Accurate Electron Affinities and Orbital Energies of Anions from a Non-Empirically Tuned Range-Separated Density Functional Theory Approach

Abstract

The treatment of atomic anions with Kohn-Sham density functional theory (DFT) has long been controversial since the highest occupied molecular orbital (HOMO) energy, $E_{HOMO}$, is often calculated to be positive with most approximate density functionals. We assess the accuracy of orbital energies and electron affinities for all three rows of elements in the periodic table (H-Ar) using a variety of theoretical approaches and customized basis sets. Among all of the theoretical methods studied here, we find that a non-empirically tuned range-separated approach (constructed to satisfy DFT-Koopmans' theorem for the anionic electron system) provides the best accuracy for a variety of basis sets - even for small basis sets where most functionals typically fail. Previous approaches to solve this conundrum of positive $E_{HOMO}$ values have utilized non-self-consistent methods; however electronic properties, such as electronic couplings/gradients (which require a self-consistent potential and energy), become ill-defined with these approaches. In contrast, the non-empirically tuned range-separated procedure used here yields well-defined electronic couplings/gradients and correct $E_{HOMO}$ values since both the potential and resulting electronic energy are computed self-consistently. Orbital energies and electron affinities are further analyzed in the context of the electronic energy as a function of electronic number (including fractional numbers of electrons) to provide a stringent assessment of self-interaction errors for these complex anion systems.

arXiv commentAccepted by the Journal of Chemical Theory and Computation

References in corpus (8)

• Theory and applications of atomic and ionic polarizabilities
• Fundamental gaps of finite systems from the eigenvalues of a generalized Kohn-Sham method
• Optoelectronic and Excitonic Properties of Oligoacenes: Substantial Improvements from Range-Separated Time-Dependent Density Functional Theory
• Non-Empirically Tuned Range-Separated DFT Accurately Predicts Both Fundamental and Excitation Gaps in DNA and RNA Nucleobases
• Coumarin Dyes for Dye-Sensitized Solar Cells - A Long-Range-Corrected Density Functional Study
• Absorption and Fluorescence Properties of Oligothiophene Biomarkers from Long-Range-Corrected Time-Dependent Density Functional Theory
• Avoiding Unbound Anions in Density Functional Calculations
• The Importance of Short- and Long-Range Exchange on Various Excited State Properties of DNA Monomers, Stacked Complexes, and Watson-Crick Pairs

Cited by in corpus (12)

• Fully numerical calculations on atoms with fractional occupations. Range-separated exchange functionals
• Fully numerical Hartree-Fock and density functional calculations. I. Atoms
• Electron-Affinity Time-Dependent Density Functional Theory: Formalism and Applications to Core-Excited States
• Approximating Quasiparticle and Excitation Energies from Ground State Generalized Kohn-Sham Calculations
• Machine learning the derivative discontinuity of density-functional theory
• Exploring electron affinities, LUMO energies, and band gaps with electron-pair theories
• Photoemission from hybrid states of Cl@$C_{60}$ before and after a stabilizing charge transfer
• Approximate Functionals in Hypercomplex Kohn-Sham Theory
• A density functional theory based comparative study of hybrid photoemissions from Cl@C60, Br@C60 and I@C60
• Density functional study of the variants of inter-Coulombic decay resonances in the photoionization of Cl@C60
• Porous carbon nitride fullerenes: a novel family of porous cage molecules
• Quantum Study of Dispersion-Corrected Electronic and Optical Properties of syn- and anti- B18H22 Clusters with/without Sulfur Doping for Tunable Optoelectronics