This is the “magic of chemistry” that even very complex systems can be reduced down to simple parameters for which we can generate general rules. In terms of advancing our ability to direct chemical process, we now have a means to directly observe these far from equilibrium motions and provide rigorous bench marks for theory. We may well uncover the basic understanding needed to gain control over barrier crossing processes to rival that of biological systems.
The above research program was initiated by our observations of the involvement of collective modes in directing biological processes at the molecular level back dating back to 1989 (see Genberg et al.). We could to some extent show that these modes were important if not dominant but we could not assign the specific, highly correlated motions, which are undoubtedly linked to the highly optimized structures of proteins. There is no spectroscopy that can cast out these highly damped low frequency modes. The same issue holds for observing the far from equilibrium motions involved barrier crossing events we call chemistry. We now have the tools in place to observe these motions directly – at the atomic level of detail. The main quest of the group is to directly resolve the structure-function relationship of biological molecules, i.e. how chemistry is wired up to direct biology. This is the main quest of the group. We are getting close.