Corrective First-Principles Approaches for the Theoretical Spectroscopy of Transition-Metal Systems

Abstract

Density-functional theory within its practical, widespread Kohn-Sham formalism (KS-DFT), is an effective approach for providing the starting point for advanced first-principles spectroscopy simulations of molecules and solids in the linear-response regime. Within available approximations for the electronic exchange-correlation energy, however, KS-DFT exhibits certain systematic errors such as self-interaction error (SIE), which dominates the error in insulating and optical gaps. Particularly, transition-metal systems in general have large SIE that manifest as large delocalisation error of 3d states of such systems. Consequently, spectroscopy simulations of these systems starting from KS-DFT are unreliable. Here, we introduce computationally feasible and quantitatively accurate corrective approaches to encounter such errors in first-principles spectroscopy simulations, particularly with a view to enabling future high-throughput spectroscopy for transition-metal systems.

Accurate spectra of selected noble-metal solids and their alloys were obtained using the random-phase approximation (RPA) on top of G0W0 quasiparticle-corrected band-structures using the first-principle stretching operators, which modify the electronic bands around the Fermi level to imitate the non-local many-body effects. Quantitative accuracy is achieved while preserving minimal additional costs. A number of promising candidate alloys are predicted for plasmonic applications.

The time-domain extension of DFT+U, namely TDDFT+U, was developed and implemented with a linear-scaling framework. This corrects SIE of particle-hole pairs built from localised orbitals in the context of linear-response time-dependent DFT (TDDFT) within adiabatic semi-local approximations for transition-metal systems. It is demonstrated using representative three coordination complexes that TDDFT+U can significantly improve the descriptions of low-lying excitations accurately from first-principles.

Despite its great success, conventional DFT+U fails to predict the insulating gap of TiO2 as its valance edge states are dominated by 2p states of O atoms. Hence, a +U correction is required for both the 3d states of Ti and the 2p states of O, giving DFT+Ud+Up. The insulating gaps of TiO2-rutile and TiO2-anatase were calculated accurately within DFT+Ud+Up with Hubbard U and Hund's J parameters calculated from first-principles. Furthermore, the defect states of neutral O vacancies in TiO2-rutile and TiO2-anatase were investigated within the same approach. Our calculations provide a first-principles assessment of the vacancy states in these important materials, and show that DFT+U can behave well for closed-shell transition-metal systems if used with appropriate care.