Molecular simulations have largely contributed to the emergence of Metal Organic Frameworks (MOFs) not only for the resolution of the crystal structures of the most complex and poorly crystallized solids but also to enumerate all the plausible structures constructed by the assembly of a large diversity of inorganic and organic building blocks. Besides this in silico design of novel MOFs which has been only rarely validated so far by the post-synthesis of the desired material, a computational effort has been deployed to modulate the chemical and topological features of existing architectures specifically targeted for societally-relevant applications. Molecular modelling has been also frequently used to guide interpretation of the experimental data by providing a deep understanding of the microscopic adsorption/separation mechanism with the objective to drive the synthesis effort towards tuned materials with the required features for an optimization of their properties. This presentation will highlight the invaluable contribution of the computational approaches from the birth of novel MOFs and their structure elucidations to the characterization and understanding of their properties, throughout recent advances our groups have made in this field. A special emphasizes will be devoted to a series of recent MOFs that show promising adsorption/separation performances for natural gas upgrading, carbon capture and interesting features for mechanical energy storage and proton conduction.

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of wavespeeds that are a linear combination of piecewise constant functions (following a domain partition) and gives a framework in which the scheme converges. The stability constant grows exponentially as the number of subdomains in the domain partition increases. We establish an order optimal upper bound for the stability constant. We eventually realize computational experiments to demonstrate the stability constant evolution for three-dimensional wavespeed reconstruction

The proton-conduction performances of the chemically stable porous zirconium phenolate MIL-163 MOF were characterized for the first time by complex impedance spectroscopy. Whereas this large square-shaped channel-like MOF exhibits very poor conductivity under anhydrous conditions, measurements performed at 90 °C and 95% relative humidity evidenced a superprotonic behavior with a conductivity of 2.1 × 10 −3 S•cm −1 , among the highest values reported so far for waterstable MOFs. This experimental investigation was further supported by Monte Carlo simulations to shed light on the effects of both the guest molecules (i.e., dimethylamine and water) and the acidic protons from the constitutive inorganic chains on the conduction properties of this porous hybrid solid. It was found that the water molecules form a three-dimensional hydrogen-bond network leading to the formation of multiple pathways that bridge the acidic Zrbonded phenol groups of the organic linker, which act as a proton source. The dimethylamine molecules were revealed to form single hydrogen bonds with H 2 O without leading to a disruption of the water hydrogen-bond network. This offers an optimal situation for the water-mediated transfer of protons over long distances at the origin of the good proton-conducting performance of MIL-163.

In this paper, we study the performance of Full Waveform Inversion (FWI) from timeharmonic Cauchy data via conditional well-posedness driven iterative regularization. The Cauchy data can be obtained with dual sensors measuring the pressure and the normal velocity. We define a novel misfit functional which, adapted to the Cauchy data, allows the independent location of experimental and computational sources. The conditional well-posedness is obtained for a hierarchy of subspaces in which the inverse problem with partial data is Lipschitz stable. Here, these subspaces yield piecewise linear representations of the wave speed on given domain partitions. Domain partitions can be adaptively obtained through segmentation of the gradient. The domain partitions can be taken as a coarsening of an unstructured tetrahedral mesh associated with a finite element discretization of the Helmholtz equation. We illustrate the effectiveness of the iterative regularization through computational experiments with data in dimension three. In comparison with earlier work, the Cauchy data do not suffer from eigenfrequencies in the configurations.

In this paper, we provide an a priori optimizability analysis of nonlinear least squares problems that are solved by local optimization algorithms. We define attraction (convergence) basins where the misfit functional is guaranteed to have only one local -and hence global -stationary point, provided the data error is below some tolerable error level. We use geometry in the data space (strictly quasiconvex sets) in order to compute the size of the attraction basin (in the parameter space) and the associated tolerable error level (in the data space). These estimates are defined a priori, i.e., they do not involve any least squares minimization problem, and only depend on the forward map. The methodology is applied to the comparison of the optimizability properties of two methods for the seismic inverse problem for a timeharmonic wave equation: the Full Waveform Inversion (FWI) and its Migration Based Travel Time (MBTT) reformulation. Computation of the size of attraction basins for the two approaches allows to quantify the benefits of the latter, which can alleviate the requirement of low-frequency data for the reconstruction of the background velocity model.

In this paper, we study the time-harmonic scalar equation describing the propagation of acoustic waves in the Sun’s atmosphere under ideal atmospheric assumptions. We use the Liouville change of unknown to conjugate the original problem to a Schrödinger equation with a Coulomb-type potential. This transformation makes appear a new wavenumber, k, and the link with the Whittaker’s equation. We consider two different problems: in the first one, with the ideal atmospheric assumptions extended to the whole space, we construct explicitly the Schwartz kernel of the resolvent, starting from a solution given by Hostler and Pratt in punctured domains, and use this to construct outgoing solutions and radiation conditions. In the second problem, we construct exact Dirichlet-to-Neumann map using Whittaker functions, and new radiation boundary conditions (RBC), using gauge functions in terms of k. The new approach gives rise to simpler RBC for the same precision compared to existing ones. The robustness of our new RBC is corroborated by numerical experiments.

The determination of background velocity by full-waveform inversion (FWI) is known to be hampered by the local minima of the data misfit caused by the phase shifts associated with background perturbations. Attraction basins for the underlying optimization problems can be computed around any nominal velocity model, and they guarantee that the misfit functional has only one (global) minimum. The attraction basins are further associated with tolerable error levels representing the maximal allowed distance between the (observed) data and the simulations (i.e., the acceptable noise level). The estimates are defined a priori, and they only require the computation of (possibly many) the first- and second-order directional derivatives of the (model to synthetic) forward map. The geometry of the search direction and the frequency influence the size of the attraction basins, and the complex frequency can be used to enlarge the basins. The size of the attraction basins for the perturbation of background velocities in classic FWI (global model parameterization) and the data-space reflectivity reformulation (migration-based traveltime [MBTT]) are compared: The MBTT reformulation substantially increases the size of the attraction basins (by a factor of 4–15). Practically, this reformulation compensates for the lack of low-frequency data. Our analysis provides guidelines for a successful implementation of the MBTT reformulation.

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