Density Functional Prediction of Quasiparticle, Excitation, and Resonance Energies of Molecules With a Global Scaling Correction Approach

Abstract

Molecular quasiparticle and excitation energies determine essentially the spectral characteristics measured in various spectroscopic experiments. Accurate prediction of these energies has been rather challenging for ground-state density functional methods, because the commonly adopted density function approximations suffer from delocalization error. In this work, by presuming a quantitative correspondence between the quasiparticle energies and the generalized Kohn–Sham orbital energies, and employing a previously developed global scaling correction approach, we achieve substantially improved prediction of molecular quasiparticle and excitation energies. In addition, we also extend our previous study on temporary anions in resonant states, which are associated with negative molecular electron affinities. The proposed approach does not require any explicit self-consistent field calculation on the excited-state species, and is thus highly efficient and convenient for practical purposes.

LibSC: Library for Scaling Correction Methods in Density Functional Theory

“…Note that the original consideration of HOMO and LUMO 41 has been generalized to all the orbitals. 46,50 The coefficient κ pσ in the original work of GSC 41 is approximated explicitly as…”

“…40 In addition to these aforementioned approaches, a series of scaling correction (SC) methods, [41][42][43][44][45][46] including the global scaling correction (GSC), 41,46 the local scaling correction (LSC) 42 and the localized orbital scaling correction (LOSC) [43][44][45] methods, have been developed in the Yang laboratory to tackle the delocalization error in conventional DFAs. With extensive numerical results, [41][42][43]43,[47][48][49][50][51] these SC methods have been demonstrated to be capable of reducing the delocalization error effectively and producing accurate descriptions for many critical and challenging problems, including the fundamental gap, 41,43,47 photoemission spectroscopy, 43,47,50 photoexcitation energies [47][48][49] and polarizability. 42,51 Therefore, a reliable and stable implementation for the SC methods can be very beneficial and meaningful to the electronic structure theory community, which helps to promote DFT with commonly used DFAs and with the SC methods for broader applications.…”

The Exact Second Order Corrections and Accurate Quasiparticle Energy Calculations in Density Functional Theory

“…To improve the accuracy of the GSC method, Xiao and coworkers developed a correction form that utilizes higher order density expansions to go beyond the frozen orbital approximation in the original GSC work. 47,48 Up to third-order orbital derivatives were calculated, and remarkable improvements had been achieved. However, the exchange-correlation component was still treated approximately as the LDA exchange energy, regardless of the DFA used.…”

“…However, the exchange-correlation component was still treated approximately as the LDA exchange energy, regardless of the DFA used. All works 39,47,48 up to now are approximate second-order corrections to the DFA total energy for fractional-electron systems.…”

“…45,50 Therefore, a natural extension to excited states is necessary, and similar constructions for the correction to all orbitals have already been established in LOSC 41 and recent work from Xiao and coworkers on GSC. 48 To facilitate the discussion to orbitals above LUMO and under the HOMO, we need to extend the ground state energy E(N ), as a function of N , the total number of electron, to E({n pσ }), the total energy as a function of the canonical orbital occupation numbers {n pσ }, which can correspond to some excited states. This energy function is what was used in Janak's work, 3,4 and it is given by the following minimum…”