Ligand Effects on the Linear Response Hubbard U: The Case of Transition Metal Phthalocyanines

Graphene-Molecule Hybridization at a Ferromagnetic Interface

The introduction of a graphene (Gr) buffer layer between a ferromagnetic substrate and a metallorganic molecule is known to mediate the magnetic coupling between them, an effect attributed to a weak hybridization between graphene and molecule. In this paper, we present experimental evidence of this effect through a detailed investigation of the frontier electronic properties of iron phthalocyanine deposited on cobalt-supported graphene. Despite being physisorbed, the molecular adsorption on Gr/Co induces a sizeable charge transfer from graphene to the molecular macrocycle leading to the partial occupation of the LUMO and the appearance of an energetically localized hybrid state, which can be attributed to the overlap between the graphene pz state and the molecular macrocycle. Graphene is not inert either; the adsorption of the molecule induces doping and alters the Fermi velocity of both the hybrid minicone state and the Dirac cone. Similar effects are observed when the molecular periphery is decorated with fluorine atoms, known for their electron-withdrawing properties, with minimal changes in the energy alignment.

The antiferromagnetic phase of a wurtzite nickel sulfide monolayer

Two-dimensional intrinsic long-range magnetic monolayers with high transition temperatures have attracted great interest in both fundamental studies and practical applications. In this study, we use a combination of first-principles calculations based on density functional theory (DFT), and unitary transformation of the effective Heisenberg model to investigate the electronic structure and magnetic properties of a [NiS]2 monolayer. The phonon calculations reveal that the [NiS]2 monolayer is dynamically stable in the wurtzite phase. This material is an out-of-plane easy-axis antiferromagnetically ordered monolayer with the Néel temperature close to room temperature. The intrinsic AFM ground state arises from the presence of top and bottom FM sublattices coupled together via AFM coupling, in which the net magnetic moment of each Ni atom is evaluated as 0.5μB. The spectrum of the spin-wave of [NiS]2 is investigated within the spin-wave theory of antiferromagnets in terms of the first-order Holstein-Primakoff approximation of the anisotropic Heisenberg model combined with the Bogoliubov diagonalization transformation. For the long wavelength limit, the magnon dispersion shows linear behavior with the wave vector, which is expected for conventional antiferromagnetism. The magnon velocity of approximately ∼600 m s-1 is predicted for the [NiS]2 monolayer by calculating the slope of the magnon spectrum. Due to strong spin-orbit coupling, the [NiS]2 monolayer has relatively large magnetic anisotropy energy, causing the existence of the 12 meV gap at the Γ point in the magnon spectrum. The magnon energy gap limits the number of thermally excited states, which is essential for maintaining intrinsic long-range antiferromagnetic order in two dimensions.

Proton-Coupled Electron Transfer Mechanisms for CO2 Reduction to Methanol Catalyzed by Surface-Immobilized Cobalt Phthalocyanine

Immobilized cobalt phthalocyanine (CoPc) is a highly promising architecture for the six-proton, six-electron reduction of CO2 to methanol. This electroreduction process relies on proton-coupled electron transfer (PCET) reactions that can occur by sequential or concerted mechanisms. Immobilization on a conductive support such as carbon nanotubes or graphitic flakes can fundamentally alter the PCET mechanisms. We use density functional theory (DFT) calculations of CoPc adsorbed on an explicit graphitic surface model to investigate intermediates in the electroreduction of CO2 to methanol. Our calculations show that the alignment of the CoPc and graphitic electronic states influences the reductive chemistry. These calculations also distinguish between charging the graphitic surface and reducing the CoPc and adsorbed intermediates as electrons are added to the system. This analysis allows us to identify the chemical transformations that are likely to be concerted PCET, defined for these systems as the mechanism in which protonation of a CO2 reduction intermediate is accompanied by electron abstraction from the graphitic surface to the adsorbate without thermodynamically stable intermediates. This work establishes a mechanistic pathway for methanol production that is consistent with experimental observations and provides fundamental insight into how immobilization of the CoPc impacts its CO2 reduction chemistry.

Molecular orbital projectors in non-empirical jmDFT recover exact conditions in transition-metal chemistry

Low-cost, non-empirical corrections to semi-local density functional theory are essential for accurately modeling transition-metal chemistry. Here, we demonstrate the judiciously modified density functional theory (jmDFT) approach with non-empirical U and J parameters obtained directly from frontier orbital energetics on a series of transition-metal complexes. We curate a set of nine representative Ti(III) and V(IV) d1 transition-metal complexes and evaluate their flat-plane errors along the fractional spin and charge lines. We demonstrate that while jmDFT improves upon both DFT+U and semi-local DFT with the standard atomic orbital projectors (AOPs), it does so inefficiently. We rationalize these inefficiencies by quantifying hybridization in the relevant frontier orbitals. To overcome these limitations, we introduce a procedure for computing a molecular orbital projector (MOP) basis for use with jmDFT. We demonstrate this single set of d1 MOPs to be suitable for nearly eliminating all energetic delocalization error and static correlation error. In all cases, MOP jmDFT outperforms AOP jmDFT, and it eliminates most flat-plane errors at non-empirical values. Unlike DFT+U or hybrid functionals, jmDFT nearly eliminates energetic delocalization error and static correlation error within a non-empirical framework.

Eliminating Delocalization Error to Improve Heterogeneous Catalysis Predictions with Molecular DFT + U

Approximate semilocal density functional theory (DFT) is known to underestimate surface formation energies yet paradoxically overbind adsorbates on catalytic transition-metal oxide surfaces due to delocalization error. The low-cost DFT + U approach only improves surface formation energies for early transition-metal oxides or adsorption energies for late transition-metal oxides. In this work, we demonstrate that this inefficacy arises due to the conventional usage of metal-centered atomic orbitals as projectors within DFT + U. We analyze electron density rearrangement during surface formation and O atom adsorption on rutile transition-metal oxides to highlight that a standard DFT + U correction fails to tune properties when the corresponding density rearrangement is highly delocalized across both metal and oxygen sites. To improve both surface properties simultaneously while retaining the simplicity of a single-site DFT + U correction, we systematically construct multi-atom-centered molecular-orbital-like projectors for DFT + U. We demonstrate this molecular DFT + U approach for tuning adsorption energies and surface formation energies of minimal two-dimensional models of representative early (i.e., TiO₂) and late (i.e., PtO₂) transition-metal oxides. Molecular DFT + U simultaneously corrects adsorption energies and surface formation energies of multilayer models of rutile TiO₂(110) and PtO₂(110) to resolve the paradoxical description of surface stability and surface reactivity of semilocal DFT.

Molecular DFT+U: A Transferable, Low-Cost Approach to Eliminate Delocalization Error

While density functional theory (DFT) is widely applied for its combination of cost and accuracy, corrections (e.g., DFT+U) that improve it are often needed to tackle correlated transition-metal chemistry. In principle, the functional form of DFT+U, consisting of a set of localized atomic orbitals (AOs) and a quadratic energy penalty for deviation from integer occupations of those AOs, enables the recovery of the exact conditions of piecewise linearity and the derivative discontinuity. Nevertheless, for practical transition-metal complexes, where both atomic states and ligand orbitals participate in bonding, standard DFT+U can fail to eliminate delocalization error (DE). Here, we show that by introducing an alternative valence-state (i.e., molecular orbital or MO) basis to the DFT+U approach, we recover exact conditions in cases for which standard DFT+U corrections have no error-reducing effect. This MO-based DFT+U also eliminates DE where standard AO-based DFT+U is already successful. We demonstrate the transferability of our approach on representative transition-metal complexes with a range of ligand field strengths, electron configurations (i.e., from Sc to Zn), and spin states.