Revitalizing Spin Natural Orbital Analysis: Electronic Structures of Mixed‐Valence Compounds, Singlet Biradicals, and Antiferromagnetically Coupled Systems

Abstract

Chemical systems with open-shell electronic structure have been gaining attention these days. Their potential applications in firstrow transition metal catalysis, molecular wires, photovoltaics and other potential applications have urged the adoption of a simple analysis tool to better understand their open-shell electronic structures, especially the role played by the unpaired electrons. Despite its lack of popularity, spin natural orbital (SNO) analysis is a tool we found to well-suit this purpose. We have therefore re-examined how the SNO could help us analyze some interesting open-shell systems, including mixed-valence compounds, singlet biradicals, and antiferromagnetically coupled systems. We found that some interesting patterns emerge from SNO analysis, especially those associated with exchange interaction.The SNO analysis, the main method we wish to discuss in this article, approaches the "correspondence" problem from a different angle. Although at the first glance the definition does not suggest a correspondence relationship, we will present its intimate connection with the COT and why it will always give such correspondence in a single-determinant calculation.

Principal interacting spin orbital: understanding the fragment interactions in open-shell systems

“…VCl4 is a simple molecule with one unpaired electron on the vanadium center. From our chemical intuition, the unpaired electron is localized on the vanadium (a fact that can be easily verified from the examination of spin density [4] ) and would have minimal effect on V-Cl bond. If we examine a V-Cl bond by PISO analysis, considering one Cl as fragment A and the remaining VCl3 as fragment B, we can see three significant interactions for both alpha and beta electrons Specifically, we found one sigma-type and two pi-type interactions as the top 3 PISO pairs (Figure 5).…”

“…To make things more complicated, the role of unpaired electron on the interactions of different chemical fragments is often hard to analyze, but they do play a key part in catalytic reactions. Even though we can often identify "spin polarization" in many transition metal systems, [4] how/whether these polarizations affect the interaction between fragments are still not well studied, and handy tools for analyzing such chemical interactions involving unpaired electron are quite limited. The fact that electrons of different spin can behave differently in a chemical system causes quite a hassle because different patterns may emerge.…”

Remote Bonding in Clusters [Pd3Ge18R6]2–: Modular Bonding Model for Large Clusters via Principal Interacting Orbital Analysis

“…31 Spin natural orbitals (SNOs) are calculated via in-house code. 44 All orbital plots have an isolvalue of 0.05 unless particularly specified. To verify the relativistic effect does not significantly affect calculation results, we have also performed single-point calculations incorporating DKH2 Hamiltonian 45,46 on the optimized structures of different isomers of cluster 1′.…”

“…Natural population analysis (NPA) is performed by NBO6.0 software. , Principal interacting orbital (PIO) analysis is carried out using the publicly available code on GitHub . Spin natural orbitals (SNOs) are calculated via in-house code . All orbital plots have an isolvalue of 0.05 unless particularly specified.…”

Hyperfine-Coupling Tensors from Projected Hartree–Fock Theory

“…The very pronounced overestimation of A iso ( 17 O) by SUHF can be attributed to excessive spin polarization. This issue is analyzed in more detail in section 5 of the Supporting Information (there, following ref , we employ the sum of the total spin-occupation numbers as a measure of spin polarization). It is worth noting that SUHF (and post-SUHF) results for isotropic HFCs in BO, CO + , and CN were reported in ref .…”