Oxidation-State Constrained Density Functional Theory for the Study of Electron-Transfer Reactions

The energy landscape of magnetic materials

Magnetic materials can display many solutions to the electronic-structure problem, corresponding to different local or global minima of the energy functional. In Hartree-Fock or density-functional theory different single-determinant solutions lead to different magnetizations, ionic oxidation states, hybridizations, and inter-site magnetic couplings. The vast majority of these states can be fingerprinted through their projection on the atomic orbitals of the magnetic ions. We have devised an approach that provides an effective control over these occupation matrices, allowing us to systematically explore the landscape of the potential energy surface. We showcase the emergence of a complex zoology of self-consistent states; even more so when semi-local density-functional theory is augmented - and typically made more accurate - by Hubbard corrections. Such extensive explorations allow to robustly identify the ground state of magnetic systems, and to assess the accuracy (or not) of current functionals and approximations.

Orbital-Resolved DFT+U for Molecules and Solids

We present an orbital-resolved extension of the Hubbard U correction to density-functional theory (DFT). Compared to the conventional shell-averaged approach, the prediction of energetic, electronic and structural properties is strongly improved, particularly for compounds characterized by both localized and hybridized states in the Hubbard manifold. The numerical values of all Hubbard parameters are readily obtained from linear-response calculations. The relevance of this more refined approach is showcased by its application to bulk solids pyrite (FeS2) and pyrolusite (β-MnO2), as well as to six Fe(II) molecular complexes. Our findings indicate that a careful definition of Hubbard manifolds is indispensable for extending the applicability of DFT+U beyond its current boundaries. The present orbital-resolved scheme aims to provide a computationally undemanding yet accurate tool for electronic structure calculations of charge-transfer insulators, transition-metal (TM) complexes and other compounds displaying significant orbital hybridization.

Simulating Electron Transfer Reactions in Solution: Radical-Polar Crossover

Single-electron transfer (SET) promotes a wide variety of interesting chemical transformations, but modeling of SET requires a careful treatment of electronic and solvent effects to give meaningful insight. Therefore, a combined constrained density functional theory and molecular mechanics (CDFT/MM) tool is introduced specifically for SET-initiated reactions. Mechanisms for two radical-polar crossover reactions involving the organic electron donors tetrakis(dimethylamino)ethylene (TDAE) and tetrathiafulvalene (TTF) were studied with the new tool. An unexpected tertiary radical intermediate within the TDAE system was identified, relationships between kinetics and substitution in the TTF system were explained, and the impact of the solvent environments on the TDAE and TTF reactions were examined. The results highlight the need for including solvent dynamics when quantifying SET kinetics and thermodynamics, as a free energy difference of >20 kcal/mol was observed. Overall, the new method informs mechanistic analysis of SET-initiated reactions and therefore is envisioned to be useful for studying reactions in the condensed phase.

Hybrid Functional and Plane Waves based Ab Initio Molecular Dynamics Study of the Aqueous Fe2+ /Fe3+ Redox Reaction

Kohn-Sham density functional theory and plane wave basis set based ab initio molecular dynamics (AIMD) simulation is a powerful tool for studying complex reactions in solutions, such as electron transfer (ET) reactions involving Fe²⁺ /Fe³⁺ ions in water. In most cases, such simulations are performed using density functionals at the level of Generalized Gradient Approximation (GGA). The challenge in modelling ET reactions is the poor quality of GGA functionals in predicting properties of such open-shell systems due to the inevitable self-interaction error (SIE). While hybrid functionals can minimize SIE, standard plane-wave based AIMD at that level of theory is typically 150 times slower than GGA for systems containing ∼100 atoms. Among several approaches reported to speed-up AIMD simulations with hybrid functionals, the noise-stabilized MD (NSMD) procedure, together with the use of localized orbitals to compute the required exchange integrals, is an attractive option. In this work, we demonstrate the application of the NSMD approach for studying the Fe²⁺ /Fe³⁺ redox reaction in water. It is shown here that long AIMD trajectories at the level of hybrid density functionals can be obtained using this approach. Redox properties of the aqueous Fe²⁺ /Fe³⁺ system computed from these simulations are compared with the available experimental data for validation.

Implementation and Validation of Constrained Density Functional Theory Forces in the CP2K Package

Constrained density functional theory (CDFT) is a powerful tool for the prediction of electron transfer parameters in condensed phase simulations at a reasonable computational cost. In this work we present an extension to CDFT in the popular mixed Gaussian/plane wave electronic structure package CP2K, implementing the additional force terms arising from a constraint based on Hirshfeld charge partitioning. This improves upon the existing Becke partitioning scheme, which is prone to give unphysical atomic charges. We verify this implementation for a variety of systems: electron transfer in (H₂O)₂⁺ in a vacuum, electron tunnelling between oxygen vacancy centers in solid MgO, and electron self-exchange in aqueous Ru²⁺–Ru³⁺. We find good agreement with previous plane-wave CDFT results for the same systems, but at a significantly lower computational cost, and we discuss the general reliability of condensed phase CDFT calculations.

Reversing the Catalytic Selectivity of Single-Atom Ru via Support Amorphization

Supported single-atom catalysts (SACs), with the extremely homogenized active sites could achieve high hydrogenation selectivity toward one of the functional groups coexisting in the reactant molecule. However, as to the target group, the control of selective recognition and activation by SACs still remains a challenge. Herein, the phase engineering of the support is adopted to control the chemo-recognition behavior of SACs in selective hydrogenation. Single-atom Ru on amorphous porous ultrathin TiO₂ nanosheets (Ru₁/a-TiO₂) is constructed, in which Ru is more positively charged than that in the crystalline counterpart (Ru₁/c-TiO₂). Moreover, in the nitro/vinyl selective hydrogenation process, Ru₁/a-TiO₂ shows superior nitro selectivity, opposite to the vinyl selectivity of Ru₁/c-TiO₂. Density functional theory calculations for single-atom Ru of different charge states show that the reactant adsorption configuration could be inverted in the amorphous TiO₂, accounting for the chemo-recognition behavior controlled by the phase of support.

Evaluation of optical band gaps and dopant state energies in transition metal oxides using oxidation-state constrained density functional theory

We report the use of oxidation-state constrained density functional theory (OS-CDFT) to calculate the optical band gaps of transition metal oxides and dopant state energies of different doped anatase. OS-CDFT was used to control electron transfer from the valence band maximum of the transition metal system to the conduction band minimum or to the dopant state in order to calculate the band gap or the dopant state energies respectively. The calculation of the dopant state energies also allows identification of the transition responsible for the reduced band gap of the doped system in ambiguous cases. We applied this approach to the band gap calculation in TiO₂anatase and rutile, vanadium pentoxide (V₂O₅), chromium(III) oxide (Cr₂O₃), manganese(IV) oxide (MnO₂), ferric oxide (Fe₂O₃), ferrous oxide (FeO) and cobalt(II) oxide (CoO). The dopant state energies calculations were carried out in the V-, Cr-, Mn-, and Fe-doped anatase.