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

Abstract

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.

Delocalization error: The greatest outstanding challenge in density‐functional theory

“…This can be resolved by using localized orbitals, but there are many possible localization schemes and the magnitude of the SIC will depend on the particular one selected. Recent development work has focused on Fermi‐Löwdin orbitals (FLO), 139,156–158 which provide a convenient framework for general application of the SIC to chemical systems of any size 159–163 . Ongoing development has involved orbital‐dependent scaling, 150,164 as well as use of FLOSIC with the density‐consistent effective potential 165,166 or the Krieger‐Li‐Iafrate 167,168 approximation to the optimized effective potential.…”

“…Recent development work has focused on Fermi-Löwdin orbitals (FLO), 139,[156][157][158] which provide a convenient framework for general application of the SIC to chemical systems of any size. [159][160][161][162][163] Ongoing development has involved orbital-dependent scaling, 150,164 as well as use of FLOSIC with the densityconsistent effective potential 165,166 or the Krieger-Li-Iafrate 167,168 approximation to the optimized effective potential.…”

Characterizing Excited States of a Copper-Based Molecular Qubit Candidate with Correlated Electronic Structure Methods

“…The 3d−σ, and 3d−σ–π active spaces each fail to predict the experimentally expected spin density, predicting about 90% of the unpaired electron on the Cu center. A previous study has suggested a large range between about 50 and 70% of spin density on the metal; ,, however, it is clear that these two active spaces predict a nearly completely localized spin on the copper center.…”

“…Computational studies of these complexes and their analogs are rather numerous, especially when considering DFT results. − Metal dithiolates have long been studied as a paradigmatic case of ligand-noninnocent redox behavior, as well as consistent examples of strong metal–ligand covalency . In the context of the [Cu­(II)­(mnt)] 2 2– qubit candidate, the strong covalency has been linked to the relatively long vibrational relaxation times .…”

How Do Self-Interaction Errors Associated with Stretched Bonds Affect Barrier Height Predictions?

“…In a FLOSIC calculation, the FODs are optimized to produce FLOs corresponding to the minimum FLOSIC total energy. More details on obtaining FLOs can be found in previous publications , and in the work of Mishra et al…”