The Monomer Electron Density Force Field (MEDFF) : a physically inspired model for noncovalent interactions

We propose a methodology to derive pairwise-additive noncovalent force fields from monomer electron densities without any empirical input. Energy expressions are based on the symmetry-adapted perturbation theory (SAPT) decomposition of interaction energies. This ensures a physically motivated force field featuring an electrostatic, exchange repulsion, dispersion, and induction contribution, which contains two types of parameters. First, each contribution depends on several fixed atomic parameters, resulting from a partitioning of the monomer electron density. Second, each of the last three contributions (exchange-repulsion, dispersion, and induction) contains exactly one linear fitting parameter. These three so-called interaction parameters in the model are initially estimated separately using SAPT reference calculations for the S66x8 database of noncovalent dimers. In a second step, the three interaction parameters are further refined simultaneously to reproduce CCSD(T)/CBS interaction energies for the same database. The limited number of parameters that are fitted to dimer interaction energies (only three) avoids ill-conditioned fits that plague conventional parameter optimizations. For the exchange repulsion and dispersion component, good results are obtained for all dimers in the S66x8 database using one single value for the associated interaction parameters. The values of those parameters can be considered universal and can also be used for dimers not present in the original database used for fitting. For the induction component such an approach is only viable for the dispersion dominated dimers in the S66x8 database. For other dimers (such as hydrogen-bonded complexes), we show that our methodology remains applicable. However, the interaction parameter needs to be determined on a case-specific basis. As an external validation:, the force field predicts interaction energies in good agreement with CCSD(T)/CBS values for dispersion dominated dimers extracted from an HIV-II protease crystal structure with a bound ligand (indinavir). Furthermore, experimental second virial coefficients of small alkanes and alkenes are well reproduced

Extension of the QuickFF force field protocol for an improved accuracy of structural, vibrational, mechanical and thermal properties of metal-organic frameworks

QuickFF was originally launched in 2015 to derive accurate force fields for isolated and complex molecular systems in a quick and easy way. Apart from the general applicability, the functionality was especially tested for metal-organic frameworks (MOFs), a class of hybrid materials consisting of organic and inorganic building blocks. Herein, we launch a new release of the QuickFF protocol which includes new major features to predict structural, vibrational, mechanical and thermal properties with greater accuracy, without compromising its robustness and transparent workflow. First, the ab initio data necessary for the fitting procedure may now also be derived from periodic models for the molecular system, as opposed to the earlier cluster-based models. This is essential for an accurate description of MOFs with one-dimensional metal-oxide chains. Second, cross terms that couple internal coordinates (ICs) and anharmonic contributions for bond and bend terms are implemented. These features are essential for a proper description of vibrational and thermal properties. Third, the fitting scheme was modified to improve robustness and accuracy. The new features are tested on MIL-53(Al), MOF-5, CAU-13 and NOTT-300. As expected, periodic input data are proven to be essential for a correct description of structural, vibrational and thermodynamic properties of MIL-53(Al). Bulk moduli and thermal expansion coefficients of MOF-5 are very accurately reproduced by static and dynamic simulations using the newly derived force fields which include cross terms and anharmonic corrections. For the flexible materials CAU-13 and NOTT-300, the transition pressure is accurately predicted provided cross terms are taken into account

The group of dyadic unitary matrices

We introduce the group DU(m) of m x m dyadic unitary matrices, i.e. unitary matrices with all entries having a real and an imaginary part that are both rational numbers with denominator of the form 2(p) (with p a non-negative integer). We investigate in detail the finite groups DU(1) and DU(2) and the discrete, but infinite groups DU(3) and DU(4). We further introduce the subgroup XDU(m) of DU(m), consisting of those members of DU(m) that have constant line sum 1. The study of XDU(2) and XDU(4) leads to conclusions concerning the synthesis of quantum computers acting on one and two qubits, respectively

Ab initio evaluation of Henry coefficients using importance sampling

We present a new algorithm that allows for an efficient evaluation of the Henry coefficient of a guest molecule inside a porous material, which permits to use ab initio energy calculations. The Widom insertion method, which is currently used to compute these Henry coefficients, typically requires millions of energy evaluations. Our new methodology reduces this number by more than 1 order of magnitude, enabling the use of an ab initio potential energy surface. The methodology we propose is reminiscent of the well-known importance sampling technique which is frequently used in Monte Carlo integrations. First, a conventional Widom insertion simulation is performed using a force field. In the second step, the Widom results are used to select a limited number of configurations and only for these configurations the ab initio evaluation of the energy is required. Finally, by appropriately reweighting the latter energies, an accurate estimation of the ab initio Henry coefficient is possible at a moderate computational cost. We apply our methodology to the adsorption of CO, in Mg-MOF-74, a prototypical case where interactions of a polar guest molecule with unsaturated metal sites dominate the adsorption mechanism. In this case generic force fields such as UFF or Dreiding are inappropriate and the use of ab initio methods is indispensable. In a second case study, we compute Henry coefficients of methane in UiO-66 using different levels of theory. We pay particular attention to the influence of the dispersion corrections and the role of many-body effects. For the final example, we qualitatively investigate adsorption features for a series of functionalized UiO-66 frameworks. Overall the cases we present show that accurate computations of Henry coefficients is extremely challenging, as different levels of theory provide strongly varying results. At the same time ab initio calculations have added value compared to force fields, as they provide a physically more sound description of the adsorption mechanism and in some cases clearly improve correspondence with experiment

Thermodynamic insight into stimuli-responsive behaviour of soft porous crystals

Knowledge of the thermodynamic potential in terms of the independent variables allows to characterize the macroscopic state of the system. However, in practice, it is difficult to access this potential experimentally due to irreversible transitions that occur between equilibrium states. A showcase example of sudden transitions between (meta) stable equilibrium states is observed for soft porous crystals possessing a network with long-range structural order, which can transform between various states upon external stimuli such as pressure, temperature and guest adsorption. Such phase transformations are typically characterized by large volume changes and may be followed experimentally by monitoring the volume change in terms of certain external triggers. Herein, we present a generalized thermodynamic approach to construct the underlying Helmholtz free energy as a function of the state variables that governs the observed behaviour based on microscopic simulations. This concept allows a unique identification of the conditions under which a material becomes flexible

Thermodynamic insight in the high-pressure behavior of UiO-66: effect of linker defects and linker expansion

In this Article, we present a molecular-level understanding of the experimentally observed loss of crystallinity in UiO-66-type metal organic frameworks, including the pristine UiO-66 to-68 as well as defect-containing UiO-66 materials, under the influence of external pressure. This goal is achieved by constructing pressure-versus-volume profiles at finite temperatures using a thermodynamic approach relying on ab initio derived force fields. On the atomic level, the phenomenon is reflected in a sudden drop in the number of symmetry operators for the crystallographic unit cell because of the disordered displacement of the organic linkers with respect to the inorganic bricks. For the defect-containing samples, a reduced mechanical stability is observed, however, critically depending on the distribution of these defects throughout the material, hence demonstrating the importance of judiciously characterizing defects in these materials

Influence of a confined methanol solvent on the reactivity of active sites in UiO-66

UiO-66, composed of Zr-oxide bricks and terephthalate linkers, is currently one of the most studied metal-organic frameworks due to its exceptional stability. Defects can be introduced in the structure, creating undercoordinated Zr atoms which are Lewis acid sites. Here, additional BrOnsted sites can be generated by coordinated protic species from the solvent. In this Article, a multilevel modeling approach was applied to unravel the effect of a confined methanol solvent on the active sites in UiO-66. First, active sites were explored with static periodic density functional theory calculations to investigate adsorption of water and methanol. Solvent was then introduced in the pores with grand canonical Monte Carlo simulations, followed by a series of molecular dynamics simulations at operating conditions. A hydrogen-bonded network of methanol molecules is formed, allowing the protons to shuttle between solvent methanol, adsorbed water, and the inorganic brick. Upon deprotonation of an active site, the methanol solvent aids the transfer of protons and stabilizes charged configurations via hydrogen bonding, which could be crucial in stabilizing reactive intermediates. The multilevel modeling approach adopted here sheds light on the important role of a confined solvent on the active sites in the UiO-66 material, introducing dynamic acidity in the system at finite temperatures by which protons may be easily shuttled from various positions at the active sites

Minimal Basis Iterative Stockholder: Atoms in Molecules for Force-Field Development

Atomic partial charges appear in the Coulomb term of many force-field models and can be derived from electronic structure calculations with a myriad of atoms-in-molecules (AIM) methods. More advanced models have also been proposed, using the distributed nature of the electron cloud and atomic multipoles. In this work, an electrostatic force field is defined through a concise approximation of the electron density, for which the Coulomb interaction is trivially evaluated. This approximate "pro-density" is expanded in a minimal basis of atom-centered s-type Slater density functions, whose parameters are optimized by minimizing the Kullback-Leibler divergence of the pro-density from a reference electron density, e.g. obtained from an electronic structure calculation. The proposed method, Minimal Basis Iterative Stockholder (MBIS), is a variant of the Hirshfeld AIM method but it can also be used as a density-fitting technique. An iterative algorithm to refine the pro-density is easily implemented with a linear-scaling computational cost, enabling applications to supramolecular systems. The benefits of the MBIS method are demonstrated with systematic applications to molecular databases and extended models of condensed phases. A comparison to 14 other AIM methods shows its effectiveness when modeling electrostatic interactions. MBIS is also suitable for rescaling atomic polarizabilities in the Tkatchenko-Sheffler scheme for dispersion interactions.Comment: 61 pages, 12 figures, 2 table

Light olefin diffusion during the MTO process on H-SAPO-34 : a complex interplay of molecular factors

The methanol-to-olefins process over H-SAPO-34 is characterized by its high shape selectivity toward light olefins. The catalyst is a supramolecular system consisting of nanometer-sized inorganic cages, decorated by Bronsted acid sites, in which organic compounds, mostly methylated benzene species, are trapped. These hydrocarbon pool species are essential to catalyze the methanol conversion but may also clog the pores. As such, diffusion of ethene and propene plays an essential role in determining the ultimate product selectivity. Enhanced sampling molecular dynamics simulations based on either force fields or density functional theory are used to determine how molecular factors influence the diffusion of light olefins through the 8-ring windows of H-SAPO-34. Our simulations show that diffusion through the 8-ring in general is a hindered process, corresponding to a hopping event of the diffusing molecule between neighboring cages. The loading of different methanol, alkene, and aromatic species in the cages may substantially slow down or facilitate the diffusion process. The presence of Bronsted acid sites in the 8-ring enhances the diffusion process due to the formation of a favorable pi-complex host-guest interaction. Aromatic hydrocarbon pool species severely hinder the diffusion and their spatial distribution in the zeolite crystal may have a significant effect on the product selectivity. Herein, we unveil how molecular factors influence the diffusion of light olefins in a complex environment with confined hydrocarbon pool species, high olefin loadings, and the presence of acid sites by means of enhanced molecular dynamics simulations under operating conditions