Machine learned Force-Fields for an ab-initio Quality Description of Metal-Organic Frameworks

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

Electrostatic design of polar metal–organic framework thin films

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 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. The observed one dimensional gradient of the electrostatic potential causes a closure of the global energy gap and also shifts core-level energies by an amount equaling the size of the original band gap. The realization of such assemblies could be based on so-called pillared layer MOFs fabricated 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

Distinguishing between Charge-Transfer Mechanisms at Organic/Inorganic Interfaces Employing Hybrid Functionals

When modeling inorganic/organic interfaces with density functional theory (DFT), the outcome often depends on the chosen functional. Hybrid functionals, which employ a fraction of Hartree–Fock exchange α, tend to give better results than the more commonly applied semilocal functionals, because they remove or at least mitigate the unphysical electron self-interaction. However, the choice of α is not straightforward, as its effect on observables depends on the physical properties of the investigated system, such as the size of the molecule and the polarizability of the substrate. In this contribution, we demonstrate this impact exemplarily for tetrafluoro-1,4-benzoquinone on semiconducting (copper-I-oxide Cu₂O) and metallic (Cu) substrates and explore how the simulated charge transfer depends on α. We determine the value α* that marks the transition point between spurious over-localization and over-delocalization of charges. This allows us to shed light on the interplay between the value of α* and the physical properties of the interface. We find that on the inert semiconducting substrate, α* strongly depends on surface screening. Furthermore, α has a significant impact on the amount of charge transfer and, in particular, the charge localization. Conversely, for the adsorption on Cu, α affects only the amount of transferred charge, but not its localization, which is a consequence of strong hybridization. Finally, we discuss limitations to the predictive power of DFT for modeling charge transfer at inorganic/organic interfaces and explain why the choice of a “correct” amount of Hartree–Fock exchange is difficult, if not impossible. However, we argue why simulations still provide valuable insights into the charge-transfer mechanism at organic/inorganic interfaces and describe how α can be chosen sensibly to simulate any given system

Understanding the Origin of the Particularly Small and Anisotropic Thermal Expansion of MOF-74

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

Unconventional Current Scaling and Edge Effects for Charge Transport through Molecular Clusters

Metal–molecule–metal junctions are the key components of molecular electronics circuits. Gaining a microscopic understanding of their conducting properties is central to advancing the field. In the present contribution, we highlight the fundamental differences between single-molecule and ensemble junctions focusing on the fundamentals of transport through molecular clusters. In this way, we elucidate the collective behavior of parallel molecular wires, bridging the gap between single molecule and large-area monolayer electronics, where even in the latter case transport is usually dominated by finite-size islands. On the basis of first-principles charge-transport simulations, we explain why the scaling of the conductivity of a junction has to be distinctly nonlinear in the number of molecules it contains. Moreover, transport through molecular clusters is found to be highly inhomogeneous with pronounced edge effects determined by molecules in locally different electrostatic environments. These effects are most pronounced for comparably small clusters, but electrostatic considerations show that they prevail also for more extended systems.We thank D. A. Egger, E. Lortscher, and M. Brandbyge for stimulating discussions and G. Nascimbeni for performing additional test calculations. The authors are also grateful for the thoughtful and detailed comments of the referees, which helped us to compile a more insightful manuscript. We are grateful for financial support by the Austrian Science Fund (FWF): P24666-N20, P28631-N36, and P28051-N36. N.P. acknowledges support from the Center for Nanostructured Graphene, sponsored by the Danish National Research Foundation, Project No. DNRF103, from Villum fonden (Grant 00013340), and from the EU H2020 Project No. 676598, ‘‘MaX: Materials at the eXascale’’ Center of Excellence in Supercomputing Applications. ICN2 is funded by the CERCA Programme/Generalitat de Catalunya and is supported by the Severo Ochoa program from the Spanish MINECO (Grant SEV-2013-0295). Electronic structure calculations have been performed using the cluster of the division for high-performance computing at the Graz University of Technology and the Vienna Scientific Cluster. Transport calculations have been performed using the Marenostrum supercomputer of the Barcelona Supercomputing Center (BSC).Peer ReviewedPostprint (published version

Exciton Coupling and Conformational Changes Impacting the Excited State Properties of Metal Organic Frameworks

In recent years, the photophysical properties of crystalline metal-organic frameworks (MOFs) have become increasingly relevant for their potential application in light-emitting devices, photovoltaics, nonlinear optics and sensing. The availability of high-quality experimental data for such systems makes them ideally suited for a validation of quantum mechanical simulations, aiming at an in-depth atomistic understanding of photophysical phenomena. Here we present a computational DFT study of the absorption and emission characteristics of a Zn-based surface-anchored metal-organic framework (Zn-SURMOF-2) containing anthracenedibenzoic acid (ADB) as linker. Combining band-structure and cluster-based simulations on ADB chromophores in various conformations and aggregation states, we are able to provide a detailed explanation of the experimentally observed photophysical properties of Zn-ADB SURMOF-2: The unexpected (weak) red-shift of the absorption maxima upon incorporating ADB chromophores into SURMOF-2 can be explained by a combination of excitonic coupling effects with conformational changes of the chromophores already in their ground state. As far as the unusually large red-shift of the emission of Zn-ADB SURMOF-2 is concerned, based on our simulations, we attribute it to a modification of the exciton coupling compared to conventional H-aggregates, which results from a relative slip of the centers of neighboring chromophores upon incorporation in Zn-ADB SURMOF-2

Magnetic configurations of open-shell molecules on metals: The case of CuPc and CoPc on silver

For nanostructured interfaces between open-shell molecules and metal surfaces that involve charge transfer upon adsorption, the investigation of molecular magnetic properties is an interesting yet difficult task, because in principle different magnetic configurations with distinct properties can be found. Here, we study the magnetic properties of CuPc-Ag and CoPc-Ag interfaces, which constitute interesting test cases because charge is transferred to the initially open-shell Pc molecules upon adsorption. Using hybrid density functional theory, we examine the stability of the various magnetic configurations occurring at these nanoscale interfaces, as well as for the corresponding gas-phase anions, and compare our findings to those of previous experimental studies. For CuPc-Ag, we identify a high-spin triplet configuration as the most likely configuration at the interface, whereas for CoPc-Ag a quenching of the total magnetic moment is found. Interestingly, such quenching is consistent with two distinctly different interfacial electronic configurations. These important differences in the magnetic properties of CuPc and CoPc on Ag are rationalized by variations in the interaction of their central metal atoms with the substrate. Our work facilitates a deeper understanding of the magnetic configuration and interlinked electronic-structure properties of molecule-metal interfaces. Furthermore, it highlights the necessity of an appropriate choice of methodology in tandem with a detailed evaluation of the different emerging magnetic properties

Breakdown of the mirror image symmetry in the optical absorption/emission spectra of oligo(para-phenylene)s

The absorption and emission spectra of most luminescent, pi-conjugated, organic molecules are the mirror image of each other. In some cases, however, this symmetry is severely broken. In the present work, the asymmetry between the absorption and fluorescence spectra in molecular systems consisting of para-linked phenyl rings is studied. The vibronic structure of the emission and absorption bands is calculated from ab-initio quantum chemical methods and a subsequent, rigorous Franck-Condon treatment. Good agreement with experiment is achieved. A clear relation can be established between the strongly anharmonic double-well potential for the phenylene ring librations around the long molecular axis and the observed deviation from the mirror image symmetry. Consequences for related compounds and temperature dependent optical measurements are also discussed.Comment: 12 pages, 13 Figure