Time-Resolved Single-Crystal X-Ray Crystallography

Abstract

In this chapter the development of time-resolved crystallography is traced from its beginnings more than 30 years ago. The importance of being able to “watch” chemical processes as they occur rather than just being limited to three-dimensional pictures of the reactant and final product is emphasised, and time-resolved crystallography provides the opportunity to bring the dimension of time into the crystallographic experiment. The technique has evolved in time with developments in technology: synchrotron radiation, cryoscopic techniques, tuneable lasers, increased computing power and vastly improved X-ray detectors. The shorter the lifetime of the species being studied, the more complex is the experiment. The chapter focusses on the results of solid-state reactions that are activated by light, since this process does not require the addition of a reagent to the crystalline material and the single-crystalline nature of the solid may be preserved. Because of this photoactivation, time-resolved crystallography is often described as “photocrystallography”.

The initial photocrystallographic studies were carried out on molecular complexes that either underwent irreversible photoactivated processes where the conversion took hours or days. Structural snapshots were taken during the process. Materials that achieved a metastable state under photoactivation and the excited (metastable) state had a long enough lifetime for the data from the crystal to be collected and the structure solved. For systems with shorter lifetimes, the first time-resolved results were obtained for macromolecular structures, where pulsed lasers were used to pump up the short lifetime excited state species and their structures were probed by using synchronised X-ray pulses from a high-intensity source. Developments in molecular crystallography soon followed, initially with monochromatic X-ray radiation, and pump-probe techniques were used to establish the structures of photoactivated molecules with lifetimes in the micro- to millisecond range. For molecules with even shorter lifetimes in the sub-microsecond range, Laue diffraction methods (rather than using monochromatic radiation) were employed to speed up the data collections and reduce crystal damage. Future developments in time-resolved crystallography are likely to involve the use of XFELs to complete “single-shot” time-resolved diffraction studies that are already proving successful in the macromolecular crystallographic field.

1 Introduction

Over the last century, single-crystal X-ray crystallography has developed into the optimum method for determining the molecular structure of materials in the crystalline state and, as this volume of Structure and Bonding shows, now underpins many aspects of the physical and life sciences. What the standard crystallographic method provides is a full three-dimensional picture of the structure of the starting material and of the product of the reaction if both can be obtained in a crystalline form. What it does not do is provide a pathway by which the starting material is converted into the product, and, since the reaction may not occur in the solid state, the immediate relevance to a solution or gas phase chemical reaction may not be apparent [1].

The reason for this inability to follow a solid-state chemical process is because the single-crystal X-ray crystallographic experiment is both space and time averaged. In terms of space averaging, every unit cell in the crystal contributes to the diffraction pattern obtained, so if some molecules within the crystal are changing and others are not, an average of the structures will be obtained. This is commonly observed in crystal structures when, for example, various parts of the molecule adopt different orientations in different unit cells or lattice solvent molecules adopt different orientations; this is termed disorder [2]. The crystallographic experiments are also time averaged. Although a single X-ray photon may interact with the electron cloud that surrounds an atomic nucleus in crystal in 10⁻¹⁸ s, it has to be remembered that in a single-crystal X-ray crystallographic experiment, the whole crystal has to be sampled. Typically, the crystal may contain 10¹⁵ molecules or more, and even with modern laboratory-based diffractometers, the sampling process takes between minutes and hours, so that the crystal structure obtained is an average over the whole duration of the data collection [3].

A further problem associated with following chemical or biological processes within a single crystal is the retention of crystallinity throughout the process since a loss of crystallinity caused by degradation of the crystal means that a single-crystal diffraction experiment is no longer viable. This limits the type of reaction that can be followed. Adding a reagent to a crystal to facilitate a chemical reaction will usually destroy the crystal, although there are an increasing number of examples, often associated with crystals of framework structure materials, where small molecules (liquids or gases) can be introduced into the crystal and can undergo a reversible or irreversible physical or chemical process [4,5,6]. A much easier way of facilitating a single-crystal-to-single-crystal reaction is to use an external medium such as irradiation with light [7,8,9], application of pressure [10,11,12] or change in temperature [13,14,15] which is less likely to disrupt the crystalline lattice, and such experiments have been becoming more feasible over the last few decades because of advances in technology.

Over the last three decades, developments in synchrotron facilities, X-ray detectors, cryogenic apparatus, laser technology, computing power and data storage capacity have all enabled single-crystal X-ray studies to provide information about solid-state reactions and dynamic processes that occur in crystals. Now chemical and biological processes that occur in crystals can be monitored in “real time”, and three-dimensional structural information on species that exist in the solid state for only fractions of a second may be obtained [16,17,18]. Regarding the external media for inducing reactions in crystals, the use of “light” has proved the most popular and is arguably the least likely to cause crystal degradation. Photochemically induced chemical reactions are relatively easy to control. The size, shape and intensity of the incident beam can be controlled using a wide variety of optical equipment and, when using a tuneable source, the wavelength can be varied to match the process involved. This has led to the development of “photocrystallography” [19], a term attributed to Philip Coppens [20], one of the pioneers in the area, although the crystallography of photoactivated species is also included in the description of “photosalient” processes [21] or, more generally, as “time-resolved” crystallography. With all the technological developments, the speed of a full single-crystal X-ray data collection has been reduced to minutes particularly when a high-intensity synchrotron source is used. This has provided the opportunity to undertake a whole range of new crystallographic experiments that can follow the dynamics of a chemical process and obtain a full three-dimensional picture of photoactivated species. This chapter will highlight some of the technological and experimental results that have been obtained in the first 20 years of the twenty-first century.

Of all the technological advances that have facilitated the growth of photocrystallography, it is the more general availability of synchrotrons as research tools that has proved to be most important. They have been used to apply a range of analytical techniques to study chemical and biological samples by providing high-intensity electromagnetic radiation as the probe. A synchrotron is a storage ring in which electrons are accelerated around the ring at speeds approaching the speed of light and, as a consequence, are subject to relativistic effects. This causes the electrons to circulate around the ring in discrete bunches. The resultant radiation is used in different experimental stations which are at the end of beamlines radiating out tangentially from the storage ring. Some of these beamlines are dedicated to crystallographic experiments and use X-rays with wavelengths in the range 0.4–2.5 Å [22]. A schematic representation of a synchrotron ring is illustrated in Fig. 1 which shows how the electrons are initially accelerated from their source through a linear accelerator, through a booster synchrotron into the main storage ring where their circular orbits are controlled by magnetic fields and their energies are controlled by insertion devices which guide the X-ray beam to the experimental hutch where the X-ray diffractometer sits.

Fig. 1

A schematic of a synchrotron ring showing a tangential beamline

2 Photocrystallographic Methodology

The type of photocrystallographic experiment that can be carried out is dependent on the lifetime of the photoactivated species that is being studied. The lifetimes of the various processes can range from hours to femtoseconds as are summarised in Fig. 2 so that the type of experiment that can be carried out and the results that can be obtained must be considered carefully beforehand. The photoactivated “excited state” (ES) must exist for longer than the time required for the data collection, although it can be maintained by repeatedly or continuously pumping light into the system. The experiment and the chemical process that is being studied must be brought on to a common timescale for the experiment to be successful. This can be achieved either by slowing the photoreaction down to the timeframe of the crystallographic experiment or speeding up the experiment to match the lifetime of the excited state species. The photoreaction can be slowed down by effectively using trapping strategies, e.g. chemical- or cryo-trapping methods, which involve a sudden change in the reaction conditions in order to “freeze” the reactant in a transient state for a period of time long enough to permit the analysis. While there are some advantages to this approach, the trapping process may change the natural progress of the solid-state reaction. To be sure of observing the true reaction pathway, it may be advisable to adopt the second strategy and speed up the data collection methodology so that the photoinduced process can be followed in real time.

Fig. 2

Timescales of the dynamic processes that occur in chemistry

In summary, the shorter the lifetime of the photoexcited species, the more challenging is the photocrystallographic experiment that is required to characterise the structure of the excited state. Photocrystallographic experiments can be characterised into three types depending on the lifetime of the excited state species.

2.1 Steady-State and Pseudo-Steady-State Methodologies

At longer timescales, from milliseconds upwards, “steady-state” or “pseudo-steady-state” experiments can be carried out using standard single-crystal X-ray diffraction methods [8, 18, 23] with monochromated X-ray radiation. The steady-state methodology is used typically to study metastable excited states, those with lifetimes of hours up to infinity, if the excited state is generated and maintained at the appropriate low temperature [24]. The metastable state is generated, at a given temperature, by irradiating the sample for a period long enough to maximise the conversion from the ground state. The irradiation is then stopped, and a standard single-crystal X-ray data collection is performed. Under these experimental conditions, there are no concerns about sample heating from the irradiation source since this has been switched off prior to the start of the data collection. This process is illustrated in Fig. 3a where the ground state, unexcited structure is collected first (in order to provide a benchmark against which changes in the photogenerated excited state can be compared), then the excited state is generated with light irradiation and finally the structure is redetermined using X-rays, the light source having been turned off. Pseudo-steady-state methodology is used to study samples with slightly shorter excited state lifetimes, usually in the range of milliseconds to minutes. In these experiments the crystalline sample is irradiated throughout the data collection to maintain a constant excited state occupancy, as illustrated in Fig. 3b. This shows the excited state being pumped up to a “steady state” with repeated pulses of light before the X-ray data collection commences, the excited state being maintained throughout the data collection by continued pulses of light. Thus, this method requires an effective means of illuminating the crystal fully throughout the data collection without the movement of the diffractometer blocking the illumination source at any point. Since the sample is irradiated throughout the experiment, heating effects at the sample resulting from the irradiation source may result and have to be mitigated.

Fig. 3

Schematic diagrams to show the timing sequences used in the different types of photocrystallographic experiments: (a) steady-state methods, (b) pseudo-steady-state methods and (c) pump-probe methods. Taken from Ref. [18] with permission from Elsevier

2.2 Stroboscopic or Pump-Probe Methodologies

In order to study transient photoinduced species, with lifetimes of microseconds and below, “stroboscopic” or “pump-probe” photocrystallographic methods are required as shown in Fig. 3c, the sample being repeatedly re-excited and only probed by the X-rays when in the excited state. The experiments generally require short-duration light and monochromatic X-ray pulses to be generated that are synchronised to arrive at the sample position in a specific time sequence [25] or to use a time-gated detector which is synchronised with the light pulses [26] so that X-ray data is only recorded when the crystal is activated. The light source for these experiments is usually a pulsed laser that generates pulses on the nanosecond or picosecond timescale. The X-ray source can be pulsed in a number of ways. Initially, for experiments involving crystalline species with lifetimes in the nanosecond to microsecond range, the X-ray pulses were generated by placing a mechanical chopper in the incident beam [25, 27] which interrupts the beam so that the X-rays are only “on” in synchronisation with the laser pulse. When using these short pulses, the X-ray flux that impinges on the crystal is limited, and in order to overcome this problem, high-intensity synchrotron radiation is normally required. Even with this higher X-ray intensity, many pump-probe laser and X-ray cycles are required per data collection frame to build up a sufficiently strong diffraction image, and many frames are required in order to obtain a complete X-ray data set. The repeated pumping and probing usually has a detrimental effect on the crystalline sample, and significant sample heating effects may also be a problem.

One development to overcome the crystal degradation problem has been devised and used effectively in the macromolecular crystallographic community, and that is the pump-multi-probe method based on the Hadamard transformation [28]. In the conventional pump-probe approach described above, the photoactivation event is initiated by a laser pulse and then probed at a later time by an X-ray pulse, so that every laser (pump) pulse is followed by a single probe (X-ray) pulse after a predetermined time delay (see Fig. 4a). Therefore, to measure n time points, n pump-probe pairs are required. In contrast, in the Hadamard approach, each pump pulse is followed by a sequence of probe pulses, and the total signal from each sequence is recorded in a single measurement (see Fig. 4b). The sensitivity of the experiment is thus defined by the total number of photons in the complete probe sequence, with the time resolution defined as the total probe sequence length divided by the number of pulses. This method no longer limits the time resolution that can be achieved to the brilliance of the X-ray source by summing the time points across the probe sequence. It also gives an improved signal-to-noise ratio because of the larger number of photons recorded during the measurement.

Fig. 4

(a) The time sequence for the classical pump-probe method showing three time delays. (b) The simplest Hadamard pulse sequence set up to measure three time points. (c) The 3 × 3 Hadamard S matrix showing how each row produces a single summed intensity for each reflection on the detector (w₁, …, w_n) forming the vector W. Figure reproduced from Ref. [28] with permission from Nature Methods

As in standard pump-probe experiments, n pump-probe sequences are required to measure n time points. The pattern of the probe sequence is represented as rows of a nxn matrix (S) obtained from the Hadamard sequence. The simplest case is shown in Fig. 4b where each row of the matrix (and the probe sequence) is obtained by cycling by one element from the previous row to the left (see Fig. 4c).

For the Hadamard time-resolved experiment, the photoactivation is initiated and then the complete probe sequence (first row of the S matrix) is recorded as a single image. This process is repeated on the sample after relaxation but with the probe sequence now defined by the second row of the S matrix, until all the rows have been completed. The resulting encoded signals from the n excitations are then collated to form a vector W of length n. The time-dependent signal, I_t, is then obtained by reversing the probe sequence encoding by multiplying the vector W by the inverse of the matrix S, so that I_t = S⁻¹W. A time-resolved crystallographic Hadamard experiment has been dubbed a HATRX experiment.

2.3 Laue Methods

The time-resolved experiments described so far have used monochromatic X-ray radiation. An alternative way of overcoming the limited flux in short-duration time-resolved crystallographic experiments is to change from monochromatic radiation to the Laue method where polychromatic X-ray radiation is used [29, 30]. The main advantage of the Laue method is the broader energy range used, compared with the narrow beam from a monochromator. This results in a substantial increase in intensity. The method used in both molecular [31] and macromolecular [32] crystallographic experiments is often called the pink-Laue method as “pink” indicates quite a small range of wavelengths as opposed to all the wavelengths available in the full “white” beam. The pink-Laue method eliminates the need for the thousands of pump-probe cycles required in the stroboscopic method used for monochromatic data sets [33]. Because of the reduced time for the experiment, the crystal deterioration caused by laser and X-ray exposure may be reduced and the heating caused by the repeated laser pulses may also be reduced. In the best possible case, a single synchrotron pulse is sufficient to record a good enough diffraction pattern to solve the crystal structure [34]. In other examples several pump-probe cycles are required before a sufficiently intense diffraction pattern is obtained.

For pink-Laue data, a wavelength dependence correction has to be applied to the intensity data, because diffraction spots are being obtained from many wavelengths, and there also has to be a fitting of intensities of equivalent reflections that appear. With molecular crystals having relatively small unit cells, this scaling of intensities is challenging because there are relatively few of them. To avoid this difficulty, the RATIO method can be used [35], a method that will be explained in further detail below. A second complication with pink-Laue data is that there is a steep slope of wavelength distribution on the high-energy side of the pink-Laue spectrum. A small change in the unit cell dimensions on exposure, as would be expected with excitation, might lead to anomalous values of the on/off ratios of reflections scattered by wavelengths in this narrow region. The effect would be small if the conversion percentage from the ground to the excited state is small and also if the temperature increase is small. The affected reflections can be identified in the analysis of equivalent reflections and confirmed by checking the calculated wavelength from the Bragg angle and the hkl index after indexing. These can be removed from the averaging procedures and used to establish the structural changes that have taken place in the excited state.

As indicated above, the most sensitive measure of the structural change in a crystal when it is photoactivated into an excited state is the observed change in intensity of each of the reflections. In the RATIO method [35], this intensity difference is identified by using the on/off ratios as the observables in the activated structure refinement program LASER [36]. As explained in the previous paragraph, the advantage of the RATIO method when used in a Laue data collection is the elimination of the need to have a spectral curve to determine the wavelength at which each reflection is observed. To exploit the method, the laser-on and laser-off intensities for each reflection need to be collected immediately after one another. This eliminates variations in the intensity of the X-ray beam over time. This, in turn, adds an error to the intensity of the individual reflections and also eliminates the effect of any slow deterioration of the crystalline sample. In addition, slight differences in the absorption correction may occur if the laser-on and laser-off reflections were collected at different times in different settings. Finally, scaling is not required as the paired frames are collected at the same temperature and under the same conditions.

Even with these advances, it is often necessary to use multiple crystals of a crystalline sample, because of crystal deterioration, in order to obtain a complete data set. Scaling of the data sets is then required before electron density maps can be calculated and the structure solved and refined. Various scaling methods have been applied from the simplest form which is based on the fractional change of each of the reflections on exposure to light to more sophisticated weighted least-squares scaling [31, 37].

Once the Laue data has been collected and the data set corrected, as with monochromatic photocrystallographic experiments, it is usual to compute a Fourier photodifference map to evaluate the structural changes that occur upon photoexcitation [38]. When using the RATIO method, the photodifference Fourier map is simply based on the difference between the observed laser-on and laser-off structure factors [29, 39]. These calculations are based on the fact that the crystal does not change phase (crystal system or space group) upon excitation which is generally true because percentage conversions from ground to excited state structures upon excitation are low for the short-lived species generated.

In an alternative approach to the pump-probe experiments, rather than synchronising the laser pump pulses with X-ray probe pulses generated by use of a mechanical chopper, new detector technology has allowed the X-ray detector to be synchronised with the laser pulse so that the detector only records X-ray intensity while the laser is on (or records after a designated time delay). These new detectors have fast read-out times, have the ability to internally stack series of recorded images and, most importantly, provide very fast and reliable “gating” affording fine control of when the detector is recording or not. With the efficiency of these detectors, some of the limitations of the X-ray flux can be minimised, and it is possible to consider the use of laboratory X-ray sources instead of synchrotrons for some longer lifetime photocrystallographic experiments. The use of a gated hybrid pixel detector, mounted on a conventional laboratory X-ray diffractometer, has been proven in an analysis of the photoinduced linkage isomerism of sodium nitroprusside [26]. The light-induced intensity variation between ground and excited states was detected at the 1% level, caused by the photoswitching of the nitrosyl group, and this change could be detected in a 6 microsecond window. The experimental approach is illustrated in Fig. 5. In the experiment a continuous X-ray beam impinges on the sample, and during the pump-probe cycle, with the structure continuously changing, the scattered diffraction pattern is sampled by the gated detector. The X-ray signal is only detected during a short adjustable window X(t). The laser pulse serves as a trigger for the gating of the detector and synchronisation with a tuneable time delay Δt. The maximum time resolution possible is also dependent on the electronic response time of the X-ray detector.

Fig. 5

A continuous X-ray beam with a scattered signal sampled by a fast-gated detector (only one delay time shown). The figure is reproduced from Ref. [26] with permission from the IUCr

With the gated hybrid pixel detector, the photon counting statistics determine the quality of the data, and there is no dark current or read-out noise as with a conventional CCD detector. The signal acquisition is defined by a tuneable measurement time window (X(t) in Fig. 5) whose temporal width is only limited by the detector response time, which is the order of 100–200 ns. Also, with the pixel detector, it is possible to have a number of simultaneous measurement windows, with different delay times that can be acquired by the detector at the same time. This means that multiple time-resolved experiments could be carried out at the same time.

2.4 Sub-picosecond and XFEL Methodologies

The interest in studying chemical and biological processes with shorter and shorter lifetimes using time-resolved crystallographic techniques continues to grow as technological advances make the picosecond and sub-picosecond time regimes accessible. The structure of the synchrotron beam itself can help with these developments. The relativistic effects on the electrons circulating the storage ring at speeds approaching that of light mean that they orbit the ring in discrete bunches [22]. Thus, the synchrotron radiation produced is naturally pulsed with a repetition rate that is determined by the period of the electron orbit around the ring. For third-generation synchrotrons, this is typically in the nanosecond to picosecond time regime. Therefore, pump-probe time-resolved experiments on species with lifetimes within this timeframe can be carried out without the need for a mechanical or electronic shutter to pulse the X-rays, and the laser repetition rate is synchronised with the repetition rate of the storage ring [40].

In order to cover all dynamic chemical processes, the ultimate aim must be to use photocrystallographic methods to investigate the initial stages of a chemical reaction that occur on femtosecond timescales [41]. The study of species with sub-picosecond lifetimes requires the development of “single-shot” diffraction methods where the whole diffraction pattern of the crystal is obtained in one X-ray pulse. Here the flux of the X-ray pulse needs to be extremely high in order to achieve a measurable pattern. Laue techniques provide sufficient flux to obtain the result, but the development of X-ray free-electron lasers (XFELs) with several orders of magnitude more flux than the most powerful synchrotrons is the obvious tool to use to achieve this goal. The “diffract-and-destroy” approach has been developed at XFELs to study macromolecular systems [42,43,44,45]. From these and related studies, it is apparent that the direction-controlling, initial stages of a chemical reaction appear at timescales faster than are accessible through the use of synchrotrons which effectively have a 100 ps limit. The volume of data that is collected in one of these studies is enormous. For example, in the study of the initial stages of the photoexcitation of the photoactive yellow protein (PYP), which is triggered by the trans-cis isomerisation of the coumarin chromophore, 2.5 × 10⁶ snapshots were recorded to 1.6 Å [46]. With these advances, and with the large number of data sets being collected accurate scaling between these data sets is required to obtain reliable results. It has been found from scaling analyses that the anisotropy of absorption following sample excitation can be pronounced and depends on the orientation of the crystals in the laser beam [47] so that this factor has to be taken into consideration if accurate analysis of molecular samples is to be achieved in the future.

3 The Beginnings of Time-Resolved Crystallography

3.1 Macromolecular Photocrystallography

The initial developments in time-resolved crystallography came in the area of macromolecular crystallography because of the interest in important biological processes. These studies required faster data collection and processing techniques than had been standard. Biological crystals are also prone to decomposition particularly as a result of X-ray radiation damage, so the use of Laue methods could achieve faster data collection with less crystal decay.

The first nanosecond time-resolved macromolecular crystallographic study using Laue techniques, with a broad range of wavelengths (white beam), was reported in 1996 when Moffat and co-workers reported a study of the photodissociation mechanism of carbon monoxide in carbon monoxy-myoglobin (MbCO) [48]. The MbCO system had previously been studied in depth by ultra-fast spectroscopic techniques, and, as a result, the photoactivity of the complex in solution had been established [49,50,51]. In the experiments carried out at the European Synchrotron Radiation Facility (ESRF), Moffat et al. employed a pump-probe strategy consisting of an initial 7.5 nm-wide laser pump pulse at λ = 630 nm, followed by an X-ray probe pulse timed to arrive after a specific delay (τ). This delay was varied so that six different data sets were completed at intervals of between τ = 4 ns and 1.9 ms. The analysis of the data from the 4 ns and 1 μs data sets showed that regions of negative electron density appeared where the coordinated CO molecule had been. These observations confirmed the results of the earlier solution-based spectroscopic studies that photolysis of the Fe–CO bond had occurred and indicated that a similar occurs in the single crystal. The crystallographic data also showed a region of positive electron density below the heme centre, suggesting that the iron atom moves out of the heme plane as a result of the Fe–CO bond cleavage. This is consistent with the CO group having dissociated from the iron and moved away from its binding position. The data sets collected with longer delays of above 1 μm did not show these electron density features, which is consistent with the CO recombining with the heme unit and the whole system re-relaxing back to the ground state, the whole process being completed within a few milliseconds. In a subsequent study, by the same research team, in 2001, further data sets were obtained with time delays of between 1 ns and 1 μm, and analysis of these data showed the position of transient docking sites within the heme pocket in which the photodisassociated CO sat [52]. The relative positions of these docking sites provided information on the photodissociation process and kinetic data describing the ligand recombination process.

The success of this time-resolved approach in establishing the pathways of biological processes led to further ground-breaking studies of proteins in photoactivated states with lifetimes down to hundreds of picoseconds [53, 54]. Using these pioneering techniques, it has proved possible to construct “molecular movies” that describe the full biological process in three dimensions [55].

While macromolecular time-resolved crystallography is not the focus of this chapter, the research area has continued to lead the discipline in terms of innovation taking full advantage of developments of, initially, synchrotron facilities [56,57,58] and, more recently, of the power of the XFELs [59,60,61,62,63,64]. The molecular crystallographers have much to learn from their macromolecular colleagues not least in the area of the treatment of crystal damage in high-intensity X-ray beams [65,66,67] and in the adaption of multi-crystal data collection techniques [68].

3.2 Molecular Photocrystallography

Research into photoactivated changes in single crystals of molecular compounds commenced in the 1960s when Schmidt and Cohen reported that a series of trans-cinnamic acid derivatives underwent irreversible [2 + 2] photodimerization cycloaddition reactions in the solid state [69,70,71]. In these pioneering studies, the authors highlighted the importance of the surrounding crystalline environment on the pathway of the photodimerization reaction. They presented a series of key criteria that needed to be satisfied if a single-crystal-to-single-crystal transformation was to take place without significant crystal deterioration. These criteria were generalised in the Topochemical Postulate, stating that the photoreaction will follow a minimum energy pathway that imparts the lowest level of steric strain to the surrounding crystal environment. This meant that only transformations that proceeded topotactically, that is, with the minimum amount of movement at the atomic level could occur without crystal decay. Some subsequent improvements have been made [72] and several exceptions found [73], but the Topochemical Postulate remains an effective guide in the design of systems that undergo high levels of photoactivated [2 + 2] cycloaddition. More recently, crystal engineering techniques have been applied to the design of systems [73] that readily undergo photoactivated [2 + 2] cycloaddition reactions in the solid state, but the basis of the Postulate remains largely intact. The crystal engineering methodologies applied to the design of monomers with suitable separations and orientations have included templating methods using both metal ions and hydrogen bonds and co-crystallisations and host-guest chemistry. Because the solid-state [2 + 2] cycloaddition process is irreversible, diffraction data can be collected at various stages throughout the reaction simply by pausing the irradiation at convenient intervals. Solid-state kinetic data has been obtained in this way on cycloaddition reactions by following the photoreaction as a function of irradiation time using single-crystal X-ray diffraction methods [74,75,76].

Irreversible solid-state photoreactions permit the full three-dimensional structures of the starting material and of the product to be determined using conventional single-crystal X-ray crystallographic methods as long as crystal integrity is maintained throughout the process. However, for reversible dynamic processes in the solid state, effectively snapshots of the structures in their excited states must be obtained, taking into account the lifetime of the activated species. Over the last four decades, the importance of fully reversible photoactivated processes has been realised because of their application in real-world technologies [77], including sensors, read-write data storage media, non-linear optics [78], molecular switches, amphidynamic materials [77] and molecular actuators [79,80,81]. Examples of reversible photochemical processes include metal-metal bond-length changes [82, 83], linkage isomerisation processes [8, 23, 84, 85] and light-induced spin-state trapping behaviour [13]. The photocrystallographic studies have established that the structural changes can be promoted and controlled in the solid state, with the concomitant control over physical properties such as colour [86, 87], luminescence [8, 17, 24, 86, 87] and refractive index [88,89,90].

Steady-state and pseudo-steady-state photocrystallographic techniques have been used to identify metastable species with much of the research focussing on the identification of metastable linkage isomers and on the products of light-induced excited spin-state trapping (LIESST) experiments. This work is covered in previous chapter of this book by Skelton et al. and will not be discussed in detail here other than to give a brief outline of the overall findings that can be related to the faster time-resolved photocrystallographic experiments that will be described in the next section.

The majority of photocrystallographic studies of transition metal complexes that undergo linkage isomerism under photoactivation have focussed on nitrosyl [91,92,93,94], sulphur dioxide [17, 85, 95] and nitro complexes [8]. Some general conclusions as to the processes involved can be drawn from these studies. In all cases the percentage of conversion obtained and the isomer formed are highly dependent on the wavelength of light used and the temperature at which the experiment is carried out. For a single-crystal-to-single-crystal process to occur, there is no change in the crystal system and the unit cell parameters do not change by more than 2%. There is a temperature at which the metastable limit is reached above which the excited state has a finite lifetime before returning to the ground state. The interconversion is also dependent on the flexibility of the crystal lattice and on the steric and electronic environment of the ambidentate ligand and the metal centre, as evidenced by only small changes in cell volume being observed. There needs to be sufficient space in the lattice for the ligand to switch between one form and the other, and intermolecular interactions should either not be particularly strong or be flexible perhaps through a change in temperature [88, 96]. The accessible volume within the lattice and the flexibility of the lattice under experimental conditions relates back to the concept of the reaction cavity first proposed by Cohen [72] and then exemplified by Ohashi who showed subsequently that the reaction cavity could flex during the course of the reaction and that changes in temperature could significantly affect the process [97]. For example, lowering the temperature would cause lattice contraction, reducing the cavity size, and might thus “switch off” the reaction.

Light-induced excited spin-state trapping (LIESST) studies map the low spin-high spin interconversions in transition metal complexes with d⁴-d⁷ electronic configurations. The spin crossover phenomenon, with the associated change in magnetic properties, is usually activated thermally with the high spin (HS) to low spin (LS) interconversion occurring on cooling the complex to below some critical temperature. A significant number of these complexes can then undergo a photoactivated conversion from the LS state to a metastable HS state, via a long-lived triplet excited state. The photoinduced phenomenon was first identified in a study of [Fe(1-ptopyltetrazole)₆][BF₄]₂ using Mössbauer spectroscopy [98]. The phenomenon is observable in both solution and in the solid state.

Single-crystal crystallographic and powder diffraction studies of the LIESST phenomenon soon followed [99,100,101,102,103,104,105], taking advantage of cryoscopic advances that allowed crystals to be relatively easily cooled below liquid nitrogen temperatures; many LIESST transitions occurring below 80 K. Since the early 2000s, the topic has continued to develop with a range of techniques being used to analyse the LIESST phenomenon [13, 106]. Of additional interest are LIESST complexes that display reverse switching from their photoinduced HS state back to a low temperature LS state which is induced via both temperature changes and “reverse-LIESST” processes, involving further irradiation of the excited LIESST state with a different excitation wavelength [107]. This two-way switching using different wavelengths of light has potential applications, making these metastable state species potential candidates for photoswitchable molecular devices.

3.3 Time-Resolved Molecular Photocrystallographic Studies

For successful pump-probe molecular photocrystallographic studies, a material in which the molecules can undergo a fast, fully reversible switching process is required, and there should only be a small change in unit cell dimensions during the process. The robustness of the crystal under light and X-ray radiation is of primary importance if sufficient data is to be obtained and the excited state structure solved to atomic resolution.

3.3.1 Studies with Monochromatic X-Ray Radiation

Pump-probe X-ray experiments on molecular species, using monochromatic radiation rather than Laue techniques, were first described in 2001. Techert et al. reported a time-resolved study of transient changes in N,N-dimethylaminonitrile (DMABN) using stroboscopic X-ray powder diffraction (XRPD) methods [108]. Photoactivation of DMABN at λ = 267 nm resulted in an ultra-fast structural change as a result of the electronic excitation, and relaxation back to the ground state occurs on the picosecond timescale. The relaxation process was structurally analysed using synchrotron radiation with the beam being chopped mechanically and synchronised with light pulses from a Ti:sapphire laser, with pump-probe delay times ranging from −240 to 1,500 ps, allowing for several data points to be collected. The reflections that showed the greatest intensity changes during the structural rearrangement were identified, and the authors followed these intensity changes with increasing delay times. The data showed a conversion level to the excited state of between 28 and 32% at short time delays, which is consistent with spectroscopic data. Refinement of the powder data using the Rietveld method showed that the relaxation occurred via a change in the inversion angle of the molecule and a rotation of the methyl group (as shown in Fig. 6), with a total structural relaxation time of 520 ps.

Fig. 6

Top: The principle of TR X-ray diffraction on the excited state PES of DMABN crystals. Bottom: the intramolecular degrees of freedom, which contribute to the relaxation process (inversion qinv and torsion ftors). C atoms of the phenyl moiety are given as open, N atoms as black and the amino C as grey circles. Note that the H atoms are not shown, since they do not contribute to the X-ray diffraction signal. Reproduced from Ref. [108] with permission from the ACS

Coppens was among the first to take advantage of the higher intensity of synchrotron X-ray radiation and in 2002 reported the first single-crystal X-ray diffraction study of a species with a microsecond lifetime. The results of pump-probe experiments on salts of the [Pt₂(pop)₄]⁴⁻ anion (pop = [H₂P₂O₅]²⁻) showed that structural distortions in the anion are induced by photoactivation with 355 nm light, producing a triplet excited state with a microsecond lifetime [83]. The key change in the structure upon excitation was the shortening of the Pt–Pt bond which has previously been proposed from electronic [109] and Raman spectroscopy [110] and XAFS [111] studies, the latter suggesting a reduction in Pt–Pt bond length of 0.52 Å. The pump-probe time-resolved single-crystal X-ray study was carried out on the tetra-tetraethylammonium salt of [Pt₂(pop)₄]⁴⁻ at a temperature of 17 K and 33 μs wide light pulses from a Nd/YAG laser, at a repetition rate of 5,100 Hz, and using the “light-on/light-off” data collection strategy. Analysis of the excited state data showed a 2% level of excitation under the experimental conditions. Upon refinement of the Pt positions, the rest of the structure being treated as a rigid group, the Pt–Pt distance was found to shorten by 0.28(9) Å with a concomitant rotation of 3° about the Pt–Pt vector. The Pt–Pt distance has subsequently been confirmed by a second diffraction experiment [112] on the related salt (n-Bu₄N)₂H₂[Pt₂(pop)₄] where the Pt–Pt reduction in length was recorded at 0.23 Å. More recently, further confirmation has come from scattering measurements of an aqueous solution [113] and a time-resolved EXAFS study [114] that showed the reduction in Pt–Pt distance from that found in the ground state structure were 0.24 Å and 0.31 Å, respectively.

Another substantial reduction in metal-metal bond length was reported for the Rh–Rh bond length in [Rh₂(dimen)₄][PF₆]₂.MeCN (dimen = 1,8-diisocyanomethane) upon photoactivation at 23 K using 335 nm laser pulses. The maximum level of excitation reached was 2.5%, and the Rh–Rh bond length reduction was a remarkable 0.86 Å and a bond rotation of ca. 13° [82]. Previous spectroscopic studies on the cation had indicated a lifetime of ca. 11 μs for the triplet excited state species [115] which is in excellent agreement with the experimental value of 11.7 μs at 23 K. DFT calculations conducted at the same time as the photocrystallography experiment proposed a slightly greater decrease in the Rh–Rh distance upon excitation as illustrated in Fig. 7. The difference between the experimental and theoretical results may indicate that the steric effects from the crystalline environment may modify the structural response to the excitation process.

Fig. 7

Theoretical ground state (in pink) and excited state (green and blue colours) geometries of the [Rh₂(1,8-diisocyanomenthane)₄]²⁺ cation. Reproduced from Ref. [82] with permission from the Royal Society of Chemistry

Further photocrystallographic studies employing stroboscopic methods were reported by Coppens et al. including an investigation of photoinduced structural changes in the trimeric complex [Cu₃(3,5-(CF₃)₂pyrazolate)₃] [116]. This system differs from the examples discussed above because the photoexcitation occurs intermolecularly between two neighbouring copper trimer molecules, as opposed to the intramolecular processes in the di-nuclear species. Photoactivation at λ = 355 nm and 17 K promotes the production of excited state species with microsecond lifetimes, involving a rearrangement of the trimer molecules into pairs such that one inter-planar Cu…Cu distance is reduced by 0.65 Å while the next Cu…Cu contact lengthens by ca. 0.30 Å. In a separate study, conducted in 2009, significant structural distortions in the complex [Cu(dmp)(dppe)](PF₆), (dmp = 2,9-dimethyl-1,10-phenanthroline) are described [117]. The complex crystallises with two, crystallographically independent molecules in the asymmetric unit, whose structural response on photoactivation is interestingly different. These differences have been attributed to different constraining effects from the surrounding crystalline environment for each of the independent molecules. In general, upon irradiation the Cu cation is observed to “flatten out”, and a concomitant increase in the average Cu–P bond length is observed by comparison of the diffraction data from the ground and excited states (Fig. 8). The changes are expected to be the result of charge-transfer between the dmp and dppe ligands and were determined from an excited state population of ca. 7–10% in the single crystal.

Fig. 8

Excited state geometries of the two independent molecules (orange) superimposed on the ground state of the complex (Cu, green; C, black; P, purple; N, blue). Slightly different views are shown to illustrate the change in rocking distortion (left) and the displacement of the phenanthroline ligand from its ground state plane (molecule 2, right) upon excitation. Reproduced from Ref. [117] with permission from the American Chemical Society

These studies highlighted the importance of the crystalline environment on the solid-state photoactivation process and confirmed the significance of the “reaction cavity” hypothesis discussed earlier [97, 118]. In order to exploit this aspect and to use it to increase the level of conversion to the excited state species, photoactive complexes have been embedded as guests into arrays and framework materials. It is of importance that the host frameworks should be inert to photoactivation but effectively dilute the concentration of the photoactive species in the material. The host-guest arrangement has significant advantages for promoting the retention of crystal integrity during the process and provides greater freedom for the guest to rearrange without resulting in steric clashes with adjacent molecules in the pure material. Additionally, the dilution of the photoactive species reduces the number of photons that are required to maximise excitation, leading to more efficient photoactivation and, hopefully, increased conversion percentages [119]. It should also be noted that this approach has the effect of isolating the photoactive molecules from one another, producing quite a different environment to that experienced in crystals of the guest molecule, so differences in the physical properties of the pure compound and of the host-guest complex should be expected. Coppens et al. have investigated a number of species by this approach, via both static and dynamic photocrystallographic techniques [94, 119,120,121].

There have been a number of other studies using “crystal engineering” techniques involving the use of molecular cages and flasks [122] and metal organic frameworks (MOFs) to trap transient and highly reactive species [123]. Kawano et al. used synchrotron X-ray radiation to identify the coordinatively unsaturated “η⁵-(C₅H₄Me)Mn(CO)₂” moiety in a designed self-assembled coordination cage [124]. Photoirradiation of a [η⁵-(C₅H₄Me)Mn(CO)₃] guest molecule, within a single crystal, at 100 K, using 365 nm light, resulted in the dissociation of a carbonyl ligand remarkably without loss of crystallinity, and peaks in the electron density difference map could be attributed to free carbon monoxide. The crystallographic results were supported by a solid-state IR study. The same group has subsequently gone on to identify an unstable imine [125] and a transient hemiaminal [126], both trapped in pre-designed porous networks. They have also demonstrated the suppression of rapid cis-trans isomerism in the dimeric coordination complex [(η⁵-indenyl)Ru(CO)₂]₂ when this molecule is trapped in a self-assembled coordination cage [127] and the conversion of an overcrowded chromic alkene to a metastable twisted conformation, upon photoactivation, when incorporated into a tetrahedrally symmetric coordination cage [128]. Champness et al. have also exploited the power of synchrotron-based X-ray crystallography to support time-resolved IR studies to probe the fac-mer isomerism of [M(diimine)(CO)₃X] (M = Re or Mn; X = Cl or Br) units immobilised in a MOF and shown the presence of the mer-isomer in the photoactivated crystalline solid [129]. Subsequently, they have shown that the coordination polymer [(Cu(DMF)(H₂O)][LRe(CO)₃Cl].DMF]͚ (L = 2,2′-bipyridine-5,5′-dicarboxylic acid) undergoes an irreversible photoinduced charge transfer process. Time-resolved IR spectroscopy was used to identify the nature of this photoinduced process and how, under suitable conditions, it is possible to initiate irreversible modification of the crystal through induction of the charge transfer process. By using the photoinduced process, which arises purely as a result of the structure of the coordination network, it was possible to write on the surfaces of crystals [130].

3.3.2 Studies Using Laue Diffraction Techniques

Among the first time-resolved photocrystallographic studies using Laue diffraction techniques, designed to probe shorter timescales and reduce crystal damage, was carried out on a di-rhodium complex, [Rh₂(μ-PNP)₂(PNP)₂][BPh₄] (PNP = CH₃N(P(OCH₃)₂)₂), which was studied photocrystallographically on the 100 ps timescale [29] using Laue diffraction methods. The crystal was pumped with 35 ps pulses of a Ti:sapphire laser tuned to a wavelength of 337 nm, at a temperature of 225 K, followed by a single 100 ps-wide X-ray pulse after a 100 ps delay. The lifetime of the excited state species was ca. 35 μs. In this case, the experimental results showed a shortening of the Rh–Rh distance of 0.136(8) Å upon excitation, and the results are quantitatively supported by quantum-mechanical calculations. The study shows similar, but smaller, trends to those described for [Rh₂(dimen)₄][PF₆]₂.MeCN above [82]. The deconvolution of the overlapping reflections was achieved during the data reduction, and the structure was refined using the RATIO method [36].

A Cu(I) complex, [Cu(1,10-phenanthroline)(PPh₃)₂][BPh₄], was also studied using Laue diffraction methods [131] and compared to the [Cu(dmp)(dppe)]⁺ cation that had been studied previously using monochromatic methods [117]. This phenanthroline complex also crystallises with two independent cations in the asymmetric unit, with one molecule in a more sterically constrained environment. Photoactivation in the single crystal was expected to induce a MLCT transition, resulting in transient structural changes. The two independent molecules are again observed to undergo different structural responses upon activation with λ = 390 nm light at 90 K. Data were collected using the single-pulse Laue method, the data was analysed [132], and the results showed considerable distortion in the less restricted Cu molecule, while no significant changes were observed in the cation adopting the second, more confined arrangement (Fig. 9). Theoretical studies confirmed that the different responses were to be expected resulting from the interaction of the photoactive species with the surrounding lattice, with far greater distortions predicted in the free molecule than those observed experimentally in the solid state. For both this and the study on [Rh₂(μ-PNP)₂(PNP)₂][BPh₄], the experimental standard deviations for data collected by the Laue method are much improved compared to those seen with monochromatic time-resolved techniques. These improvements highlight the greater accuracy of time-resolved diffraction data collected by Laue methods for short lifetime species, which is mainly attributed to reduced levels of laser heating when adopting the single-shot approach [133].

Fig. 9

Comparison of the ground state (in blue) and the excited state (in red) structures of the two independent molecules at 90 K. (a) Molecule A; (b) molecule B. Reproduced from Ref. [131] with permission from the American Chemical Society

The use of pink-beam Laue diffraction has also been applied to the time-resolved photocrystallographic study of mixed metal polynuclear complexes. The triplet excited state of the tetranuclear d¹⁰-d¹⁰ complex Ag₂Cu₂L₄ (L = 2-diphenylphosphino-3-methylindole) has been investigated with a Laue pump-probe technique with an 80 ps time resolution at 90 K [134]. The lifetime of 1 μs is accompanied by significant changes in the metal framework, with an Ag…Cu distance shortening by 0.59(3) Å, which suggests an increase in the argentophilic interactions (Fig. 10). The photocrystallographic study was accompanied by theoretical calculations which confirm that the strengthening of the Ag…Ag interaction is caused by ligand-to-metal charge transfer (LMCT).

Fig. 10

(a) Photodifference map (F_o^ON−F_o^OFF) of the complex showing atomic shifts upon excitation (solid isosurfaces, ±0.55 e·Å⁻³; semi-transparent, ±0.35 e·Å⁻³; blue, positive; red, negative). (b) Refined excited state geometry related to that of the ground state crystal structure (green, ground state; red, excited state; methylindole ligands were omitted for clarity). (c) Photodeformation map (F_c^ON−F_c^OFF) based on the refined model parameters (isosurfaces, ± 0.30 e·Å⁻³; blue, positive; red, negative; k_B = 1.06). Reproduced from Ref. [134] with permission from the American Chemical Society

Most recently, the luminescent properties of a tetranuclear Cu(I) benzoate complex have been investigated by a combination of time-resolved spectroscopy and crystallography. The complex [Cu₄(PhCO₂)₄] displays luminescent thermochromism, with red phosphorescence at room temperature that turns green on lowering the temperature to 90 K [135]. The low-energy triplet state has been assigned to a cluster-centred triplet state, and the emission from this state matches the experimental red band observed at 660–715 nm. The computed next highest triplet excited state occurs close to the experimental value at 545 nm. The two excited states exhibit MLCT and LMCT characteristics, particularly in their solid-state geometries, as evidenced from the Laue photocrystallographic study, at 90 and 225 K, with 355 and 360 nm light irradiation, which shows the expected Cu…Cu contraction. Again, there are two independent molecules in the crystallographic asymmetric unit, and they show slightly different distortions because of their different crystalline environments.

With recent technological advances, it is not just very fast timescale photocrystallographic molecular transformations that have been carried out. It has become possible to study the dynamics of LIESST [136], and the results show significant differences to results obtained from those of conventional diffraction studies of long-lived photoinduced high spin states. Ultra-fast spin-state photoswitching in two crystalline polymorphs of the octahedral Fe(III) complex [(TPA)Fe(TCC)] (TPA = tris(2-pyridylmethyl)amine and TCC = 3,4,5,6-tetrachloroactecholate dianion) (Fig. 11) has been studied by femtosecond optical spectroscopy and picosecond X-ray diffraction [39]. In these experiments the X-ray pulses were generated by a fast chopper, and data was collected with a series of different delay times between the laser pump and the X-ray probe. The time dependence of the lattice parameters was measured using partial data collected for each delay time with 60 frames with 10 s of exposure for every 1° step of the diffractometer ϕ axis. Typical excitation densities were 150 μm⁻², with a laser diameter of ca. 500 μm (FWHM). After data processing of the full data sets for the monoclinic polymorph, photodifference maps were calculated for the 500 ps and 50 μs time delays. The maps show significant changes in electron density upon excitation (Fig. 11). The response to the excitation at 500 ps is shown by the sideways shift of electron density from the Fe1 atom towards O2 (Fig. 11a). This shift becomes even more pronounced at the 50 μs time point (Fig. 11b). There is also an increase in the Fe–N distances by ca. 0.05 Å. The estimated population of the excited state at 500 ps is in the range 1.5–2%, and this increases to ca. 10.5% after 50 μs. Overall, the results show significant shifts of the Fe atom and the two O atoms upon excitation, and the results are consistent with the complementary spectroscopy that was undertaken.

Fig. 11

Photodifference maps obtained for the monoclinic polymorph with isosurfaces (red positive, blue negative) of (a) ±0.14 eų for the 500 ps data and (b) ±0.46 eų for the 50 μs data. Reproduced from Ref. [39] with permission from the Royal Society of Chemistry

In a subsequent study of the Fe(III) spin-crossover material, [Fe(3-MeO-SalEen)₂][PF₆], the switch from LS to HS only occurs at the molecular level as clearly shown by the linear dependence of the fraction of photoswitched molecules with the excitation density as well as with the initial fraction of low spin molecules. The inter-system crossing from the photoexcited LS (S = 1/2) to HS (S = 5/2) occurs within approximately 200 fs and is accompanied by coherent non-equilibrium vibrational relaxation in the photoinduced HS state. These results reveal similar dynamical features to those already reported for LIESST in related Fe(II) systems [137]. The activation of coherent molecular vibrations is an essential requirement for reaching the HS potential on the timescale of molecular motions, whereas their fast damping allows an efficient trapping in the HS potential [138]. The observed coherent oscillations are attributed to photoinduced molecules in the HS states, and the results are supported by Raman spectroscopy at thermal equilibrium and DFT analyses of molecular vibrations and TD-DFT calculations of optical absorption.

4 Conclusions

Time-resolved crystallography has developed extensively over the last three decades, and the results presented in this chapter show that under favourable conditions it is possible to obtain full three-dimensional structural data on chemical species that have lifetimes of microseconds or less [139]. These advances, coupled with similar advances in instrumentation and computer power, open up possibilities for monitoring chemical processes in the solid state in a way that has not previously been possible. At present the restrictions of maintaining crystal integrity remain, and the reactions and processes are mostly limited to the interaction of the solid to external media such as light, as discussed in this chapter, but also to changes in temperature and pressure and the influence of magnetic and electric fields (although crystal integrity is retained in some solid-gas reactions). The potential is enormous, and the topic is ripe for development. As has already been indicated, the new frontier in photocrystallography over the next several decades is the use of X-ray free-electron laser sources to carry out serial femtosecond studies [41]. The use of XFELs to track chemical reactions by serial femtosecond pump-probe X-ray crystallography by rapidly recording diffraction patterns at closely spaced time intervals has already proved successful in macromolecular crystallography [42, 43, 45]. Once the scaling issues related to using multiple crystals in serial processes are resolved and diffraction patterns better than atomic resolution [47] are obtained, the prospect for carrying out molecular crystallography at an XFEL is extremely promising.

In the meantime, for the slower timescale processes (milliseconds to minutes), detector development will facilitate the use of laboratory sources [26, 140], rather than the need for synchrotrons. This will mean that many more “routine” time-resolved experiments can be carried out and there are thousands of systems which would benefit from structural dynamic studies. Additionally, the monitoring of dynamic processes using multiple techniques simultaneously, such as the combination of photocrystallography with emission spectroscopy or Raman spectroscopy, will allow the detailed processes within the molecule as well as changes in the crystalline environment to be monitored in exquisite detail.