Unconventional mechanical and thermal behaviours of MOF CALF-20

CALF-20 was recently identified as a benchmark sorbent for CO2 capture at the industrial scale, however comprehensive atomistic insight into its mechanical/thermal properties under working conditions is still lacking. In this study, we developed a general-purpose machine-learned potential (MLP) for the CALF-20 MOF framework that predicts the thermodynamic and mechanical properties of the structure at finite temperatures within first-principles accuracy. Interestingly, CALF-20 was demonstrated to exhibit both negative area compression and negative thermal expansion. Most strikingly, upon application of the tensile strain along the [001] direction, CALF-20 was shown to display a distinct two-step elastic deformation behaviour, unlike typical MOFs that undergo plastic deformation after elasticity. Furthermore, this MOF was shown to exhibit a fracture strain of up to 27% along the [001] direction at room temperature comparable to that of MOF glasses. These abnormal thermal and mechanical properties make CALF-20 as attractive material for flexible and stretchable electronics and sensors.


Introduction
2][3][4] In particular the intriguing mechanical and thermal properties of this family of materials serve as an important cornerstone in expanding their potential application domains. 2,3,5,6Notably, some of the flexible MOFs, possess counterintuitive mechanical properties, including negative linear compressibility (NLC), 7 negative area compressibility (NAC), stretch densification, 8 and push/pull-twisted among others. 9These abnormal pressureresponsive behavior defies the well-known "compression-contraction" effect and opens new avenues in many applications, e.g.optoelectronic devices, 10 pressure sensors and intelligent body armor. 8,11In addition, some of these materials also exhibit negative thermal expansion (NTE) behavior, which refers to the phenomenon where a material contracts rather than expands upon heating, of potential importance for further development in the field of thermal expansion compensator.
Recently, a Zn2(1,2,4-triazolate)2(oxalate) framework named as CALF-20, was proposed as a novel benchmark sorbent for CO2 capture combining excellent CO2/N2 separation performance in flue gas condition, high hydrolytic stability and easy scalable that made it promotable at the industrial scale. 124][15][16][17] The structure of this MOF consists of 2D layers of 1,2,4-triazolate-bridged zinc ions pillared by oxalate linkers, forming a three-dimensional (3D) framework. 12The pillars of the oxalate linker acting as hinges, are connected by zinc triazolate grids parallel to the ac plane, offering potentially high flexibility to the 3D framework that might pave the way towards intriguing physical properties (Fig. 1a).However, so far, the mechanical/thermal behaviors of this MOF have been completely overlooked.Beyond a fundamental interest, the lack of understanding on the pressure/thermal-induced structure change of CALF-20 is critical in the context of using this MOF under diverse operating conditions.The determination of MOF mechanical/thermal properties generally requires the deployment of high-tech and specialized equipment as well as high-quality samples making the whole testing process far to be trivial. 18,191][22] Herein, the unprecedented computational exploration of the physical properties of the emblematic CALF-20 MOF calls for the development and application of cost-effective and accurate molecular simulation tools and the expected outcomes might reveal new phenomena paving the way towards novel prospective for this MOF.
In this context, the mechanical and thermal behaviors of CALF-20 was explored in-depth by combining extensive Density Functional Theory (DFT) calculations and high-precision machine-learning potential molecular dynamics (MLP-MD) simulations.
CALF-20 was demonstrated to exhibit anomalous structural response to both temperature and pressure stimuli, resulting in the coexistence of NAC and NTE effects.This makes this material highly attractive for mechanical/thermal sensing, besides its actual application in the field of CO2 capture.Decisively our simulations revealed that CALF-20 exhibits an abnormal strain-softening at both 0K and room temperature under uniaxial tensile strain that eventually leads to the formation of a new metastable structure.From a methodology perspective, the MLP-MD approach was demonstrated to be a powerful tool for anticipating unconventional structural features of CALF-20 upon stimuli at finite temperature.

Results
Negative area compressibility behavior.DFT calculations were first performed at0K to determine the elastic properties of CALF-20 via a comprehensive tensorial analysis based on a finite difference approach, 23 as implemented in the VASP code. 24These calculations evidenced that CALF-20 exhibits a large anisotropy in its linear compressibility, with a positive contribution along the c axis (170 TPa -1 ) (see Fig. 1b), while both a and b axis show a negative contribution (maximum of −24 and −32 TPa - 1 respectively, see Supplementary Fig. S1).This unusual mechanical response of the MOF framework corresponds to a rather rare NAC behavior.This implies that as the MOF is compressed, the ab-plane expands spontaneously to maintain the minimum energy principle of the system, while the c-axis shrinks.These calculations revealed that the predicted Young's modulus (Fig. 1b) and Poisson's ratio (Fig. 1c) are also highly anisotropic, with both maxima observed quasi along the a-axis (Supplementary Fig. S2) corresponding to the direction of the pillared oxalate ligands, allowing a stronger resilience of the MOF framework, whereas the bc plane corresponds to the more flexible rhombic-shaped zinc triazolate grid.It is worth noting that the [100] and [010] directions are the principal axes of the rhombic shaped zinc triazolate grid, therefore, when b-axis is elongated (compressed), the zinc triazolate layer is deformed by reducing (stretching) the length of all the connectors along the c-axis to minimize the energy of the overall system.Therefore, the unique flexible behavior of CALF-20 originates from its topology: Each oxalate ligand utilizes its tetradentate oxygen atoms to vertically stretch two independent zinc triazolate ligand forming a crossed 3D configuration with zinc triazolate grids and oxalate pillars.(j) Overall elastic properties simulated by MD calculations using different force fields including MLP as well as UFF and UFF-modified referring to an adjusted UFF parameterization reported in our previous work. 17and compared to DFT calculations at 0K.
Besides the stiffness tensor-based analysis, the impact of applying a mechanical pressure on the structure was equally examined.Compressibility of material is typically denoted as the relative rate of changes in dimensions with pressure at a fixed , where  can be assigned as volume, area, or linear compressibility, respectively. 8The compressibility coefficients of the principal axes can be determined within the pressure range. 26 The NAC behavior is much more marked along the a-axis with -188.77TPa -1 strain tensor eigenvector compared to that along the b-axis (-75.52 TPa -1 ).The highest positive linear compressibility (PLC) is observed along the direction perpendicular to the ab plane with a corresponding eigenvector of 501.53 TPa -1 , which leads to a substantial compression of the oxalate pillars under pressure (cf.Fig. 1f, Supplementary Table S1).Remarkably, in contrast to other conventional uniaxial NLC materials, CALF20 exhibits a biaxial (or in-plane) NLC behavior, and its compressibility is higher than that of the most extreme existing NLC inorganic materials including Ag3[Co(CN)6]-I (Kc = -76 TPa -1 ) 25 and [Ag(en)]NO3-I (Kc = -28.4TPa -1 ), 27 as well as the most representative flexible MIL-53 MOF material (Kb = −27 TPa −1 ). 28The CALF-20 structures simulated upon different applied mechanical pressure are illustrated in Fig. 1g.It is evident that as the pressure increases, the c-axis shrinks significantly, eventually leading to a decrease in unit cell volume derived from the larger PLC along the axis.Notably, the applied pressure up to 1 GPa does not induce any structure collapse.Therefore, besides its previously-demonstrated promise as CO2 sorbent at the industrial level, CALF-20 owing to its unconventional mechanical properties, is predicted to be attractive in pressure-sensitive devices, shock-absorbing materials, artificial muscles, and shape-memory applications among others.Supplementary Figs.
S3-S4 that reports the pressure-induced evolution of the CALF-20 lattice parameters further demonstrates that above 1 GPa, a metastable high-pressure phase for CALF-20 exists.Supplementary Fig. S4 shows that such phase is non porous and is associated with a very high density (3.58 g cm -3 ).This novel phase is also demonstrated to remain stable even after releasing the pressure stimulus.
We then developed a MLP-MD strategy (Supplementary Note1 and Figs.S5-S14 for details) to explore the pressure-driven structural flexibility of CALF-20 at room temperature, which is almost unfeasible within the DFT formalism.For all MLP-MD simulations, the 2 × 2 × 2 supercell was used and the structural parameters were finally collected from the last 500 picosecond (ps) (1 nanosecond [ns] in total with 0.5 femtosecond [fs] time steps).Figs.1h-1i report the MLP-MD derived evolution of the CALF-20 lattice parameters at room temperature upon different applied pressure.These simulations evidenced that both a-and b-axis dimensions decrease with increasing pressure below 0.30 GPa range in line with the NAC phenomenon revealed above by DFT calculations at 0K.An apparent phase transition is equally observed at 0.30 GPa (Fig. 1d).Moreover, when pressure exceeds 0.50 GPa, a-and b-axis dimensions remain almost unchanged upon pressure increase, while the c-axis dimension decreases linearly (Fig. 1h).This later prediction slightly deviates from the DFT predictions at 0K. Indeed at room temperature, CALF-20 is expected to display a tiny NAC behavior above 0.50 GPa, where the structure evolves as a rigid backbone.The reliability of MLP vs generic UFF force field to describe the mechanical properties of CALF-20 was further assessed using DFT results as benchmark data.Fig. 1i and Supplementary Table S2 evidence that UFF force field leads to a substantial overestimation of both bulk modulus and Young's modulus while it significantly underestimates the shear modulus by a factor of 3 and 4 respectively compared to the corresponding DFT value.
Remarkably, the use of MLP enables to reproduce well the DFT values, especially for the Young's modulus and shear modulus.This comparison emphasizes the reliability of the MLP-MD approach to accurately probe the flexible behavior of CALF-20 at finite temperature at a computational cost far below that of DFT calculations (Supplementary Note2).
Negative thermal expansion behavior.The temperature-dependent thermal properties of CALF-20 were first assessed using the quasi-harmonic approximation (QHA) approach, 29 where the influence of temperature is considered through the volume response of the vibrational frequency via the use of phonon anharmonicity. 30Note that conventional QHA approach based on DFT calculations requires the determination of the phonon spectrum under several independent volume deformation of the structure, which requires huge computing resources.The implementation of MLP in the QHA scheme enables a much faster assessment of the corresponding data reported in Fig. 2a (see Supplementary Figs.S15-S16 for details).CALF-20 is thus predicted to exhibit a NTE behavior at low temperature, the lowest NTE value of −10.56 × 10 -6 K -1 at 40K being within the same range than that reported for typical NTE MOFs. 6,31,32Notably, a nearly negligible unit cell volume change versus temperature is obtained, indicating that as the temperature increases, the lattice shrinks in different orientations to ensure an energy equilibrium, confirming a relatively high flexibility of the CALF-20 framework.Since QHA does not explicitly include anharmonicity 33 , its reliability is almost exclusively limited to the low temperature domain.One possibility to extend the applicability of QHA to higher temperature is to carry out AIMD simulations, however, this is extremely time-consuming.Herein, we privileged the implementation of our newly derived MLP validated above on the mechanical properties of CALF-20 to run MLP-MD simulations in the NPT ensemble at 1bar and room temperature (298.15K) with a total simulation time of 1 ns with the use of 0.5 fs time steps to determine the equilibrium lattice parameters of CALF-20, as shown in Figs.2b-2c.We evidenced that the b-axis dimension decreases linearly as the temperature increases, while the overall unit-cell volume remains almost unchanged, which is in excellent agreement with the prediction based on the QHA approach.Fig. 3c delivers a 3D-representation of the contribution to thermal expansion along each axis (also see Supplementary Table S3).
The blue region refers to the NTE behavior domain with negative linear thermal expansion ranging from −4.22 MK −1 and −60.81 MK −1 .This coefficient is comparable to that exhibited by MOF DUT-60 (−65.0MK −1 ) 34 while it is higher than most other NTE MOFs, e.g.Ag(mim) (−24.5 MK −1 ), 35 and DUT-49 (−32.778MK −1 ) 36 .This suggests that CALF-20 offers promise for applications in the fields of ultrasensitive temperature sensing.Abnormal tension strain response.Typically, a material with multiple negative phenomena, e.g.NLC combined with NTE exhibits other peculiar strain-stress behaviors. 37,38We therefore examined the deformation behavior of CALF-20 upon the application of ideal tensile strain.The strain-stress curve was first simulated at 0K by DFT calculations (Fig. 3a).The three directions show anisotropic changes, among which the [100] and [010] directions show rapid strain-stiffening after a short elastic deformation. 39,40As a result, the [100] and [010] growth directions are predicted to be relatively brittle with failure strains lower than 11% and 22% respectively.However, two independent elastic deformation regions were found with the tensile strain along [001] direction, namely before and after strain-softening to MOF fracture respectively.
The first peak at 18.43% strain is associated with a structural transition, i.e. strainsoftening point, while the second one at 40.25% corresponds to MOF fracture.The rapid change in the stress-strain curve suggest a phase transition.Therefore, the structure near the strain-softening point was considered to calculate the phonon spectrum.Figs.3b-3c and Supplementary Figs.S17-S19, reveal that there is not any imaginary frequency in the entire Brillouin zone and this confirms the dynamic stability of CALF-20 during the deformation process.In the meantime, we demonstrated that this MOF maintains its structure integrity at very high strain level up to 36.13% (Supplementary Fig. S20).This behavior significantly differs with that exhibited by most of MOF crystals like Ni-TCPP 41 and ZIF-8 42 etc, that all undergo a fracture above 30% strain.Among them, ϕ and θ are defined as the angles of the lozenge lattice formed by triazolate grids, and ω represents the angle between the triazolate grids and oxalate ligands.As shown in Supplementary Fig. S27 and Figs. 4b-4c, the corresponding results indicate that all the angular changes of CALF-20 are linear before the critical strain regardless of the strained direction.This implies that the MOF is sufficiently robust to resist to mechanical deformation.It is particularly interesting to highlight that before and after the strain softening-point when the tensile strain is applied along the [001] direction, such deformation mechanism remains unchanged, suggesting that the CALF_20 structure presents a high flexibility in conjunction with a good mechanical strength.In particular, the linear relationship between the angular changes and the applied tensile strain is still preserved at >30% strain as shown in Fig. 4c and Supplementary Movie S1.This behavior is attractive for potential ultra-sensitive sensing applications.
To further elucidate the phase transition mechanism driven by the uniaxial tensile strain along the [001] direction, we conducted orbital Hamilton population (COHP) analysis, 45 which allows quantitative analysis of changes in interatomic couplings during stretching.As shown in Figs.4d-4e, the broken symmetry in CALF-20 leads to independent changes in the chemical bonds between Zn atoms and its coordinated atoms.Fig. 4e evidences that the interactions between Zn and the oxalate ligands change only slightly in the whole strain range.Notably, the structural differences before/after the strain-softening point are mainly due to the different orientation of the oxalate ligands, as shown in Fig. 4d.The negative integrated COHP analysis revealed that the interactions between the single O or N atoms of the ligand and Zn metal change significantly before and after the phase transition, while the interactions between the overall Zn and the two ligands only slightly change, as shown in Figs.4e-4f.This is because during the stretching process along [001] direction, the main deformation is the bending of the Zinc triazolate grid, and the oxalate ligand acts like a hinge during the deformation process.Therefore, CALF-20 is demonstrated to exhibit a distinct two-step elastic deformation behavior when stretched along the [001] direction, as well as a switching from auxetic to non-auxetic behavior.This phenomenon is rarely reported in crystal, 46 indicating that CALF-20 may be promising in the fields of engineering materials, motion memory devices and strain sensors among others. 47,48etastable phase identified by generalized solid-state nudged elastic band (SS-NEB) approach. 49ange of unit cell volume (Å 3 ) relative is given by black lines.(i) Unit-cell volume vs energy plot for pristine structure and metastable phase from DFT and MLP-MD simulations, respectively.
The strained crystal structure is inherently unstable at ambient pressure.We therefore considered the structure after the strain-softening point and re-optimized it at the DFT level.Interestingly, it was found that the total energy of such configuration at 0K is only 83 meV unit-cell -1 slightly higher than that of the pristine structure.
Therefore, this new phase (termed as metastable CALF-20) is rearranged by applying uniaxial strain, showing strain-induced reversible phase transition behavior, as shown in Fig. 4g.These calculations indicate that the energy barrier for the phase transition from pristine to metastable CALF-20 is only 0.11 eV unit-cell -1 , whereas for the reverse phase transition the energy barrier is even lower (0.03 eV unit-cell -1 ) (Fig. 4h and Supplementary Movie S2).This suggests that the newly identified structure is indeed a metastable phase that can readily switch towards the pristine structure by overcoming a very low energy barrier.

Discussions
In conclusion, high-accuracy DFT and MLP-MD simulations enabled to systematically explore the flexible behavior of CALF-20.This MOF was demonstrated to exhibit a coexistence of multiple negative phenomena simultaneously, including NAC, negative Poisson's ratio, and NTE, resulting in a unique dynamic response of the structure upon temperature and pressure stimuli.From a methodology standpoint, the development of an accurate MLP for the MOF framework was proved to be a key strategy to predict the mechanical properties at finite temperature with comparable numerical accuracy to DFT calculations and a much lower computational cost.Decisively CALF-20 was shown to possess a very unique strain-softening behavior along the [001] direction with two nearly linear strain-stress curves under the ideal tensile strain applied, demonstrating an uncommon elastic deformation during the whole extension process.
Importantly, the fracture strain of CALF-20 was determined to be 27% along the [001] direction at room temperature, a magnitude nearly twofold greater than the hitherto reported value for a MOF, specifically 14% in the case of Ni-TCPP 41 ).This highlights that this material is very promising for biomechanical systems, flexible electronics and nanomechanical devices.Finally, the deformation of CALF-20 along the [001]   direction was demonstrated to induce a newly metastable phase owing to its unique anisotropic flexibility.This observation is reminiscent to the phase β-CALF-20 very recently reported upon exposure of this MOF to humid environments. 50Notably, the structural parameters of our computed metastable phase are in excellent agreement with the experimental parameters of β-CALF-20, 50 as show in Fig. 4g and Supplementary Table S4.In this respect, the developed MLP enabled to predict the energy landscape of this metastable phase accurately, as shown in Fig. 4i.Particularly considering the fact that such metastable phase has not been incorporated in the initial data set and MLP training, this suggests that the developed MLP can serve as a general-purpose potential to expand the computational exploration of CALF-20 towards new avenues.

DFT calculations
All DFT calculations were carried out using the Vienna Ab-initio Simulation Package (VASP) code (Version: 5.4.4). 24The projector augmented wave (PAW) potential and the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional was adopted. 51,52 energy cutoff of 650 eV and a Monkhorst-Pack 3 × 4 × 3 k-point grid 53 was chosen to ensure convergence of total energy and forces below 10 -5 eV and 10 -3 eV/Å, respectively.We also used the DFT-D3 Van der Waals (vdW) correction 54 .The computed lattice parameters of the pristine CALF-20 were found in good agreement with the experimental values (Supplementary Table S5).

Dataset preparation
In order to obtain the training data for the MLPs introduced in this study, finitetemperature ab-initio molecular dynamics (AIMD) simulations were performed using the VASP code.These simulations involved > 30,000 snapshots within a 2 × 2 × 2 supercell of CALF-20, using a time step of 0.5 fs.Brillouin zone sampling was performed using a Monkhorst-Pack k-point grid 53 of size 1 × 1 × 1.All AIMD simulations adhered to the NVT ensemble framework, incorporating the Nosé-Hoover thermostat 55 to maintain a constant temperature of 100 ~800 K.

MLP development
To construct the MLP for CALF-20, the DeePMD-kit code (version 2.0.1) 56was employed with the DeepPot-SE model. 56,57The size of the embedding network was set to {25, 50, 100}, while the fitting section consisted of {240, 240, 240}.Both networks utilize the ResNet architecture.ResNet architecture is utilized in both networks. 58ring the training process, a cutoff distance of 7.9 Å was applied, and a smoothing value of 2.1 Å was used.To ensure model robustness, the training and test data were allocated in a 3:1 ratio, effectively mitigating the risk of overfitting.

MLP-MD simulations
The MLP derived from the DFT was implemented in the following MLP-MD simulations through integration with the DeepMD-kit interface coupled with the LAMMPS code. 56,59In the MLP-MD simulations, the trained model served as a pair style within the LAMMPS framework, enabling the computation of both energy and force profiles during the MD simulations.The phonon dispersion spectra were calculated under strict convergence criteria with the Phonopy code, by using Lammps as the calculator. 30,59assical MD simulations MD simulations employing classical force fields were executed using the Lammps code. 59CALF-20 was treated as fully flexible with the potential parameters and 12-6 Lennard-Jones (LJ) site contributions from the universal force field (UFF). 60The computation of 12-6 LJ parameters involved the application of Lorentz-Berthelot mixing rules. 61The distance cutoff for LJ interactions was set as 12 Å.Electrostatic interactions were determined using the Ewald summation method, 62 with a tolerance level of 10⁻⁶.Atomic charges were determined utilizing the DDEC6 method. 63To accommodate the simulation, a supercell with dimensions of 3 × 3 × 3 was employed, thereby ensuring that the box size was twice the cutoff radius.
More detailed methodologies are provided in the Supplementary Information.

Fig. 1 |
Fig. 1 | Anisotropic mechanical properties of CALF-20 predicted by DFT and finite temperature NPT MLP-MD simulations.(a) DFT-optimized structure of CALF-20 viewed along different perspectives.(b) Three dimensional representations of the linear compressibility (left) and Young's modulus (right).Positive and negative values for linear compressibility are indicated as green and red respectively.(c) The elastic constant derived from the spatial dependence of the Poisson's ratio in ac plane.Positive and negative contributions are indicated in blue and red lines respectively.Green shadow represents the maximum positive value for Poisson's ratio.(d) Unitcell parameters changes and corresponding (e) compressibility changes during hydrostatic Figs. 1d-1e show that the most striking giant NAC phenomenon along a and b axis continues monotonically up to 0.3 GPa.

Fig. 2 |
Fig. 2 | Anisotropic Negative Thermal Expansion of CALF-20 revealed by finite temperature NPT MLP-MD simulations.(a) Thermal expansion coefficient and volume change calculated at different temperatures using the quasi-harmonic approximation.(b, c) Equilibrium lattice parameters calculated at various temperatures based on MLP-MD simulations.The error bars indicate the statistical deviation from the collected trajectories.(d) Illustration of the 3D expansivity (MK −1) derived from the empirical potential fitting method using MLP-MD outputs.

Fig. 3 |
Fig. 3 | Unconventional strain-stress behavior determined by DFT and finite temperature NPT MLP-MD simulations.(a) Tensile strain-stress response along the three directions from DFT calculations at0K.The green circle indicates the strain-softening region.(b, c) Phonon dispersion spectrum under tensile strain (around the strain-softening range) along the [001] direction calculated based on MLP.Only below 8 THz curves are displayed for clarity.Stress-strain curves at (d) 200 K and (e) 298.15K derived from MLP-MD simulations.(f) MLP-MD derived volume changes of the CALF-20 at 298.15 K during the application of tensile strain along the three directions.(g) Schematic illustration of the CALF-20 structural evolution upon tensile strain applied along the [001] direction.

Fig. 4 |
Fig. 4 | Strain-induced phase transition of CALF-20.(a) Scheme of CALF-20 along the bc (top) and ac (bottom) planes, where the angle ϕ and θ denote the angle between adjacent triazolate ligands in the lozenge lattice of CALF-20, and the angle ω represents the angle between the triazolate ligand and oxalate ligand.Relative angle changes (ϕ, θ, and ω) for the applied tension strain along the [001] direction (b) before strain-softening and (c) after strain-softening, respectively.(d) Typical CALF-20 structure component containing three 1,2,4-triazole and one oxalate functions.The five atoms coordinated to Zn metal are labelled (left: pristine CALF-20; right: CALF-20 after strain-softening.(e, f) Negative integrated crystal orbital Hamilton population (−ICOHP) values reported as a function of the strain applied along [001] direction for various Zn-coordinated atom pairs.The −ICOHP values are scaled with the strength of the interactions.Color code: Zn, orange; N, blue; O,