Quantum chemical modeling of hydrogen binding in metal-organic frameworks: validation, insight, predictions and challenges.

A detailed chemical understanding of H2 interactions with binding sites in the nanoporous crystalline structure of metal-organic frameworks (MOFs) can lay a sound basis for the design of new sorbent materials. Computational quantum chemical calculations can aid in this quest. To set the stage, we review general thermodynamic considerations that control the usable storage capacity of a sorbent. We then discuss cluster modeling of H2 ligation at MOF binding sites using state-of-the-art density functional theory (DFT) calculations, and how the binding can be understood using energy decomposition analysis (EDA). Employing these tools, we illustrate the connections between the character of the MOF binding site and the associated adsorption thermodynamics using four experimentally characterized MOFs, highlighting the role of open metal sites (OMSs) in accessing binding strengths relevant to room temperature storage. The sorbents are MOF-5, with no open metal sites, Ni2(m-dobdc), containing Lewis acidic Ni(II) sites, Cu(I)-MFU-4l, containing π basic Cu(I) sites and V2Cl2.8(btdd), also containing π-basic V(II) sites. We next explore the potential for binding multiple H2 molecules at a single metal site, with thermodynamics useful for storage at ambient temperature; a materials design goal which has not yet been experimentally demonstrated. Computations on Ca2+ or Mg2+ bound to catecholate or Ca2+ bound to porphyrin show the potential for binding up to 4 H2; there is precedent for the inclusion of both catecholate and porphyrin motifs in MOFs. Turning to transition metals, we discuss the prediction that two H2 molecules can bind at V(II)-MFU-4l, a material that has been synthesized with solvent coordinated to the V(II) site. Additional calculations demonstrate binding three equivalents of hydrogen per OMS in Sc(I) or Ti(I)-exchanged MFU-4l. Overall, the results suggest promising prospects for experimentally realizing higher capacity hydrogen storage MOFs, if nontrivial synthetic and desolvation challenges can be overcome. Coupled with the unbounded chemical diversity of MOFs, there is ample scope for additional exploration and discovery.

Selective Adsorption of Oxygen from Humid Air in a Metal-Organic Framework with Trigonal Pyramidal Copper(I) Sites.

High or enriched-purity O2 is used in numerous industries and is predominantly produced from the cryogenic distillation of air, an extremely capital- and energy-intensive process. There is significant interest in the development of new approaches for O2-selective air separations, including the use of metal-organic frameworks featuring coordinatively unsaturated metal sites that can selectively bind O2 over N2 via electron transfer. However, most of these materials exhibit appreciable and/or reversible O2 uptake only at low temperatures, and their open metal sites are also potential strong binding sites for the water present in air. Here, we study the framework CuI-MFU-4l (CuxZn5-xCl4-x(btdd)3; H2btdd = bis(1H-1,2,3-triazolo[4,5-b],[4',5'-i])dibenzo[1,4]dioxin), which binds O2 reversibly at ambient temperature. We develop an optimized synthesis for the material to access a high density of trigonal pyramidal CuI sites, and we show that this material reversibly captures O2 from air at 25 °C, even in the presence of water. When exposed to air up to 100% relative humidity, CuI-MFU-4l retains a constant O2 capacity over the course of repeated cycling under dynamic breakthrough conditions. While this material simultaneously adsorbs N2, differences in O2 and N2 desorption kinetics allow for the isolation of high-purity O2 (>99%) under relatively mild regeneration conditions. Spectroscopic, magnetic, and computational analyses reveal that O2 binds to the copper(I) sites to form copper(II)-superoxide moieties that exhibit temperature-dependent side-on and end-on binding modes. Overall, these results suggest that CuI-MFU-4l is a promising material for the separation of O2 from ambient air, even without dehumidification.

A Free Energy Decomposition Analysis: Insight into Binding Thermodynamics from Absolutely Localized Molecular Orbitals.

Traditional energy decomposition analysis (EDA) methods can provide an interpretive decomposition of non-covalent electronic binding energies. However, by definition, they neglect entropic effects and nuclear contributions to the enthalpy. With the objective of revealing the chemical origins of trends in free energies of binding, we introduce the concept of a Gibbs decomposition analysis (GDA) by coupling the absolutely localized molecular orbital treatment of electrons in non-covalent interactions with the simplest possible quantum rigid rotor-harmonic oscillator treatment of nuclear motion at finite temperature. The resulting pilot GDA is employed to decompose enthalpic and entropic contributions to the free energy of association of the water dimer, fluoride-water dimer, and water binding to an open metal site in the metal-organic framework Cu(I)-MFU-4l. The results show enthalpic trends that generally track the electronic binding energy and entropic trends that reveal the increasing price of loss of translational and rotational degrees freedom with temperature.

Prediction of Multiple Hydrogen Ligation at a Vanadium(II) Site in a Metal-Organic Framework.

Densifying hydrogen in a metal-organic framework (MOF) at moderate pressures can circumvent challenges associated with high-pressure compression. The highly tunable structural and chemical composition in MOFs affords vast possibilities to optimize binding interactions. At the heart of this search are the nanoscale characteristics of molecular adsorption at the binding site(s). Using density functional theory (DFT) to model binding interactions of hydrogen to the exposed metal site of cation-exchanged MFU-4l, we predict multiple hydrogen ligation of H2 at the first coordination sphere of V(II) in V(II)-exchanged MFU-4l. We find that the strength of this binding between the metal site and H2 molecules can be tuned by altering the halide counterion adjacent to the metal site and that the fluoride containing node affords the most favorable interactions for high-density H2 storage. Using energy decomposition analysis, we delineate electronic contributions that enable multiple hydrogen ligation and demonstrate its benefits for hydrogen adsorption and release at modest pressures.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package.

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Observation of an Intermediate to H2 Binding in a Metal-Organic Framework.

Coordinatively unsaturated metal sites within certain zeolites and metal-organic frameworks can strongly adsorb a wide array of substrates. While many classical examples involve electron-poor metal cations that interact with adsorbates largely through physical interactions, unsaturated electron-rich metal centers housed within porous frameworks can often chemisorb guests amenable to redox activity or covalent bond formation. Despite the promise that materials bearing such sites hold in addressing myriad challenges in gas separations and storage, very few studies have directly interrogated mechanisms of chemisorption at open metal sites within porous frameworks. Here, we show that nondissociative chemisorption of H2 at the trigonal pyramidal Cu+ sites in the metal-organic framework CuI-MFU-4l occurs via the intermediacy of a metastable physisorbed precursor species. In situ powder neutron diffraction experiments enable crystallographic characterization of this intermediate, the first time that this has been accomplished for any material. Evidence for a precursor intermediate is also afforded from temperature-programmed desorption and density functional theory calculations. The activation barrier separating the precursor species from the chemisorbed state is shown to correlate with a change in the Cu+ coordination environment that enhances π-backbonding with H2. Ultimately, these findings demonstrate that adsorption at framework metal sites does not always follow a concerted pathway and underscore the importance of probing kinetics in the design of next-generation adsorbents.

Ambient-Temperature Hydrogen Storage via Vanadium(II)-Dihydrogen Complexation in a Metal-Organic Framework.

The widespread implementation of H2 as a fuel is currently hindered by the high pressures or cryogenic temperatures required to achieve reasonable storage densities. In contrast, the realization of materials that strongly and reversibly adsorb hydrogen at ambient temperatures and moderate pressures could transform the transportation sector and expand adoption of fuel cells in other applications. To date, however, no adsorbent has been identified that exhibits a binding enthalpy within the optimal range of -15 to -25 kJ/mol for ambient-temperature hydrogen storage. Here, we report the hydrogen adsorption properties of the metal-organic framework (MOF) V2Cl2.8(btdd) (H2btdd, bis(1H-1,2,3-triazolo[4,5-b],[4',5'-i])dibenzo[1,4]dioxin), which features exposed vanadium(II) sites capable of backbonding with weak π acids. Significantly, gas adsorption data reveal that this material binds H2 with an enthalpy of -21 kJ/mol. This binding energy enables usable hydrogen capacities that exceed that of compressed storage under the same operating conditions. The Kubas-type vanadium(II)-dihydrogen complexation is characterized by a combination of techniques. From powder neutron diffraction data, a V-D2(centroid) distance of 1.966(8) Å is obtained, the shortest yet reported for a MOF. Using in situ infrared spectroscopy, the H-H stretch was identified, and it displays a red shift of 242 cm-1. Electronic structure calculations show that a main contribution to bonding stems from the interaction between the vanadium dπ and H2 σ* orbital. Ultimately, the pursuit of MOFs containing high densities of weakly π-basic metal sites may enable storage capacities under ambient conditions that far surpass those accessible with compressed gas storage.

Quantum Chemical Modeling of Pressure-Induced Spin Crossover in Octahedral Metal-Ligand Complexes.

Spin state switching on external stimuli is a phenomenon with wide applicability, ranging from molecular electronics to gas activation in nanoporous frameworks. Here, we model the spin crossover as a function of the hydrostatic pressure in octahedrally coordinated transition metal centers by applying a field of effective nuclear forces that compress the molecule towards its centroid. For spin crossover in first-row transition metals coordinated by hydrogen, nitrogen, and carbon monoxide, we find the pressure required for spin transition to be a function of the ligand position in the spectrochemical sequence. While pressures on the order of 1 GPa are required to flip spins in homogeneously ligated octahedral sites, we demonstrate a fivefold decrease in spin transition pressure for the archetypal strong field ligand carbon monoxide in octahedrally coordinated Fe2+ in [Fe(II)(NH3 )5 CO]2+ .

Sparsity of the wavefunction from the generalized Pauli exclusion principle.

Electron occupations that arise from pure quantum states are restricted by a stringent set of conditions that are said to generalize the Pauli exclusion principle. These generalized Pauli constraints (GPCs) define the boundary of the set of one-electron reduced density matrices (1-RDMs) that are derivable from at least one N-electron wavefunction. In this paper, we investigate the sparsity of the Slater-determinant representation of the wavefunction that is a necessary, albeit not sufficient, condition for its 1-RDM to lie on the boundary of the set of pure N-representable 1-RDMs or in other words saturate one of the GPCs. The sparse wavefunction, we show, is exact not only for 3 electrons in 6 orbitals but also for 3 electrons in 8 orbitals. For larger numbers of electrons and/or orbitals in the lowest spin state, the exact wavefunction does not generally saturate one of the GPCs, and hence, the sparse representation is typically an approximation. Because the sparsity of the wavefunction is a necessary but not sufficient condition for saturation of one of the GPCs, optimization of the sparse wavefunction Ansatz to minimize the ground-state energy does not necessarily produce a wavefunction whose 1-RDM exactly saturates one of the GPCs. While the sparse Ansatz can be employed with arbitrary orbitals or optimized orbitals, in this paper, we explore the Ansatz with the natural orbitals from full configuration interaction, which yields an upper bound to the ground-state energy that equals the exact energy for a given basis set if the full-configuration-interaction wavefunction saturates the Ansatz's GPC. With calculations on the boron isoelectronic sequence, the dinitrogen cation N2+, hydrogen chains, and cyclic conjugated π systems, we examine the quality of the sparse wavefunction Ansatz from the amount of correlation energy recovered.