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A linker extension strategy for generating metal-organic frameworks (MOFs) with superior moisture-capturing properties is presented. Applying this design approach involving experiment and computation results in MOF-LA2-1 {[Al(OH)(PZVDC)], where PZVDC2- is (E)-5-(2-carboxylatovinyl)-1H-pyrazole-3-carboxylate}, which exhibits an approximately 50% water capacity increase compared to the state-of-the-art water-harvesting material MOF-303. The power of this approach is the increase in pore volume while retaining the ability of the MOF to harvest water in arid environments under long-term uptake and release cycling, as well as affording a reduction in regeneration heat and temperature. Density functional theory calculations and Monte Carlo simulations give detailed insight pertaining to framework structure, water interactions within its pores, and the resulting water sorption isotherm.

Grafting metal cations to missing linker defect sites in zirconium-based metal-organic frameworks, such as UiO-66, produces a uniquely well-defined and homotopic catalytically active site. We present here the synthesis and characterization of a group of UiO-66-supported metal catalysts, M-UiO-66 (M = Ni, Co, Cu, and Cr), for the catalytic dimerization of alkenes. The hydrogen-deuterium exchange via deuterium oxide adsorption followed by infrared spectroscopy showed that the last molecular water ligand desorbs from the sites after evacuation at 300 °C leading to M(OH)-UiO-66 structures. Adsorption of 1-butene is studied using calorimetry and density functional theory techniques to characterize the interactions of the alkene with metal cation sites that are found active for alkene oligomerization. For the most active Ni-UiO-66, the removal of molecular water from the active site significantly increases the 1-butene adsorption enthalpy and almost doubles the catalytic activity for 1-butene dimerization in comparison to the presence of water ligands. Other M-UiO-66 (M = Co, Cu, and Cr) exhibit 1-3 orders of magnitude lower catalytic activities compared to Ni-UiO-66. The catalytic activities correlate linearly with the Gibbs free energy of 1-butene adsorption. Density functional theory calculations probing the Cossee-Arlman mechanism for all metals support the differences in activity, providing a molecular level understanding of the metal site as the active center for 1-butene dimerization.

Multireference electronic structure methods, like the complete active space (CAS) self-consistent field model, have long been used to characterize chemically interesting processes. Important work has been done in recent years to develop modifications having a lower computational cost than CAS, but typically these methods offer no more chemical insight than that from the CAS solution being approximated. In this paper, we present the localized active space-state interaction (LASSI) method that can be used not only to lower the intrinsic cost of the multireference calculation but also to improve interpretability. The localized active space (LAS) approach utilizes the local nature of the electron-electron correlation to express a composite wave function as an antisymmetrized product of unentangled wave functions in local active subspaces. LASSI then uses these LAS states as a basis from which to express complete molecular wave functions. This not only makes the molecular wave function more compact but also permits flexibility in choosing those states to be included in the basis. Such selective inclusion of states translates to the selective inclusion of specific types of interactions, thereby allowing a quantitative analysis of these interactions. We demonstrate the use of LASSI to study charge migration and spin-flip excitations in multireference organic molecules. We also compute the

The adsorption of simple gas molecules to metal oxide surfaces is a primary step in many heterogeneous catalysis applications. Quantum chemical modeling of these reactions is a challenge both in terms of cost and accuracy, and quantum-embedding methods are promising, especially for localized chemical phenomena. In this work, we employ density matrix embedding theory (DMET) for periodic systems to calculate the adsorption energy of CO to the MgO(001) surface. Using coupled-cluster theory with single and double excitations and second-order Møller-Plesset perturbation theory as quantum chemical solvers, we perform calculations with embedding clusters up to 266 electrons in 306 orbitals; the largest embedding models agreeing to within 1.2 kcal/mol of the non-embedding references. Due to the need of large impurity clusters for surface chemistry, we present a memory-efficient procedure of storing and manipulating electron repulsion integrals in the embedding space within the framework of periodic DMET.

Two possible explanations for the temperature-dependence of spin crossover (SCO) behavior in the dimeric triple-decker Cr(II) complex ([(C5Me5)Cr(P5)Cr(C5Me5)]+) have been offered. One invokes variations in antiferromagnetic interactions between the two Cr(II) ions, while the other posits the development of a strong ligand-field effect favoring the low-spin ground state. We perform multireference electronic structure calculations based on multiconfiguration pair-density functional theory to resolve these effects. We find quintet, triplet, and singlet electronic ground states, respectively, for the experimental geometries at high, intermediate, and low temperatures. The ground-state transition from quintet to triplet at intermediate temperature derives from increased antiferromagnetic interactions between the two Cr(II) ions. By contrast, the ground-state transition from triplet to singlet at low temperature is attributable to increased ligand-field effects, which dominate with continued variations in antiferromagnetic coupling. This study provides quantitative detail for the degree to which these two effects can act in concert for the observed SCO behavior in this complex and others subject to temperature dependent variations in geometry.

Iron(II) porphyrins play critical roles in enzymes and synthetic catalysts. Computationally determining the spin-state ordering for even the unsubstituted iron(II) porphyrin (FeP) is challenging due to its large size. Multiconfiguration pair-density functional theory (MC-PDFT), a method capable of accurately capturing correlation with lower cost than comparably accurate methods, was previously used to predict a triplet ground state for FeP across a wide range of active spaces up to (34e, 35o). The purpose of this present MC-PDFT study is to determine the effects of including nonlocal exchange in the energy calculation and of using a larger active space size [DMRG(40e, 42o) and RAS(40, 2, 2; 16, 6, 20)] on the calculated FeP spin-state ordering. The recently developed hybrid MC-PDFT method, which uses a weighted average of the MC-PDFT energy and the energy expectation value of the reference wave function, is applied with a weight of the reference wave function energy of λ. We find that increasing λ stabilizes the quintet relative to the triplets. The hybrid tPBE0 functional (tPBE with λ set to 0.25) consistently predicts a triplet ground state with the quintet lying above by 0.10-0.16 eV, depending on the reference wave function. These values are particularly interesting in light of tPBE0's very strong performance for a diverse set of other systems.

Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn-Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin-orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.

Summary Energetically driven reduction of porosity through entanglement is ubiquitous in nature and synthetic systems. This entanglement decreases valuable internal pore space useful for applications, such as catalysis, storage, and sensing. Here, we describe the discovery of spontaneous de-interpenetration in a 6-fold interpenetrated uranium-based metal-organic framework (MOF), NU-1303-6. De-interpenetration transforms NU-1303-6 (14.2 and 19.8 A pores) to its larger pore (40.7 A) non-interpenetrated counterpart, which possesses a record-high 96.6% void fraction and 9.2 cm3g−1 pore volume. Density functional theory calculations reveal that charged point-point repulsions between anionic, closely positioned uranium-based nodes drive this phenomenon. These repulsions compete with water molecules that hydrogen bond nearby networks together, favoring interpenetration. Controlling the interplay between these intermolecular forces enables the reversal of omnipresent energetic equilibria, leading to thermodynamically favored open pore structures. The discovery of charged point-point repulsion will likely lead to the re-evaluation of non-interpenetrated network design, synthesis, and wide-reaching applications.

We present a quantum embedding method for ground and excited states of extended systems that uses multiconfiguration pair-density functional theory (MC-PDFT) with densities provided by periodic density matrix embedding theory (pDMET). We compute local excitations in oxygen mono- and di-vacancies on a magnesium oxide (100) surface and find absolute deviations within 0.05 eV between pDMET using the MC-PDFT, denoted as pDME-PDFT, and the more expensive, non-embedded MC-PDFT approach. We further use pDME-PDFT to calculate local excitations in larger supercells for the mono-vacancy defect, for which the use of non-embedded MC-PDFT is prohibitively costly.

We investigate the negatively charged nitrogen-vacancy center in diamond using periodic density matrix embedding theory (pDMET). To describe the strongly correlated excited states of this system, the complete active space self-consistent field (CASSCF) followed by n-electron valence state second-order perturbation theory (NEVPT2) was used as impurity solver. Since the NEVPT2-DMET energies show a linear dependence on the inverse of the size of the embedding subspace, we performed an extrapolation of the excitation energies to the non-embedding limit using linear regression. The extrapolated NEVPT2-DMET first triplet-triplet excitation energy is 2.31 eV and that for the optically inactive singlet-singlet transition is 1.02 eV, both in agreement with the experimentally observed vertical excitation energies of ~2.18 eV and ~1.26 eV, respectively. This is the first application of pDMET to a charged periodic system and the first investigation of the NV- defect using NEVPT2 for periodic supercell models.

Multiconfiguration pair-density functional theory (MC-PDFT) is a post-SCF multireference method that has been successful at computing ground- and excited-state energies. However, MC-PDFT is a single-state method in which the final MC-PDFT energies do not come from diagonalization of a model-space Hamiltonian matrix, and this can lead to inaccurate topologies of potential energy surfaces near locally avoided crossings and conical intersections. Therefore, in order to perform physically correct ab initio molecular dynamics with electronically excited states or to treat Jahn-Teller instabilities, it is necessary to develop a PDFT method that recovers the correct topology throughout the entire nuclear configuration space. Here we construct an effective Hamiltonian operator, called the linearized PDFT (L-PDFT) Hamiltonian, by expanding the MC-PDFT energy expression to first order in a Taylor series of the wave function density. Diagonalization of the L-PDFT Hamiltonian gives the correct potential energy surface topology near conical intersections and locally avoided crossings for a variety of challenging cases including phenol, methylamine, and the spiro cation. Furthermore, L-PDFT outperforms MC-PDFT and previous multi-state PDFT methods for predicting vertical excitations from a variety of representative organic chromophores.

Two-dimensional (2D) inorganic materials have emerged as exciting platforms for (opto)electronic, thermoelectric, magnetic, and energy storage applications. However, electronic redox tuning of these materials can be difficult. Instead, 2D metal-organic frameworks (MOFs) offer the possibility of electronic tuning through stoichiometric redox changes, with several examples featuring one to two redox events per formula unit. Here we demonstrate that this principle can be extended over a far greater span with the isolation of four discrete redox states in the 2D MOFs LixFe3(THT)2 (x = 03, THT = triphenylene hexathiol). This redox modulation results in 10,000-fold greater conductivity, p- to n-type carrier switching, and modulation of antiferromagnetic coupling. Physical characterization suggests that changes in carrier density drive these trends with relatively constant charge transport activation energies and mobilities. This series illustrates that 2D MOFs are uniquely redox flexible, making them an ideal materials platform for tunable and switchable applications.

The unsaturated hexathia-18-crown-6 (UHT18C6) molecule was investigated for the extraction of Hg(II) in HCl and HNO

Accurate and affordable methods to characterize the electronic structure of solids are important for targeted materials design. Embedding-based methods provide an appealing balance in the trade-off between cost and accuracy─particularly when studying localized phenomena. Here, we use the density matrix embedding theory (DMET) algorithm to study the electronic excitations in solid-state defects with a restricted open-shell Hartree-Fock (ROHF) bath and multireference impurity solvers, specifically, complete active space self-consistent field (CASSCF) and n-electron valence state second-order perturbation theory (NEVPT2). We apply the method to investigate the electronic excitations in an oxygen vacancy (OV) on a MgO(100) surface and find absolute deviations within 0.05 eV between DMET using the CASSCF/NEVPT2 solver, denoted as CAS-DMET/NEVPT2-DMET, and the nonembedded CASSCF/NEVPT2 approach. Next, we establish the practicality of DMET by extending it to larger supercells for the OV defect and a neutral silicon vacancy in diamond where the use of nonembedded CASSCF/NEVPT2 is extremely expensive.

We present the active learning configuration interaction (ALCI) method for multiconfigurational calculations based on large active spaces. ALCI leverages the use of an active learning procedure to find important electronic configurations among the full configurational space generated within an active space. We tested it for the calculation of singlet–singlet excited states of acenes and pyrene using different machine learning algorithms. The ALCI method yields excitation energies within 0.2–0.3 eV from those obtained by traditional complete active-space configuration interaction (CASCI) calculations (affordable for active spaces up to 16 electrons in 16 orbitals) by including only a small fraction of the CASCI configuration space in the calculations. For larger active spaces (we tested up to 26 electrons in 26 orbitals), not affordable with traditional CI methods, ALCI captures the trends of experimental excitation energies. Overall, ALCI provides satisfactory approximations to large active-space wave functions with up to 10 orders of magnitude fewer determinants for the systems presented here. These ALCI wave functions are promising and affordable starting points for the subsequent second-order perturbation theory or pair-density functional theory calculations.

Although the positions of water guests in porous crystals can be identified, determination of their filling sequence remains challenging. We deciphered the water-filling mechanism for the state-of-the-art water-harvesting metal-organic framework MOF-303 by performing an extensive series of single-crystal x-ray diffraction measurements and density functional theory calculations. The first water molecules strongly bind to the polar organic linkers; they are followed by additional water molecules forming isolated clusters, then chains of clusters, and finally a water network. This evolution of water structures led us to modify the pores by the multivariate approach, thereby precisely modulating the binding strength of the first water molecules and deliberately shaping the water uptake behavior. This resulted in higher water productivity, as well as tunability of regeneration temperature and enthalpy, without compromising capacity and stability.

Understanding direct metal-metal bonding between actinide atoms has been an elusive goal in chemistry for years. We report for the first time the anion photoelectron spectrum of U2-. The threshold of the lowest electron binding energy (EBE) spectral band occurs at 1.0 eV, which corresponds to the electron affinity (EA) of U2, whereas the vertical detachment energy of U2- is found at EBE ∼ 1.2 eV. Electronic structure calculations on U2 and U2- were carried out with state-of-the-art theoretical methods. The computed values of EA(U2) and EA(U) and the difference between the computed dissociation energies of U2 and U2- are found to be internally consistent and consistent with experiment. Analysis of the bonds in U2 and U2- shows that while U2 has a formal quintuple bond, U2- has a quadruple bond, even if the effective bond orders differ only by 0.5 unit instead of one unit. The resulting experimental-computational synergy elucidates the nature of metal-metal bonding in U2 and U2-.

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 300 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 776 entries, the paper represents a broad snapshot of DFT, anno 2022.

Chemically functionalized series of metal-organic frameworks (MOFs), with subtle differences in local structure but divergent properties, provide a valuable opportunity to explore how local chemistry can be coupled to long-range structure and functionality. Using

We have screened an array of 23 metals deposited onto the metal–organic framework (MOF) NU-1000 for propyne dimerization to hexadienes under different reaction conditions for a total of ~1400 experiments. By a first-of-its-kind study utilizing data-driven algorithms and high-throughput experimentation (HTE) in MOF catalysis, yields on Cu-deposited NU-1000 were improved from 4.2% to 24.4%. Characterization of the most-performant catalysts reveal conversion to hexadiene to be due to the formation of large Cu nanoparticles, which is further supported by reaction mechanisms calculated with density functional theory (DFT). Our results demonstrate both the strengths and weaknesses of the HTE approach. As a strength, HTE excels at being able to find interesting and novel catalytic activity; any a priori theoretical approach would be hard-pressed to find success, as high-performing catalysts required highly specific operating conditions difficult to model theoretically, and initial naïve single-atom models of the active site did not prove representative of the nanoparticle catalysts responsible for conversion to hexadiene. As a weakness, our results show how the HTE approach must be designed and monitored carefully to find success; in our initial campaign (~six months and over half of the total experiments conducted) only minor catalytic performances (up to 4.2% yield) were achieved, which was only improved following a complete overhaul of our HTE approach and questioning our initial assumptions. Thus, the HTE approach is much less automated than it may seem, even if driven by machine learning algorithms – one must carefully design their HTE campaign to find success.

The emergence of conductive 2D and less commonly 3D coordination polymers (CPs) and metal-organic frameworks (MOFs) promises novel applications in many fields. However, the synthetic parameters for these electronically complex materials are not thoroughly understood. Here we report a new 3D semiconducting CP Fe

Spin-orbit coupling is especially critical for the description of magnetic anisotropy, electron paramagnetic resonance spectroscopy of inorganic radicals and transition-metal complexes, and intersystem crossing. Here, we show how spin-orbit coupling may be included in multiconfiguration pair-density functional theory (MC-PDFT), and we apply the resulting formulation to the calculation of magnetic g tensors (which govern the Zeeman effect) of molecules containing transition metals. MC-PDFT is an efficient method for including static and dynamic electronic correlation in the quantum mechanical treatment of molecules; here, we apply it with spin-orbit coupling by using complete active space self-consistent field (CASSCF) and complete active space configuration interaction (CASCI) wave functions and on-top density functionals. We propose a systematic CASCI scheme for the g tensor calculation of the ground state of the systems under consideration, and we show its superiority over the conventional CASSCF scheme. State interaction, which is important for degenerate and nearly degenerate states, is included by extended multi-state PDFT (XMS-PDFT). Applications are reported for the ground doublet states of 25 transition-metal complexes with d1, d5, d7, and d9 configurations. The MC-PDFT methods are shown to be both efficient and accurate as compared with complete active space second-order perturbation theory.