Informative Training Data for Efficient Property Prediction in Metal-Organic Frameworks by Active Learning.

In recent data-driven approaches to material discovery, scenarios where target quantities are expensive to compute and measure are often overlooked. In such cases, it becomes imperative to construct a training set that includes the most diverse, representative, and informative samples. Here, a novel regression tree-based active learning algorithm is employed for such a purpose. It is applied to predict the band gap and adsorption properties of metal-organic frameworks (MOFs), a novel class of materials that results from the virtually infinite combinations of their building units. Simpler and low dimensional descriptors, such as those based on stoichiometric and geometric properties, are used to compute the feature space for this model owing to their ability to better represent MOFs in the low data regime. The partitions given by a regression tree constructed on the labeled part of the data set are used to select new samples to be added to the training set, thereby limiting its size while maximizing the prediction quality. Tests on the QMOF, hMOF, and dMOF data sets reveal that our method constructs small training data sets to learn regression models that predict the target properties more efficiently than existing active learning approaches, and with lower variance. Specifically, our active learning approach is highly beneficial when labels are unevenly distributed in the descriptor space and when the label distribution is imbalanced, which is often the case for real world data. The regions defined by the tree help in revealing patterns in the data, thereby offering a unique tool to efficiently analyze complex structure-property relationships in materials and accelerate materials discovery.

CO and CO2 adsorption mechanism in Fe(pz)[Pt(CN)4] probed by neutron scattering and density-functional theory calculations.

We study the binding mechanism of CO and CO2 in the porous spin-crossover compound Fe(pz)[Pt(CN)4] by combining neutron diffraction (ND), inelastic neutron scattering (INS) and density-functional theory (DFT) calculations. Two adsorption sites are identified, above the open-metal site and between the pyrazine rings. For CO adsorption, the guest molecules are parallel to the neighboring gas molecules and perpendicular to the pyrazine planes. For CO2, the molecules adsorbed on-top of the open-metal site are perpendicular to the pyrazine rings and those between the pyrazines are almost parallel to them. These configurations are consistent with the INS data, which are in good agreement with the computed generalized phonon density of states. The most relevant signatures of the binding occur in the spectral region around 100 cm-1 and 400 cm-1. The first peak blue-shifts for both CO and CO2 adsorption, while the second red-shifts for CO and remains nearly unchanged for CO2. These spectral changes depend both from steric effects and the nature of the interaction. The interpretation of the INS data as supported by the computed binding energy and the molecular orbital analysis are consistent with a physisorption mechanism for both gases. This work shows the strength of the combination of neutron techniques and DFT calculations to characterize in detail the gas adsorption mechanism in this type of materials.

Assessing the Role of the Kohn-Sham Density in the Calculation of the Low-Lying Bethe-Salpeter Excitation Energies.

We adopt the GW many-body perturbation theory in conjunction with the Bethe-Salpeter equation (BSE) to compute 57 excitation energies of a set of 37 molecules. By using the PBEh global hybrid functional and a self-consistent scheme on the eigenvalues in GW, we show a strong dependence of the BSE energy on the starting Kohn-Sham (KS) density functional. This arises from both the quasiparticle energies and the spatial localization of the frozen KS orbitals employed to compute the BSE. In order to address the arbitrariness in the mean field choice, we adopt an orbital-tuning scheme where the amount of Fock exchange, α, is tuned to impose that the KS HOMO matches the GW quasiparticle eigenvalue, thus fulfilling the ionization potential theorem in DFT. The performance of the proposed scheme yields excellent results and it is similar to M06-2X and PBEh with α = 75%, consistent with tuned values of α ranging between 60% and 80%.

Cooperative insertion of CO2 in diamine-appended metal-organic frameworks.

The process of carbon capture and sequestration has been proposed as a method of mitigating the build-up of greenhouse gases in the atmosphere. If implemented, the cost of electricity generated by a fossil fuel-burning power plant would rise substantially, owing to the expense of removing CO2 from the effluent stream. There is therefore an urgent need for more efficient gas separation technologies, such as those potentially offered by advanced solid adsorbents. Here we show that diamine-appended metal-organic frameworks can behave as 'phase-change' adsorbents, with unusual step-shaped CO2 adsorption isotherms that shift markedly with temperature. Results from spectroscopic, diffraction and computational studies show that the origin of the sharp adsorption step is an unprecedented cooperative process in which, above a metal-dependent threshold pressure, CO2 molecules insert into metal-amine bonds, inducing a reorganization of the amines into well-ordered chains of ammonium carbamate. As a consequence, large CO2 separation capacities can be achieved with small temperature swings, and regeneration energies appreciably lower than achievable with state-of-the-art aqueous amine solutions become feasible. The results provide a mechanistic framework for designing highly efficient adsorbents for removing CO2 from various gas mixtures, and yield insights into the conservation of Mg(2+) within the ribulose-1,5-bisphosphate carboxylase/oxygenase family of enzymes.

Electric field-induced oxygen vacancies in YBa2Cu3O7.

The microscopic doping mechanism behind the superconductor-to-insulator transition of a thin film of YBa2Cu3O7 was recently identified as due to the migration of O atoms from the CuO chains of the film. Here, we employ density-functional theory calculations to study the evolution of the electronic structure of a slab of YBa2Cu3O7 in the presence of oxygen vacancies under the influence of an external electric field. We find that, under massive electric fields, isolated O atoms are pulled out of the surface consisting of CuO chains. As vacancies accumulate at the surface, a configuration with vacancies located in the chains inside the slab becomes energetically preferred, thus providing a driving force for O migration toward the surface. Regardless of the defect configuration studied, the electric field is always fully screened near the surface, thus negligibly affecting diffusion barriers across the film.

In operando evidence of deoxygenation in ionic liquid gating of YBa2Cu3O7-X.

Field-effect experiments on cuprates using ionic liquids have enabled the exploration of their rich phase diagrams [Leng X, et al. (2011) Phys Rev Lett 107(2):027001]. Conventional understanding of the electrostatic doping is in terms of modifications of the charge density to screen the electric field generated at the double layer. However, it has been recently reported that the suppression of the metal to insulator transition induced in VO2 by ionic liquid gating is due to oxygen vacancy formation rather than to electrostatic doping [Jeong J, et al. (2013) Science 339(6126):1402-1405]. These results underscore the debate on the true nature, electrostatic vs. electrochemical, of the doping of cuprates with ionic liquids. Here, we address the doping mechanism of the high-temperature superconductor YBa2Cu3O7-X (YBCO) by simultaneous ionic liquid gating and X-ray absorption experiments. Pronounced spectral changes are observed at the Cu K-edge concomitant with the superconductor-to-insulator transition, evidencing modification of the Cu coordination resulting from the deoxygenation of the CuO chains, as confirmed by first-principles density functional theory (DFT) simulations. Beyond providing evidence of the importance of chemical doping in electric double-layer (EDL) gating experiments with superconducting cuprates, our work shows that interfacing correlated oxides with ionic liquids enables a delicate control of oxygen content, paving the way to novel electrochemical concepts in future oxide electronics.

Tuning Gas Adsorption by Metal Node Blocking in Photoresponsive Metal-Organic Frameworks.

By combining first-principles calculations and classical molecular simulations, an atomistic-level of understanding was provided towards the notable change in CO2 adsorption upon light treatment in two recently reported photoactive metal-organic frameworks, PCN-123 and Cu2 (AzoBPDC)2 (AzoBiPyB). It was demonstrated that the reversible decrease in gas adsorption upon isomerization can be primarily attributed to the blocking of the strong adsorbing sites at the metal nodes by azobenzene molecules in a cis configuration. The same mechanism was found to apply also to other molecules, for example, alkanes and toxic gases. Such understandings are instrumental to the future design of photoresponsive metal-organic frameworks. For example, the metal node-blocking mechanism can be leveraged to achieve optimal adsorption properties as a function of metal substitution and/or ligand functionalization. As a proof of concept, it was shown that the working capacity could be increased by a factor of two in PCN-123 by replacing the Zn4 O node with the more strongly adsorbing Mg4 O.

Probing the electric field-induced doping mechanism in YBa2Cu3O7 using computed Cu K-edge x-ray absorption spectra.

We recently demonstrated that the superconductor-to-insulator transition induced by ionic liquid gating of the high temperature superconductor YBa2Cu3O7 (YBCO) is accompanied by a deoxygenation of the sample [A. M. Perez-Munoz et al., Proc. Natl. Acad. Sci. U. S. A. 114, 215 (2017)]. Density functional theory calculations helped establish that the pronounced changes in the spectral features of the Cu K-edge absorption spectra measured in situ during the gating experiment arise from a decrease of the Cu coordination within the CuO chains. In this work, we provide a detailed analysis of the electronic structure origin of the changes in the spectra resulting from three different types of doping: (i) the formation of oxygen vacancies within the CuO chains, (ii) the formation of oxygen vacancies within the CuO2 planes, and (iii) the electrostatic doping. For each case, three stoichiometries are studied and compared to the stoichiometric YBa2Cu3O7, i.e., YBa2Cu3O6.75, YBa2Cu3O6.50, and YBa2Cu3O6.25. Computed vacancy formation energies further support the chain-vacancy mechanism. In the case of doping by vacancies within the chains, we study the effect of oxygen ordering on the spectral features and we clarify the connection between the polarization of the x-rays and this doping mechanism. Finally, the inclusion of the Hubbard U correction on the computed spectra for antiferromagnetic YBa2Cu3O6.25 is discussed.

Long-range magnetic order in the porous metal-organic framework Ni(pyrazine)[Pt(CN)4].

A combined study involving DFT calculations, neutron scattering, heat capacity and magnetic measurements at very low temperatures demonstrates the long-range magnetic ordering of Ni(pyrazine)[Pt(CN)4] below 1.9 K, describing its antiferromagnetic spin arrangement. This compound belongs to the family of porous coordination polymers M(pyrazine)[Pt(CN)4] (M = divalent metal), renowned for showing interesting combinations of porosity and magnetic properties. The possibility of including long-range magnetic ordering, one of the most pursued functional properties, opens new perspectives for the multifunctionality of this class of compounds.

Probing gas adsorption in MOFs using an efficient ab initio widom insertion Monte Carlo method.

We propose a novel biased Widom insertion method that can efficiently compute the Henry coefficient, KH , of gas molecules inside porous materials exhibiting strong adsorption sites by employing purely DFT calculations. This is achieved by partitioning the simulation volume into strongly and weakly adsorbing regions and selectively biasing the Widom insertion moves into the former region. We show that only few thousands of single point energy calculations are necessary to achieve accurate statistics compared to many hundreds of thousands or millions of such calculations in conventional random insertions. The methodology is used to compute the Henry coefficient for CO2 , N2 , CH4 , and C2 H2 in M-MOF-74(M = Zn and Mg), yielding good agreement with published experimental data. Our results demonstrate that the DFT binding energy and the heat of adsorption are not accurate enough indicators to rank the guest adsorption properties at the Henry regime. © 2016 Wiley Periodicals, Inc.

Probing the mechanism of CO2 capture in diamine-appended metal-organic frameworks using measured and simulated X-ray spectroscopy.

Diamine-appended metal-organic frameworks display great promise for carbon capture applications, due to unusual step-shaped adsorption behavior that was recently attributed to a cooperative mechanism in which the adsorbed CO2 molecules insert into the metal-nitrogen bonds to form ordered ammonium carbamate chains [McDonald et al., Nature, 2015, 519, 303]. We present a detailed study of this mechanism by in situ X-ray absorption spectroscopy and density functional theory calculations. Distinct spectral changes at the N and O K-edges are apparent upon CO2 adsorption in both mmen-Mg2(dobpdc) and mmen-Mn2(dobpdc), and these are evaluated based upon computed spectra from three potential adsorption structures. The computations reveal that the observed spectral changes arise from specific electronic states that are signatures of a quasi-trigonal planar carbamate species that is hydrogen bonded to an ammonium cation. This eliminates two of the three structures studied, and confirms the insertion mechanism. We note the particular sensitivity of X-ray absorption spectra to the insertion step of this mechanism, underpinning the strength of the technique for examining subtle chemical changes upon gas adsorption.

Probing adsorption interactions in metal-organic frameworks using X-ray spectroscopy.

We explore the local electronic signatures of molecular adsorption at coordinatively unsaturated binding sites in the metal-organic framework Mg-MOF-74 using X-ray spectroscopy and first-principles calculations. In situ measurements at the Mg K-edge reveal distinct pre-edge absorption features associated with the unique, open coordination of the Mg sites which are suppressed upon adsorption of CO2 and N,N'-dimethylformamide. Density functional theory shows that these spectral changes arise from modifications of local symmetry around the Mg sites upon gas uptake and are strongly dependent on the metal-adsorbate binding strength. The expanded MOF Mg2(dobpdc) displays the same behavior upon adsorption of CO2 and N,N'-dimethylethylenediamine. Similar sensitivity to local symmetry is expected for any open metal site, making X-ray spectroscopy an ideal tool for examining adsorption in such MOFs. Qualitative agreement between ambient-temperature experimental and 0 K theoretical spectra is good, with minor discrepancies thought to result from framework vibrational motion.

The mechanism of carbon dioxide adsorption in an alkylamine-functionalized metal-organic framework.

The mechanism of CO2 adsorption in the amine-functionalized metal-organic framework mmen-Mg2(dobpdc) (dobpdc(4-) = 4,4'-dioxidobiphenyl-3,3'-dicarboxylate; mmen = N,N'-dimethylethylenediamine) was characterized by quantum-chemical calculations. The material was calculated to demonstrate 2:2 amine:CO2 stoichiometry with a higher capacity and weaker CO2 binding energy than for the 2:1 stoichiometry observed in most amine-functionalized adsorbents. We explain this behavior in the form of a hydrogen-bonded complex involving two carbamic acid moieties resulting from the adsorption of CO2 onto the secondary amines.

Artificial Neural Network-Based Density Functional Approach for Adiabatic Energy Differences in Transition Metal Complexes.

During the past decades, approximate Kohn-Sham density functional theory schemes have garnered many successes in computational chemistry and physics, yet the performance in the prediction of spin state energetics is often unsatisfactory. By means of a machine learning approach, an enhanced exchange and correlation functional is developed to describe adiabatic energy differences in transition metal complexes. The functional is based on the computationally efficient revision of the regularized, strongly constrained, and appropriately normed functional and improved by an artificial neural network correction trained over a small data set of electronic densities, atomization energies, and/or spin state energetics. The training process, performed using a bioinspired nongradient-based approach adapted for this work from the particle swarm optimization, is analyzed and discussed extensively. The resulting machine learned meta-generalized gradient approximation functional is shown to outperform most known density functionals in the prediction of adiabatic energy differences for a diverse set of transition metal complexes with varying local coordinations and metal choices.

Ligand-assisted enhancement of CO2 capture in metal-organic frameworks.

Using density functional theory with a van der Waals-corrected functional, we elucidate how CO(2) binds to a novel "BTT-type" metal-organic framework (MOF) featuring open metal centers. We show that CO(2) binds most favorably to open metal cation sites, but with an adsorption energy that can be three times more sensitive to the choice of the bridging ligand than to metal cation choice. A strong, three-site interaction between CO(2) and the open-metal site is predicted, with the binding energy enhanced by up to a factor of 2, depending on the ligand. The CO(2)-MOF binding can be attributed to a combination of electrostatics and vdW dispersive interactions, both of which are critically sensitive to the local environment, and both of which contribute nearly equally to the overall binding strength. We show that a judicious choice of the organic linker and the metal center allows the binding energy to be tuned from 34.8 kJ/mol (for CaBTTri) to a maximum of 64.5 kJ/mol (MgBTT).

CO2 capture by metal-organic frameworks with van der Waals density functionals.

We use density functional theory calculations with van der Waals corrections to study the role of dispersive interactions on the structure and binding of CO(2) within two distinct metal-organic frameworks (MOFs): Mg-MOF74 and Ca-BTT. For both classes of MOFs, we report calculations with standard gradient-corrected (PBE) and five van der Waals density functionals (vdW-DFs), also comparing with semiempirical pairwise corrections. The vdW-DFs explored here yield a large spread in CO(2)-MOF binding energies, about 50% (around 20 kJ/mol), depending on the choice of exchange functional, which is significantly larger than our computed zero-point energies and thermal contributions (around 5 kJ/mol). However, two specific vdW-DFs result in excellent agreement with experiments within a few kilojoules per mole, at a reduced computational cost compared to quantum chemistry or many-body approaches. For Mg-MOF74, PBE underestimates adsorption enthalpies by about 50%, but enthalpies computed with vdW-DF, PBE+D2, and vdW-DF2 (40.5, 38.5, and 37.4 kJ/mol, respectively) compare extremely well with the experimental value of 40 kJ/mol. vdW-DF and vdW-DF2 CO(2)-MOF bond lengths are in the best agreement with experiments, while vdW-C09(x) results in the best agreement with lattice parameters. On the basis of the similar behavior of the reduced density gradients around CO(2) for the two MOFs studied, comparable results can be expected for CO(2) adsorption in BTT-type MOFs. Our work demonstrates for this broad class of molecular adsorbate-periodic MOF systems that parameter-free and computationally efficient vdW-DF and vdW-DF2 approaches can predict adsorption enthalpies with chemical accuracy.

Improved Spin-State Energy Differences of Fe(II) Molecular and Crystalline Complexes via the Hubbard U-Corrected Density.

We recently showed that the DFT+U approach with a linear-response U yields adiabatic energy differences biased toward high spin [Mariano et al. J. Chem. Theory Comput. 2020, 16, 6755-6762]. Such bias is removed here by employing a density-corrected DFT approach where the PBE functional is evaluated on the Hubbard U-corrected density. The adiabatic energy differences of six Fe(II) molecular complexes computed using this approach, named PBE[U] here, are in excellent agreement with coupled cluster-corrected CASPT2 values for both weak- and strong-field ligands resulting in a mean absolute error (MAE) of 0.44 eV, smaller than that of the recently proposed Hartree-Fock density-corrected DFT (1.22 eV) and any other tested functional, including the best performer TPSSh (0.49 eV). We take advantage of the computational efficiency of this approach and compute the adiabatic energy differences of five molecular crystals using PBE[U] with periodic boundary conditions. The results show, again, an excellent agreement (MAE = 0.07 eV) with experimentally extracted values and a superior performance compared with the best performers M06-L (MAE = 0.08 eV) and TPSSh (MAE = 0.31 eV) computed on molecular fragments.

Strongly Bound Excitons in Metal-Organic Framework MOF-5: A Many-Body Perturbation Theory Study.

During the past years, one of the most iconic metal-organic frameworks (MOFs), MOF-5, has been characterized as a semiconductor by theory and experiments. Here we employ the GW many-body perturbation theory in conjunction with the Bethe-Salpeter equation to compute the electronic structure and optical properties of this MOF. The GW calculations show that MOF-5 is a wide-band-gap insulator with a fundamental gap of ∼8 eV. The strong excitonic effects, arising from highly localized states and low screening, result in an optical gap of 4.5 eV and in an optical absorption spectrum in excellent agreement with experiments. The origin of the incorrect conclusion reported by past studies and the implication of this result are also discussed.

Tunable Proton Conductivity and Color in a Nonporous Coordination Polymer via Lattice Accommodation to Small Molecules.

Nonporous coordination polymers (npCPs) able to accommodate molecules through internal lattice reorganization are uncommon materials with applications in sensing and selective gas adsorption. Proton conduction, extensively studied in the analogue metal-organic frameworks under high-humidity conditions, is however largely unexplored in spite of the opportunities provided by the particular sensitivity of npCPs to lattice perturbations. Here, AC admittance spectroscopy is used to unveil the mechanism behind charge transport in the nonporous 1·2CH3 CN. The conductance in the crystals is found to be of protonic origin. A vehicle mechanism is triggered by the dynamics of the weakly coupled acetonitrile molecules in the lattice that can be maintained by a combination of thermal cycles, even at low humidity levels. An analogue 1·pyrrole npCP is formed by in situ exchange of these weakly bound acetonitrile molecules by pyrrole. The color and conduction properties are determined by the molecules weakly bonded in the lattice. This is the first example of acetonitrile-mediated proton transport in an npCP showing distinct optical response to different molecules. These findings open the door to the design of switchable protonic conductors and capacitive sensors working at low humidity levels and with selectivity to different molecules.

Twin boundary migration in an individual platinum nanocrystal during catalytic CO oxidation.

At the nanoscale, elastic strain and crystal defects largely influence the properties and functionalities of materials. The ability to predict the structural evolution of catalytic nanocrystals during the reaction is of primary importance for catalyst design. However, to date, imaging and characterising the structure of defects inside a nanocrystal in three-dimensions and in situ during reaction has remained a challenge. We report here an unusual twin boundary migration process in a single platinum nanoparticle during CO oxidation using Bragg coherent diffraction imaging as the characterisation tool. Density functional theory calculations show that twin migration can be correlated with the relative change in the interfacial energies of the free surfaces exposed to CO. The x-ray technique also reveals particle reshaping during the reaction. In situ and non-invasive structural characterisation of defects during reaction opens new avenues for understanding defect behaviour in confined crystals and paves the way for strain and defect engineering.