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Metal-organic frameworks (MOFs) are an incredibly diverse group of highly porous hybrid materials, which are interesting for a wide range of possible applications. For a reliable description of many of their properties accurate computationally highly efficient methods, like force-field potentials (FFPs), are required. With the advent of machine learning approaches, it is now possible to generate such potentials with relatively little human effort. Here, we present a recipe to parametrize two fundamentally different types of exceptionally accurate and computationally highly efficient machine learned potentials, which belong to the moment-tensor and kernel-based potential families. They are parametrized relying on reference configurations generated in the course of molecular dynamics based, active learning runs and their performance is benchmarked for a representative selection of commonly studied MOFs. For both potentials, comparison to a random set of validation structures reveals close to DFT precision in predicted forces and structural parameters of all MOFs. Essentially the same applies to elastic constants and phonon band structures. Additionally, for MOF-5 the thermal conductivity is obtained with full quantitative agreement to single-crystal experiments. All this is possible while maintaining a high degree of computational efficiency, with the obtained machine learned potentials being only moderately slower than the extremely simple UFF4MOF or Dreiding force fields. The exceptional accuracy of the presented FFPs combined with their computational efficiency has the potential of lifting the computational modelling of MOFs to the next level.

Metal-organic frameworks often display large positive or negative thermal expansion coefficients. MOF-74, a material envisioned for many applications does not display such a behavior. For this system, temperature-dependent x-ray diffraction reveals particularly small negative thermal expansion coefficients perpendicular and positive ones parallel to the hexagonally arranged pores. The observed trends are explained by combining state-of-the-art density-functional theory calculations with the Gr\"uneisen theory of thermal expansion, which allows tracing back thermal expansion to contributions of individual phonons. On the macroscopic level, the small thermal expansion coefficients arise from two aspects: compensation effects caused by the large coupling between stress and strain perpendicular to the pores and the small magnitudes of the mean Gr\"uneisen tensor elements, $\langle\gamma\rangle$, which provide information on how strains in the material influence its phonon frequencies. To understand the small mean Gr\"uneisen tensor in MOF-74, the individual mode contributions are analyzed based on the corresponding atomic motions. This reveals that only the lowest frequency modes up to ~3 THz provide non-negligible contributions, such that $\langle\gamma\rangle$ drops sharply at higher temperatures. These considerations reveal how the details of the anharmonic properties of specific phonon bands determine the magnitude and sign of thermal expansion in a prototypical material like MOF-74.

Covalent organic frameworks (COFs) have attracted significant attention due to their chemical versatility combined with a significant number of potential applications. Of particular interest are two-dimensional COFs, where the organic building units are linked by covalent bonds within a plane. Most properties of these COFs are determined by the relative arrangement of neighboring layers. These are typically found to be laterally displaced, which, for example, reduces the electronic coupling between the layers. In the present contribution, we use dispersion-corrected density-functional theory to elucidate the origin of that displacement, showing that the common notion that the displacement is a consequence of electrostatic repulsions of polar building blocks can be misleading. For the representative case of COF-1, we find that electrostatic and van der Waals interactions would, actually, favor a cofacial arrangement of the layers and that Pauli repulsion is the crucial factor causing the serrated AA stacking. A more in-depth analysis of the electrostatic contribution reveals that the "classical" Coulomb repulsion between the boroxine building blocks of COF-1 suggested by chemical intuition does exist, but is overcompensated by attractive effects due to charge-penetration in the phenylene units. The situation becomes more involved when additionally allowing the interlayer distance to relax for each displacement, as then the different distance-dependences of the various types of interactions come into play. The overall behavior calculated for COF-1 is recovered for several additional COFs with differently sized pi-systems and topologies, implying that the presented results are of more general relevance.

In recent years, optical and electronic properties of metal-organic frameworks (MOFs) have increasingly shifted into the focus of interest of the scientific community. Here, we discuss a strategy for conveniently tuning these properties through electrostatic design. More specifically, based on quantum-mechanical simulations, we suggest an approach for creating a gradient of the electrostatic potential within a MOF thin film exploiting collective electrostatic effects. With a suitable orientation of the polar apical linkers, the resulting non-centrosymmetric packing results in an energy staircase of the frontier electronic states reminiscent of the situation in a pin-photodiode. This 1-D gradient of the electrostatic potential causes a closure of the global energy gap and also shifts core-level energies by an energy equaling the size of the original band gap. The realization of such assemblies could be based on so-called pillared layer MOFs, grown in an oriented fashion on a solid substrate employing layer by layer growth techniques. In this context, the simulations provide guidelines regarding the design of the polar apical linker molecules that would allow the realization of MOF thin films with the (vast majority of the) molecular dipole moments pointing in the same direction.

In recent years, charge transport in metal-organic frameworks (MOFs) has shifted into the focus of scientific research. In this context, systems with efficient through-space charge transport pathways resulting from pi-stacked conjugated linkers are of particular interest. In the current manuscript, we use density functional theory based simulations to provide a detailed understanding of such MOFs, which in the present case are derived from the prototypical Zn2(TTFTB) system. In particular we show that factors like the relative arrangement of neighboring linkers and the details of the structural conformations of the individual building blocks have a profound impact on band widths and charge transfer. Considering the helical stacking of individual tetrathiafulvalene (TTF) molecules around a screw axis as the dominant symmetry element in Zn2(TTFTB)-derived materials, the focus here is primarily on the impact of the relative rotation of neighboring molecules. Not unexpectedly, also changing the stacking distance in the helix plays a distinct role, especially for structures, which display large electronic couplings to start with. The presented results provide guidelines for achieving structures with improved electronic couplings. It is, however, also shown that structural defects (especially missing linkers) provide major obstacles to charge transport in the studied, essentially one-dimensional systems. This suggests that especially the sample quality is a decisive factor for ensuring efficient through-space charge transport in MOFs comprising stacked pi-systems.

Controlling the transport of thermal energy is key to most applications of metal-organic frameworks. Analyzing the evolution of the effective local temperature, the interfaces between the metal nodes and the organic linkers are identified as the primary bottlenecks for heat conduction. Consequently, changing the bonding strength at that node-linker interface and the mass of the metal atoms can be exploited to tune the thermal conductivity. This insight is generated employing molecular dynamics simulations in conjunction with advanced, ab initio parametrized force fields. The focus of the present study is on MOF-5 as a prototypical example of an isoreticular MOF. Still, the key findings prevail for different node structures and node-linker bonding chemistries. The presented results lay the foundation for developing detailed structure-to-property relationships for thermal transport in MOFs with the goal of devising strategies for the application-specific optimization of heat conduction.

Phonons crucially impact a variety of properties of organic semiconductor materials. For instance, charge- and heat transport depend on low-frequency phonons, while for other properties, such as the free energy, especially high-frequency phonons count. For all these quantities one needs to know the entire phonon band structure, whose simulation becomes exceedingly expensive for more complex systems when using methods like dispersion-corrected density functional theory (DFT). Therefore, in the present contribution we evaluate the performance of more approximate methodologies, including density functional tight binding (DFTB) and a pool of force fields (FF) of varying complexity and sophistication. Beyond merely comparing phonon band structures, we also critically evaluate to what extent derived quantities, like temperature-dependent heat capacities, mean squared thermal displacements and temperature-dependent free energies are impacted by shortcomings in the description of the phonon bands. As a benchmark system, we choose (deuterated) naphthalene, as the only organic semiconductor material for which to date experimental phonon band structures are available in the literature. Overall, the best performance amongst the approximate methodologies is observed for a system-specifically parametrized second-generation force field. Interestingly, in the low-frequency regime also force fields with a rather simplistic model for the bonding interactions (like the General Amber Force Field) perform rather well. As far as the tested DFTB parametrization is concerned, we obtain a significant underestimation of the unit cell volume resulting in a pronounced overestimation of the phonon energies in the low frequency region. This cannot be mended by relying on the DFT-calculated unit cell, since with this unit cell the DFTB phonon frequencies significantly underestimate the experiments., Comment: Supporting Information is available free of charge at https://pubs.acs.org/doi/abs/10.1021/acs.jctc.0c00119

Metal-organic frameworks (MOFs) are crystalline materials consisting of metal centers and organic linkers forming open and porous structures. They have been extensively studied due to various possible applications exploiting their large amount of internal surface area. Phonon properties of MOFs are, however, still largely unexplored, despite their relevance for thermal and electrical conductivities, thermal expansion, and mechanical properties. Here, we use quantum-mechanical simulations to provide an in-depth analysis of the phonon properties of isoreticular MOFs. We consider phonon band structures, spatial confinements of modes, projected densities of states, and group velocity distributions. We find that more complex linkers shift the spectral weight of the phonon density of states towards higher frequencies, while increasing the mass of the metal atoms in the nodes has the opposite effect. Due to the high porosity of MOFs, we observe a particularly pronounced polarization dependence of the dispersion of acoustic phonons with rather high group velocities for longitudinal acoustic modes. Interestingly, also for several optical phonon modes group velocities amounting to several thousand m/s are obtained. For heterogeneous systems like MOFs, correlating group velocities and the displacement of modes is particularly relevant. Here we find that high group velocities are generally associated with delocalized vibrations, while the inverse correlation does not necessarily hold. To quantify anharmonicities, we calculate mode Gr\"uneisen parameters, which we find to be significant only for phonons with frequencies below ~3 THz. The presented results provide the foundations for an in-depth understanding of the vibrational properties of MOF, and, thus, pave the way for a future rational design of systems with well-defined phonon properties., Comment: Supplemental Material available (http://link.aps.org/supplemental/10.1103/PhysRevMaterials.3.116003 )

A crucial factor determining charge transport in organic semiconductors is the electronic coupling between the molecular constituents, which is heavily influenced by the relative arrangement of the molecules. This renders quinacridone, with its multiple, structurally fundamentally different polymorphs and their diverse intermolecular interactions an ideal test case for analyzing the correlation between the electronic coupling in a specific configuration and the configuration's energetic stability. To provide an in-depth analysis of this correlation, starting from the $\alpha$-polymorph of quinacridone, we also construct a coplanar model crystal. This allows us to systematically compare the displacement-dependence of the electronic coupling with that of the total energy. In this way, we identify the combination of Pauli repulsion and orbital rehybridization as the driving force steering the system towards a structure in which the electronic coupling is minimal (especially for the valence band and at small displacements). The general nature of these observations is supported by equivalent trends for an analogous pentacene model system. This underlines that the design of high-performance materials cannot rely on the "natural" assembly of the $\pi$-conjugated backbones of organic semiconductors into their most stable configurations. Rather, it must include the incorporation of functional groups that steer crystal packing towards more favorable structures, where aiming for short-axis displacements or realizing comparably large long-axis displacements appear as strategies worthwhile exploring., Comment: This article has been removed by arXiv administrators because the submitter did not have the rights to agree to the license at the time of submission