Spin Currents via the Gauge Principle for Meta-Generalized Gradient Exchange-Correlation Functionals.

The prominence of density functional theory in the field of electronic structure computation stems from its ability to usefully balance accuracy and computational effort. At the base of this ability is a functional of the electron density: the exchange-correlation energy. This functional satisfies known exact conditions that guide the derivation of approximations. The strongly constrained and appropriately normed (SCAN) approximation stands out as a successful, modern, example. In this Letter, we demonstrate how the SU(2) gauge invariance of the exchange-correlation functional in spin current density functional theory allows us to add an explicit dependence on spin currents in the SCAN functional (here called JSCAN)-and similar meta-generalized-gradient functional approximations-solely invoking first principles. In passing, a spin-current dependent generalization of the electron localization function (here called JELF) is also derived. The extended forms are implemented in a developer's version of the crystal23 program. Applications on molecules and materials confirm the practical relevance of the extensions.

Synthesis, Crystal Structure, and Photocatalytic Properties of Two Isoreticular Ce(IV)-MOFs with an Infinite Rod-Shaped Inorganic Building Unit.

The use of the V-shaped linker molecules 4,4'-oxydibenzoic acid (H2ODB) and 4,4'-carbonyldibenzoic acid (H2CDB) led to the discovery of two isoreticular Ce(IV)-based metal-organic frameworks (MOFs) of composition [CeO(H2O)(L)], L = ODB2-, CDB2-, denoted CAU-58 (CAU = Christian-Albrechts-University). The recently developed Ce-MOF synthesis approach in acetonitrile as the solvent proved effective in accessing Ce(IV)-MOF structures with infinite rod-shaped inorganic building units (IBUs) and circumventing the formation of the predominantly observed hexanuclear [Ce6O8] cluster. For the structure determination of the isoreticular MOFs, three-dimensional electron diffraction (3D ED) and powder X-ray diffraction (PXRD) data were used in combination with density functional theory (DFT) calculations. [CeO(H2O)(CDB)] shows reversible H2O adsorption by stirring in water and thermal treatment at 190 °C, which leads to a unit cell volume change of 11%. The MOFs feature high thermal stabilities (T > 290 °C), which exceed those of most Ce(IV)-MOFs and can be attributed to the infinite rod-shaped IBU. Surface and bulk oxidation states of the cerium ions were analyzed via X-ray photoelectron spectroscopy (XPS) and X-ray absorption near-edge spectroscopy (XANES). While Ce(III) ions are observed by the highly surface-sensitive XPS method, the bulk material contains predominantly Ce(IV) ions according to XANES. Application of the MOFs as catalysts for the catalytic degradation of methyl orange in aqueous solutions was also studied. While degradation activity for both MOFs was observed, only CAU-58-ODB revealed enhanced photocatalytic activity under ultraviolet (UV) light. The photocatalytic mechanism likely involves a ligand-to-metal charge transfer (LMCT) from the linkers to the Ce(IV) centers. Analyses by XANES and inductively coupled plasma-optical emission spectroscopy (ICP-OES) demonstrate that leaching of Cerium ions as well as partial reduction of Ce(IV) to Ce(III) takes place during catalysis. At the same time, PXRD data confirm the structural stability of the remaining MOF catalysts.

The Structure of Monomeric Hydroxo-CuII Species in Cu-CHA. A Quantitative Assessment.

Using EPR and HYSCORE spectroscopies in conjunction with ab initio calculations, we assess the structure of framework-bound monomeric hydroxo-CuII in copper-loaded chabazite (CHA). The species is an interfacial distorted square-planar [CuIIOH(O-8MRs)3] complex located at eight-membered-ring windows, displaying three coordinating bonds with zeolite lattice oxygens and the hydroxo ligand hydrogen-bonded to the cage. The complex has a distinctive EPR signature with g = [2.072 2.072 2.290], CuA= [30 30 410] MHz, and HA = [-13.0 -4.5 +11.5] MHz, distinctively different from other CuII species in CHA.

Metal-organic frameworks properties from hybrid density functional approximations.

The chemical versatility and modular nature of Metal-Organic Frameworks (MOFs) make them unique hybrid inorganic-organic materials for several important applications. From a computational point of view, ab initio modeling of MOFs is a challenging and demanding task, in particular, when the system reaches the size of gigantic MOFs as MIL-100 and MIL-101 (where MIL stands for Materials Institute Lavoisier) with several thousand atoms in the unit cell. Here, we show how such complex systems can be successfully tackled by a recently proposed class of composite electronic structure methods revised for solid-state calculations. These methods rely on HF/density functional theory hybrid functionals (i.e., PBEsol0 and HSEsol) combined with a double-zeta quality basis set. They are augmented with semi-classical corrections to take into account dispersive interactions (D3 scheme) and the basis set superposition error (gCP). The resulting methodologies, dubbed "sol-3c," are cost-effective yet reach the hybrid functional accuracy. Here, sol-3c methods are effectively applied to predict the structural, vibrational, electronic, and adsorption properties of some of the most common MOFs. Calculations are feasible even on very large MOFs containing more than 2500 atoms in the unit cell as MIL-100 and MIL-101 with reasonable computing resources. We propose to use our composite methods for the routine in silico screening of MOFs targeting properties beyond plain structural features.

Mechanisms for Pressure-Induced Isostructural Phase Transitions in EuO.

We study pressure-induced isostructural electronic phase transitions in the prototypical mixed valence and strongly correlated material EuO using the global-hybrid density functional theory. The simultaneous presence in the valence of highly localized d- and f-type bands and itinerant s- and p-type states, as well as the half-filled f-type orbital shell with seven unpaired electrons on each Eu atom, have made the description of the electronic features of this system a challenge. The electronic band structure, density of states, and atomic oxidation states of EuO are analyzed in the 0-50 GPa pressure range. An insulator-to-metal transition at about 12 GPa of pressure was identified. The second isostructural transition at approximately 30-35 GPa, previously believed to be driven by an oxidation from Eu(II) to Eu(III), is shown instead to be associated with a change in the occupation of the Eu d orbitals, as can be determined from the analysis of the corresponding atomic orbital populations. The Eu d band is confined by the surrounding oxygens and split by the crystal field, which results in orbitals of e_{g} symmetry (i.e., d_{x^{2}-y^{2}} and d_{2z^{2}-x^{2}-y^{2}}, pointing along the Eu-O direction) being abruptly depopulated at the transition as a means to alleviate electron-electron repulsion in the highly compressed structures.

Analytical calculation of the solvent-accessible surface area and its nuclear gradients by stereographic projection: A general approach for molecules, polymers, nanotubes, helices, and surfaces.

In this article, we explore an alternative to the analytical Gauss-Bonnet approach for computing the solvent-accessible surface area (SASA) and its nuclear gradients. These two key quantities are required to evaluate the nonelectrostatic contribution to the solvation energy and its nuclear gradients in implicit solvation models. We extend a previously proposed analytical approach for finite systems based on the stereographic projection technique to infinite periodic systems such as polymers, nanotubes, helices, or surfaces and detail its implementation in the Crystal code. We provide the full derivation of the SASA nuclear gradients, and introduce an iterative perturbation scheme of the atomic coordinates to stabilize the gradients calculation for certain difficult symmetric systems. An excellent agreement of computed SASA with reference analytical values is found for finite systems, while the SASA size-extensivity is verified for infinite periodic systems. In addition, correctness of the analytical gradients is confirmed by the excellent agreement obtained with numerical gradients and by the translational invariance achieved, both for finite and infinite periodic systems. Overall therefore, the stereographic projection approach appears as a general, simple, and efficient technique to compute the key quantities required for the calculation of the nonelectrostatic contribution to the solvation energy and its nuclear gradients in implicit solvation models applicable to both finite and infinite periodic systems.

Structural and Optical Properties of Struvite. Elucidating Structure of Infrared Spectrum in High Frequency Range.

Study of structure and optical properties of magnesium ammonium phosphate hexahydrate crystal known as struvite is presented. Experimentally determined infrared (IR) and ultraviolet-visible (UV-vis) spectra are compared with the theoretical predictions of density functional methods. Examination of the interatomic bond lengths, Mulliken atomic charges, and binding energies of water in the magnesium hexahydrate cation, together with the analysis of the hydrogen bond pattern have allowed us to explain a special feature of the IR spectrum of struvite, a blueshift of the band corresponding to the O-H stretching mode. This mode has been assigned to a "dangling" hydroxyl group in one of the water molecules in magnesium hexahydrate. Using experimentally obtained UV-vis spectrum and performing Tauc plots analysis, optical bandgap of struvite has been narrowed to a range from 5.92 to 6.06 eV.

The CRYSTAL code, 1976-2020 and beyond, a long story.

CRYSTAL is a periodic ab initio code that uses a Gaussian-type basis set to express crystalline orbitals (i.e., Bloch functions). The use of atom-centered basis functions allows treating 3D (crystals), 2D (slabs), 1D (polymers), and 0D (molecules) systems on the same grounds. In turn, all-electron calculations are inherently permitted along with pseudopotential strategies. A variety of density functionals are implemented, including global and range-separated hybrids of various natures and, as an extreme case, Hartree-Fock (HF). The cost for HF or hybrids is only about 3-5 times higher than when using the local density approximation or the generalized gradient approximation. Symmetry is fully exploited at all steps of the calculation. Many tools are available to modify the structure as given in input and simplify the construction of complicated objects, such as slabs, nanotubes, molecules, and clusters. Many tensorial properties can be evaluated by using a single input keyword: elastic, piezoelectric, photoelastic, dielectric, first and second hyperpolarizabilities, etc. The calculation of infrared and Raman spectra is available, and the intensities are computed analytically. Automated tools are available for the generation of the relevant configurations of solid solutions and/or disordered systems. Three versions of the code exist: serial, parallel, and massive-parallel. In the second one, the most relevant matrices are duplicated on each core, whereas in the third one, the Fock matrix is distributed for diagonalization. All the relevant vectors are dynamically allocated and deallocated after use, making the code very agile. CRYSTAL can be used efficiently on high performance computing machines up to thousands of cores.

CRYSPLOT: A new tool to visualize physical and chemical properties of molecules, polymers, surfaces, and crystalline solids.

CRYSPLOT is a web-oriented tool (http://crysplot.crystalsolutions.eu) to visualize computed properties of periodic systems, in particular, as computed with the CRYSTAL code. Along with plotting, CRYSPLOT also permits the modification and customization of plots to meet the standards required for scientific graphics. CRYSPLOT has been designed with advanced and freely available graphical Javascript libraries as Plotly. The programming language used is Javascript. The code parses the input files, reads the data, and organizes them into objects ready to be plotted with the plotly.js library. It is modular and flexible so that it is very simple to add other input data formats. The new graphical tool is presented in details along with selected applications on metal-organic frameworks to show some of its capabilities. © 2019 Wiley Periodicals, Inc.

Interfacing CRYSTAL/AMBER to Optimize QM/MM Lennard⁻Jones Parameters for Water and to Study Solvation of TiO2 Nanoparticles.

Metal oxide nanoparticles (NPs) are regarded as good candidates for many technological applications, where their functional environment is often an aqueous solution. The correct description of metal oxide electronic structure is still a challenge for local and semilocal density functionals, whereas hybrid functional methods provide an improved description, and local atomic function-based codes such as CRYSTAL17 outperform plane wave codes when it comes to hybrid functional calculations. However, the computational cost of hybrids are still prohibitive for systems of real sizes, in a real environment. Therefore, we here present and critically assess the accuracy of our electrostatic embedding quantum mechanical/molecular mechanical (QM/MM) coupling between CRYSTAL17 and AMBER16, and demonstrate some of its capabilities via the case study of TiO2 NPs in water. First, we produced new Lennard⁻Jones (LJ) parameters that improve the accuracy of water⁻water interactions in the B3LYP/TIP3P coupling. We found that optimizing LJ parameters based on water tri- to deca-mer clusters provides a less overstructured QM/MM liquid water description than when fitting LJ parameters only based on the water dimer. Then, we applied our QM/MM coupling methodology to describe the interaction of a 1 nm wide multilayer of water surrounding a spherical TiO2 nanoparticle (NP). Optimizing the QM/MM water⁻water parameters was found to have little to no effect on the local NP properties, which provide insights into the range of influence that can be attributed to the LJ term in the QM/MM coupling. The effect of adding additional water in an MM fashion on the geometry optimized nanoparticle structure is small, but more evident effects are seen in its electronic properties. We also show that there is good transferability of existing QM/MM LJ parameters for organic molecules⁻water interactions to our QM/MM implementation, even though these parameters were obtained with a different QM code and QM/MM implementation, but with the same functional.

Detecting Molecular Rotational Dynamics Complementing the Low-Frequency Terahertz Vibrations in a Zirconium-Based Metal-Organic Framework.

We show clear experimental evidence of cooperative terahertz (THz) dynamics observed below 3 THz (∼100 cm^{-1}), for a low-symmetry Zr-based metal-organic framework structure, termed MIL-140A [ZrO(O_{2}C-C_{6}H_{4}-CO_{2})]. Utilizing a combination of high-resolution inelastic neutron scattering and synchrotron radiation far-infrared spectroscopy, we measured low-energy vibrations originating from the hindered rotations of organic linkers, whose energy barriers and detailed dynamics have been elucidated via ab initio density functional theory calculations. The complex pore architecture caused by the THz rotations has been characterized. We discovered an array of soft modes with trampolinelike motions, which could potentially be the source of anomalous mechanical phenomena such as negative thermal expansion. Our results demonstrate coordinated shear dynamics (2.47 THz), a mechanism which we have shown to destabilize the framework structure, in the exact crystallographic direction of the minimum shear modulus (G_{min}).

The unique Raman fingerprint of boron nitride substitution patterns in graphene.

Boron nitride-substituted graphene (BNsG) two-dimensional structures are new materials of wide technological interest due to the rich variety of electronic structures and properties they can exploit. The ability to accurately characterize them is key to their future success. Here we show, by means of ab initio simulations, that the vibrational Raman spectra of such compounds are extremely sensitive to substitution motifs and concentration, and that each structure has unique and distinct features. This result can be useful as a guide for the optimization of production processes.

Isoreticular zirconium-based metal-organic frameworks: discovering mechanical trends and elastic anomalies controlling chemical structure stability.

Understanding the mechanical properties of metal-organic frameworks (MOFs) is crucial not only to yield robust practical applications, but also to advance fundamental research underpinning the flexibility of a myriad of open-framework chemical compounds. Herein we present one of the most comprehensive structural analyses yet on MOF-mechanics: elucidating the complex elastic response of an isoreticular series of topical Zr-based MOFs, explaining all the important mechanical properties, and identifying major trends arising from systematic organic linker exchange. Ab initio density functional theory (DFT) was employed to establish the single-crystal elastic constants of the nanoporous MIL-140(A-D) structures, generating a complete 3-D representation of the principal mechanical properties, encompassing the Young's modulus, shear modulus, linear compressibility and Poisson's ratio. Of particular interest, we discovered significantly high values of both positive and negative linear compressibility and Poisson's ratio, whose framework molecular mechanisms responsible for such elastic anomalies have been fully revealed. In addition to pinpointing large elastic anisotropy and unusual physical properties, we analyzed the bulk modulus of isoreticular Zr-MOF compounds to understand the framework structural resistance against the hydrostatic pressure, and determined the averaged mechanical behaviour of bulk (polycrystalline) MOF materials important for the design of emergent applications.

Prediction uncertainty of density functional approximations for properties of crystals with cubic symmetry.

The performance of a method is generally measured by an assessment of the errors between the method's results and a set of reference data. The prediction uncertainty is a measure of the confidence that can be attached to a method's prediction. Its estimation is based on the random part of the errors not explained by reference data uncertainty, which implies an evaluation of the systematic component(s) of the errors. As the predictions of most density functional approximations (DFA) present systematic errors, the standard performance statistics, such as the mean of the absolute errors (MAE or MUE), cannot be directly used to infer prediction uncertainty. We investigate here an a posteriori calibration method to estimate the prediction uncertainty of DFAs for properties of solids. A linear model is shown to be adequate to address the systematic trend in the errors. The applicability of this approach to modest-size reference sets (28 systems) is evaluated for the prediction of band gaps, bulk moduli, and lattice constants with a wide panel of DFAs.

Range-separated double-hybrid density-functional theory applied to periodic systems.

Quantum chemistry methods exploiting density-functional approximations for short-range electron-electron interactions and second-order Møller-Plesset (MP2) perturbation theory for long-range electron-electron interactions have been implemented for periodic systems using Gaussian-type basis functions and the local correlation framework. The performance of these range-separated double hybrids has been benchmarked on a significant set of systems including rare-gas, molecular, ionic, and covalent crystals. The use of spin-component-scaled MP2 for the long-range part has been tested as well. The results show that the value of µ = 0.5 bohr(-1) for the range-separation parameter usually used for molecular systems is also a reasonable choice for solids. Overall, these range-separated double hybrids provide a good accuracy for binding energies using basis sets of moderate sizes such as cc-pVDZ and aug-cc-pVDZ.

Benchmarking dispersion and geometrical counterpoise corrections for cost-effective large-scale DFT calculations of water adsorption on graphene.

The physisorption of water on graphene is investigated with the hybrid density functional theory (DFT)-functional B3LYP combined with empirical corrections, using moderate-sized basis sets such as 6-31G(d). This setup allows to model the interaction of water with graphene going beyond the quality of classical or semiclassical simulations, while still keeping the computational costs under control. Good agreement with respect to Coupled Cluster with singles and doubles excitations and perturbative triples (CCSD(T)) results is achieved for the adsorption of a single water molecule in a benchmark with two DFT-functionals (Perdew/Burke/Ernzerhof (PBE), B3LYP) and Grimme's empirical dispersion and counterpoise corrections. We apply the same setting to graphene supported by epitaxial hexagonal boron nitride (h-BN), leading to an increased interaction energy. To further demonstrate the achievement of the empirical corrections, we model, entirely from first principles, the electronic properties of graphene and graphene supported by h-BN covered with different amounts of water (one, 10 water molecules per cell and full coverage). The effect of h-BN on these properties turns out to be negligibly small, making it a good candidate for a substrate to grow graphene on.

Identifying the role of terahertz vibrations in metal-organic frameworks: from gate-opening phenomenon to shear-driven structural destabilization.

We present an unambiguous identification of low-frequency terahertz vibrations in the archetypal imidazole-based metal-organic framework (MOF) materials: ZIF-4, ZIF-7, and ZIF-8, all of which adopt a zeolite-like nanoporous structure. Using inelastic neutron scattering and synchrotron radiation far-infrared absorption spectroscopy, in conjunction with density functional theory (DFT), we have pinpointed all major sources of vibrational modes. Ab initio DFT calculations revealed the complex nature of the collective THz modes, which enable us to establish detailed correlations with experiments. We discover that low-energy conformational dynamics offers multiple pathways to elucidate novel physical phenomena observed in MOFs. New evidence demonstrates that THz modes are intrinsically linked, not only to anomalous elasticity underpinning gate-opening and pore-breathing mechanisms, but also to shear-induced phase transitions and the onset of structural instability.

Double-hybrid density-functional theory applied to molecular crystals.

We test the performance of a number of two- and one-parameter double-hybrid approximations, combining semilocal exchange-correlation density functionals with periodic local second-order Møller-Plesset (LMP2) perturbation theory, for calculating lattice energies of a set of molecular crystals: urea, formamide, ammonia, and carbon dioxide. All double-hybrid methods perform better on average than the corresponding Kohn-Sham calculations with the same functionals, but generally not better than standard LMP2. The one-parameter double-hybrid approximations based on the PBEsol density functional give lattice energies per molecule with an accuracy of about 6 kJ/mol, which is similar to the accuracy of LMP2. This conclusion is further verified on molecular dimers and on the hydrogen cyanide crystal.