TDDFT plus U: A critical assessment of the Hubbard U correction to exchange-correlation kernels and potentials

Article

关键词: DENSITY-FUNCTIONAL THEORY;    STATE PERTURBATION-THEORY;    ELECTRONIC-STRUCTURE;    EXCITATION-ENERGIES;    EXCITED-STATES;    AB-INITIO;    EFFICIENT IMPLEMENTATION;    TIO2 NANOPARTICLES;    OPTICAL-SPECTRA;    BAND THEORY;   

DOI  :  10.1103/PhysRevB.99.165120

来源: SCIE

【 摘 要 】

We develop a generalization of the Kohn-Sham density-functional theory (KS-DFT)+Hubbard U (DFT+U) method to the excited-state regime. This has the form of Hubbard U corrected linear-response time-dependent DFT, or TDDFT+U. Combined with calculated linear-response Hubbard U parameters, it may provide a computationally light, first-principles method for the simulation of tightly bound excitons on transition-metal ions. Our presented implementation combines linear-scaling DFT+U and linear-scaling TDDFT, but the approach is broadly applicable. In detailed benchmark tests on two Ni-centered diamagnetic coordination complexes with variable U values, it is shown that the Hubbard U correction to an approximate adiabatic semilocal exchange-correlation interaction kernel lowers the excitation energies of transitions exclusively within the targeted localized subspace by increasing the exciton binding of the corresponding electron-hole pairs. This partially counteracts the Hubbard U correction to the exchange-correlation potential in KS-DFT, which increases excitation energies into, out of, and within the targeted localized subspace by modifying the underlying KS-DFT eigenspectrum. This compensating effect is most pronounced for optically dark transitions between localized orbitals of the same angular momentum, for which experimental observation may be challenging, and theoretical approaches are at their most necessary. Interestingly, we find that first-principles TDDFT+U seems to offer a remarkably good agreement with experiment for a perfectly closed-shell complex on which approximate TDDFT underperforms, but only when TDDFT+U is applied to the DFT eigenspectrum and not to the DFT+U one. In tests on an open-shell, noncentrosymmetric, high-spin cobalt coordination complex, we find that first-principles TDDFT+U again compensates for the DFT+U blueshift in 3d -> 3d transitions, but that using the DFT eigenspectrum is not viable due to the emergence of a singlet instability. Overall, our results point to shortcomings in the contemporary DFT+U corrective potential, either in its functional form, or when applied to transition-metal orbitals but not to ligand ones, or both.

【 授权许可】

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