Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals

Abstract

Excitation gaps are of considerable significance in electronic structure theory. Two different gaps are of particular interest. The fundamental gap is defined by charged excitations, as the difference between the first ionization potential and the first electron affinity. The optical gap is defined by a neutral excitation, as the difference between the energies of the lowest dipole-allowed excited state and the ground state. Within many-body perturbation theory, the fundamental gap is the difference between the corresponding lowest quasi-hole and quasi-electron excitation energies, and the optical gap is addressed by including the interaction between a quasi-electron and a quasi-hole. A long-standing challenge has been the attainment of a similar description within density functional theory (DFT), with much debate on whether this is an achievable goal even in principle. Recently, we have constructed and applied a new approach to this problem. Anchored in the rigorous theoretical framework of the generalized Kohn-Sham equation, our method is based on a range-split hybrid functional that uses exact long-range exchange. Its main novel feature is that the range-splitting parameter is not a universal constant but rather is determined from first principles, per system, based on satisfaction of the ionization potential theorem. For finite-sized objects, this DFT approach mimics successfully, to the best of our knowledge for the first time, the quasi-particle picture of many-body theory. Specifically, it allows for the extraction of both the fundamental and the optical gap from one underlying functional, based on the HOMO-LUMO gap of a ground-state DFT calculation and the lowest excitation energy of a linear-response time-dependent DFT calculation, respectively. In particular, it produces the correct optical gap for the difficult case of charge-transfer and charge-transfer-like scenarios, where conventional functionals are known to fail. In this perspective, we overview the formal and practical challenges associated with gap calculations, explain our new approach and how it overcomes previous difficulties, and survey its application to a variety of systems.

Assessment of Tuning Methods for Enforcing Approximate Energy Linearity in Range-Separated Hybrid Functionals

“…A similar form for the tuning norm has also been proposed, 35,38 differing from eq. 16 only in the cross-terms of its square, which we write as…”

Modelling materials for solar fuel synthesis by artificial photosynthesis; predicting the optical, electronic and redox properties of photocatalysts

“…There is no guarantee that the amount of HF-like exchange (HFLE) required to achieve a good match to the true band gap is the same for all systems, but at least for simple binary semiconductors this seems to be the case [85,86]. In this context, we feel it is also opportune to mention the optimally tuned range-separated hybrid functional method of Kronik and co-workers [87,88]. In their approach, the range-separation parameter of a range-separated XC functional is tuned, such that for a given system, the KS gap found with this XC functional is equal to the difference between the IP and EA potentials obtained in Δ-SCF calculations using the same XC functional.…”

Range-Separation Parameter in Tuned Exchange–Correlation Functionals: Successive Ionizations and the Fukui Function

“…The value of µ can be fixed or it can be 'tuned' on a system-by-system basis by minimising some tuning norm. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] Whether the parameter is fixed or tuned, it is well established that such functionals yield improvements in many long-range properties, most notably charge-transfer excitation energies, and they have become the functional of choice in many studies.…”