A new computational method can predict the crystal structures that strongly influence organic semiconductor performance, starting from the molecular design stage. A joint research team from the University of Tokyo and Yamagata University focused on the symmetry and layered structure of molecular crystals. By optimizing the variables that define molecular arrangement step by step, they reproduced four crystal structures known from experiments. Rather than generating a large number of candidate structures and searching for stable ones, as conventional approaches do, the team examined molecular tilt, rotation, and layer stacking in sequence, and in doing so clarified why each structure is stable.
The research was carried out by a group including Ryota Ohno, a graduate student at the University of Tokyo Graduate School of Engineering; Seiji Tsuzuki, project researcher; Professor Tatsuo Hasegawa; and Satoru Inoue, research associate professor at Yamagata University. The results were published in the journal Communications Chemistry on October 23, 2026 (DOI: 10.1038/s42004-026-02252-8). The study targeted five polyacene molecules with two to six linked benzene rings, and reproduced their molecular arrangements without providing known crystal structures as starting points for the calculations. This was not a study that synthesized new crystals; it advanced the prediction of crystal structures and the understanding of the intermolecular interactions that govern their formation.
From Exhaustive Searches of Vast Candidates to Stepwise Optimization of Molecular Arrangement
In organic semiconductors, even the same molecule can show greatly different electrical properties depending on how it is arranged in the crystal. For example, the ease with which charge moves in pentacene, which is used in organic transistors, varies with the crystal structure the molecules form. If a stable crystal structure could be predicted before a molecule is synthesized, it might reduce the trial and error needed in materials development. However, the combinations of positions and orientations that many molecules can adopt are enormous, and identifying stable structures by calculation is not easy.
Conventional crystal structure prediction (CSP) has widely relied on generating a large number of candidate structures, calculating the energy of each, and searching for stable ones. This approach is effective, but even once a final structure is obtained, explaining why that molecular arrangement is stable requires additional analysis. To address this problem, the research team used the geometric regularity of crystals to organize the variables to be explored in a systematic way.
The keys are "glide symmetry" and "layeredness." Glide symmetry refers to a geometric relationship in which combining a reflection across a plane with a translation along that plane makes the molecular arrangement coincide with itself. Layeredness, meanwhile, is the property whereby rod-shaped molecules align their long axes in roughly the same direction and line up side by side to form molecular layers. Many organic semiconductors form crystals with such regularities.
The team chose as test subjects the polyacene series, in which benzene rings are linked in a straight line: naphthalene (two rings), anthracene (three), tetracene (four), pentacene (five), and hexacene (six). These are rigid, rod-like molecules, well suited for validating a computational model that exploits layered structure and symmetry.
The method first determines the basic structure of a simple molecular layer, then tilts the long axes of the molecules, and further optimizes the rotation of the molecular planes and the relative positions of the layers. At each stage, the intermolecular interaction energy is calculated to trace how stable arrangements emerge. This makes it possible not only to obtain the final crystal structure but also to visualize the rise and fall of energy accompanying structural changes as a "potential map."
A "Herringbone" Structure Stabilized When Molecules Tilt About 25 Degrees
The first calculation assumed a two-dimensional molecular layer in which the long axes of the molecules are parallel to one another, with no relative shift along the long-axis direction. A molecular pair with glide symmetry served as the basic unit, and arranging it periodically represents the whole layer. This arrangement can be described by the angle between the molecular plane and the glide plane, together with lattice constants expressing the relative positions of the molecules.
The team calculated intermolecular interaction energies using density functional theory (DFT) with dispersion corrections. Dispersion forces are attractive forces produced by instantaneous fluctuations in electron distribution, and they are an important factor governing the stability of molecular crystals. When the energy of the molecular layer was examined while varying the angle , symmetry-equivalent stable structures were obtained near about 25 and 65 degrees.
In this case, the herringbone angle formed by adjacent molecular planes is about 51 degrees. This is close to the roughly 53 degrees observed in experimental pentacene crystals. The team named this basic stable molecular arrangement the "R structure (Regular)."
In the R structure, adjacent molecules sit at an angle to each other, forming a fishbone-like pattern. This is called a "Layered Herringbone (LHB)" structure, a representative molecular arrangement widely seen in organic semiconductors. The calculations confirmed that the stability of this structure is determined by the balance between attraction from dispersion and electrostatic forces and the exchange repulsion that arises when molecules come too close.
Particularly important is the contact between a hydrogen atom at the edge of a molecule and the vicinity of the center of an adjacent benzene ring. When molecules adopt a nearly T-shaped arrangement, the hydrogen atom approaches the ring center of the neighboring molecule, strengthening stabilization from dispersion forces and others. On the other hand, when molecules approach each other too closely, the exchange repulsion associated with overlapping electron clouds rises sharply. The angle of about 25 degrees can be explained as a stable arrangement arising from the balance of this attraction and repulsion.
The team next introduced an operation that uniformly tilts the long axes of the molecules in the R-structure layer. When the azimuthal angle \phi_} indicating the tilt direction and the tilt angle \theta_} were varied, adjacent molecules shifted relative to one another along the long-axis direction, and new energy minima appeared at positions corresponding to a displacement of about one benzene ring.
This operation yielded two metastable structures: the "G structure (Glide)," which retains glide symmetry, and the "N structure (Non-glide)," in which glide symmetry is broken. In other words, simply tilting the molecules from the basic R structure led to two stable arrangements that connect to different crystal structures.
Four Crystal Structures That Change With the Number of Benzene Rings
Having obtained the three types of molecular layers, R, G, and N, the team further incorporated into the calculations rotation about the axis perpendicular to the molecular plane and the way layers stack on one another. Optimizing these arrangements step by step reproduced the four crystal structure types (I to IV) known experimentally in the polyacene series.
| Crystal structure | Main geometric features | Representative experimental examples | Main stabilizing factors |
|---|---|---|---|
| Polymorph I | Layered structure based on the R structure, with molecular long axes nearly parallel | Thin-film phases of tetracene and pentacene | Balance of in-layer T-shaped contacts with dispersion, electrostatic forces, and exchange repulsion |
| Polymorph II | Stacking based on the N structure, with glide symmetry broken | Pentacene single crystals, hexacene | Shift along the molecular long axis and close contact between layers |
| Polymorph III | Molecular planes rotated from the G structure, maintaining glide symmetry | Naphthalene, anthracene | Filling of interlayer gaps by molecular rotation and new intermolecular contacts |
| Polymorph IV | Different interlayer arrangement of the N structure, with slight non-uniform tilt of the molecular long axes | Bulk phase of tetracene, another crystal phase of pentacene | Interlocking of layers and increased interlayer interaction |
For naphthalene and anthracene, which have fewer rings, rotating the molecules from the G structure yielded polymorph III, which agrees well with the experimental structure. Rotating the molecular planes creates gaps within the layer, and molecules of the adjacent layer fit into them. New contacts between hydrogen atoms and benzene rings also form, strengthening interlayer interaction. This stabilization is particularly effective for polyacenes with short molecular length; for longer molecules, the energetic benefit of the same rotation becomes smaller.
For longer molecules such as pentacene and hexacene, on the other hand, stacking based on the N structure is advantageous. When N-structure molecular layers are shifted horizontally, the lattice volume decreases in arrangements where the surface irregularities of the layers interlock, and two energy minima appear. These arrangements corresponded to the experimentally known polymorphs II and IV.
The team also took into account slight non-uniform tilt of the molecular long axes and compared the stability of the two structures. As a result, polymorph IV was favored for tetracene with four rings, while polymorph II prevailed for pentacene (five rings) and hexacene (six rings). This is thought to be because, as molecules get longer, it becomes easier to maintain contact between molecules in arrangements shifted along the long axis, stabilizing the dense stacking based on the N structure.
These calculations explain the tendency in the polyacene series for the most stable crystal structure to change from polymorph III to IV and then II as the number of rings increases. This agrees well with the structural differences known from experiments.
The team also compared, for the four polymorphs, the intermolecular interaction between molecules in T-shaped contact within a layer and that between molecules arranged in parallel. The ratio of their strengths was kept at roughly 2 to 1 in every polymorph. This indicates that even when molecular tilt and layer stacking differ, the basic balance of intermolecular interactions supporting the herringbone structure is common.
Crystal Structures Reproduced, but Substrate and Thermal Effects Remain
The method reproduced the crystal structure types seen in the five polyacenes without using known crystal structures as initial arrangements for the calculations. However, this cannot be taken as an achievement that makes it possible to fully predict the crystal structures of unknown compounds. The targets were molecules whose structures were already established experimentally, and the study validated the effectiveness of a model that assumes layeredness and high symmetry.
The calculation results also showed differences depending on how far interactions were taken into account. Interactions between neighboring molecules alone sometimes could not adequately explain the slight differences in stability among polymorphs, but incorporating contributions from more distant molecules brought the results closer to the experimentally known stability trends. While local molecular arrangement is determined mainly by interactions with nearby molecules, interactions extending over a wider range are also important in determining which polymorph is stable for the crystal as a whole.
In addition, for polymorph I seen in pentacene thin films, slight differences were found between the computationally ideal R structure and the experimental structure. This is because in actual thin films, molecular arrangement may change due to interactions with the substrate and interface effects. The team believes such substrate and interface effects are involved in the gap between the calculated and experimental structures. A model that treats only intermolecular interactions cannot fully reproduce conditions during thin-film growth.
Thermodynamic limitations also remain. The calculations mainly evaluated interaction energies of static molecular arrangements, and judging phase stability at finite temperature rigorously requires considering the Gibbs free energy including entropy, $G=H-TS$. The team points out that, because the calculated stability agrees well with experimental results, the effect of entropy may be relatively small for this polyacene series. However, this assumption cannot necessarily be applied as is to flexible molecules or more complex crystals.
Furthermore, although the study introduces the geometric variables for determining crystal structures step by step, the choice of some variables also draws on knowledge gained from comparison with known experimental structures. It is therefore necessary to distinguish between not using experimental structures as initial values and predicting unknown structures without using any experimental information. Whether the same procedure can lead to correct crystal structures for unknown molecules remains a subject for future verification.
Small Differences in Molecular Position Greatly Change Charge Transport Properties
The team also calculated the intermolecular "transfer integral" for the reproduced crystal structures, which relates to charge transport in semiconductors. The transfer integral is an indicator of how strongly the electron orbitals of adjacent molecules are coupled, and it relates to the strength of the electronic coupling when charge moves between molecules.
The results showed that, although the basic balance of intermolecular interactions is nearly common across the four crystal structures, the magnitude of the transfer integral differed markedly. For pentacene in particular, the transfer integral was large for polymorph I and tended to be smaller for polymorphs II and IV.
The main factor producing this difference is the relative shift of adjacent molecules along the long-axis direction. When molecules shift, the way the molecular orbitals involved in charge transport overlap changes. In these calculations, the transfer integral became small at a shift corresponding to about half a benzene ring, and became large again as it reached about one ring. The wavefunctions of molecular orbitals have parts with positive and negative phase, so depending on the positional relationship of the molecules, coupling between orbitals is strengthened or they cancel each other out.
This shows that minute differences in crystal structure greatly affect the electronic properties of organic semiconductors. However, a large transfer integral does not necessarily mean higher charge mobility in an actual transistor. Device performance also depends on grain boundaries, defects, thin-film morphology, contact resistance with electrodes, scattering by lattice vibrations, and more. What was clarified here is the theoretical relationship between crystal structure and the electronic coupling relevant to charge transport, not the result of measuring actual device performance.
Extending to Organic Semiconductors With Flexible Side Chains Is the Next Challenge
According to the University of Tokyo's announcement, the team plans to extend the method to organic semiconductor materials with flexible side chains such as alkyl chains. Many practical organic semiconductors have long side chains introduced onto the molecular backbone to make it easier to form thin films from solution. In such materials, not only the arrangement of the rigid main backbone but also the shape and motion of the side chains affect the crystal structure, increasing the degrees of freedom to be explored.
What this study confirmed to be effective is the polyacene series, made of highly symmetric, rigid rod-shaped molecules. Whether the arrangement variables can be organized in the same way and stable structures derived for molecules with flexible side chains or for more complex crystals is not yet known. If substrate interactions and temperature-dependent changes in free energy can also be incorporated, it would be an important step toward predicting crystal structures in environments closer to actual manufacturing conditions.
The significance of this work lies not only in reproducing crystal structures by calculation but also in systematically explaining through which interactions changes in molecular shape and arrangement stabilize a crystal. Rather than replacing conventional exhaustive crystal structure prediction, it is best positioned as a new method that adds physical understanding to it. If its predictive accuracy for unknown molecules is verified, it could become a powerful means of rationally developing organic semiconductors with desired crystal structures and charge transport properties from the molecular design stage.