Through-space spin-spin coupling propagated by $$\pi $$-orbitals

Abstract Conventional analyses of indirect nuclear spin–spin coupling (SSC or J -coupling) in molecular systems typically focus on propagation through the framework of formal covalent bonds. However, in systems featuring functional groups in close proximity but separated by multiple covalent bonds, measurable through-space (TS) coupling can occur. Different mechanisms of TS coupling are commonly distinguished by the types of orbitals dominating them (e.g. lone-pair orbitals) or the type of non-covalent interaction keeping the coupling moieties in close proximity (e.g. hydrogen bonds). This article investigates the significance of the propagation of coupling specifically through $$\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> -orbitals. Using a novel approach for the evaluation of direct and indirect contributions of $$\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> -orbitals to SSC in the framework of non-hybrid density functional theory (DFT), we analyse the role of $$\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> ­-orbitals in TS coupling across small molecular gaps between two $$\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> -orbital containing moieties. Therein, we make special use of Komorovský’s version of the spin-spin coupling constant density to confirm the TS character, and of Malkina’s approach to the "indirect" $$\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> -orbital contribution to SSC via the transfer of spin polarisation ( $$\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> -TSP effect) to evaluate the $$\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> -character of the investigated SSCs. Our results demonstrate that measurable C–C TS SSC between $$\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> -carbons can occur. However, $$\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> -orbitals, beyond their structural role in enabling close proximity between the coupling moieties via $$\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> – $$\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> stacking interactions and CH $$\cdots \pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>⋯</mml:mo> <mml:mi>π</mml:mi> </mml:mrow> </mml:math> hydrogen bonds, appear to play only a minor role in the TS transfer of SSC between those moieties.