Abstract
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 pointcan lead to artifactual dipole moments of up to 1D, 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.
Highlights
One of the simplest descriptions of chemistry is given by Lewis theory (LT) of chemical bonding.1 The main focus of LT is the octet rule, which states that the valence electrons of main group elements are arranged in four pairs that imitate the electron configuration of noble gas atoms.1 While LT is probably the best-known, most extensively taught, and most widely used theory of chemical bonding, there are several cases in which LT does not suffice for an accurate understanding of chemical bonding.2 For instance, as LT assumes that the electrons are always paired—thereby forming a closed-shell singlet state—LT is not able to describe molecules with non-singlet ground states, such as the oxygen molecule
As the Linnett’s double-quartet (LDQ) configuration can be thought of as a superposition of the two LT configurations, in which the spinup Fermi-orbital descriptors (FODs) are picked from one LT structure, while the spin-down FODs are picked from the other LT structure, the LDQ structure is expected to prefer a symmetric molecular geometry
We have shown that Fermi-orbital descriptors (FODs) and the corresponding Fermi–Löwdin orbitals (FLOs) can be used to guide selfinteraction corrected calculations toward the wanted type of solution, that is, the wanted type of local minimum
Summary
One of the simplest descriptions of chemistry is given by Lewis theory (LT) of chemical bonding. The main focus of LT is the octet rule, which states that the valence electrons of main group elements are arranged in four pairs that imitate the electron configuration of noble gas atoms. While LT is probably the best-known, most extensively taught, and most widely used theory of chemical bonding, there are several cases in which LT does not suffice for an accurate understanding of chemical bonding. For instance, as LT assumes that the electrons are always paired—thereby forming a closed-shell singlet state—LT is not able to describe molecules with non-singlet ground states, such as the oxygen molecule. As LT assumes that the electrons are always paired—thereby forming a closed-shell singlet state—LT is not able to describe molecules with non-singlet ground states, such as the oxygen molecule. This shortcoming of LT, the lack of electronic spin, is solved by Linnett’s double-quartet (LDQ) theory that explicitly includes the electronic spin in the formalism. The nearly forgotten LDQ replaces the octet of LT by scitation.org/journal/jcp two quartets—one quartet per spin channel— the name of the theory. Schwalbe et al. revived LDQ theory in the context of the Perdew–Zunger (PZ) self-interaction correction (SIC) to density functional theory (DFT)..
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