Comparative Analysis of Nickel–Phosphine Complexes with Cumulated Double Bond Ligands: Structural Insights and Electronic Interactions via ETS-NOCV and QTAIM Approaches

This study presents a comprehensive analysis of nickel–phosphine complexes, specifically Ni(PH₃)₂(OCCH₂), Ni(PH₃)₂(H₂CCO), Ni(PH₃)₂(H₂CCCH₂), Ni(PH₃)₂(NNCH₂), and Ni(PH₃)₂(<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>η</mi><mn>1</mn></msup></semantics></math></inline-formula>-H₂CNN). Utilizing ETS-NOCV analysis, we explored orbital energy decomposition and the Hirshfeld charges of the ligands, providing insights into the electronic structures and donor–acceptor interactions within these complexes. The interactions in the ketene and allene complexes exhibit similar deformation densities and NOCV orbital shapes to those calculated for Ni(PH₃)₂(NNCH₂), indicating consistent interaction characteristics across these complexes. The total interaction energy for all <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>η</mi><mn>2</mn></msup></semantics></math></inline-formula> complexes is observed to be over 60 kcal/mol, slightly exceeding that of the analogous carbon dioxide complex reported earlier. Furthermore, the study highlights the stronger back-donation as compared to donor interactions across all <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>η</mi><mn>2</mn></msup></semantics></math></inline-formula> complexes. This is further corroborated by Hirshfeld analysis, revealing the charge distribution dynamics within the ligand fragments. The research offers new perspectives on the electron distribution and interaction energies in nickel–phosphine complexes, contributing to a deeper understanding of their catalytic and reactive behaviors.