The Fermi–Löwdin self-interaction correction for ionization energies of organic molecules

Introducing a new exchange functional by altering the electron density's ionization dependency in density functional theory

Each of the exchange-correlation functionals in the density functional theory has been customized to particular systems or elements and has unique advantages and disadvantages. In one of the most recent research on exchange-correlation functionals, Chachiyo et al. present a relationship for exchange-correlation functional by assuming the simplest form of electron density. Their utilized electron density causes a systematic inaccuracy in the energy of the molecules since it does not fully account for the variation of the ionization energy for different atoms. We offer a novel relationship for exchange functional that improves the precision of the energy calculations for molecules by using the basic assumptions of the Chachiyo approach and correcting the electron density. Our density is directly related to the atom's ionization energy. Our suggested functional was implemented for 56 molecules composed of atoms from the first, second, and third rows of the periodic table using Siam Quantum package. We discussed about the role of our functional on the reducing the computation error of dipole moment along with total, bonding and zero point energies. We also increased the portion of core electrons to improve the accuracy of the results.

Slater transition methods for core-level electron binding energies

Methods for computing core-level ionization energies using self-consistent field (SCF) calculations are evaluated and benchmarked. These include a "full core hole" (or "ΔSCF") approach that fully accounts for orbital relaxation upon ionization, but also methods based on Slater's transition concept in which the binding energy is estimated from an orbital energy level that is obtained from a fractional-occupancy SCF calculation. A generalization that uses two different fractional-occupancy SCF calculations is also considered. The best of the Slater-type methods afford mean errors of 0.3-0.4 eV with respect to experiment for a dataset of K-shell ionization energies, a level of accuracy that is competitive with more expensive many-body techniques. An empirical shifting procedure with one adjustable parameter reduces the average error below 0.2 eV. This shifted Slater transition method is a simple and practical way to compute core-level binding energies using only initial-state Kohn-Sham eigenvalues. It requires no more computational effort than ΔSCF and may be especially useful for simulating transient x-ray experiments where core-level spectroscopy is used to probe an excited electronic state, for which the ΔSCF approach requires a tedious state-by-state calculation of the spectrum. As an example, we use Slater-type methods to model x-ray emission spectroscopy.

Spin-crossover complexes: Self-interaction correction vs density correction

Complexes containing a transition metal atom with a 3d⁴-3d⁷ electron configuration typically have two low-lying, high-spin (HS) and low-spin (LS) states. The adiabatic energy difference between these states, known as the spin-crossover energy, is small enough to pose a challenge even for electronic structure methods that are well known for their accuracy and reliability. In this work, we analyze the quality of electronic structure approximations for spin-crossover energies of iron complexes with four different ligands by comparing energies from self-consistent and post-self-consistent calculations for methods based on the random phase approximation and the Fermi-Löwdin self-interaction correction. Considering that Hartree-Fock densities were found by Song et al., J. Chem. Theory Comput. 14, 2304 (2018), to eliminate the density error to a large extent, and that the Hartree-Fock method and the Perdew-Zunger-type self-interaction correction share some physics, we compare the densities obtained with these methods to learn their resemblance. We find that evaluating non-empirical exchange-correlation energy functionals on the corresponding self-interaction-corrected densities can mitigate the strong density errors and improves the accuracy of the adiabatic energy differences between HS and LS states.

Chemical bonding theories as guides for self-interaction corrected solutions: Multiple local minima and symmetry breaking

Fermi-Löwdin orbitals (FLOs) are a special set of localized orbitals, which have become commonly used in combination with the Perdew-Zunger self-interaction correction (SIC) in the FLO-SIC method. The FLOs are obtained for a set of occupied orbitals by specifying a classical position for each electron. These positions are known as Fermi-orbital descriptors (FODs), and they have a clear relation to chemical bonding. In this study, we show how FLOs and FODs can be used to initialize, interpret, and justify SIC solutions in a common chemical picture, both within FLO-SIC and in traditional variational SIC, and to locate distinct local minima in either of these approaches. We demonstrate that FLOs based on Lewis theory lead to symmetry breaking for benzene-the electron density is found to break symmetry already at the symmetric molecular structure-while ones from Linnett's double-quartet theory reproduce symmetric electron densities and molecular geometries. Introducing a benchmark set of 16 planar cyclic molecules, we show that using Lewis theory as the starting point can lead to artifactual dipole moments of up to 1 D, while Linnett SIC dipole moments are in better agreement with experimental values. We suggest using the dipole moment as a diagnostic of symmetry breaking in SIC and monitoring it in all SIC calculations. We show that Linnett structures can often be seen as superpositions of Lewis structures and propose Linnett structures as a simple way to describe aromatic systems in SIC with reduced symmetry breaking. The role of hovering FODs is also briefly discussed.

Self-interaction-corrected Kohn-Sham effective potentials using the density-consistent effective potential method

Density functional theory (DFT) and beyond-DFT methods are often used in combination with photoelectron spectroscopy to obtain physical insights into the electronic structure of molecules and solids. The Kohn-Sham eigenvalues are not electron removal energies except for the highest occupied orbital. The eigenvalues of the highest occupied molecular orbitals often underestimate the electron removal or ionization energies due to the self-interaction (SI) errors in approximate density functionals. In this work, we adapt and implement the density-consistent effective potential method of Kohut, Ryabinkin, and Staroverov [J. Chem. Phys. 140, 18A535 (2014)] to obtain SI-corrected local effective potentials from the SI-corrected Fermi-Löwdin orbitals and density in the Fermi-Löwdin orbital self-interaction correction scheme. The implementation is used to obtain the density of states (photoelectron spectra) and HOMO-LUMO gaps for a set of molecules and polyacenes. Good agreement with experimental values is obtained compared to a range of SI uncorrected density functional approximations.

Electronic structure of mononuclear Cu-based molecule from density-functional theory with self-interaction correction

We investigate the electronic structure of a planar mononuclear Cu-based molecule [Cu(C₆H₄S₂)₂]^z in two oxidation states (z = -2, -1) using density-functional theory (DFT) with Fermi-Löwdin orbital (FLO) self-interaction correction (SIC). The dianionic Cu-based molecule was proposed to be a promising qubit candidate. Self-interaction error within approximate DFT functionals renders severe delocalization of electron and spin densities arising from 3d orbitals. The FLO-SIC method relies on optimization of Fermi-Löwdin orbital descriptors (FODs) with which localized occupied orbitals are constructed to create SIC potentials. Starting with many initial sets of FODs, we employ a frozen-density loop algorithm within the FLO-SIC method to study the Cu-based molecule. We find that the electronic structure of the molecule remains unchanged despite somewhat different final FOD configurations. In the dianionic state (spin S = 1/2), FLO-SIC spin density originates from the Cu d and S p orbitals with an approximate ratio of 2:1, in quantitative agreement with multireference calculations, while in the case of SIC-free DFT, the orbital ratio is reversed. Overall, FLO-SIC lowers the energies of the occupied orbitals and, in particular, the 3d orbitals unhybridized with the ligands significantly, which substantially increases the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) compared to SIC-free DFT results. The FLO-SIC HOMO-LUMO gap of the dianionic state is larger than that of the monoanionic state, which is consistent with experiment. Our results suggest a positive outlook of the FLO-SIC method in the description of magnetic exchange coupling within 3d-element-based systems.

Describing adsorption of benzene, thiophene, and xenon on coinage metals by using the Zaremba-Kohn theory-based model

Semilocal (SL) density functional approximations (DFAs) are widely applied but have limitations due to their inability to incorporate long-range van der Waals (vdW) interaction. Non-local functionals (vdW-DF, VV10, and rVV10) or empirical methods (DFT+D, DFT+vdW, and DFT+MBD) are used with SL-DFAs to account for such missing interaction. The physisorption of a molecule on the surface of the coinage metals (Cu, Ag, and Au) is a typical example of systems where vdW interaction is significant. However, it is difficult to find a general method that reasonably describes both adsorption energy and geometry of even the simple prototypes of cyclic and heterocyclic aromatic molecules such as benzene (C₆H₆) and thiophene (C₄H₄S), respectively, with reasonable accuracy. In this work, we present an alternative scheme based on Zaremba-Kohn theory, called DFT+vdW-dZK. We show that unlike other popular methods, DFT+vdW-dZK and particularly SCAN+vdW-dZK give an accurate description of the physisorption of a rare-gas atom (xenon) and two small albeit diverse prototype organic molecules on the (111) surfaces of the coinage metals.