arXiv subjects
Publications and source records attributed to François-Xavier Coudert.
Based on first principles calculations, we predict and characterize the flexibility of two aluminium-based Metal-Organic Frameworks (MOFs), CAU-13 and NOTT-300. Both materials have a wine rack topology similar to that of MIL-53(Al), the archetypal breathing MOF, yet their flexibility has not been demonstrated so far.
We study the energetic stability and structural features of bimetallic metal-organic frameworks. Such heterometallic MOFs, which can result from partial substitutions between two types of cations, can have specific physical or chemical properties used for example in catalysis or gas adsorption. We work here to provide through computational chemistry a microscopic understanding of bimetallic MOFs and the distribution of cations within their structure. We develop a methodology based on a systematic study of possible cation distributions at all cation ratios by means of quantum chemistry calculations at the density functional theory level. We analyze the energies of the resulting bimetallic frameworks and correlate them with various disorder descriptors (functions of the bimetallic framework topology, regardless of exact atomic positions). We apply our methodology to two families of MOFs known for heterometallicity: MOF-5 (with divalent metal ions) and UiO-66 (with tetravalent metal ions). We observe that bimetallicity is overall more favorable for pairs of cations with sizes very close to each other, owing to a charge transfer mechanism inside secondary building units. For cation pairs with significant mutual size difference, metal mixing is globally less favorable, and the energy signifantly correlates with the coordination environment of linkers, determining their ability to adapt the mixing-induced strains. This effect is particularly strong in the UiO-66 family because of high cluster coordination number.
Recent years have seen a large increase in the number of reported framework materials, including the nowadays-ubiquitous metal-organic frameworks (MOFs). Many of these materials show flexibility and stimuli-responsiveness, i.e. their structure can undergo changes of large amplitude in response to physical or chemical stimulation. We describe here a toolbox of theoretical approaches, developed in our group and others, to shed light into these materials' properties. We focus on their behavior under mechanical constraints, temperature changes, adsorption of guest molecules, and exposure to light. By means of molecular simulation at varying scale, we can now probe, rationalize and predict the behavior of stimuli-responsive materials, producing a coherent description of soft porous crystals from the unit cell scale all the way to the behavior of the whole crystal. In particular, we have studied the impact of defects in soft porous crystals, and developed a methodology for the study of their disordered phases (presence of correlated disorder, MOF glasses, and liquid MOFs).
Highly flexible nanoporous materials, exhibiting for instance gate opening or breathing behavior, are often presented as candidates for separation processes due to their supposed high adsorption selectivity. But this view, based on "classical" considerations of rigid materials and the use of the Ideal Adsorbed Solution Theory (IAST), does not necessarily hold in the presence of framework deformations. Here, we revisit some results from the published literature and show how proper inclusion of framework flexibility in the osmotic thermodynamic ensemble drastically changes the conclusions, in contrast to what intuition and standard IAST would yield. In all cases, the IAST method does not reproduce the gate-opening behavior in the adsorption of mixtures, and may overestimates the selectivity by up to two orders of magnitude.
Here we highlight recent progress in the field of computational chemistry of nanoporous materials, focusing on methods and studies that address the extraordinary dynamic nature of these systems: the high flexibility of their frameworks, the large-scale structural changes upon external physical or chemical stimulation, and the presence of defects and disorder. The wide variety of behavior demonstrated in soft porous crystals, including the topical class of metal-organic frameworks, opens new challenges for computational chemistry methods at all scales.
We use a combination of X-ray diffraction, total scattering and quantum mechanical calculations to determine the mechanism responsible for hydration-driven contraction in ZrW$_2$O$_8$. Inclusion of H$_2$O molecules within the ZrW$_2$O$_8$ network drives the concerted formation of new W--O bonds to give one-dimensional (--W--O--)$_n$ strings. The topology of the ZrW$_2$O$_8$ network is such that there is no unique choice for the string trajectories: the same local changes in coordination can propagate with a large number of different periodicities. Consequently, ZrW$_2$O$_8$ is heavily disordered, with each configuration of strings forming a dense aperiodic `spaghetti'. This new connectivity contracts the unit cell \emph{via} large shifts in the Zr and W atom positions. Fluctuations of the undistorted parent structure towards this spaghetti phase emerge as the key NTE phonon modes in ZrW$_2$O$_8$ itself. The large relative density of NTE phonon modes in ZrW$_2$O$_8$ actually reflect the degeneracy of volume-contracting spaghetti excitations, itself a function of the particular topology of this remarkable material.
Metal--organic frameworks (MOFs) are a family of chemically diverse materials, with applications in a wide range of fields covering engineering, physics, chemistry, biology and medicine. Research so far has focused almost entirely on crystalline structures, yet a clear trend has emerged shifting the emphasis onto disordered states of MOFs, including "defective by design" crystals, as well as amorphous phases such as glasses and gels. Here we introduce a MOF liquid, a strongly associated liquid obtained by melting a zeolitic imidazolate framework (ZIF), with retention of chemical configuration, coordinative bonding modes, and porosity of the parent crystalline framework. We combine in-situ variable temperature X-ray, ex-situ neutron pair distribution function experiments, and first principles molecular dynamics simulations to study the melting phenomenon and the nature of the liquid obtained, focusing on structural characterization at the molecular scale, dynamics of the species, and thermodynamics of the solid--liquid transition.
Theoretical studies on the experimental feasibility of hypothetical Zeolitic Imidazolate Frameworks (ZIF) have focused so far on relative energy of various polymorphs, by energy minimization at the quantum chemical level. We present here a systematic study of stability of 18 ZIFs as a function of temperature and pressure, by molecular dynamics simulations. This approach allows us to better understand the limited stability of some experimental structures upon solvent or guest removal. We also find that many of the hypothetical ZIFs proposed in the literature are not stable at room temperature. Mechanical and thermal stability criteria thus need to be considered for the prediction of new MOF structures. Finally, we predict a variety of thermal expansion behavior for ZIFs as a function of framework topology, with some materials showing large negative volume thermal expansion.
We report on the implementation of a tool for the analysis of second-order elastic stiffness tensors, provided with both an open-source Python module and a standalone online application providing visualization tools of anisotropic mechanical properties. After describing the software features, how we compute the conventional elastic constants and how we represent them graphically, we explain our technical choices for the implementation. In particular, we focus on why a Python module is used to generate the HTML web page with embedded Javascript for dynamical plots.
In this work, we use molecular dynamics simulations to study the thermodynamics, structure and dynamics of the Li$_2$CO$_3$-K$_2$CO$_3$ (62:38 mol%) eutectic mixture. We present a new classical non-polarizable force field for this molten salt mixture, optimized using experimental and first principles molecular dynamics simulations as reference data. This simple force field allows efficient molecular simulations of phenomena at long timescales. We use this optimized force field to describe the behavior of the eutectic mixture in the 900-1100 K temperature range, at pressures between 0 and 5 GPa. After studying the equation of state in these thermodynamic conditions, we present molecular insight into the structure and dynamics of the melt. In particular, we present an analysis of the temperature and pressure dependence of the eutectic mixture's self diffusion coefficients, viscosity and ionic conductivity.
At the heart of systems chemistry lies the idea that supramolecular interactions can give rise to complex and unexpected collective states that emerge on a fundamentally different lengthscale to that of the interactions themselves. While in certain cases - e.g. the self-assembly of virus-like polyhedral cages from coordination building blocks - it is possible to control emergence in a systematic manner, the development of general approaches remains a fundamental challenge in the field. In the conceptually-related domain of frustrated magnetism - where collective states give rise to exotic physics of relevance to data storage and spintronics - the task of predicting emergent behaviour is simplified through control over the geometry and form of the magnetic interactions from which complexity arises. Seeking to combine approaches from these two fields, we study here the solid phases of inorganic polymer chains assembled from non-magnetic gold(I)/silver(I) cations and cyanide anions. We show the periodic inter-chain potential encodes a supramolecular interaction that can be tuned to mimic different magnetic interactions between XY spins ("spin rotors"). Because the chains pack on a triangular lattice, the crystal structures of gold(I)/silver(I) cyanides can be interpreted in terms of the phase behaviour of triangular XY magnets. Complex magnetic states predicted for this family - including hidden quadrupolar order and emergent spin-vortex quasiparticles - are realised for the first time in the structural chemistry of these cyanide polymers. In this way we demonstrate both how simple inorganic materials might behave as structural analogues of otherwise-unrealisable "toy" spin models, and also how a theoretical understanding of those models might be used to predict and control emergent phenomena in chemical systems.
In this introductory review, we give an overview of the computational chemistry methods commonly used in the field of metal-organic frameworks (MOFs), to describe or predict the structures themselves and characterize their various properties, either at the quantum chemical level or through classical molecular simulation. We discuss the methods for the prediction of crystal structures, geometrical properties and large-scale screening of hypothetical MOFs, as well as their thermal and mechanical properties. A separate section deals with the simulation of adsorption of fluids and fluid mixtures in MOFs.
We investigate the feasibility of four-connected nets as hypothetical zinc cyanide polymorphs, as well as their thermal and mechanical properties, through quantum chemical calculations and molecular dynamics simulations. We confirm the metastability of the two porous phases recently discovered experimentally (Lapidus, S. H.; et al. J. Am. Chem. Soc. 2013, 135, 7621-7628), suggest the existence of seven novel porous phases of Zn(CN)2, and show that isotropic negative thermal expansion is a common occurrence among all members of this family of materials, with thermal expansion coefficients close to that of the dense dia-c phase. In constrast, we find a wide variety in the mechanical behavior of these porous structures with framework-dependent anisotropic compressibilities. All porous structures, however, show pressure-induced softening leading to a structural transition at modest pressure.
Breathing transitions represent recently discovered adsorption-induced structural transformations between large-pore and narrow-pore conformations in bistable metal-organic frameworks, such as MIL-53. We present a multiscale physical mechanism of the dynamics of breathing transitions. We show that due to interplay between host framework elasticity and guest molecule adsorption, these transformations on the crystal level occur via layer-by-layer shear. We construct a simple Hamiltonian that describes the physics of host-host and host-guest interactions on the level of unit cells and reduces to one effective dimension due to the long-range elastic cell-cell interactions. We then use this Hamiltonian in Monte Carlo simulations of adsorption-desorption cycles to study how the behavior of unit cells is linked to the transition mechanism at the crystal level through three key physical parameters: the transition energy barrier, the cell-cell elastic coupling, and the system size.
Soft porous crystals present a challenge to molecular dynamics simulations with flexible size and shape of the simulation cell (i.e., in the NPT ensemble), since their framework responds very sensitively to small external stimuli. Hence, all interactions have to be described very accurately in order to obtain correct equilibrium structures. Here, we report a methodological study on the nanoporous metal-organic framework MIL-53(Ga), which undergoes a large-amplitude transition between a narrow- and a large-pore phase upon a change in temperature. Since this system has not been investigated by density functional theory (DFT)-based NPT simulations so far, we carefully check the convergence of the stress tensor with respect to computational parameters. Furthermore, we demonstrate the importance of dispersion interactions and test two different ways of incorporating them into the DFT framework. As a result, we propose two computational schemes which describe accurately the narrow- and the large-pore phase of the material, respectively. These schemes can be used in future work on the delicate interplay between adsorption in the nanopores and structural flexibility of the host material.
We performed ab initio calculations of the elastic constants of five flexible metal-organic frameworks: MIL-53(Al), MIL-53(Ga), MIL-47 and the square and lozenge structures of DMOF-1. Tensorial analysis of the elastic constants reveal a highly anisotropic elastic behavior, some deformation directions exhibiting very low Young's modulus and shear modulus. This anisotropy can reach a 400:1 ratio between the most rigid and weakest directions, in stark contrast with the case of non-flexible MOFs such as MOF-5 and ZIF-8. In addition, we show that flexible MOFs can display extremely large negative linear compressibility (NLC). These results uncover the microscopic roots of stimuli-induced structural transitions in flexible MOFs, by linking the local elastic behavior of the material and its multistability.
While the Born elastic stability criteria are well-known for cubic crystals, there is some confusion in the literature about the form it should take for lower symmetry crystal classes. We present here closed form necessary and sufficient conditions for elastic stability in all crystal classes, as a concise and pedagogical reference to stability criteria in non-cubic materials.
Molecular dynamics simulations are used to study the mechanism and kinetics of hydrated electron diffusion. The electron center of mass is found to exhibit Brownian-type behavior with a diffusion coefficient considerably greater than that of the solvent. As previously postulated by both experimental and theoretical works, the instantaneous response of the electron to the librational motions of surrounding water molecules constitutes the principal mode of motion. The diffusive mechanism can be understood within the traditional framework of transfer diffusion processes, where the diffusive step is akin to the exchange of an extramolecular electron between neighboring water molecules. This is a second-order process with a computed rate constant of 5.0 ps^{-1} at 298 K. In agreement with experiment the electron diffusion exhibits Arrhenius behavior over the temperature range of 298-400 K. We compute an activation energy of 8.9 kJ/mol. Through analysis of Arrhenius plots and the application of a simple random walk model it is demonstrated that the computed rate constant for exchange of an excess electron is indeed the phenomenological rate constant associated with the diffusive process.