Bridging photochemistry and photomechanics with NMR crystallography: the molecular basis for the macroscopic expansion of an anthracene ester nanorod

Spiers Memorial Lecture: NMR crystallography

Chemical function is directly related to the spatial arrangement of atoms. Consequently, the determination of atomic-level three-dimensional structures has transformed molecular and materials science over the past 60 years. In this context, solid-state NMR has emerged to become the method of choice for atomic-level characterization of complex materials in powder form. In the following we present an overview of current methods for chemical shift driven NMR crystallography, illustrated with applications to complex materials.

The interplay of density functional selection and crystal structure for accurate NMR chemical shift predictions

Ab initio chemical shift prediction plays a central role in nuclear magnetic resonance (NMR) crystallography, and the accuracy with which chemical shifts can be predicted relative to experiment impacts the confidence with which structures can be assigned. For organic crystals, periodic density functional theory calculations with the gauge-including projector augmented wave (GIPAW) approximation and the PBE functional are widely used at present. Many previous studies have examined how using more advanced density functionals can increase the accuracy of predicted chemical shifts relative to experiment, but nearly all of those studies employed crystal structures that were optimized with generalized-gradient approximation (GGA) functionals. Here, we investigate how the accuracy of the predicted chemical shifts in organic crystals is affected by replacing GGA-level PBE-D3(BJ) crystal geometries with more accurate hybrid functional PBE0-D3(BJ) ones. Based on benchmark data sets containing 132 13C and 35 15N chemical shifts, plus case studies on testosterone, acetaminophen, and phenobarbital, we find that switching from GGA-level geometries and chemical shifts to hybrid-functional ones reduces 13C and 15N chemical shift errors by ∼40-60% versus experiment. However, most of the improvement stems from the use of the hybrid functional for the chemical shift calculations, rather than from the refined geometries. In addition, even with the improved geometries, we find that double-hybrid functionals still do not systematically increase chemical shift agreement with experiment beyond what hybrid functionals provide. In the end, these results suggest that the combination of GGA-level crystal structures and hybrid-functional chemical shifts represents a particularly cost-effective combination for NMR crystallography in organic systems.

Improved Description of Intra- and Intermolecular Interactions through Dispersion-Corrected Second-Order Møller-Plesset Perturbation Theory

ConspectusThe quantum chemical modeling of organic crystals and other molecular condensed-phase problems requires computationally affordable electronic structure methods which can simultaneously describe intramolecular conformational energies and intermolecular interactions accurately. To achieve this, we have developed a spin-component-scaled, dispersion-corrected second-order Møller-Plesset perturbation theory (SCS-MP2D) model. SCS-MP2D augments canonical MP2 with a dispersion correction which removes the uncoupled Hartree-Fock dispersion energy present in canonical MP2 and replaces it with a more reliable coupled Kohn-Sham treatment, all evaluated within the framework of Grimme's D3 dispersion model. The spin-component scaling is then used to improve the description of the residual (nondispersion) portion of the correlation energy.The SCS-MP2D model improves upon earlier corrected MP2 models in a few ways. Compared to the highly successful dispersion-corrected MP2C model, which is based solely on intermolecular perturbation theory, the SCS-MP2D dispersion correction improves the description of both inter- and intramolecular interactions. The dispersion correction can also be evaluated with trivial computational cost, and nuclear analytic gradients are computed readily to enable geometry optimizations. In contrast to earlier spin-component scaling MP2 models, the optimal spin-component scaling coefficients are only mildly sensitive to the choice of training data, and a single global parametrization of the model can describe both thermochemistry and noncovalent interactions.The resulting dispersion-corrected, spin-component-scaled MP2 (SCS-MP2D) model predicts conformational energies and intermolecular interactions with accuracy comparable to or better than those of many range-separated and double-hybrid density functionals, as is demonstrated on a variety of benchmark tests. Among the functionals considered here, only the revDSD-PBEP86-D3(BJ) functional gives consistently smaller errors in benchmark tests. The results presented also hint that further improvements of SCS-MP2D may be possible through a more robust fitting procedure for the seven empirical parameters.To demonstrate the performance of SCS-MP2D further, several applications to molecular crystal problems are presented. The three chosen examples all represent cases where density-driven delocalization error causes GGA or hybrid density functionals to artificially stabilize crystals exhibiting more extended π-conjugation. Our pragmatic strategy addresses the delocalization error by combining a periodic density functional theory (DFT) treatment of the infinite lattice with intramolecular/conformational energy corrections computed with SCS-MP2D. For the anticancer drug axitinib, applying the SCS-MP2D conformational energy correction produces crystal polymorph stabilities that are consistent with experiment, in contrast to earlier studies. For the crystal structure prediction of the ROY molecule, so named for its colorful red, orange, and yellow crystals, this approach leads to the first plausible crystal energy landscape, and it reveals that the lowest-energy polymorphs have already been found experimentally. Finally, in the context of photomechanical crystals, which transform light into mechanical work, these techniques are used to predict the structural transformations and extract design principles for maximizing the work performed.

Organic Crystal Packing Is Key to Determining the Photomechanical Response

Organic photomechanical crystals have great promise as molecular machines, but their development has been hindered by a lack of clear theoretical design principles. While much research has focused on the choice of the molecular photochrome, density functional theory calculations here demonstrate that crystal packing has a major impact on the work densities that can be produced by a photochrome. Examination of two diarylethene molecules reveals that the predicted work densities can vary by an order of magnitude across different experimentally known crystal structures of the same species. The highest work densities occur when molecules are aligned in parallel, thereby producing a highly anisotropic photomechanical response. These results suggest that a greater emphasis on polymorph screening and/or crystal engineering could improve the work densities achieved by photomechanical engines. Finally, an inherent thermodynamic asymmetry is identified that biases photomechanical engines to exhibit higher work densities in the forward stroke direction.

Photocrystallography of [Ru(bpy)2(dmso)2]2+ reveals an O-bonded metastable state

We report the first instance of observing the phototriggered isomerization of dmso ligands on a bis sulfoxide complex, [Ru(bpy)₂(dmso)₂], in the crystalline solid state. The solid-state UV-vis spectrum of the crystal demonstrates an increase in optical density around 550 nm after irradiation, which is consistent with the solution isomerization results. Digital images of the crystal before and after irradiation display a notable color change (pale orange to red) and cleavage occurs along planes, (1̄01) and (100), during irradiation. Single crystal X-ray diffraction data also confirms that isomerization is occurring throughout the lattice and a structure that contains a mix of the S,S and O,O/S,O isomer was attained from a crystal irradiated ex situ. In situ irradiation XRD studies reveal that the percentage of the O-bonded isomer increases as a function of 405 nm exposure time.

An Elastic Organic Crystal Enables Macroscopic Photoinduced Crystal Elongation

Among the various types of photomechanical deformations of organic crystals, photoinduced elongation of millimeter-scale crystals has yet to be demonstrated. Here we report that the millimeter-sized crystalline rods of an anthracene-pentiptycene hybrid organic π-system (1) are highly elastic and able to elongate up to 21.6% or 0.40 mm without fragmentation upon undergoing [4 + 4] photodimerization reactions. Both the mechanical and photomechanical effects reveal a strong cohesion of the system, even at the interface of 1 and its photodimer 2 and under the conditions of randomized molecular packing, representing a new class of mechanically adaptive organic crystals.

Do Models beyond Hybrid Density Functionals Increase the Agreement with Experiment for Predicted NMR Chemical Shifts or Electric Field Gradient Tensors in Organic Solids?

Ab initio predictions of chemical shifts and electric field gradient (EFG) tensor components are frequently used to help interpret solid-state nuclear magnetic resonance (NMR) experiments. Typically, these predictions employ density functional theory (DFT) with generalized gradient approximation (GGA) functionals, though hybrid functionals have been shown to improve accuracy relative to experiment. Here, the performance of a dozen models beyond the GGA approximation are examined for the prediction of solid-state NMR observables, including meta-GGA, hybrid, and double-hybrid density functionals and second-order Møller-Plesset perturbation theory (MP2). These models are tested on organic molecular crystal data sets containing 169 experimental ¹³C and ¹⁵N chemical shifts and 114 ¹⁷O and ¹⁴N EFG tensor components. To make these calculations affordable, gauge-including projector augmented wave (GIPAW) Perdew-Burke-Ernzerhof (PBE) calculations with periodic boundary conditions are combined with a local intramolecular correction computed at the higher level of theory. Within the context of typical NMR property calculations performed on a static, DFT-optimized crystal structure, the benchmarking finds that the double-hybrid DFT functionals produce errors versus experiment that are no smaller than those of hybrid functionals in the best cases, and they can be larger. MP2 errors versus experiment are even bigger. Overall, no practical advantages are found for using any of the tested double-hybrid functionals or MP2 to predict experimental solid-state NMR chemical shifts and EFG tensor components for routine organic crystals, especially given the higher computational cost of those methods. This finding likely reflects error cancellation benefiting the hybrid functionals. Improving the accuracy of the predicted chemical shifts and EFG tensors relative to experiment would probably require more robust treatments of the crystal structures, their dynamics, and other factors.

Cooperative Photochemical Reaction Kinetics in Organic Molecular Crystals

Photoreactive molecular crystals have been intensively investigated as next-generation functional materials. Changes in physicochemical properties are usually interpreted in terms of static pre- and post-reaction molecular structures and packings determined by X-ray structure analysis. However, to elucidate the dynamic properties, it is necessary to understand the dynamic nature of photochemical kinetics in crystals. Reaction dynamics in the crystal phase can be dramatically different from those in dilute solution because the local molecular environment evolves as the surrounding reactant molecules are transformed into products. In this Review article, we summarize multiple examples of photochemical reactions in the crystalline phase that do not follow classical kinetic behavior. We also discuss different theoretical methods that can be used to describe this behavior. This Review article should help provide a foundation for future workers to understand and analyze photochemical reaction kinetics in crystals.

TensorView for MATLAB: Visualizing tensors with Euler angle decoding

TensorView for MATLAB is a GUI-based visualization tool for depicting second-rank Cartesian tensors as surfaces on three-dimensional molecular models. Both ellipsoid and ovaloid tensor display formats are supported, and the software allows for easy conversion of Euler angles from common rotation schemes (active, passive, ZXZ, and ZYZ conventions) with visual feedback. In addition, the software displays all four orientation-equivalent Euler angle solutions for the placement of a single tensor in the molecular frame and can report relative orientations of two tensors with all 16 orientation-equivalent Euler angle sets that relate them. The salient relations are derived and illustrated through several examples. TensorView for MATLAB expands and complements the earlier implementation of TensorView within the Mathematica programming environment and can be run without a MATLAB license. TensorView for MATLAB is available through github at https://github.com/LeoSvenningsson/TensorViewforMatlab, and can also be accessed directly via the NMRbox resource.

A theoretical framework for the design of molecular crystal engines

Photomechanical molecular crystals have garnered attention for their ability to transform light into mechanical work, but difficulties in characterizing the structural changes and mechanical responses experimentally have hindered the development of practical organic crystal engines. This study proposes a new computational framework for predicting the solid-state crystal-to-crystal photochemical transformations entirely from first principles, and it establishes a photomechanical engine cycle that quantifies the anisotropic mechanical performance resulting from the transformation. The approach relies on crystal structure prediction, solid-state topochemical principles, and high-quality electronic structure methods. After validating the framework on the well-studied [4 + 4] cycloadditions in 9-methyl anthracene and 9-tert-butyl anthracene ester, the experimentally-unknown solid-state transformation of 9-carboxylic acid anthracene is predicted for the first time. The results illustrate how the mechanical work is done by relaxation of the crystal lattice to accommodate the photoproduct, rather than by the photochemistry itself. The large ∼10⁷ J m^-3 work densities computed for all three systems highlight the promise of photomechanical crystal engines. This study demonstrates the importance of crystal packing in determining molecular crystal engine performance and provides tools and insights to design improved materials in silico.

Photomechanical Structures Based on Porous Alumina Templates Filled with 9-Methylanthracene Nanowires

9-Methylanthracene (9MA) undergoes a concerted [4 + 4] photodimerization in its crystal form that can be harnessed in order to generate photomechanical motions such as bending, twisting, and expansion. As described in this paper, 9MA nanowires were grown in anodic aluminum oxide (AAO) templates with the goal of using the crystal expansion to generate a net increase in the height of the composite disk. The growth conditions were optimized in order to raise the filling amount from 28% to 77% of the available volume in the porous AAO. A new experimental method for detecting motion, based on the analysis of data from a dynamically misaligned Michelson interferometer, was developed. Template bending was observed, showing that the photodimerization of the confined nanowires generated mechanical work, but no conclusive evidence for surface disruption or vertical translation was observed. Optical measurements, as well as atomic force and scanning electron microscopy, showed that incomplete filling, crystal orientation, and debris from template polishing likely prevented the observation of vertical actuation in these nanocrystal composites. This work highlights some of the practical challenges that are involved in creating photomechanical actuators using the organic–inorganic composite approach, with the two most significant being (1) the uniform filling of the porous template with the organic active material and (2) the removal of excess organic material from the template’s surface.

Structural Phase Transitions in Anthracene Crystals

Anthracene (C14 H10 ) and its derivatives, π-conjugated molecules in acenes, have been widely researched in terms of their reactions, physical properties, and self-assembly (or crystal engineering). These molecules can be functionalized to tune reactivities, optoelectronic properties, and self-assembling abilities. Structural changes in the molecular assemblies, solid states, and crystals have recently been discovered. Therefore, a systematic discussion of anthracene's molecular structure, packing, and optical properties based on its intermolecular structure and phase transitions is important for future chemical and structural design. In the present review, we discuss anthracene's molecular design, dimer packing, and crystal structure, focusing on the structural phase transitions of its crystals. We also provide examples of the phase transitions of anthracene crystals. Changes to edge-to-face of CH-π interaction and face-to-face packing of π-π interaction affect the thermodynamic stabilities of various crystal structures. These structures can inform the prediction of structural and physical properties.

Engineering Photomechanical Molecular Crystals to Achieve Extraordinary Expansion Based on Solid-State [2 + 2] Photocycloaddition

Photomechanical molecular crystals are promising candidates for photoactuators and can potentially be implemented as smart materials in various fields. Here, we synthesized a new molecular crystal, (E)-3-(naphthalen-1-yl)acrylaldehyde malononitrile ((E)-NAAM), that can undergo a solid-state [2 + 2] photocycloaddition reaction under visible light (≥400 nm) illumination. (E)-NAAM microcrystals containing symmetric twinned sealed cavities were prepared using a surfactant-mediated crystal seeded growth method. When exposed to light, the hollow microcrystals exhibited robust photomechanical motions, including bending and dramatic directional expansion of up to 43.1% elongation of the original crystal length before fragmentation due to the photosalient effect. The sealed cavities inside the microcrystals could store different aqueous dye solutions for approximately one month and release the solutions instantly upon light irradiation. A unique slow-fast-slow crystal elongation kinematic process was observed, suggesting significant molecular rearrangements during the illumination period, leading to an average anisotropic crystal elongation of 37.0% (±3.8%). The significant molecular structure and geometry changes accompanying the photocycloaddition reaction, which propels photochemistry to nearly 100% completion, also facilitate photomechanical crystal expansion. Our results provide a possible way to rationally design molecular structures and engineer crystal morphologies to promote more interesting photomechanical behaviors.

Photomechanical crystalline materials: new developments, property tuning and applications

This highlight gives an overview of the mechanism development, property tuning and application exploration of photomechanical crystalline materials.

Correlating Reaction Dynamics and Size Change during the Photomechanical Transformation of 9-Methylanthracene Single Crystals

Photomechanical molecular crystals that expand under illumination could potentially be used as photon-powered actuators. In this study, we find that the use of high-quality single crystals of 9-methylanthracene (9MA) leads to more homogeneous reaction kinetics than that previously seen for polycrystalline samples, presumably due to a lower concentration of defects. Furthermore, simultaneous observation of absorbance and shape changes in single crystals revealed that the dimensional change mirrors the reaction progress, resulting in a smooth expansion of 7 % along the c-axis that is linearly correlated with reaction progress. The same expansion dynamics are highly reproducible across different single crystal samples. Organic single crystals exhibit well-defined linear expansions during 100 % photoconversion, suggesting that this class of solid-state phase change material could be used for actuation.

Recent Development of Photodeformable Crystals: From Materials to Mechanisms

Photodeformable materials are a class of molecules that can convert photon energy into mechanical energy, which have attracted tremendous attention in the last few decades. Owing to their unique photoinduced deformable properties, including fast light-response and diverse mechanical behaviors, photodeformable materials have exhibited great potential in many practical applications such as actuators, photoswitches, artificial muscles, and bioimaging. In this review, we sort out the current state of photodeformable crystals and classify them into six categories by molecular structures: diarylethenes, azobenzenes, anthracenes, olefins, triarylethylenes, and other systems. Three distinct light-responsive mechanisms, photocyclization, trans-cis isomerization, and photodimerization, are revealed to play significant roles in the molecular photodeformation. Their corresponding photodeformable behaviors such as twisting, bending, hopping, bursting, and curling, as well as the potential applications, are also discussed. Furthermore, the challenges and prospective development directions of photodeformable crystals are highlighted.

Fast and Accurate Electric Field Gradient Calculations in Molecular Solids With Density Functional Theory

Modern approaches for calculating electric field gradient (EFF) tensors in molecular solids rely upon plane-wave calculations employing periodic boundary conditions (PBC). In practice, models employing PBCs are limited to generalized gradient approximation (GGA) density functionals. Hybrid density functionals applied in the context of gauge-including atomic orbital (GIAO) calculations have been shown to substantially improve the accuracy of predicted NMR parameters. Here we propose an efficient method that effectively combines the benefits of both periodic calculations and single-molecule techniques for predicting electric field gradient tensors in molecular solids. Periodic calculations using plane-wave basis sets were used to model the crystalline environment. We then introduce a molecular correction to the periodic result obtained from a single-molecule calculation performed with a hybrid density functional. Single-molecule calculations performed using hybrid density functionals were found to significantly improve the agreement of predicted 17O quadrupolar coupling constants (C q ) with experiment. We demonstrate a 31% reduction in the RMS error for the predicted 17O C q values relative to standard plane-wave methods using a carefully constructed test set comprised of 22 oxygen-containing molecular crystals. We show comparable improvements in accuracy using five different hybrid density functionals and find predicted C q values to be relatively insensitive to the choice of basis set used in the single molecule calculation. Finally, the utility of high-accuracy 17O C q predictions is demonstrated by examining the disordered 4-Nitrobenzaldehyde crystal structure.