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

Universal Generalization of Density Functional Theory for Static Correlation

A major challenge for density functional theory (DFT) is its failure to treat static correlation, yielding errors in predicted charges, band gaps, van der Waals forces, and reaction barriers. Here we combine one- and two-electron reduced density matrix (1- and 2-RDM) theories with DFT to obtain a universal O(N^{3}) generalization of DFT for static correlation. Using the lowest unitary invariant of the cumulant 2-RDM, we generate a 1-RDM functional theory that corrects the convexity of any DFT functional to capture static correlation in its fractional orbital occupations. Importantly, the unitary invariant yields a predictive theory by revealing the dependence of the correction's strength upon the trace of the two-electron repulsion matrix. We apply the theory to the barrier to rotation in ethylene, the relative energies of the benzynes, as well as an 11-molecule, dissociation benchmark. By inheriting the computational efficiency of DFT without sacrificing the treatment of static correlation, the theory opens new possibilities for the prediction and interpretation of significant quantum molecular effects and phenomena.

Regulating the Electronic Configuration of Spinel Zinc Manganate Derived from Metal-Organic Frameworks: Controlled Synthesis and Application in Anode Materials for Lithium-Ion Batteries

In recent years, transition metal oxides have been considered as the most promising anode materials due to their high theoretical capacity, low price, and abundant natural reserves. Among them, zinc manganate is used as an electrode material for anodes, whose application is mostly hindered due to its poor ionic/electronic conductivity. In this work, a series of ZnMn₂O₄ (ZMO) are synthesized by a hydrothermal technique coordinated with a metal-organic framework-based high-temperature calcination process for their application as an anode in lithium-ion batteries (LIBs). Meanwhile, this study systematically explores the influence of carbon doping and the types of organic ligands and oxygen vacancies on the electrochemical properties of the synthesized ZMO. Density functional theory (DFT) calculations and experimental investigations reveal that the introduction of carbon and oxygen vacancies can enhance electronic conductivity, more active sites and faster Li⁺ adsorption, resulting in better electrochemical performances. As expected, all ZMOs with carbon doping (PMA-ZMO, MI-ZMO, and BDC-ZMO) derived from 1,2,4,5-benzenetetracarboxylic acid, 2-methylimidazole, and 1,4-dicarboxybenzene achieve outstanding electrochemical performance. Meanwhile, the introduction of oxygen vacancies can enhance the electronic conductivity and can significantly reduce the activation energy of Li⁺ transport, thereby accelerating the Li⁺ diffusion kinetics in the lithiation/delithiation process. Furthermore, an optimal ZMO anode material synthesized by 2-methylimidazole delivers a high reversible capacity of 1174.7 mA h g^-1 after 300 cycles at 0.1 A g^-1 and 600 mA h g^-1 at 0.5 A g^-1 after 300 cycles. After high-rate charge and discharge cycles, the specific capacity rapidly recovers to a value greater than the initial value, which proves the unusual activation and thereby an excellent rate property of the electrode. Hence, we conclude that ZMO provides potential application prospects as an anode electrode material for LIBs.

Ligand Additivity and Divergent Trends in Two Types of Delocalization Errors from Approximate Density Functional Theory

The predictive accuracy of density functional theory (DFT) is hampered by delocalization errors, especially for correlated systems such as transition-metal complexes. Two complementary strategies have been developed to reduce delocalization error: eliminating the global curvature with change in charge, and applying a linear response Hubbard U as a measure of local curvature at a metal center at fixed charge in a DFT+U framework. We investigate the relationship between the two delocalization error measures as the ligand field strength is varied with the number of strong-field ligands in a series of heteroleptic complexes or by geometrically constraining the metal-ligand bond length in homoleptic octahedral complexes. We show that across these sets of complexes an inverse relationship generally exists between global and local curvatures. We find that effects of ligand substitution on both measures of delocalization are typically additive, but the quantities seldom coincide.

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.