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1. Strong electron correlation from partition density functional theory

   https://doi.org/10.1063/5.0175538  

   Shi, Yi; Shi, Yuming; Wasserman, Adam (December 2023, The Journal of Chemical Physics)

   Standard approximations for the exchange–correlation functional in Kohn–Sham density functional theory (KS-DFT) typically lead to unacceptably large errors when applied to strongly correlated electronic systems. Partition-DFT (PDFT) is a formally exact reformulation of KS-DFT in which the ground-state density and energy of a system are obtained through self-consistent calculations on isolated fragments, with a partition energy representing inter-fragment interactions. Here, we show how typical errors of the local density approximation (LDA) in KS-DFT can be largely suppressed through a simple approximation, the multi-fragment overlap approximation (MFOA), for the partition energy in PDFT. Our method is illustrated on simple models of one-dimensional strongly correlated linear hydrogen chains. The MFOA, when used in combination with the LDA for the fragments, improves LDA dissociation curves of hydrogen chains and produces results that are comparable to those of spin-unrestricted LDA, but without breaking the spin symmetry. MFOA also induces a correction to the LDA electron density that partially captures the correct density dimerization in strongly correlated hydrogen chains. Moreover, with an additional correction to the partition energy that is specific to the one-dimensional LDA, the approximation is shown to produce dissociation energies in quantitative agreement with calculations based on the density matrix renormalization group method. 

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2. Integrating density functional theory with machine learning for enhanced band gap prediction in metal oxides

   https://doi.org/10.1039/D4CP03397C  

   Ezeakunne, Chidozie; Lamichhane, Bipin; Kattel, Shyam (March 2025, Physical Chemistry Chemical Physics)

   In this study, we used a combination of density functional theory with Hubbard U correction (DFT+U) and machine learning (ML) to accurately predict the band gaps and lattice parameters of metal oxides: TiO2 (rutile and anatase), cubic ZnO, cubic ZnO2, cubic CeO2, and cubic ZrO2. Our results show that including Up values for oxygen 2p orbitals alongside Ud/f for metal 3d or 4f orbitals significantly enhances the accuracy of these predictions. Through extensive DFT+U calculations, we identify optimal (Up, Ud/f) integer pairs that closely reproduce experimentally measured band gaps and lattice parameters for each oxide: (8 eV, 8 eV) for rutile TiO2; (3 eV, 6 eV) for anatase TiO2; (6 eV, 12 eV) for c-ZnO; (10 eV, 10 eV) for c-ZnO2; (9 eV, 5 eV) for c-ZrO2; and (7 eV, 12 eV) for c-CeO2. Our ML analysis showed that simple supervised ML models can closely reproduce these DFT+U results at a fraction of the computational cost and generalize well to related polymorphs. Our approach builds on existing high-throughput DFT+U frameworks by providing fast pre-DFT estimates of structural properties and band gaps. Since this work does not aim to improve the underlying DFT+U method, the ML model shares its limitations. We also note that the reported values of Up strongly depend on the choice of correlated orbitals, and caution is recommended with a different choice of correlated orbitals. 

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3. Extensive Benchmarking of DFT+U Calculations for Predicting Band Gaps

   https://doi.org/10.3390/app11052395  

   Kirchner-Hall, Nicole E.; Zhao, Wayne; Xiong, Yihuang; Timrov, Iurii; Dabo, Ismaila (March 2021, Applied Sciences)

   null (Ed.)

   Accurate computational predictions of band gaps are of practical importance to the modeling and development of semiconductor technologies, such as (opto)electronic devices and photoelectrochemical cells. Among available electronic-structure methods, density-functional theory (DFT) with the Hubbard U correction (DFT+U) applied to band edge states is a computationally tractable approach to improve the accuracy of band gap predictions beyond that of DFT calculations based on (semi)local functionals. At variance with DFT approximations, which are not intended to describe optical band gaps and other excited-state properties, DFT+U can be interpreted as an approximate spectral-potential method when U is determined by imposing the piecewise linearity of the total energy with respect to electronic occupations in the Hubbard manifold (thus removing self-interaction errors in this subspace), thereby providing a (heuristic) justification for using DFT+U to predict band gaps. However, it is still frequent in the literature to determine the Hubbard U parameters semiempirically by tuning their values to reproduce experimental band gaps, which ultimately alters the description of other total-energy characteristics. Here, we present an extensive assessment of DFT+U band gaps computed using self-consistent ab initio U parameters obtained from density-functional perturbation theory to impose the aforementioned piecewise linearity of the total energy. The study is carried out on 20 compounds containing transition-metal or p-block (group III-IV) elements, including oxides, nitrides, sulfides, oxynitrides, and oxysulfides. By comparing DFT+U results obtained using nonorthogonalized and orthogonalized atomic orbitals as Hubbard projectors, we find that the predicted band gaps are extremely sensitive to the type of projector functions and that the orthogonalized projectors give the most accurate band gaps, in satisfactory agreement with experimental data. This work demonstrates that DFT+U may serve as a useful method for high-throughput workflows that require reliable band gap predictions at moderate computational cost. 

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4. Optimizing the orbital occupation in the multiple minima problem of magnetic materials from the metaheuristic firefly algorithm

   https://doi.org/10.1039/C9CP03618K  

   Payne, Adam; Avedaño-Franco, Guillermo; He, Xu; Bousquet, Eric; Romero, Aldo H. (October 2019, Physical Chemistry Chemical Physics)

   We present the use and implementation of the firefly algorithm to help in scanning the multiple metastable minima of orbital occupations in density functional theory (DFT) plus Hubbard U correction and to identify the ground state occupations in strongly correlated materials. We show the application of this implementation with the Abinit code on KCoF 3 and UO 2 crystals, which are typical d and f electron systems with numerous occupation minima. We demonstrate the validity and performance of the method by comparing with previous methodologies. The method is general and can be applied to any code using constrained occupation matrices. 

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5. Density functional theory study of bulk properties of transition metal nitrides

   https://doi.org/10.1039/D2CP06082E  

   Lynn, Michael O.; Ologunagba, Damilola; Dangi, Beni B.; Kattel, Shyam (February 2023, Physical Chemistry Chemical Physics)

   Density functional theory (DFT) calculations are performed to compute the lattice constants, formation energies and vacancy formation energies of transition metal nitrides (TMNs) for transition metals (TM) ranging from 3d–5d series. The results obtained using six different DFT exchange and correlation potentials (LDA, AM05, BLYP, PBE, rPBE, and PBEsol) show that the experimental lattice constants are best predicted by rPBE, while the values obtained using AM05, PBE, rPBE and PBEsol lie between the LDA and BLYP calculated values. A linear relationship is observed between the lattice constants and formation energies with the mean radii of TM and the difference in the electronegativity of TM and N in TMNs, respectively. Our calculated vacancy formation energies, in general, show that N-vacancies are more favorable than TM-vacancies in most TMNs. We observe that N-vacancy formation energies are linearly correlated with the calculated bulk formation energies indicating that TMNs with large negative formation energies are less susceptible to the formation of N-vacancies. Thus, our results from this extensive DFT study not only provide a systematic comparison of various DFT functionals in calculating the properties of TMNs but also serve as reference data for the computation-driven experimental design of materials. 

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