Predicting and Rationalizing Piezoelectricity in Racemic Bioorganic Molecular Crystals

ABSTRACT

Racemic crystals, often presumed to favour centrosymmetric packing and lack polar functionality, conceal an unlikely and underexplored capacity for longitudinal piezoelectricity. Here, we report a broad computational exploration demonstrating that certain bioorganic racemic systems exhibit pronounced piezoelectric responses, comparable to leading single‐crystal materials. Despite their inherent mirror symmetry at the molecular level, the modelled crystal structures lack inversion symmetry, giving rise to significant electrical polarisation under mechanical stress, as predicted by our density functional theory (DFT) calculations. Our top‐performing stable racemic crystals exhibit effective longitudinal piezoelectric strain response of up to 28 pC/N, more than twice that of benchmark DL‐alanine (12.5 pC/N), combined with low dielectric constants (<5) and high mechanical flexibility. These results position our modelled racemic molecular systems as a promising, bio‐friendly platform for soft, sustainable and lead‐free piezoelectric devices. Our findings overturn conventional assumptions about the structural and functional limitations of racemic crystals as a material class, revealing their suitability for next‐generation piezoelectric applications. Six of the racemic organic systems studied exhibit piezoelectric strain coefficients exceeding 10 pC/N, highlighting their viability as efficient and environmentally friendly alternatives to conventional inorganic materials.

Racemic molecular crystals, composed of equal mixtures of chiral enantiomeric components, are predicted to exhibit significant piezoelectric responses and favourable mechanical flexibility. This study identifies organic and bioorganic racemates as promising candidates for sustainable, lead‐free materials, enabling next‐generation applications in energy harvesting, soft electronics and responsive biomedical devices through their intrinsic electromechanical coupling.

1. Introduction

Chirality is a fundamental property of organic molecules and a defining feature of biological systems, referring to molecular asymmetry in which a structure cannot be superimposed on its mirror image [1]. In nature, homochirality prevails: L‐amino acids form proteins, whilst D‐sugars (D‐deoxyribose and D‐ribose) constitute the backbones of nucleic acids [2]. Racemic mixtures, composed of equal quantities of left‐ and right‐handed enantiomers (DL‐ or (±)‐type), are less common in biology but are of increasing interest in materials science due to their distinct crystallisation behaviour [3]. Unlike their enantiopure counterparts, racemic molecular crystals can adopt unique packing arrangements and symmetry properties, including rare subcategories of non‐centrosymmetric space groups that are essential for longitudinal piezoelectricity [4, 5, 6, 7]. Recent studies reveal that racemic amino acid assemblies can switch their supramolecular β‐sheet arrangements from antiparallel to parallel configurations, thereby introducing new structural degrees of freedom. This chiral interplay enables modulation of optical, mechanical and piezoelectric responses, providing a molecular basis for property tuning in bioorganic crystals [8]. This makes racemic organic and bioorganic crystals promising candidates for next‐generation piezoelectric materials that are inherently biocompatible, flexible and potentially biodegradable [9, 10].

Piezoelectricity in molecular crystals arises from the absence of inversion symmetry and the presence of a polar axis within the lattice [11]. Although most known organic piezoelectrics are based on enantiopure or achiral compounds [7], recent studies highlighted that certain racemic crystals also exhibit significant piezoelectric responses [10, 12]. For example, DL‐alanine crystallises in a polar space group and exhibits an experimental longitudinal piezoelectric coefficient of approximately 4‐6 pC/N in its polycrystalline form, with associated voltage outputs reaching up to 0.8 V under mechanical stress [12, 13]. Piezoresponse force microscopy (PFM) measurements on single crystals reveal higher responses, with coefficients of 11.5 pC/N for DL‐alanine and 8.1 pC/N for DL‐tyrosine [14]. Complementary density functional theory (DFT) calculations predict shear piezoelectric responses as high as 18 pC/N for DL‐alanine, indicating that racemic molecular crystals can support effective electromechanical coupling via symmetry‐breaking molecular arrangements [12]. Previously reported polyethylene oxide nanofiber arrays incorporating DL‐alanine and L‐lysine hemihydrate nanocrystals exhibit piezoelectric currents up to 7 µA/m², energy conversion efficiencies of 3%–5%, and a pyroelectric coefficient of 150 µC/m²K, underscoring their promise as scalable, biocompatible energy‐harvesting materials [15]. Similarly, PVA/DL‐alanine polycrystals, with DL‐alanine domains aligned along the polar axis, display composition‐dependent piezoelectricity with d₃₃ values reaching ∼5 pC/N, highlighting their potential for bio‐friendly piezoelectric devices [16]. Although amino acids have been the primary focus of such investigations, the implications of racemisation extend far beyond the proteinogenic set [17]. Racemic mixtures of small organic and bioorganic molecules, particularly those featuring hydrogen bonding, ionic interactions or π─π stacking, can crystallise in non‐centrosymmetric lattices [18], potentially enabling macroscopic polarisation. Recent work shows that chirality and co‐assembly critically influence supramolecular packing in amino acid‐based assemblies. Racemic mixtures of N‐terminally capped alanine‐based assemblies (Ac‐Ala) with a bipyridine coformer (BPA/Ac‐DL‐Ala) form distinct motifs that enhance mechanical stability but suppress piezoelectricity, whereas enantiopure co‐assemblies of BPA/Ac‐L‐Ala and BPA/Ac‐D‐Ala achieve higher piezoelectric coefficients and power outputs [19]. However, overall, the influence of chirality and racemic composition on supramolecular order, polarisation and piezoelectric properties remains poorly understood, limiting the development of general design principles.

Despite these early findings and growing interest in sustainable piezoelectrics [9, 10, 20], no systematic investigation has yet explored the broader landscape of racemic bioorganic molecular crystals for piezoelectric applications. Key questions remain regarding the structural features that enable piezoelectricity in racemates and the extent to which racemic systems can achieve piezoelectric responses comparable to, or surpassing, those of enantiopure materials. Although the benchmark racemic systems such as DL‐alanine and DL‐tyrosine have demonstrated promising responses, the general potential of racemates to achieve functional piezoelectric properties remains unexplored on a large scale. Addressing these questions is essential for establishing racemic crystallisation as a viable design strategy in electromechanical materials. Broader studies are needed to assess how often racemic crystallisation leads to piezoelectricity through non‐centrosymmetric packing and to identify candidate materials with desirable electromechanical and dielectric characteristics. In this context, we present a comprehensive computational study of racemic organic and bioorganic crystals, focusing on their structural, dielectric and piezoelectric properties, and evaluating their suitability for sustainable piezoelectric applications.

2. Results and Discussion

To address this research gap, we carried out a comprehensive computational study of racemic organic and bioorganic molecular crystals, combining crystal structure analysis with first‐principles modelling. Using high‐throughput density functional theory (DFT) [10, 21, 22, 23, 24]. We evaluated the piezoelectric and dielectric properties of racemic systems containing DL‐ and (±)‐type components, spanning both amino acid and organic (non‐amino acid) chemistries. Our dataset focused on racemates that crystallise in non‐centrosymmetric space groups, identified through prior pre‐screening (Note S1). These non‐centrosymmetric packings are driven by hydrogen bonding, asymmetric charge distribution and chirality‐mediated packing frustration [12], which enable net polarisation and piezoelectric activity absent in centrosymmetric systems. Moreover, the supramolecular packing of racemic crystals often deviates from the helical or layered motifs typical of enantiopure assemblies [25], giving rise to novel polar architectures. This enhanced structural diversity allows for chirality‐driven design strategies in organic crystalline materials [26, 27]. Although there are cases where racemic crystals outperform their enantiopure counterparts in piezoelectric output due to favourable crystal packing and mechanical anisotropy, this is not always the case, as the racemic form may crystallise in a centrosymmetric structure that suppresses piezoelectricity [7, 12, 14].

The piezoelectric properties presented in this study are obtained using our CrystalDFT high‐throughput computational framework [10] that has been applied to a diverse set of crystalline materials with experimentally quantified piezoelectric behaviour [22, 23, 28]. The scope of these benchmarks spans inorganic, organic and metal‐organic framework crystals, encompassing well‐known inorganic piezoelectrics such as zinc oxide, aluminium nitride, potassium niobate and lithium niobate, as well as racemic bioorganic crystals including DL‐alanine and DL‐tyrosine for which single crystal piezoelectric measurements have been reported (Figure 1A,C). For these systems, calculated piezoelectric strain coefficients were quantitatively compared with experimental data for 16 materials, covering 30 independent components of the piezoelectric tensor, and were shown to capture both the magnitude and symmetry of the measured responses.

FIGURE 1.

Benchmarking, structural characteristics and three‐dimensional piezoelectric strain tensor visualisations of high‐performing racemic crystals and reference materials. (A) Correlation between experimentally reported and computationally predicted piezoelectric responses across representative bioorganic and inorganic materials drawn from the literature (Ref. [10, 23]). Data points are colour coded by material class, with bioorganic systems shown in green, inorganic materials in blue and metal organic frameworks in red. The dotted black line denotes the linear regression fit and illustrates overall agreement between experimental measurements and theoretical predictions. For visual clarity, materials with piezoelectric coefficients exceeding 40 pC/N are excluded. (B) Unit‐cell highlights the structural diversity and molecular packing motifs of non‐centrosymmetric racemates. (C) Computationally predicted piezoelectric properties of representative inorganic and organic single‐crystal piezoelectric materials, reproduced from our previous work [23], provide a benchmark for comparison with the racemic systems examined in this study. (D) Three‐dimensional representations of the piezoelectric strain tensor (d_ij , pC/N) depict the directional dependence and magnitude of the predicted electromechanical responses (Scheme S4). The surface contours illustrate anisotropic behaviour arising from crystal symmetry and atomic arrangement, revealing how mechanical deformation induces electric polarisation along distinct crystallographic directions.

The present work applies the same computational protocol to racemic bioorganic crystals, enabling predictive assessment of their piezoelectric responses within a consistent theoretical framework. The predicted trends are in line with experimentally reported behaviour for racemic materials (Figure 1), supporting the transferability of the approach to this class of compounds. All crystal structures were fully optimised using the PBE exchange correlation functional with Grimme dispersion corrections. The sensitivity of the calculated piezoelectric properties to the choice of dispersion treatment, including PBE D3 (benchmarked for CrystalDFT), PBE‐D3‐BJ and PBE‐D2 relative to dispersion‐free PBE, has been systematically analysed in earlier studies [10, 22, 28] and informs the methodological choices adopted here.

An initial collection of ∼2100 DL‐ or (±)‐labelled crystal structures was compiled from the Cambridge Structural Database (CSD). Structures were selected based on the availability of complete three‐dimensional atomic coordinates, and an R‐factor of 0.075 or lower to ensure crystallographic quality and the exclusion of disordered, polymeric or erroneous entries. Only organic compounds with racemic components that met quality criteria were retained, representing approximately 0.17% of the entire CSD. Crystallographic point group analysis of these structures identified 245 racemic crystals comprising organic and bioorganic compounds, with approximately 15% representing amino acids and their derivatives. Applying a unit cell size filter to include only structures containing 150 atoms or fewer per unit cell for computational cost, narrowed the selection to 118 non‐centrosymmetric crystals (Scheme S1). To enable a broader chemical and functional context, all modelled racemic crystals were tagged by compound class, including amino acids and derivatives, bioorganic molecules, carbohydrates and glycomimetics, heterocyclic compounds, pharmaceuticals and drug candidates, organosulfur compounds, organic acids and esters, and salts, solvates and hydrates (Note S1 and Scheme S2). These candidates were then subjected to full geometry optimisation using DFT under symmetry constraints, followed by elastic stability analyses to confirm their mechanical viability (Note S2). Electromechanical properties were calculated using density functional perturbation theory (DFPT) to compute dielectric and Born effective charge tensors, combined with finite difference methods to obtain the elastic tensor and estimate piezoelectric responses (Scheme S3). Figure S1 displays the electromechanical property spectrum of modelled racemic structures after excluding those flagged for negative material stiffness (Note S3), highlighting the most canonically explored piezoelectric strain coefficients, which reach an upper fence of 40 pC/N, indicating significant device potential [28, 29]. These values still fall short of the strain coefficients of ceramics and other classes of inorganic materials, the majority of which exceed 100 pC/N [10].

Amongst the non‐centrosymmetric racemates, seven are predicted to exhibit effective longitudinal piezoelectric response ($d_{33}^{eff}$) values exceeding 10 pC/N, with two surpassing 25 pC/N (Figure 1B and Table 1). Although the Cartesian $d_{33}$ is defined along the z axis, $d_{33}^{eff}$ represents the maximum amongst the diagonal tensor components ($d_{11}$, $d_{22}$ and $d_{33}$). This value reflects the anisotropic nature of racemic molecular packings, where the direction of maximum measurable piezoelectric strain does not necessarily coincide with the conventional 3‐axis. Instead, an experimentalist can obtain the largest longitudinal signal by aligning the measurement or electrode axis along the crystallographic direction that maximises piezoelectric response. The corresponding three‐dimensional piezoelectric strain tensor (d_ij ) visualisations further reveal the strong anisotropy and directional dependence of the electromechanical response, highlighting how crystal symmetry governs the magnitude and orientation of induced polarisation under mechanical stress (Figure 1D and Scheme S4). The top‐performing material, (±)‐Phenyl 3‐methyl‐2‐oxoindolyl‐3‐carboxylate, achieved a $d_{33}^{eff}$ of 27.2 pC/N, rivalling commercial piezoelectric polymer PVDF and its derivatives. Predicted dielectric constants for the top candidates ranged from 2.8 to 5.1, enabling high voltage output per unit stress. Elastic tensors were used to derive Young's moduli ranging from approximately 5 to 28.5 GPa, Bulk moduli (9.5 to 30 GPa) and Shear moduli (1.5 to 12.5 GPa), confirming that the screened materials possess sufficient mechanical resilience under device‐relevant conditions. Young's and Bulk Modulus (GPa, Hill averages) values for the top‐performing piezoelectric racemates are shown in Table 1. All predicted properties, including piezoelectric charge, strain and voltage tensors, as well as the full elastic tensors and associated mechanical properties, are provided in Table S1. The top‐performing racemates exhibit a combination of mechanical softness with elastic anisotropy, features that are advantageous for bending and flexible applications.

TABLE 1.

Top racemic crystals ranked by predicted effective longitudinal (${\mathit{d}}_{33}^{\mathit{eff}}$) and shear piezoelectric responses (${\mathit{d}}_{15}$) along with their predicted dielectric constant (ε), Young's modulus (E), bulk modulus (K) and dipole moment, excluding crystals flagged for negative material stiffness or unstable eigenvalues.

Serial no.	CSD ID	Crystal name	Crystal system	Space group	Young's Modulus (GPa)	Bulk Modulus (GPa)	Net Dipole Moment (Debye)	${\mathit{d}}_{33}^{\mathit{eff}}$ (pC/N)	${\mathit{d}}_{15}$ (pC/N)	Dielectric constant (ε)
1	JOKKUQ	(+‐)‐Phenyl 3‐methyl‐2‐oxoindolyl‐3‐carboxylate	Trigonal	P32	5.01	13.68	23.69	27.18	12.32	3.15
2	WIBLID	(+‐)‐5,6a‐Dimethyl‐6,6a,7,8,9,9a‐hexahydropentaleno(2,1‐b)indol‐6,7‐dione	Monoclinic	Pc	7.01	13.61	48.44	25.42	13.1	3.56
3	QQQAGP01	Rac‐Potassium hydrogen 1‐malate.H2O	Monoclinic	Cc	27.05	22.2	9.92	12.87	4.16	5.14
4	DLALNI20	DL‐alanine	Orthorhombic	Pna21	27.05	24.96	15.95	12.51	5.27	3.99
5	TIJWIS	(3β,3aβ,7β,8aα)‐(+‐)‐6,6‐(Ethylenedioxy)‐3,8,8‐trimethyl‐1,2,3,3a,4,5,6,7,8,8a‐decahydro‐3a,7‐(methano)azulen‐2‐one	Monoclinic	P21	12.87	14.65	11.44	11.22	0	2.9
6	GEJKUC	Diammonium O‐phospho‐DL‐threoninate	Orthorhombic	Pca21	28.58	30.02	37.66	10.83	0.69	4.84
7	WOCVOZ	N‐Methyl‐DL‐aspartic acid monohydrate	Monoclinic	Cc	24.98	21.5	29.29	10.54	11	4.33
8	WIKCUO	N‐Carboxy‐DL‐valine anhydride (DL‐valine NCA)	Orthorhombic	Pca21	10.13	11.37	45.34	9.76	16.66	3.36
9	AZUSIX	(+‐)‐syn‐(6‐Methoxy‐2a,3,4,5‐tetrahydro‐2H‐naphtho(1,8‐bc)furan‐5‐yl)ammoniomethane chloride	Orthorhombic	Pna21	11.9	14.59	16.25	9.67	6.2	3.46
10	HOCYSL	DL‐Homocysteine thiolactone hydrochloride	Orthorhombic	Pbc21	16.99	14.65	13.74	9.57	24.18	4.42
11	YELJII	(2R')‐(+‐)‐1‐((1R,3R,4R,5R)‐3‐Cyano‐4,7,7,‐trimethyl‐6‐oxabicyclo(3.2.1)oct‐5‐yl)aziridin‐2'‐carboxamide	Monoclinic	P21	11.81	9.67	37.68	9.47	0	2.84
12	INUQEN	(+‐)‐2,6‐[1',11'‐(3',9'‐diaza‐4',8'‐dioxo‐6'‐oxaundeca‐1,11‐diyl)]‐cis‐1,3,5,7‐tetraoxadecalin	Monoclinic	P21	12.45	13.08	9.53	9.25	0	3.22
13	EROMOP	ammonium 2‐acetamido‐3‐methylpentanoate (ammonium DL‐alloisoleucinate)	Orthorhombic	Pna21	14.25	14.43	35.89	9.24	1.97	3.39
14	TEXSEU	2‐Trifluoromethyl‐4‐DL‐ribolactone	Monoclinic	Cc	14.27	16.11	36.49	9.04	2.57	3.1
15	NOZYOQ	(+‐)‐2,3‐Dihydro‐3‐oxo‐1H‐indeneacetic acid ((+‐)‐3‐Indanone‐1‐acetic acid)	Orthorhombic	Pca21	11.35	12.02	41.46	8.98	4.64	3.49
16	DLTYRS	DL‐tyrosine	Orthorhombic	Pna21	21.28	23.48	17.6	8.34	12.82	3.8
17	DLMALC	(±)‐Malic acid	Monoclinic	Cc	24.38	19.61	55.52	8.16	28.6	3.61

Several other racemic crystals are predicted to exhibit high $d_{33}^{eff}$ compared with experimental benchmarks such as γ‐glycine (d₃₃  = 11.3 pC/N) [10, 28] and croconic acid (d₃₃ ≈15 pC/N) [30]. For instance, (±)‐5,6a‐Dimethyl‐6,6a,7,8,9,9a‐hexahydropentaleno(2,1‐b)indol‐6,7‐dione displays a remarkable $d_{33}^{eff}$ of 25.4 pC/N alongside moderate Young's modulus of 7 GPa and bulk modulus of 13.6 GPa. Rac‐Potassium hydrogen 1‐malate monohydrate and DL‐alanine both exceed 12 pC/N longitudinal response, supported by higher stiffness values (Young's modulus ∼27 GPa). Other promising candidates include (3β,3aβ,7β,8aα)‐6,6‐ethylenedioxy‐trimethylazulenone and Diammonium O‐phospho‐DL‐threoninate, with $d_{33}^{eff}$ values of 11.2 and 10.8 pC/N, respectively, paired with Young's moduli of 12.9 and 28.6 GPa, respectively. DL‐tyrosine and N‐Methyl‐DL‐aspartic acid monohydrate also show effective piezoelectric responses around 8.3 and 10.5 pC/N. Dielectric constants for these materials span roughly 2.9 and 5.1, balancing efficient polarisation with electrical insulation. Previously, we have studied a broader dataset reaching up to 240 pC/N of predicted longitudinal piezoelectric response [10]. Compared with the previously reported organic crystal dataset, the racemic materials dataset further expands the landscape of practical organic piezoelectric candidates. Overall, these racemic crystals combine appreciable longitudinal piezoelectricity with mechanical robustness, making them strong candidates for practical piezoelectric applications.

Racemic organic crystals exhibit not only longitudinal but also significant shear piezoelectric responses, making them strong candidates for anisotropic electromechanical applications. Amongst the top racemates analysed for shear piezoelectricity (Table S2), a large proportion display strong shear coefficients, along the “canonical.” $d_{15}$, $d_{14}$, $d_{25}$ and $d_{36}$ tensor components. This is particularly evident in monoclinic and orthorhombic systems with point groups 2, m, 222 and mm2, which inherently support multiple shear‐active modes due to their lower symmetry. The highest observed shear response appears in the trigonal racemate (±)‐phenyl 3‐methyl‐2‐oxoindolyl‐3‐carboxylate, which shows $d_{14}$ = $d_{25}$ = 37.9 pC/N, far exceeding the shear coefficients typically found in enantiopure molecular crystals. This compound crystallises in space group P3₂, enabling simultaneous multi‐directional shear activity, as also reflected by its low Young's modulus of 5 GPa, indicating considerable lattice compliance. Similarly, DL‐homocysteine thiolactone hydrochloride and N‐carboxy‐DL‐valine anhydride (DL‐valine NCA), both in Pbc2₁ (mm2, orthorhombic), show strong ​$d_{15}$ values of 24.2 and 16.7 pC/N, respectively, align with the expected piezoelectric activity allowed in their polar space groups.

Across the dataset, high shear responses are not limited to any one chemical class but are observed in structurally and functionally diverse systems, from zwitterionic amino acid derivatives to halogenated and sulfoxide‐containing molecules. (±)‐((2R,3S)‐3‐(hydroxymethyl)oxiran‐2‐yl)(phenyl)methanone (Pca2₁, 9 GPa) exhibits $d_{15}$ of 21.8 pC/N whilst (±)‐3‐exo,6‐exo‐dibromo‐5‐endo‐hydroxy‐3‐endo‐nitrobicyclo[2.2.1]heptane‐2‐exo‐carbonitrile (Cc, 15.5 GPa) reaches $d_{15}$ ​ of 15.9 pC/N. These results underscore how macroscopic achirality in racemates, when paired with non‐centrosymmetric packing, can activate strong shear piezoelectricity. In many of these systems, strong shear performance correlates with moderate‐to‐low elastic stiffness, suggesting efficient mechanical‐to‐electrical conversion under shear strain. The consistent high activity along ​ $d_{15}$, in particular, highlights this mode as a frequent and dominant contributor to shear piezoelectricity in racemic crystals. These shear piezoelectric coefficients are provided in Table S2, where the shear components are included along with space group and modulus values, providing insight into structure‐property relationships guiding shear‐dominant piezoelectric behaviour.

Although canonical $d_{14}$, $d_{15}$, $d_{25}$ and $d_{36}$ generally dominate the shear behaviour of racemic crystals; certain systems exhibit exceptionally high shear responses along other off‐diagonal components. For instance, the monoclinic co‐crystal (+‐)‐5,6a‐dimethyl‐6,6a,7,8,9,9a‐hexahydropentaleno(2,1‐b)indol‐6,7‐dione (WIBLID) shows $d_{35}$ = 77.4 pC/N and $d_{26}$ = 27.2 pC/N, substantially exceeding the typical shear values (20‐40 pC/N) observed in the most racemates. Similarly, the trigonal racemate (+‐)‐phenyl 3‐methyl‐2‐oxoindolyl‐3‐carboxylate (JOKKUQ) shows $d_{14}$ = $d_{25}$= 37.9 pC/N and $d_{26}$ = 54.3 pC/N, highlighting significant contributions from multiple shear tensor elements. These extreme values emphasise that, beyond the frequently dominant modes, alternative shear components can play a major role in overall electromechanical performance, offering new directions for the design of highly anisotropic organic piezoelectric materials. Such shear‐dominant behaviour resonates with recent reports on biomolecular crystals, where shear‐piezoelectric sensitivities of up to 60 V/Nm have been measured in d₁₆ mode for β‐Glycine‐Alginate (Gly‐Alg) piezoelectric films [31]. Moreover, the exceptional d₁₆ response of β‐glycine along the 1‐6 crystallographic direction (178 pm/V) highlights the unique capacity of specific hydrogen‐bonding networks to channel polarisation into lateral shear modes [28]. Collectively, these studies suggest that carefully engineered co‐crystals and racemic systems can exploit anisotropic molecular packing to enhance shear‐coupled electromechanical effects, opening new avenues for the design of organic materials with dominant shear piezoelectricity.

The identification of racemic crystals with large shear piezoelectric coefficients opens research paths in advanced electromechanical devices. Although conventional longitudinal (d ₃₃ ^eff) and transverse (d ₃₁) responses are widely exploited in bending actuators, cantilevers and vibration energy harvesters, shear coefficients such as d ₁₅, d ₁₄ and d ₃₆ enable efficient electromechanical coupling under lateral or torsional stress [32, 33]. Materials with dominant shear responses, including zinc oxide, aluminium nitride and AT‐cut quartz, have long been used in shear‐mode resonators, surface acoustic wave devices and gyroscopes due to their high stability and low thermal noise [34, 35, 36]. The strong d ₁₅ and d ₁₄ values identified in these racemic systems suggest similar applications for high‐sensitivity shear‐mode sensors, micro/nanoscale gyroscopes and torsional actuators, whilst offering the additional tunability and structural diversity of molecular crystals (Tables 1 and S2).

Nonzero d ₃₆ coefficients further expand potential applications by directly coupling normal stress to shear strain, a mode exploited in face‐shear actuators and guided‐wave ultrasonic transducers [37]. Such responses enable precise lateral or rotational motion in micro‐positioning stages, stick‐slip motors and compact actuation systems, where conventional longitudinal or transverse piezoelectrics are less effective. The combination of specific shear‐mode responses, d ₁₅, d ₁₄ and d ₃₆, in these racemic crystals could offer multi‐axial electromechanical functionality, which is particularly valuable in devices requiring controlled multi‐directional motion or force sensing.

Beyond sensing and actuation, strong shear piezoelectricity could provide unique ways for energy harvesting in complex mechanical environments. Unlike uniaxial d ₃₃ or d ₃₁‐based harvesters, shear‐active materials can efficiently convert twisting, sliding and multi‐directional vibrations into electrical energy [38]. This capability is ideal for wearable electronics, human motion monitoring and biomechanical interfaces, where mechanical inputs are inherently nonuniform. The biocompatibility and flexibility of molecular racemic crystals further enable applications in soft electronic skins, bio‐integrated sensors, smart surgical tools and implantable devices, where mechanical compliance and electromechanical performance must coexist. Collectively, these findings highlight the technological relevance of shear piezoelectricity and position racemic molecular crystals as versatile candidates for next‐generation electromechanical systems.

From the broader high‐throughput screening of racemic molecular crystals, a subset of representative systems was selected for in‐depth analysis to illustrate diverse structural and piezoelectric features. The selection includes DL‐tyrosine and DL‐alanine, both crystallising in the polar orthorhombic space group Pna2₁ and DL‐malic acid, which adopts the monoclinic space group Cc. Although not amongst the top‐performing materials by piezoelectric response, DL‐tyrosine and DL‐alanine were selected as experimentally characterised benchmarks, whilst DL‐malic acid represents a well‐known bio‐relevant dicarboxylic acid. These racemates have a practical basis for comparing piezoelectric behaviour with their corresponding enantiopure forms.

2.1. Case Study 1: Piezoelectric Response in Racemic and Enantiopure Malic Acid Systems

Amongst the investigated systems, malic acid and its derivatives reveal a distinct division in piezoelectric performance between racemic and enantiopure forms (Table 2). Racemic compounds generally exhibit higher $d_{33}^{eff}$ and shear coefficients, with crystals including rac‐potassium hydrogen 1‐malate and (±)‐malic acid. Although enantiopure systems display lower but directionally varied shear responses, as seen in (‐)‐malic acid and its derivatives. The racemic crystal of (±)‐malic acid, adopting a monoclinic Cc space group, exhibits a longitudinal piezoelectric strain coefficient $d_{33}^{eff}$ ​of 8.16 pC/N and a shear response with $d_{15}$ = 28.6 pC/N. This behaviour is notable given the molecular‐level mirror symmetry of the racemate, suggesting the absence of macroscopic inversion symmetry within the crystal lattice. The dielectric constant is modest (ε = 3.61), contributing to an effective electromechanical coupling. In contrast, the enantiopure form of malic acid, co‐crystallised with D‐tartaric acid in a polar P2₁ space group, yields a significantly reduced $d_{33}^{eff}$ of 1.05‐1.31 pC/N, despite almost similar stiffness (Hill‐averaged Young's modulus (E_Hill ) of 25.6‐25.9 GPa). Similar reductions are observed in other enantiopure derivatives. The co‐crystal of L‐malic acid with L‐tartaric acid, crystallising in the P2₁ space group, exhibits a modest longitudinal response ($d_{33}^{eff}$ = 3.79 pC/N) but a remarkably high off‐diagonal shear component, $d_{14}$ = 51.08 pC/N, indicating strong anisotropic polarisation rotation under shear. Similar behaviour has been experimentally reported in high‐temperature enantiomeric azobenzene‐tartrate crystals, where homochirality drives polar packing in a non‐centrosymmetric space group and yields robust piezoelectric responses of around 7 pC/N sustained up to 460 K. The coexistence of photoisomerisation under 450 nm irradiation and piezoelectricity further illustrates how chiral molecular design can couple optical and electromechanical functions within a single crystalline framework [8].

TABLE 2.

Electromechanical properties of selected racemic and enantiopure malic acid systems. Representative compounds are shown to compare racemic and enantiopure forms across different space groups and piezoelectric responses, illustrating structure‐property relations. Full piezoelectric tensor data are in Table S3. Racemic compounds contain both enantiomers; enantiopure compounds contain only one chiral form. ${\mathit{d}}_{33}^{\mathit{eff}}$: Effective longitudinal piezoelectric coefficient, ${\mathit{d}}_{15}$: Shear piezoelectric coefficient.

Serial no.	CSD ID	Crystal name	Crystal type	Category	Description	Crystal system	Space group	Young's Modulus (GPa)	Bulk Modulus (GPa)	${\mathit{d}}_{33}^{\mathit{eff}}$ (pC/N)	${\mathit{d}}_{15}$ (pC/N)	Dielectric constant (ε)
1	QQQAGP01	Rac‐Potassium hydrogen 1‐malate.H2O	Racemic	Organic Salt	Inorganic cation (K+) with organic malate anion	Monoclinic	Cc	27.05	22.2	12.87	4.16	5.14
2	MOBZAE01	4,4’‐Bipyridyl (S)‐malic acid	Enantiopure	Organic Complex	Organic base with chiral organic acid	Triclinic	P1	19.38	18.98	12.73	5.68	4.98
3	DLMALC	(±)‐Malic acid	Racemic	Organic	Racemic mixture of L‐ and D‐malic acid	Monoclinic	Cc	24.38	19.61	8.16	28.6	3.61
4	AMHMAN01	Ammonium malate.H2O	Racemic	Organic Salt/Hydrate	Ammonium ion with racemic malate includes water	Monoclinic	Cc	22.87	20.06	5.98	4.84	4.67
5	YUQQOS	(S)‐Malic acid.urea	Enantiopure	Organic Co‐crystal	Chiral organic acid with a neutral organic molecule	Monoclinic	P21	13.95	17.07	3.66	0	4.15
6	COFRUK10	(‐)‐Malic acid ((S)‐malic acid)	Enantiopure	Bioorganic	Naturally occurring enantiomer involved in metabolism	Monoclinic	P21	6.2	14.77	1.82	0	3.84
7	EYOBAV	Rac‐1‐Phenylethanaminium rac‐malate	Racemic	Organic Salt	Racemic cation with racemic anion	Monoclinic	Cc	15.64	15.11	1.55	10.45	3.64
8	CECPOP03	(R)‐1‐Phenylethanaminium (S)‐malate	Enantiopure	Organic Salt	Chiral salt with diastereomeric pairing	Monoclinic	P21	16.99	16.03	1.08	0	3.7

The highest piezoelectric activity in the malate‐based systems is observed in the racemic salt, potassium hydrogen (±)‐malate monohydrate (Cc), with $d_{33}^{eff}$ = 12.87 pC/N along with a low dielectric constant of 5.14. The mechanical stiffness remains moderate (E_Hill ​ = 27.1 GPa), allowing for efficient polarisation under mechanical stress. The presence of potassium cations likely facilitates enhanced hydrogen bonding networks, enabling a cooperative polar distortion. A further enhancement is seen in a co‐crystal formed between (S)‐malic acid and 4,4’‐bipyridine, crystallising in the triclinic P1 space group. Despite being enantiopure, this system achieves a comparable $d_{33}^{eff}$ = 12.73 pC/N. However, its shear response is more complex, featuring all components with the highest shear of −18.64 pC/N ($d_{36}$). A polymorph of (±)‐malic acid crystallising in the Cm space group shows diminished piezoelectricity ($d_{33}^{eff}$ = 4.98 pC/N), likely due to its increased symmetry and reduced effective polar axes, as the Cm space group imposes a mirror plane that limits the directionality of polar distortions. Unlike Cc or P1, which permit more degrees of freedom for spontaneous polarisation, Cm restricts dipole alignment to fewer crystallographic directions, thereby suppressing net polarisation and reducing the piezoelectric response, despite the same molecular components. Despite a lower modulus (9 GPa), its electromechanical efficiency is less optimal, constrained by structural rigidity along the polar axis.

Collectively, these observations underscore the capacity of racemic systems, particularly those crystallising in Cc or P1, to support substantial piezoelectric responses. The enhanced piezoelectric response observed in racemic and multicomponent malic acid crystals arises from their ability to adopt non‐centrosymmetric packing arrangements that break inversion symmetry despite the inherent molecular mirror symmetry. This structural organisation, combined with favourable mechanical compliance as evidenced by Young's and bulk moduli values, facilitates significant polarisation under mechanical stress. As our data shows, racemic salts and co‐crystals frequently exhibit significant $d_{33}^{eff}$ that match or exceed those of enantiopure analogues, underscoring the important role of crystal engineering and multicomponent design in achieving efficient piezoelectric functionality in bio‐organic systems. This challenges the conventional emphasis on molecular chirality and highlights the potential of racemic and multicomponent crystals as viable, sustainable alternatives in piezoelectric applications.

2.2. Case Study 2: Piezoelectric Responses in DL‐Tyrosine and DL‐Alanine Versus Their Enantiopure Analogues

DL‐alanine and DL‐tyrosine both crystallise in the polar space group Pna2₁, which supports five independent piezoelectric tensor components, including the technologically relevant longitudinal $d_{33}$. This tensor component, aligned with the principal polar axis, is especially desirable due to its direct coupling between common mechanical pressing actions and electrical response (Figure 2).

FIGURE 2.

Piezoelectric responses of racemic and enantiopure amino acids. Racemates, equimolar mixtures of L‐ and D‐enantiomers, represent a distinct class within amino acids. DL‐alanine and DL‐tyrosine crystallise in the polar space group Pna2₁, allowing five independent piezoelectric tensor components, including the longitudinal d₃₃ , which is directly aligned with the principal polar axis. This alignment enables efficient conversion between mechanical stress and electric polarisation. In contrast, the enantiopure analogues exhibit markedly different piezoelectric responses, highlighting the influence of crystal symmetry on the electromechanical properties of amino acids. (A) Representative unit cell structures of DL‐alanine and DL‐tyrosine, both crystallising in the polar point group mm2, together with their enantiopure counterparts, which crystallise in the nonpolar point group 222. Overall comparison illustrates how racemisation enables access to lower symmetry polar structures that support a unique polar axis. (B) Comparison of predicted piezoelectric responses for DL and enantiopure amino acid crystals, highlighting the role of symmetry and directionality in determining the observed electromechanical response. Experimental values for racemates are indicated by a yellow star symbol. Density functional theory calculations show that the racemic systems exhibit a significant longitudinal piezoelectric strain constant that exceeds the maximum response observed in the corresponding enantiopure forms. Full details of the plotted data are provided in Tables S4 and S5.

To deepen insights following the racemic screening phase, DL‐tyrosine, was selected for further investigation and compared against its enantiopure counterparts: L‐tyrosine and D‐tyrosine. All crystallise in the orthorhombic system, yet DL‐tyrosine adopts the non‐centrosymmetric space group Pna2₁, in contrast to the P2₁2₁2₁ group shared by the enantiopure forms. DL‐tyrosine crystallises in point group mm2, which allows a nonzero longitudinal piezoelectric tensor component ($d_{33}$) aligned with polar axes. DFT calculations reveal that DL‐tyrosine exhibits a notably high longitudinal piezoelectric strain constant, with an effective $d_{33}$ of 8.3 pC/N, surpassing the highest piezoelectric response magnitude of its pure enantiomers (Table S4). The crystal symmetry (Pna2₁, mm2) and favourable zwitterionic packing, each molecule carrying both a positive (NH₃ ⁺) and a negative (COO⁻) charge, in the racemic lattice likely enables efficient dipole alignment along this axis, yielding a significantly amplified piezoelectric response. The enantiopure L‐ and D‐tyrosine crystals, though non‐centrosymmetric (222), display only minor shear components ($d_{14}$, $d_{25}$ and $d_{36}$) with magnitudes below 5.2 pC/N and no longitudinal or transverse piezoelectric response.

Mechanically, the bulk modulus of DL‐tyrosine is calculated at 23.4 GPa, comparable to the enantiopure phases (22‐24 GPa), suggesting mechanical resilience is retained. The Young's modulus of 21.2 GPa supports its elastic compliance, a key factor in flexible electronic applications. The dielectric constant (ε) of 3.8 is moderate, promoting efficient electromechanical coupling without dielectric screening. This data‐driven comparison supports the hypothesis that racemic molecular crystals can surpass their enantiopure counterparts in piezoelectric performance.

A similar comparison between racemic DL‐alanine and its enantiopure forms was carried out (Table S5). Racemic DL‐alanine crystallises in the polar space group Pna2₁ (mm2), facilitating a longitudinal piezoelectric response along the polar c‐axis (nonzero $d_{33}$). In comparison, enantiopure L‐alanine adopts the chiral space group P2₁2₁2₁ (222), which doesn't allow longitudinal piezoelectricity ($d_{33}=0$). Due to the absence of polar symmetry elements along any principal axis. Our dataset reveals $d_{33}$ values for DL‐alanine consistently exceeding 11 pC/N, with a peak response of 12.52 pC/N, placing it amongst the most piezoelectric organic molecular crystals reported [14]. On the other hand, all L‐alanine entries within the P2₁2₁2₁ group show $d_{33}$ of 0, as expected from symmetry restrictions; only shear coefficients ($d_{14}$, $d_{25}$, $d_{36}$) are symmetry‐allowed in class 222. The highest non‐zero piezoelectric response for enantiopure systems appears in L‐alanine phosphate (P2₁, monoclinic), with $d_{33}$ of 2.99 pC/N, attributed to the introduction of a phosphate group and a polar space group distinct from alanine's typical form.

Shear piezoelectricity in L‐alanine is consistently observed through nonzero $d_{14}$, $d_{25}$ $d_{36}$ coefficients, typically ranging from 3 to 6 pC/N, with dielectric constants from 3.9 to 4.1. However, the longitudinal coefficient $d_{33}$ remains effectively zero across all enantiopure entries. Racemic DL‐alanine exhibits significant shear and longitudinal piezoelectric response. $d_{33}$ exceed 11 pC/N in multiple entries, and $d_{15}$ ​ reaches up to 6.1 pC/N, whilst all other shear terms are suppressed. The dielectric constant remains the same. These data confirm that racemisation does not alter dielectric behaviour but activates additional tensor components allowed by the lower‐symmetry polar point group. The variation is both quantitative and also crystallographically enforced, racemisation breaks the rotational suppression of the dipole in enantiopure crystals (nonpolar 222), enabling polar point group symmetry (mm2) in racemates like DL‐alanine, which supports longitudinal $d_{33}$. In a racemic mixture, stoichiometric incorporation of both enantiomers leads to macroscopic achirality and permits access to a lower‐symmetry polar point group such as mm2. This reduction in symmetry removes the rotational constraints present in the enantiopure phase and allows longitudinal tensor components that were previously symmetry‐forbidden to become accessible. This is evident in DL‐alanine and DL‐tyrosine, which exemplify a broader trend: racemic amino acid crystals can surpass their chiral analogues in longitudinal piezoelectric performance due to symmetry‐permitted tensor elements. Thus, DL‐alanine and DL‐tyrosine stand as a prototypical candidate for symmetry‐driven enhancement of piezoelectricity in bioorganic crystals.

2.3. Structural Design Rules Governing Piezoelectric Response in Racemic Molecular Crystals

A qualitative correlation between crystal packing, elastic properties and piezoelectric coefficients reveals clear structure‐property trends governing polarisation in racemic molecular crystals. Amongst the systems examined, (±)‐phenyl 3‐methyl‐2‐oxoindolyl‐3‐carboxylate, which shows the highest effective piezoelectric coefficient (d₃₃ ^eff  = 27.18 pC/N) and a net crystal dipole moment of 23.69 D, originates from its trigonal P3₂ symmetry and a unique intermolecular hydrogen‐bond pattern combined with π─π stacking, which together enable cooperative polar alignment within the crystal. In this crystal, the predicted d₃₃ ^eff aligns with the direction of the highest predicted longitudinal mechanical stiffness (c₃₃  = 17.6 GPa) and the largest diagonal dielectric constant (ε = 3.25), consistent with the overall net dipole moment of 23.69 D. Such directional concurrence of maximum piezoelectric, elastic and dielectric responses signifies a strong intrinsic electromechanical coupling along the principal polar axis (Figure 3; Tables 1 and S6). The corresponding energy frameworks showing the supramolecular architecture, highlighting dispersion‐dominated interactions and total interaction energies (E_tot ), are shown in Figure S2, further supporting that the triangular molecular packing within the unit cell, together with intermolecular interactions, contributes to the high predicted longitudinal piezoelectric response. In comparison, (±)‐5,6a‐dimethyl‐6,6a,7,8,9,9a‐hexahydropentaleno(2,1‐b)indol‐6,7‐dione (WIBLID) exhibits a similarly high intrinsic dipole moment (48.44 D) and d₃₃ ^eff  = 25.42 pC/N, consistent with local polar distortion within its monoclinic Pc lattice. Crystals containing extended hydrogen‐bonded frameworks, such as DL‐alanine (DLALNI20) and diammonium O‐phospho‐DL‐threoninate (GEJKUC), show moderate piezoelectric responses (d₃₃ ^eff = 12.51 and 10.83 pC/N, respectively), reflecting cooperative yet spatially constrained dipole coupling within orthorhombic Pna2₁ systems. Moderately high predicted piezoelectric performance is also observed for water‐mediated hydrogen‐bond networks in rac‐potassium hydrogen 1‐malate·H₂O (QQQAGP01) and N‐methyl‐DL‐aspartic acid monohydrate (WOCVOZ), which yield d₃₃ ^eff values of 12.87 and 10.54 pC/N, respectively, supported by flexible hydrogen linkages that facilitate polar reorientation. DL‐tyrosine (DLTYRS) displays an intermediate response (d₃₃ ^eff  = 8.34 pC/N), consistent with its relatively rigid hydrogen‐bond geometry. In contrast, (3β,3aβ,7β,8aα)‐(±)‐6,6‐(ethylenedioxy)‐3,8,8‐trimethyl‐1,2,3,3a,4,5,6,7,8,8a‐decahydro‐3a,7‐(methano)azulen‐2‐one (TIJWIS), which features intramolecular hydrogen bonding, exhibits a d₃₃ ^eff of 11.22 pC/N and a high shear piezoelectric response (d₂₅ ) of 17.4 pC/N, along with a low Young's modulus of 12.8 GPa. The orthorhombic N‐carboxy‐DL‐valine anhydride (WIKCUO), with a high crystal dipole moment (45.34 D) oriented along the polar axis (z), but limited hydrogen‐bond connectivity, shows a moderate d₃₃ ^eff of 9.76 pC/N. Collectively, these data demonstrate that racemic crystals with directional and flexible hydrogen‐bond networks, particularly those incorporating water molecules or polar π─π frameworks, achieve the most effective piezoelectric response, whereas rigid lattices or isolated intramolecular dipoles yield comparatively diminished macroscopic polarisation.

FIGURE 3.

Molecular packing of top piezoelectric racemic crystals identified through high‐throughput DFT characterisation. The yellow and green arrows indicate the directions of intermolecular hydrogen bonding within the racemic crystal structures. Racemates including DL‐alanine, DL‐tyrosine and diammonium O‐phospho‐DL‐threoninate exhibit directional hydrogen‐bonded networks within the crystal lattice. The crystals of rac‐potassium hydrogen 1‐malate·H₂O and N‐methyl‐DL‐aspartic acid monohydrate display water‐mediated hydrogen‐bonding networks with distinct directional patterns. The racemate (±)‐phenyl 3‐methyl‐2‐oxoindolyl‐3‐carboxylate shows a unique hydrogen‐bonding motif, as highlighted in the inset. In contrast, (3β,3aβ,7β,8aα)‐(±)‐6,6‐(ethylenedioxy)‐3,8,8‐trimethyl‐1,2,3,3a,4,5,6,7,8,8a‐decahydro‐3a,7‐(methano)azulen‐2‐one exhibits intramolecular but no intermolecular hydrogen bonding, whilst (±)‐5,6a‐dimethyl‐6,6a,7,8,9,9a‐hexahydropentaleno(2,1‐b)indol‐6,7‐dione shows no hydrogen‐bond formation. The variation in hydrogen‐bonding motifs and their spatial directionality correlates strongly with the observed directional differences in piezoelectric response and mechanical stiffness amongst these racemic crystals. Interaction hotspots mapped on the Hirshfeld surfaces of DL‐alanine and (±)‐phenyl 3‐methyl‐2‐oxoindolyl‐3‐carboxylate further highlight regions of hydrogen‐bonding within the crystal lattice. The directional arrows next to the crystal structures of DL‐alanine and (±)‐phenyl 3‐methyl‐2‐oxoindolyl‐3‐carboxylate indicate the orientation of the electromechanical responses, including the longitudinal piezoelectric coefficient (d₃₃ ^eff ), elastic constants (C_ij ), and dielectric coefficients (ε) along the indicated directions.

The piezoelectric performance of racemic molecular crystals is linked to their structural and electronic characteristics. Crystals exhibiting non‐centrosymmetric packing with directional hydrogen bonding or π─π interactions consistently demonstrate measurable longitudinal and shear piezoelectric coefficients, highlighting controlled asymmetry in molecular arrangement as a key structural prerequisite for piezoelectricity in racemic systems. Comparative structural analyses show that cooperative hydrogen‐bond networks, either direct or water‐mediated, enhance polar coupling along defined crystallographic axes, promoting effective dipole alignment and elastic adaptability. Hirshfeld surface analysis further indicates the strong interaction hotspots that could be the regions of local strain and charge redistribution, providing microscopic evidence for the origin of macroscopic piezoelectricity in racemates. Crystals such as DL‐alanine and (±)‐phenyl 3‐methyl‐2‐oxoindolyl‐3‐carboxylate display distinct but complementary structure‐property relationships. The former stabilises polar order through linear hydrogen bonds, whereas the latter achieves enhanced response through conformational diversity, oriented hydrogen bonding and π─π stacking within its trigonal lattice (Figure 4). These observations demonstrate that anisotropic hydrogen‐bond geometry and molecular conformational flexibility act together to sustain non‐cancelling dipole orientations. A comparison of net crystal dipole moment with piezoelectric and mechanical properties reveals general trends, with d₁₅ increasing most clearly with dipole moment, as shown in Figure S3. Overall, racemic crystals screened and optimised for strong piezoelectric performance combine non‐centrosymmetric space groups, directionally persistent hydrogen‐bond frameworks, and flexible or polar π‐conjugated motifs capable of dynamic dipole reorientation. The interplay between hydrogen‐bond topology, π─π interactions, and elastic compliance defines an effective structural design strategy for achieving high longitudinal piezoelectricity in organic racemates and provides a transferable framework for the rational design of sustainable molecular piezoelectric materials.

FIGURE 4.

Structural and interaction analysis of piezoelectric response in racemic molecular crystals. DL‐alanine (orthorhombic) represents a well‐characterised reference piezoelectric racemate, whilst (±)‐Phenyl 3‐methyl‐2‐oxoindolyl‐3‐carboxylate (trigonal) is predicted to exhibit the highest longitudinal piezoelectric response (d₃₃ ^eff  = 27.2 pC/N). The unit cell views highlight molecular packing and symmetry in both systems, and the Hirshfeld surfaces mapped with d_norm (B3LYP/6‐311G(d,p)) reveal interaction hotspots dominated by hydrogen bonding and π─π contacts. Three conformers (C1, C2, C3) within the (±)‐Phenyl 3‐methyl‐2‐oxoindolyl‐3‐carboxylate unit cell contribute collectively to its enhanced longitudinal piezoelectricity through directional intermolecular interactions.

2.4. Analysis of Structures With Weak Longitudinal Piezoelectric Response

Amongst the non‐centrosymmetric racemic crystals screened in our high‐throughput DFT study, a substantial fraction exhibits no symmetry‐allowed longitudinal piezoelectric strain due to constraints imposed by their crystallographic point groups. Within the subset of structures for which a longitudinal response is permitted, 20 crystals display predicted effective $d_{33}^{eff}$ values below 2 pC/N, indicating intrinsically weak piezoelectric coupling (Table S7). Importantly, both the strongest‐ and weakest‐performing racemic crystals in our dataset frequently belong to the same common polar space groups (Pna2₁, Cc, P2₁), demonstrating that crystallographic symmetry primarily determines which piezoelectric tensor components are symmetry‐allowed, whereas the magnitude of $d_{33}^{eff}$ is governed by more subtle packing‐dependent factors and the extent of cancellation of local electromechanical contributions within the crystal lattice.

Analysis of the chemical structures underlying the low $d_{33}^{eff}$ crystals reveal a clear trend, they are predominantly small, highly hydroxylated molecules or contain multiple polar functional groups, such as polyols (DL‐mannitol, pentane‐1,2,3,4,5‐pentol) and hydroxy‐amino acids (DL‐2‐hydroxyphenylalanine) and other amino acid or sugar derivatives (Table S7). In contrast, the highest‐performing crystals tend to be more rigid and aromatic. Our highest‐performing compounds include rigid aromatic structures and simple amino acids, such as (±)‐Phenyl 3‐methyl‐2‐oxoindolyl‐3‐carboxylate and DL‐Alanine (Table 1). For instance, DL‐o‐tyrosine (2‐amino‐3‐(2‐hydroxyphenyl)propionic acid; CSD ID: DTYROS, P2₁, monoclinic) exhibits a low predicted $d_{33}^{eff}$ of 1.6 pC/N, whereas its isomer, DL‐tyrosine (CSD ID: DLTYRS, Pna2₁, orthorhombic), shows a substantially higher response of 8.3 pC/N. This example demonstrates that even closely related chemical isomers can display markedly different longitudinal piezoelectric responses depending on their crystal packing and space group. This structural distinction indicates that, even when the same space group is adopted, molecular composition and functionalisation critically influence the net longitudinal piezoelectric response.

2.5. Hydrogen Bonding Versus Predicted Longitudinal Piezoelectric Response

A linear correlation analysis was performed to investigate the relationship between the number of hydrogen bonds and the predicted $d_{33}^{eff}$ across racemic crystals. The resulting regression model is shown in Figure 5. The low coefficient of determination indicates an essentially negligible linear correlation, suggesting that increased hydrogen bonding does not essentially enhance (and may even weakly suppress) the longitudinal piezoelectric response in these racemates. This observation is consistent with previous studies reporting that hydrogen bond strength alone is not a reliable predictor of piezoelectric coefficients in hydrogen‐bonded systems, as the relationship between dipole derivative and compliance is often nonlinear and system‐dependent [39]. These findings collectively suggest that whilst hydrogen bonding can contribute to electromechanical coupling (Figure 3), its presence alone is insufficient to dictate high $d_{33}^{eff}$ values, and that other factors such as crystal symmetry, molecular orientation and elastic anisotropy likely play a more significant role.

FIGURE 5.

Correlation between the total hydrogen bond count per asymmetric unit (x) and the predicted effective longitudinal piezoelectric response (${\mathit{d}}_{33}^{\mathit{eff}}$) for racemic molecular crystals. The linear fit is described by ${\mathit{d}}_{33}^{\mathit{eff}}$= −0.22x + 5.1, with a low coefficient of determination (R ² = 0.017), indicating negligible linear correlation. This suggests that the presence of hydrogen bonding alone is not a strong predictor of longitudinal piezoelectric performance in racemic systems.

2.6. Predicted Mechanical Properties of Racemic Crystals

Mechanically flexible molecular crystals have recently gained attention as promising organic piezoelectrics, where the electromechanical response arises from the interplay between lattice polarity and mechanical compliance [40]. To quantify this relationship, full elastic tensors were computed using the finite‐difference method within our CrystalDFT high‐throughput DFT framework [10]. The resulting stiffness matrices reveal elastic anisotropy across the racemic systems, providing insight into how structural softness along specific crystallographic directions facilitates strain‐induced polarisation.

Elastic moduli derived from the stiffness tensor, including Young's, bulk and shear moduli, provide quantitative measures of this anisotropy and serve as robust descriptors of the mechanical response of racemates under applied stress (Figure S4). Stress components and their Voigt representations underpin the linear elastic framework linking stress and strain. The distribution of elastic properties (Figure 6A) spans a wide range, with most Young's and bulk moduli falling between 5 and 25 GPa, indicative of moderate stiffness across the majority of racemic systems. Variations in the eigenvalues of the stiffness tensor further underscore the directional dependence and mechanical diversity intrinsic to these crystals. To ensure the reliability of subsequent analyses, racemic structures exhibiting negative stiffness tensor eigenvalues were excluded, yielding a dataset of mechanically stable systems (see Note S3). Two‐dimensional projections of the elastic tensor for the top‐predicted racemic materials (Figure 6B) illustrate the directional dependence of Young's modulus and Poisson's ratio. These visualisations emphasise the anisotropic elastic behaviour, providing insight into how directional stiffness variations govern mechanical response across the racemics. The relationship between the diagonal elastic coefficients and macroscopic stiffness is shown in Figure S5, highlighting how variations in C₁₁‐C₆₆ correlate with Young's and bulk moduli. The full elastic tensors (C_ij ) and corresponding piezoelectric tensors (d_ij ) for these top‐predicted materials are provided in Table S1, offering a comprehensive dataset to correlate directional mechanical compliance with electromechanical performance and to guide rational design of high‐efficiency molecular piezoelectrics.

FIGURE 6.

Predicted mechanical properties of racemic molecular crystals. Materials exhibiting negative diagonal elastic stiffness coefficients or negative eigenvalues of the stiffness tensor C_ij (indicative of mechanical instability) were excluded from the analysis (see Note S3). (A) Distribution of DFT‐predicted elastic moduli across the racemic dataset, highlighting the anisotropy and mechanical diversity characteristic of racemic materials. Representative elastic moduli, including Young's modulus, bulk modulus and shear modulus, serve as practical criteria for evaluating mechanical behaviour under simple stress conditions. The corresponding formulas for these are derived in the limit of small displacement, consistent with the linear elastic rule. (B) Two‐dimensional projections of the elastic tensor C for the top screened racemic materials, illustrating the directional dependence of Young's modulus (GPa) and Poisson's ratio. First‐principles calculations were employed to systematically explore the electronic structures, elastic properties, and their anisotropic character across the racemic dataset.

Directional variations in elastic compliance influence the magnitude of the piezoelectric response along distinct crystallographic axes [28], with regions of lower stiffness contributing disproportionately to the overall piezoelectric response, although the nature of mechanical coupling differs between effective (global) and crystallographic components [40]. Extending this analysis to the diagonal components of the elastic tensor (c₁₁ , c₂₂ , c₃₃ , c₄₄ , c₅₅ , c₆₆ ) reveals a rich, direction‐dependent hierarchy in electromechanical coupling. The effective longitudinal response (d₃₃ ^eff ), representing the macroscopic electromechanical output, is most strongly influenced by shear‐dominated stiffness terms, indicating that volumetric and shear compliance along specific crystallographic planes govern the macroscopic piezoelectric output rather than purely axial rigidity. Directional longitudinal responses exhibit distinct trends, such as d₁₁, which shows minimal correlation across the diagonal elastic components, reflecting weak electromechanical coupling along that axis. In contrast, d₂₂ correlates inversely with all diagonal stiffness terms, particularly shear‐related components, highlighting that mechanically compliant directions promote b‐axis polarisation. The d₃₃ component displays moderate positive correlations, suggesting that the principal polar axis aligns along directions of intermediate stiffness that support strain‐induced polarisation. Shear‑dominated coefficients (d₁₄, d₂₅, d₃₆ ) consistently show negative correlations, emphasising that reduced shear stiffness directly enhances shear‑driven polarisation, whilst off‐diagonal terms, d_15, contribute only marginally to the overall response. Collectively, these findings delineate a subtle mechanical‐electrical hierarchy: macroscopic longitudinal output balances lattice stiffness and polarisation, directional longitudinal components respond to anisotropic stiffness, and shear‐dominated coefficients exploit lattice softness. Figure S6 summarises the component‐specific correlations, with full regression details provided in Table S8.

The d₃₃ ^eff shows its strongest dependence on bulk and shear moduli, whilst the correlation with the Young's modulus is comparatively weaker (Figure 7A and Table S9). This behaviour indicates that the measurable effective longitudinal response is primarily governed by volumetric and shear compliance of the lattice rather than only by uniaxial stiffness. In contrast, the directional longitudinal tensor elements exhibit distinct relationships (Figure 7B–D). The d₃₃ component shows moderate positive correlation with all three elastic moduli, suggesting that the principal polar axis lies along moderately stiff crystallographic directions that support elastic recovery during reversible polarisation [41]. The d₂₂ coefficient shows clear negative slopes, most notably with shear modulus, revealing that lower shear stiffness facilitates larger strain‐induced b‐axis polarisation. The d₁₁ component displays negligible correlation, consistent with weak electromechanical coupling along that axis.

FIGURE 7.

Correlation between elastic moduli and piezoelectric coefficients in racemic molecular crystals. Scatter plots with trend lines showing the relationships between the calculated elastic moduli (Young's, bulk and shear) and individual piezoelectric tensor components (d_ij ). Panel A presents the macroscopic effective longitudinal coefficient (d₃₃ ^eff ), whilst panels B‐H show the directional longitudinal (d₁₁ , d₂₂ , d₃₃ ) and shear‐dominated (d₁₄ , d₂₅ , d₃₆ ) components. The regression details and fitted slope values revealing component‐specific correlations are provided in Table S9, with d₃₃ ^eff ​ and polar axial d₃₃ scaling moderately with bulk and shear moduli, whilst d₂₂ , d₁₄ , d₂₅ and d₃₆ ​ display inverse trends, indicating enhanced piezoresponse along mechanically compliant directions. Legends denote the corresponding elastic moduli used in each fit.

The shear‐dominated tensor components (d₁₄ , d₂₅ , d₃₆ ) show a consistent inverse relationship with all elastic moduli (Figure 7E–G and Table S9). The strongest dependence occurs for d₂₅ , which exhibits correlation of −0.29, −0.34 and −0.75 with Young's, bulk and shear moduli, respectively. Similarly, d₃₆ correlates negatively with all three calculated moduli, underscoring that reduced shear stiffness directly enhances shear‐driven polarisation. The d₁₄ component follows a similar trend, further supporting that anisotropic lattice softness enables strong shear electromechanical coupling. In contrast, the off‐diagonal d₁₅ component exhibits weak positive correlation across all three moduli (Figure 7H), indicating a minor contribution to overall polarisation. Together, these results establish a subtle mechanical‐electrical hierarchy across the tensor components. Longitudinal responses (d₃₃ ^eff ) scale with intermediate lattice stiffness, balancing elastic recovery and polarisation, whereas shear‐dominated coefficients (d₁₄ , d₂₅ , d₃₆ ) benefit from mechanical softness and local compliance. The weak correlations in off‐diagonal terms confirm that piezoresponse in these racemic molecular crystals is governed by a combination of directional elastic anisotropy, lattice topology and supramolecular flexibility rather than global stiffness alone. Although the data are scattered, as expected across the diverse racemic dataset, the aim is to highlight general trends rather than provide exact quantitative predictions. This behaviour contrasts sharply with inorganic piezoelectrics, where strong ionic polarisation and rigidity dominate [40], underscoring that elastic anisotropy is the primary design lever for enhancing electromechanical efficiency in soft molecular systems.

These findings provide evidence that racemic molecular crystals, particularly those based on bio‐relevant building blocks, offer a powerful platform for developing soft, sustainable and lead‐free piezoelectric materials. By systematically evaluating over 120 racemic candidates, we identify a previously underexplored subset exhibiting non‐centrosymmetric packing and strong electromechanical coupling. Our results reveal that the flexible racemic systems display effective longitudinal strain coefficients up to 28 pC/N, over twice that of DL‐alanine (12.5 pC/N), whilst maintaining low dielectric constants below five and high mechanical flexibility. These findings emphasise that coupling mechanical flexibility with supramolecular chirality and polarity offers a viable strategy for designing soft, high‐performance piezoelectric crystals. Collectively, our work demonstrates that racemic crystallisation can support functional properties, establishing racemic architectures as a versatile design strategy for next‐generation piezoelectric materials suited to flexible electronics, biopiezoelectric sensors and energy‐harvesting applications.

3. Methods Section

Comprehensive descriptions of the computational methodology, simulation parameters and modelling approach employed in this study are provided in Note S2 of the Supporting Information.

Conflicts of Interest

The authors declare no conflicts of interest.

Code Availability Statement

All the source code used for this work is available on the Actuate Lab website at https://actuatelab.ie/actuate_tools.html.

Supporting information

Supporting File 1: Supporting Information includes Notes S1–S3, Schemes S1–S4, Tables S1–S9, and Figures S1–S6.

Data Availability Statement

All data presented in this study, along with the necessary resources to reproduce the findings, are available on the CrystalDFT—Racemates database website at https://actuatelab.ie/racemic‐piezoelectrics/index.php.