Key Points
- Developed a new method for predicting the crystal structures of molecular assemblies—a key determinant of semiconductor performance—from the molecular design stage.
- Systematically organized the variables defining molecular arrangements based on layered structures and crystal symmetry, and optimized them stepwise, beginning with the most important variables.
- Elucidated the physical mechanisms underlying the emergence of four crystal polymorphs by analyzing structural stability throughout the optimization process.
Schematic: Stepwise crystal structure optimization and prediction.
Outline
A research team comprising Graduate student Ryota Ono, Senior Researcher Seiji Tsuzuki, and Professor Tatsuo Hasegawa from the Department of Applied Physics, Graduate School of Engineering, The University of Tokyo, together with Research Associate Professor Satoru Inoue from the Innovation Center for Organic Electronics, Yamagata University, systematically analyzed the crystal structures of “polyacenes” (Note 1; see schematic, left)—a series of organic semiconductor molecules consisting of linearly fused benzene rings—using quantum chemical calculations.
By systematically organizing the configurational variables associated with the layered nature and symmetry of the crystals and optimizing them stepwise, the team successfully predicted and reproduced, using calculations alone, all four crystal polymorphs (Note 2) known experimentally for the polyacene series, without using experimentally determined crystal structures as starting points. Furthermore, detailed analysis of the optimization process revealed the physical mechanisms underlying the formation and stabilization of these crystal structures.
Conventional approaches to crystal structure prediction typically involve computationally generating vast numbers of candidate crystal structures and searching among them for stable structures. In contrast, this study presents a new perspective: experimentally observed crystal structures can be reached by systematically organizing the variables that define molecular arrangements and optimizing them sequentially, beginning with the most important ones. The approach also clarifies the relationships among molecular shape, constituent atoms, and crystal structure. By enabling molecular design that takes the anticipated crystal structure into account from the outset, this method is expected to accelerate the development of a wide range of molecular materials, including high-performance layered organic semiconductors.
The results of this research were published online in the international scientific journal Communications Chemistry on October 23, 2026 (BST).
1. Research Background
Many organic molecules form molecular crystals in which vast numbers of identical molecules are arranged in an ordered manner. The “crystal structure,” which describes the arrangement of molecules within a crystal, can be experimentally determined using techniques such as X-ray diffraction and electron diffraction. These methods provide detailed information about the positions of individual atoms within molecules, molecular shapes, and the relative spatial relationships between neighboring molecules. Crystal structure analysis therefore serves as one of the most powerful tools for linking microscopic molecular structures with macroscopic material properties across a wide range of fields, from materials science to the life sciences.
In materials and pharmaceutical development, there is strong demand for methods that can predict the crystal structure a molecule will form before the molecule is actually synthesized. For example, the solubility of a pharmaceutical compound and the performance of an electronic material depend strongly not only on the intrinsic properties of the individual molecule but also on how the molecules assemble within the crystal. The ability to predict the resulting crystal structure at the molecular design stage could therefore greatly improve the efficiency of molecular materials development. However, accurately predicting the crystal structure formed by a given molecule before experimental characterization remains difficult even for relatively simple molecules. As a result, obtaining a desired crystal structure often requires extensive trial and error, substantially increasing the time and cost involved in materials development.
The crystal structures accessible to a molecule are largely governed by its shape, constituent atoms, and the resulting intermolecular interactions. Recent advances in quantum chemical calculations have made it possible to evaluate these intermolecular interactions with very high accuracy. However, because a crystal structure is determined by numerous variables describing the positions and orientations of many molecules, identifying stable structures from the enormous number of possible combinations remains a major challenge in computational science.
To date, crystal structure prediction has largely focused on methods that generate vast numbers of candidate structures and then identify stable structures among them. Although powerful, these approaches often make it difficult to understand physically why a particular structure is stable, limiting the extent to which the resulting insights can be directly translated into the design of new molecules and materials.
2. Research Approach
Specific symmetry relationships frequently appear in the molecular arrangements of crystals. For example, neighboring molecules may be related to one another through symmetry operations such as inversion, reflection, or glide reflection (Note 3), thereby forming highly ordered crystal structures. Such “crystal symmetry” provides an important clue for organizing the many degrees of freedom associated with molecular arrangements and reducing the number of variables needed to describe the structure.
Rod-shaped molecules also frequently form molecular layers in which their long axes are approximately aligned while the molecules pack laterally. Many organic semiconductors exhibit this type of layered molecular arrangement. This “layered nature” provides another important clue for organizing the variables that determine molecular packing.
In this study, focusing on molecular materials such as organic semiconductors, the researchers investigated whether crystal structures could be predicted by using high crystal symmetry and layered packing to systematically organize the numerous configurational variables and then optimizing them stepwise, beginning with the most important variables. When the method was applied to five polyacenes containing two to six benzene rings, it successfully reproduced with high precision all four crystal polymorphs known experimentally across the polyacene series, without using experimentally determined crystal structures as starting points for the calculations.
Furthermore, by visualizing changes in the energy of the molecular assemblies during each optimization step as “potential maps,” the researchers elucidated the physical mechanisms underlying how the final crystal structures emerge and become stabilized.
3. Research Results
Figure 1 illustrates the overall workflow of the stepwise crystal structure prediction method developed in this study for rod-shaped polyacene molecules. First, an arbitrary pair of molecules was considered in which the molecular long axes were parallel and there was no displacement along the long-axis direction. By imposing glide symmetry on this pair and extending the arrangement periodically, a molecular monolayer was constructed. Minimization of its energy yielded the most stable “regular” structure, termed the R structure.
Next, a uniform tilt of the molecular long axes was introduced into the R-structure monolayer. This produced two metastable structures: the G structure, which retains glide symmetry, and the N structure (non-glide), in which glide symmetry is broken. Finally, by stacking the molecular layers and searching for stable interlayer arrangements, the researchers successfully reproduced four crystal polymorphs.
Figure 1: Conceptual diagram of the stepwise reproduction of polyacene crystal polymorphs.
Figure 2 illustrates the process by which the R structure is obtained. A molecular monolayer composed of glide-symmetric molecular pairs can be described by two variables: (1) the angle α between the molecular plane and the glide plane, and (2) the position of the molecule relative to the glide plane.
The upper panel of Figure 2 shows the most stable monolayer configuration obtained for each value of α. Intermolecular interactions between pairs of molecules were calculated using dispersion-corrected DFT (Note 4), and the total energy of the molecular layer was evaluated by summing these interactions. Energy minima appeared near α = 25° and 65°, revealing the most stable molecular arrangements corresponding to the R structure.
Notably, although no experimentally determined crystal structure information was used in the calculation, the resulting molecular arrangement closely matched the layered herringbone (LHB) structure (Note 5) of Polymorph I known experimentally for polycrystalline pentacene thin films.
Analysis of the individual interaction components revealed that stabilization of the LHB structure depends on a balance among attractive dispersion and electrostatic interactions (Note 6) and exchange repulsion (Note 6). Furthermore, analysis of the changes in molecular arrangement with α (Figure 2, lower panel) showed that hydrogen atoms at the molecular ends approach hollow regions near the centers of neighboring aromatic rings, thereby increasing the dispersion interaction and stabilizing the LHB structure composed of T-shaped molecular pairs.
Figure 2: Reproduction and stabilization mechanism of the regular LHB structure. Assuming glide symmetry, the molecular arrangement that minimizes the total interaction energy of the molecular layer was determined as a function of the angle α between the molecular plane and the glide plane (upper panel). The most stable LHB structure—the regular R structure—was obtained near α = 25° and 65°.
Next, starting from the R structure, the molecules within the layer were uniformly tilted in the same direction. The center-left panel of Figure 3 shows the molecular-layer energy as a color-coded potential map, using the tilt azimuth φincl and tilt angle θincl as configurational variables, with θincl cos(φincl) on the horizontal axis and θincl sin(φincl) on the vertical axis.
The potential map shows that, in addition to the most stable R structure, molecular tilting gives rise to two metastable structures: the G structure, which retains glide symmetry, and the N structure, in which glide symmetry is broken. Tilting the molecules produces a relative displacement of neighboring molecules along their long axes, thereby changing their interactions with surrounding molecules. New energy minima appear when neighboring molecules are displaced by approximately the length of one benzene ring; these minima correspond to the G and N structures.
Figure 3: G and N structures generated by tilting the molecular long axes. Starting from the basic R-type LHB structure, uniformly tilting the molecular long axes in the same direction while preserving the molecular layer generates two new metastable structures, the G and N structures.
Next, for each of these three layered structures, the researchers introduced rotation of the molecules around a central axis perpendicular to the molecular plane, represented by the configurational variable θtwist, and searched for stable crystal structures while also taking interlayer stacking into account (Figure 4). For naphthalene (two rings) and anthracene (three rings), which have relatively short molecular backbones, optimization starting from the G structure yielded stable structures that closely matched the experimentally determined structures.
The molecular rotation created spaces into which molecules from adjacent layers could fit, while other hydrogen atoms moved closer to hollow regions of neighboring aromatic rings in T-shaped arrangements (Figure 4, right). These additional intermolecular contacts were found to further stabilize the crystal structure.
Figure 4: Reproduction of naphthalene and anthracene crystal structures through molecular rotation. Starting from the glide-symmetric G-type LHB structure, the molecules were rotated around a central axis perpendicular to the molecular plane while maintaining glide symmetry. Optimization of the intermolecular interaction energy reproduced the experimentally observed anthracene crystal structure. Potential-map analysis showed that the crystal structure is stabilized by new hydrogen–benzene-ring contacts and additional intermolecular contacts that fill gaps between neighboring molecular layers.
Figure 5 shows how the lattice volume changes with interlayer displacement when molecular layers having the N structure are stacked. Shifting the molecular layers causes the lattice volume to decrease at positions where the corrugated surfaces of adjacent layers interlock, producing two local minima. The stacking structures corresponding to these minima closely matched Polymorphs II and IV known experimentally.
Furthermore, shifting molecules along their long axes produced additional stabilization, but the magnitude of this stabilization depended on molecular length, or the number of fused rings. Analysis of this molecular-length dependence clarified why different crystal polymorphs emerge in tetracene (four rings), pentacene (five rings), and hexacene (six rings).
For the five rod-shaped polyacenes containing two to six linearly fused benzene rings, the calculated crystal structures showed excellent agreement with experimentally determined structures. Overall, all four crystal polymorphs known experimentally across the polyacene series were successfully reproduced.
For Polymorph I of polycrystalline pentacene thin films, however, the experimentally observed structure was found to deviate slightly from the most stable calculated configuration because of interactions with the substrate. In addition, calculations including longer-range intermolecular interactions showed that the relative stabilities of the different crystal polymorphs were in good agreement with experimental observations.
Figure 5: Reproduction of pentacene single-crystal polymorphs through interlayer stacking. Starting from the N structure, which lacks glide symmetry, changes in lattice volume were calculated as a function of the relative displacement between stacked molecular layers. Configurations corresponding to minima in the lattice volume reproduced Polymorphs II and IV observed experimentally in pentacene and related systems.
Comparison of the interactions between neighboring molecules in T-shaped and parallel configurations within the molecular layers showed that their interaction strengths maintain an approximately 2:1 ratio across all four polymorphs, I–IV. This indicates that the balance of the major intermolecular interactions responsible for forming the LHB structure is maintained even though the detailed molecular arrangements differ among the polymorphs.
In contrast, intermolecular transfer integrals, which play a key role in charge-carrier transport in semiconductors, differed substantially among the polymorphs. These differences arise primarily from variations in the relative displacement of neighboring molecules along their long axes.
This study demonstrates that the crystal structures of complex molecular crystals can be predicted by systematically organizing molecular configurational variables on the basis of crystal symmetry and layered packing and then optimizing these variables stepwise. Furthermore, analysis of the optimization pathways reveals the physical mechanisms responsible for crystal-structure stabilization and provides insight into how differences in crystal structure affect semiconductor properties.
4. Future Perspectives
A key feature of this method is that, rather than merely identifying the most stable crystal structure from a vast number of candidate structures, it tracks the process by which a crystal structure becomes stabilized and thereby reveals why that particular structure forms.
In future work, the researchers will extend the method to more complex molecular materials, including organic semiconductors with flexible side chains such as alkyl chains. The ultimate goal is to develop a broadly applicable crystal structure prediction method that bridges molecular design and crystal engineering and contributes to the rational design of organic electronic materials and molecular devices.
Notes
(Note 1) Polyacene: A family of π-conjugated molecules consisting of multiple benzene rings fused linearly. Examples include naphthalene with two fused benzene rings, anthracene with three, tetracene with four, pentacene with five, and hexacene with six. Pentacene, in particular, has been widely studied as a representative organic semiconductor material.
(Note 2) Crystal polymorph: The phenomenon in which the same molecule can form multiple crystal structures because of differences in molecular arrangement or stacking. The individual crystal structures are called polymorphs. Different polymorphs of the same molecule can exhibit substantially different stability, solubility, electronic properties, and other physical characteristics.
(Note 3) Glide reflection: A symmetry operation found in crystals that combines reflection across a plane with translation by a fixed distance parallel to that plane. Put simply, it corresponds to “shifting a mirror image by a certain distance along the mirror plane.” If applying this operation to one molecule makes it coincide with another molecule, the two molecules are related by glide symmetry, and the reference plane is called the “glide plane.” In molecular crystals, glide reflection can enable dense packing in which protruding and recessed parts of neighboring molecules interlock, making glide symmetry common in organic molecular crystals.
(Note 4) Dispersion-corrected DFT: Density functional theory (DFT) is a quantum-mechanical computational method used to calculate the electronic states and energies of molecules and solids. Dispersion-corrected DFT incorporates corrections for intermolecular dispersion interactions, which are not always adequately described by conventional DFT. It is widely used for molecular crystals, in which intermolecular interactions play a major role in determining crystal structures.
(Note 5) Layered herringbone (LHB) structure: A crystal packing motif in which plate-like or rod-like π-conjugated molecules form molecular layers, with neighboring molecules within each layer arranged at an angle to one another in a pattern resembling a herringbone. It is a common packing motif in organic semiconductors and strongly influences intermolecular electronic coupling and charge-carrier transport.
(Note 6) Dispersion interactions, electrostatic interactions, and exchange repulsion: These are major components of intermolecular interactions. Dispersion interactions are attractive interactions arising from instantaneous fluctuations in electron distributions. Electrostatic interactions originate from the charge distributions within molecules and can be either attractive or repulsive depending on molecular orientation and arrangement. Exchange repulsion is a strong short-range repulsive interaction that arises when the electron clouds of neighboring molecules overlap, reflecting the quantum-mechanical requirement that electrons cannot occupy the same quantum state. The distances and relative orientations of molecules in a crystal are determined by the balance among these interactions.
Papers
Journal: Communications Chemistry
Title: Stepwise quantum chemical optimization reveals the origin of layered herringbone packing and polymorphism in polyacenes
Authors: Ryota Ono, Satoru Inoue, Mao Miyoshi, Kanata Koyama, Seiji Tsuzuki, and Tatsuo Hasegawa*