Electronic Force Density Fields: Insights into Partial Bonds, Transition States, and Chemical Structure Evolution

This paper presents the quantum-topological binding approach, in which the electrostatic and total static force density fields, <b>F</b>_es(<b>r</b>) and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>, together with the electron density gradient field ∇ρ(<b>r</b>), are simultaneously analyzed to elucidate the chemical structure of transition states and the nature of interatomic interactions for semibroken semiformed partial chemical bonds. The approach attributes the discrepancies between the force fields <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> and <b>F</b>_es(<b>r</b>) to the nonclassical electron-electron interaction effects. The internuclear gap between the zero-flux boundaries of <b>F</b>_es(<b>r</b>) and ∇ρ(<b>r</b>) indicates the interatomic charge transfer phenomenon (ICT) that occurs upon the formation of a system from free atoms. Concomitantly, the mismatch of the zero-flux surfaces defined in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>-</mml:mo><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> and ∇ρ(<b>r</b>) can be interpreted as a phenomenon of the electron-transfer-induced quantum chemical response (QCR), which originates from the electron exchange correlation. Our study permits the assertion of parallels between partial bonds and noncovalent interactions, as both typically exhibit incomplete QCRs, indicating the partial electron sharing of the transferred density. The changes in atomic and pseudoatomic charges are employed to describe the evolution of the chemical structure upon the substitution reaction. It is observed that the acquired difference in the actual atomic electronegativity causes polarization upon the heterolytic breaking of virtually nonpolar bonds. It is further proposed that the proximity of closely related stationary states along the reaction path on a potential energy hypersurface implies their similarity in the manifestation of the ICT and sympathetic QCR. Furthermore, the involvement of an electron pair in a partial bond facilitates its delocalization through the attraction by the static forces <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> and <b>F</b>_es(<b>r</b>) to a neighboring nucleus and through the smearing by the Pauli kinetic force <b>F</b>_P(<b>r</b>).