Quasiparticle energies and fundamental band gaps in particular are critical properties of molecules and materials. It was rigorously established that the generalized Kohn-Sham HOMO and LUMO orbital energies are the chemical potentials of electron removal and addition and thus good approximations to band edges and fundamental gaps from a density functional approximation (DFA) with minimal delocalization error. For other quasiparticle energies, their connection to the generalized Kohn-Sham orbital energies has not been established but remains highly interesting. We provide the comparison of experimental quasiparticle energies for many finite systems with calculations from the GW Green's function and localized orbitals scaling correction (LOSC), a recently developed correction to semilocal DFAs, which has minimal delocalization error. Extensive results with over forty systems clearly show that LOSC orbital energies achieve slightly better accuracy than the GW calculations with little dependence on the semilocal DFA, supporting the use of LOSC DFA orbital energies to predict quasiparticle energies. This also leads to the calculations of excitation energies of the N -electron systems from the ground state DFA calculations of the (N − 1)-electron systems. Results show good performance with accuracy similar to TDDFT and the delta SCF approach for valence excitations with commonly used DFAs with or without LOSC. For Rydberg states, good accuracy was obtained only with the use of LOSC DFA. This work highlights the pathway to quasiparticle and excitation energies from ground density functional calculations. 2Graphical TOC EntryQuasiparticles are a powerful concept in electronic structure theory of many-electron systems. In particular, accurate prediction of quasiparticle energies is essential for interpreting the electronic excitation spectra of molecules and materials, such as photoemission and optical experiments. Formally, quasiparticle energies can be exactly formulated in many-body perturbation theory. 1-3 In practice, the GW approximation 4-7 is most widely used for bulk simulations. Unfortunately, GW calculations are still expensive computationally. Therefore, a low-cost alternative to GW approximation that offers good accuracy for the prediction of quasiparticle energies is critical to the calculations of large-scale systems, and for efficient high throughput study of materials.Kohn-Sham (KS) density functional theory (DFT), 8-10 due to its good balance between accuracy and computational tractability, is among the most popular and versatile methods available for many-electron problems. In addition to the total electron energy, the physical interpretation of the KS eigenvalues has also attracted great interest. It has been known for decades that among the KS eigenvalues obtained from the exact functional, the highest occupied molecular orbital (HOMO) energy, ε HOMO , is negative vertical ionization potential (VIP), −I. [10][11][12][13][14][15][16][17] In 2008, it was rigorously proven 18,19 that within the generaliz...

Kohn−Sham density functional theory (KS-DFT) has been a wellestablished theoretical foundation for ground-state electronic structure and has achieved great success in practical calculations. Recently, utilizing the eigenvalues from KS or generalized KS (GKS) calculations as an approximation to the quasiparticle energies, our group demonstrated a method to calculate the excitation energies from (G)KS calculation on the ground-state (N − 1)-electron system. This method is now called QE-DFT (quasiparticle energies from DFT). In this work, we extend this QE-DFT method to describe excited-state potential energy surfaces (PESs), conical intersections, and the analytical gradients of excited-state PESs. The analytical gradients were applied to perform geometry optimization for excited states. In conjunction with several commonly used density functional approximations, QE-DFT can yield PESs in the vicinity of the equilibrium structure with accuracy similar to that from time-dependent DFT (TD-DFT). Furthermore, it describes conical intersection well, in contrast to TD-DFT. Good results for geometry optimization, especially bond length, of low-lying excitations for 14 small molecules are presented. The capability of describing excited-state PESs, conical intersections, and analytical gradients from QE-DFT and its efficiency based on just ground-state DFT calculations should be of great interest for describing photochemical and photophysical processes in complex systems.

The recently developed localized orbital scaling correction (LOSC) method shows the ability to systematically and size-consistently reduce the delocalization error existing in conventional density functional approximations (DFAs). However, the application of LOSC to DFAs was mainly through a post self-consistent field (SCF) manner, and few results from applying LOSC to DFAs in an SCF manner have been reported. The reason is that the originally proposed SCF approach to SCF–LOSC calculation uses an approximate Hamiltonian and encounters convergence problems easily in practice. In this work, we develop a new SCF approach with a correct Hamiltonian and achieve reliable SCF–LOSC calculations. We demonstrate the capability of the new SCF approach for SCF–LOSC to correctly describe the electron densities, total energies, and energy-level alignment for the molecular dissociation process, while conventional DFAs or LOSC–DFAs with post-SCF calculations show large errors. This work demonstrates that the new SCF approach for SCF–LOSC would be a promising method for studying problems for correct electron densities and energy-level alignments in large systems.

Calculating charge transfer (CT) excitation energies with high accuracy and low computational cost is a challenging task. Kohn-Sham density functional theory (KS-DFT), due to its efficiency and accuracy, has achieved great success in describing ground state problems. To extend to excited state problems, our group recently demonstrated an approach with good numerical results to calculate low-lying and Rydberg excitation energies of an N -electron system from a ground state KS or generalized KS calculations of an (N − 1)-electron system via its orbital energies.In present work, we explore further the same methodology to describe CT excitations. Numerical results from this work show that performance of conventional density functional approximations (DFAs) is not as good for CT excitations as for other excitations, due to the delocalization error. Applying localized orbital scaling correction (LOSC) to conventional DFAs, a recently developed method in our group to effectively reduce the delocalization error, can improve the results. Overall, the performance of this methodology is better than time dependant DFT (TDDFT) with conventional DFAs. In addition, it shows that results from LOSC-DFAs in this method reach similar accuracy to other methods, such as ∆SCF, G 0 W 0 with Bethe-Salpeter equations, particle-particle random phase approximation, and even high-level wavefunction method like CC2. Our analysis show that the correct 1/R trend for CT excitation can be captured from LOSC-DFA calculations, stressing that the application of DFAs with minimal delocalization error is essential within this methodology. This work provides an efficient way to calculate CT excitation energies from ground state DFT.

We develop a second-order correction to commonly used density functional approximations (DFAs) to eliminate the systematic delocalization error. The method, based on the previously developed global scaling correction (GSC), is an exact quadratic correction to the DFA for the fractional charge behavior and uses the analytical second derivatives of the total energy with respect to fractional occupation numbers of the canonical molecular orbitals. For small and medium-size molecules, this correction leads to ground-state orbital energies that are a highly accurate approximation to the corresponding quasiparticle energies. It provides excellent predictions of ionization potentials, electron affinities, photoemission spectrum, and photoexcitation energies beyond previous approximate second-order approaches, thus showing potential for broad applications in computational spectroscopy.