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. 2025 Dec 2;26(3):1219–1225. doi: 10.1021/acs.cgd.5c01295

Polymorphism and Negative Linear Compressibility in Pyrazine-d4

Christopher J Ridley 1,*, Jasmine K Hinton 1, Jamie J Molaison 1
PMCID: PMC12879538  PMID: 41659831

Abstract

Pyrazine (1,4-diazine) is a widely used linker in coordination polymers, molecular magnets, and metal–organic frameworks, yet its solid-state polymorphism is controlled by weak C–H···N interactions. Using variable-temperature and high-pressure neutron diffraction, a previously unrecognized low-temperature transition to phase IV is identified, showing that the form stabilized under pressure can also be accessed below ∼90 K at ambient pressure in the perdeuterated compound. The transition from phase III → IV involves a symmetry-breaking lattice distortion driven by the reorganization of C–H···N hydrogen bonds, accompanied by negative linear compressibility, which is primarily accommodated through the reduction in void-space within the structure. Structural analysis reveals that while the overall monoclinic framework of phase IV is preserved under both temperature and pressure routes, the evolution of hydrogen-bonded network is distinct depending on the pathway taken. These results establish pyrazine as a model molecular solid for studying pressure–temperature polymorphism and demonstrate how weak directional interactions can produce anomalous mechanical responses in organic crystals.

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Introduction

Pyrazine (1,4-diazine) is a structurally simple yet chemically versatile heteroaromatic molecule. Despite its apparent simplicity, it plays a key role in a wide range of functional materials, including metal–organic frameworks, molecular magnets, and coordination polymers, where its geometry and electronic structure influence framework topology, charge transport, and magnetic ordering. − Beyond use as a linker, it is used as a cationic component in molecular salts exhibiting large dielectric responses. In its solid-state molecular form, pyrazine serves as a model system for studying weak intermolecular interactions, such as dispersion forces and C–D···N hydrogen bonding, which significantly impact lattice dynamics and thermal behavior through introducing anisotropic interactions. , These interactions govern bulk properties such as thermal expansion, compressibility, and vibrational entropy, making pyrazine and related heterocycles valuable platforms for understanding structure–property relationships in dispersion-bound molecular solids. Its small molecular size and crystallographic tractability further support its use as a benchmark system for modeling lattice anharmonicity and low-frequency vibrational behavior in organic materials.

Comparisons between benzene (C6H6), pyridine (C5H5N), and the diazines (C4H4N2) show that the introduction of nitrogen atoms alters both the electronic distribution and the nature of intermolecular bonding. Podsiadło et al. demonstrated that, as one progresses through this series, C–D···π interactions are gradually replaced by C–D···N interactions, reflecting the increasing electronegativity and lone-pair availability of nitrogen atoms in the ring.

Under pressure, all three molecule-types show a breadth of structural diversity. − Pyrazine exhibits rich polymorphism driven by temperature and pressure, making it a compelling system for studying weak intermolecular interactions in organic solids. At ambient conditions, it adopts an orthorhombic structure (phase III, Pmnn). , Two additional polymorphs (phases I and II, both P21/c) form upon heating, with phase I later identified as a metastable phase accessible only by cooling from the melt. , Under pressure, a fourth polymorph (phase IV, P21/n) emerges above ∼1.1 GPa, as shown by Raman and single-crystal X-ray studies. , These studies also found that phase III remains stable down to 170 K, which is also assumed by earlier spectroscopic work , and phosphorescence measurements of pyrazine at 4.2 K.

Understanding pyrazine’s intermolecular interactions and polymorphism provides critical insights into the fundamental forces that govern molecular solids. Across all known phases, C–D···N hydrogen bonds dominate the intermolecular interactions, underscoring the importance of accurately locating hydrogen atoms to fully determine the bonding landscape. As a widely used linker, pyrazine’s packing and phase behavior directly influences material properties such as mechanical stability, thermal response, and charge or magnetic transport. Knowledge of these weak interactions under varying thermodynamic conditions informs the rational design of organic materials with targeted functionalities. Pyrazine can therefore serve as a benchmark system for elucidating structure–property relationships central to the development of advanced molecular materials.

In the present study, this molecular solid is revisited using neutron powder diffraction to resolve hydrogen bonding motifs and track their evolution across a range of temperatures and pressures. Remarkably, it is found that the previously reported high-pressure phase IV can also be accessed at ambient pressure at temperatures below ∼90 K. The discovery of this low-temperature boundary to phase IV reveals the importance of intermolecular packing in pyrazine; rearrangements of the hydrogen-bond network can alter lattice dynamics, suggesting that similar effects could modulate the properties and guest–host interactions in many frameworks and functional materials built from pyrazine linkers.

Results and Discussion

Low Temperature Stabilization of Phase IV

The low-temperature neutron diffraction data reveal a direct transition from orthorhombic phase III to monoclinic phase IV near 90 K (Figure S1), marked by a symmetry-breaking distortion of the unit cell (β angle increasing to a maximum of 93.2° at 4 K) (Figure S3). Despite this change in symmetry, the unit-cell volume evolves smoothly through the transition without collapse, indicating that the driving force is not packing density but the reorganization of weak C–D···N hydrogen bonds. Such sensitivity of crystal symmetry to modest shifts in bonding directionality highlights how weak interactions can reshape the mechanical response of molecular solids, a principle relevant to the design of responsive frameworks. The transition is continuous in volume, with no evidence of phase coexistence, suggesting a second-order (or weakly first-order) mechanism. Further analysis of the thermal contraction of the cell (Figure S3) confirms that the distortion is primarily accommodated by reductions along the b- and c-axes, while the a-axis remains effectively invariant, consistent with the rigidity of the pyrazine ring along this direction.

The temperature dependence of the unit-cell volume was modeled using an Einstein quasi-harmonic expression, which represents the lattice as a collection of harmonic oscillators with effective vibrational energies. In this framework, the volumetric response can be captured by a single dominant phonon mode, consistent with the molecular rigidity and localized electronic structure of pyrazine

V(T)=V0+∑i=1nCEiexp(θEi/T)−1

where V(T) is the unit-cell volume at a given temperature T, V 0 is the unit-cell volume at 0 K, C Ei is the Einstein constant and θEi is the effective Einstein temperature (where the total number of contibuting terms, n = 1, 2...). Figure a shows the fit to this model for pyrazine (d4), with the resultant parameters summarized in Table . For comparison, benzene (d6) requires a two-term description of its thermal expansion, see Figure S2, reflecting the larger role of higher-energy vibrational contributions in its lattice dynamics.

1.

1

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(upper) (a) Unit-cell volume for pyrazine (d4) determined from neutron powder diffraction. The line corresponds to the fit using the single-term Einstein model described in the main text. Temperature evolution of the deuteron bonding geometry in pyrazine (d4), as determined from neutron powder diffraction: (b) D···N intermolecular separation and (c) C–D···N bond angle. In phase IV, symmetry lowering leads to the emergence of two inequivalent bonding environments. (lower) Pressure evolution of pyrazine (d4) at 290 K, as determined from neutron powder diffraction: (d) unit-cell volume for both phases, fitted against a single Rydberg-Vinet equation of state. The bulk modulus, pressure derivative and values for V 0 are shown. (e) D···N intermolecular separation. (f) C–D···N bond angle. In all plots, dashed lines serve as a guide to the eye, and the approximate boundary between the two phases is indicated with the shaded region.

1. Parameters Obtained from Fitting the Einstein Expression to the Unit-Cell Volume Data for Pyrazine (This Work) and for Benzene (d6 and h6, Refitted from Fortes and Capelli)­ .

parameter pyrazine (d4) benzene (d6) benzene (h6)
V 0(Å3/Z) 98.366(3) 115.4300(2) 116.0100(7)
C E1 2.55(3) 4.684(7) 4.67(2)
θE1(K) 114.6(9) 123.4(2) 124.9(3)
C E2   174.2(8) 129(2)
θE2(K)   1105(2) 1018(3)
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a

For direct comparison, all volumes, and by extension C En values, are normalized by Z. Benzene data required a two-term Einstein model.

The contrast illustrates that directional C–D···N hydrogen bonding in pyrazine constrains molecular motion and simplifies its lattice vibrational spectrum, in contrast to dispersion-bound benzene. Each pyrazine molecule participates in eight such interactions; four as C–D donors and four as acceptors via the two N atoms, giving rise to low-energy lattice vibrations (∼10 meV), comparable in energy to the previously reported lattice vibrational-modes, and allowing its thermal expansion to be accurately described by a single Einstein oscillator term. In benzene, weaker and less directional intermolecular forces impose fewer constraints, making higher-energy contributions (∼95 meV), likely from intramolecular modes, more significant. As a result, two Einstein terms are required to capture both lattice and higher-energy contributions. This difference in bonding and lattice dynamics is consistent with the conclusion that hydrogen bonding dominates pyrazine aggregation in both phase III and IV, highlighting how directional interactions can govern thermal expansion in molecular solids.

The evolution of the hydrogen-bonding network across the transition can be inferred from the refined D positions (Figure ). In phase III, the D···N contact shortens, while remaining approximately unchanged in linearity, consistent with a gradual strengthening of the intermolecular hydrogen bond. At the onset of phase IV the D···N separations remain approximately constant on further cooling (∼2.45 Å), still shorter than at ambient conditions. Changes in the cell-volume are instead accommodated by a change in hydrogen-bond linearity; in the monoclinic phase IV, the average angle remains nearly constant with temperature, but the symmetry lowering creates two inequivalent environments that diverge in opposite directions, one angle increasing to ∼156.5°, the other decreasing to ∼148°. This divergence signals a more asymmetric hydrogen-bonding network arising from denser molecular packing.

A Hirshfeld surface and 2D fingerprint analysis was performed on the two ambient pressure structures, see Figure . Overall, the proportion of the surface area corresponding to D···N contacts decreases from phase III to IV by 1.4%. Full elemental decomposition of the surface (see Figure S6) shows that the other components accompany this with much smaller changes, however, the “wings” related to the D···N contact, and the central feature related to the D···D contact both shift to lower d e,i , consistent with the increase in density. This suggests that the hydrogen bonding is shortening and strengthening in the structure, while also becoming more spatially localized. Molecular electrostatic potential mapping (Figure e/f) shows that the monoclinic adjustment to the structure results in two inequivalent pairwise interactions between the central molecule and those surrounding it. The total energy for each of these is lower in phase IV than III, justifying the overall stability of this phase at lower temperatures.

2.

2

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Hirshfeld 2D fingerprint plots for phase III (a), 300 K and phase IV (b), 10 K of pyrazine (d4) at ambient pressure. (c,d) Contributions from D···N intermolecular contacts are highlighted, revealing the characteristic “wings” associated with hydrogen bonding. Insets show the full Hirshfeld surfaces viewed along the a-axis. (e,f) Molecular electrostatic potential maps for the two phases, viewed along the c-axis, illustrating pairwise intermolecular interactions. Four distinct pairwise interactions are present in the orthorhombic phase, compared with five in the monoclinic phase. The total calculated interaction energy for the hydrogen-bonded molecules is indicated.

These changes highlight that weak, directional hydrogen bonds can reorganize cooperatively under modest perturbations, inducing anisotropy and symmetry breaking in the lattice. While observed here in molecular pyrazine, such behavior is intrinsic to the pyrazine linker and therefore likely to propagate through extended frameworks. Subtle deformations and low-energy vibrational modes inherent to this motif influence macroscopic properties including thermal expansion, phase stability, and even functional electronic or mechanical responses. ,

Comparisons with High Pressure

High-pressure data show that the transition to phase IV occurs between 0.7 and 0.8 GPa, with no evidence of phase coexistence (see Figure S4). The sample remains indexed by the phase IV monoclinic cell up to the maximum pressure investigated, 9.1 GPa. As in the low-temperature study, the volume change through the transition is continuous. A single Rydberg-Vinet equation of state fitted to the unit-cell volume data (Figure d) yields a bulk modulus B 0 = 6.7(2) GPa and a pressure derivative B′ = 7.79(12). This low bulk modulus is characteristic of soft molecular solids, dominated by dispersion and, in some cases, weak hydrogen-bonding interactions. The values are comparable to those reported for pyridine and benzene. , Both phase I and phase II of benzene exhibit slightly reduced B′ relative to pyridine and pyrazine. These larger derivatives suggest that hydrogen bonding contributes to enhanced pressure-induced hardening. In all three, B′ > 4, and this behavior can be correlated with the progressive reduction of intermolecular void-space under compression (Figure c).

3.

3

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(a) Structure of pyrazine phase IV viewed along the b-axis (parallel to the principal X2-axis). The X3-and X1-axes are overlaid on the conventional unit-cell. (1/2) are used here to indicate the inequivalent bonding environments discussed in the main text. (b) Pressure dependence of the relative change in the principal strain axes, referenced to their ambient phase III values. The shaded region represents the boundary between phase III and IV. (c) Void space volume, indicating crossover region with negative linear compressibility. (inset) void space surface for ambient pressure structure.

As in the temperature-dependent study, the a-axis is the least responsive to applied pressure. In both phases, pyrazine rings stack coaxially along the c-axis, with their centroids directly aligned and rings tilted via rotation about the a-axis. In both phases, the separation between the pyrazine centroids decreases smoothly with pressure. This suggests that a larger π–π repulsion between adjacent rings may be responsible for the resultant unit-cell distortion in phase IV.

The C–D bond length remains unchanged within experimental uncertainty; however, both the D···N separation and the C–D···N bond angle exhibit clear variations across the transition (Figure e,f). Importantly, the overall monoclinic framework of phase IV is preserved regardless of whether it is accessed via pressure or temperature, yet the evolution of the hydrogen-bond geometry is pathway dependent.

Under compression, the D···N separation decreases and stabilizes at ∼2.375 Å, while the two inequivalent C–D···N angles diverge such that their average decreases continuously with pressure. In contrast, when phase IV is stabilized by cooling, the average bond angle remains essentially constant, even though the individual angles diverge in opposite directions.

These results indicate that while the molecular framework and lattice symmetry of phase IV are robust, the hydrogen-bonding network retains a degree of flexibility that allows distinct structural responses depending on thermodynamic pathway. This pathway dependence demonstrates the delicate balance between molecular rigidity and weak directional bonding, a principle with direct implications for controlling polymorphism and mechanical response in molecular solids.

When the unit-cell compression is analyzed, phase III shows the expected contraction along all three principal axes (X1, X2, X3) (Figure b). In phase IV, X1 and X2 continue to contract, but X3 exhibits an anomalous response, increasing by up to 2% by 3 GPa before decreasing linearly at higher pressures. The X3 principal axis corresponds to the separation between columns of pyrazine molecules (Figure a). The increase in separation between columns arises from the combined effects of reduced void space between molecules and the tilt of the molecules relative to the c-axis in phase IV. The rigidity of the molecular ring, together with these structural adjustments, leads to negative linear compressibility along X3, primarily due to directional electrostatic interactions. Above 3 GPa, the applied pressure overcomes this repulsion, and X3 decreases linearly. The D···N separation and C–D···N angles both show small changes near 2 GPa, reflecting this structural adjustment.

In phase III, a-axis neighboring molecules are equivalent. In phase IV, changes in symmetry and tilt around the b-axis lead to a different bonding environment depending on whether the central molecule is tilted toward or away from the neighbor, labeled 1 and 2 in Figure a. As these molecules alternate along the b-axis, both interactions are related to the compressibility along X3. The pairwise interaction energies between the central molecule and these neighbors have been decomposed into five terms (Coulomb, dispersion, exchange, polarization, repulsion), see Figure S7. The interaction energies are seen to diverge for the two bonding environments, with the levels staying approximately constant for molecule 2 through the window of negative linear compressibility, while they change continuously for molecule 1. Notably, the repulsive term for 2 is constant over this window. Above 3 GPa, where the negative linear compressibility is overcome, all terms for both molecules strengthen again. The mechanism underlying the existence of this relatively narrow window of negative linear compressibility arises from the symmetry change that permits the molecule to tilt. This tilt is accommodated by a reduction in void space within the structure, which decreases linearly from ∼6.28 Å3 to zero by 3 GPa (Figure c). The expected increase in intermolecular repulsion due to this tilt is mitigated by an expansion of the intermolecular separation along X3. Taken together, the anisotropic evolution of the pairwise interactions, with directional strengthening of some contacts and minimal change in others, in combination with the available void space, provides a plausible energetic explanation for the negative linear compressibility along X3.

The question remains: does deuteration influence the structural stability of pyrazine? It is perhaps surprising that the existence of a low-temperature phase of pyrazine has gone unnoticed until now. A key distinction between the present study and much of the prior literature is the substitution of hydrogen with deuterium, a common approach for neutron diffraction studies. This is not without precedent, as the related compound pyridine is known to exhibit isotopic polymorphism. , Given the demonstrated dominant role of hydrogen bonding in pyrazine, it would not be unexpected for H/D substitution to induce analogous changes in phase behavior through differences in zero-point energy. , Deuteration induces a characteristic shift in the transition pressure, lowering it from ∼1.1 GPa (h4) to ∼0.7 GPa (d4). The expected impact of deuteration for any given the crystal structure is nuanced, though many materials show a shift to higher transition pressures (such as in LiOD). Further investigation of the effect of deuteration in pyrazine will form the basis of future work.

Conclusions

This study establishes that phase IV of pyrazine (d4) is accessible either by cooling below ∼90 K or by compression beyond ∼0.7 GPa, revealing pathway-dependent evolution of the hydrogen-bonded geometry. The emergence of negative linear compressibility between columns of tilted molecules highlights the interplay between molecular rigidity, weak directional bonding and reductions in void space. Thermal expansion analysis confirms that intermolecular hydrogen bonding dominates pyrazine’s lattice dynamics, in sharp contrast to benzene, where intramolecular contributions play a greater role.

The positive dT/dP slope for the phase III → IV transition, combined with presence of the kinetically sluggish transitions of the lower-temperature phases, suggests the possible existence of a triple-point and alternative transition pathways (e.g., II → IV), offering avenues for future study.

Overall, these results demonstrate the flexibility of the hydrogen-bond network in pyrazine and show that pathway-dependent distortions can have profound consequences for the mechanical response of molecular solids. In this way, pyrazine serves as a model system, providing design principles for tailoring structure–property relationships in hydrogen-bonded materials.

Experimental Section

Polycrystalline pyrazine (d4) was purchased from Sigma-Aldrich. D was used over H to reduce incoherent background in the neutron diffraction patterns. Refinement of H/D occupancy of the ambient structure confirmed that the sample was fully deuterated. All neutron diffraction measurements were performed at the Spallation Neutron Source, Oak Ridge National Laboratory, using the SNAP diffractometer. The low temperature measurements were performed using a 50 mm diameter orange-cryostat, with the sample loaded within a 6 mm diameter vanadium canister. The sample was first cooled to a base temperature of 4 K and allowed to equilibrate for 30 min before starting data collection, with subsequent data collected on warming, with time to equilibrate at each temperature before starting collection. Each dataset was collected for approximately 6 min. The high pressure data were collected using a VX3 Paris-Edinburgh press, equipped with single-toroid cBN anvils. The sample was loaded within an encapsulated null-scattering TiZr gasket as a slurry, with Fluorinert used as the pressure transmitting medium, and a pellet of Pb included to determine the sample pressure. Two separate loadings were performed, both loaded in this way, one taken to a maximum pressure of ∼4.3 GPa, and the other taken to a maximum pressure of ∼9.1 GPa. Fluorinert was used as pyrazine is highly soluble in methanol/ethanol. The first loading was used to extract atomic coordinates, close to or within the hydrostatic limit of the pressure medium, while the second loading was used to investigate the possible emergence of a new phase beyond this pressure. Each high-pressure data set was collected for approximately 60 min. Data were reduced using SNAPRed reduction routines, within Mantid Workbench. Rietveld refinements were performed using Topas v7. All data were refined with soft-restraints to promote planarity of the C4N2 ring, using two detector banks positioned at either 2θ = 65° & 105°, or 2θ = 75° & 105°. Each detector bank’s data were refined independently, while global parameters were applied consistently across the crystal structures. Preferred orientation was observed in all patterns and was modeled using a global spherical harmonic correction. Despite this, some residual cross-correlation with the refined structural model could not be entirely eliminated, limiting the maximum pressure to which accurate coordinates could be extracted. Hirshfeld surfaces and 2D fingerprint plots were generated using CrystalExplorer25. Wave function calculations were performed on single molecules of pyrazine (d4) extracted from both phases to obtain pairwise intermolecular interaction energies, while retaining the positions of neighboring molecules to preserve the crystal packing environment. These calculations were carried out using the Open Computational Chemistry module within CrystalExplorer25, employing the ωB97M-V density functional with the 6-31G­(d,p) basis set. ,

Supplementary Material

cg5c01295_si_001.pdf (4.8MB, pdf)

Acknowledgments

This research used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory. The beam time was allocated to SNAP on proposal number IPTS-28913. The authors wish to thank Todd Sherline and Victor Fanelli (SNS Low Temperature Group) for their assistance with the cryostat. The authors wish to thank Phoenix Pleasant (Oak Ridge National Laboratory) for their assistance with preparing the graphics.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.cgd.5c01295.

  • This shows stack plots of diffraction data, representative Rietveld fits, Einstein-model fits to the unit-cell volume, lattice parameters and information supporting the Hirshfeld surface analysis; Refined models are available as crystallographic information files via the Cambridge Crystallographic Data Centre (CCDC), deposition numbers 2482071–2482119; The raw experimental data are available online at DOI 10.14461/oncat.data/2587282 (PDF)

The authors declare no competing financial interest.

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