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

Abstract

The treatment of atomic anions with Kohn-Sham density functional theory (DFT) has long been controversial because the highest occupied molecular orbital (HOMO) energy, E, 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 nonempirically 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 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 nonempirically tuned range-separated procedure used here yields well-defined electronic couplings/gradients and correct E values because 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.

Fully numerical Hartree‐Fock and density functional calculations. I. Atoms

“…In order to study the accuracy of the results obtained with an extended Gaussian basis set in Ref. , we decided to repeat the calculations in the finite element approach. We chose to study the species H − , He, Li + , Li − , Be, B + , C − , N, O + , F – , Ne, Na + , Na − , Mg, Al + , Si − , P, S + , Cl − , and Ar, as each of them has only fully filled subshells.…”

“…Surprisingly, symmetry breaking can sometimes also be seen for cases with fully filled shells, such as in the case of the Ne atom and the F − anion . We chose the above systems for the present work, as the study by Anderson and coworkers explicitly considered broken symmetry solutions by the use of wave function stability analysis, which is not currently implemented in HelFEM .…”

“…Our second application is the benchmark of Gaussian basis set energies for a variety of neutral, cationic, and anionic species with HF and the BHHLYP functional. Atomic anions are especially challenging to model with DFT . For instance, it has been shown that calculations on the well‐bound F − anion may require extremely diffuse basis functions with exponents as small as (!)…”

“… α = 6.9 × 10 −9 to achieve converged results . The use of such small exponents requires extensive modifications to the used Gaussian‐basis quantum chemistry program to ensure sufficient numerical accuracy . In contrast, the finite element method (FEM) has none of these issues: because the basis set has local support and is never ill‐conditioned, calculations are extremely stable numerically.…”

“…We will show below that the absolute energies reproduced by the large Gaussian basis set used in Refs. are too large by several microhartrees for most systems. The second part of the present series presents analogous applications to diatomic molecules, where the deficiencies of Gaussian basis sets are considerably more noticeable …”