Sublinear scaling second-order polarization propagator approximation (SOPPA) for the calculation of indirect spin-spin coupling constants

Indirect spin–spin coupling constants (SSCCs) are fundamental parameters in nuclear magnetic resonance (NMR) spectroscopy, providing critical insights into molecular structure and electronic environments. Although high-accuracy SSCC simulation methods, such as the second-order polarization propagator approximation (SOPPA), offer superior accuracy compared to density functional theory (DFT), their application to large molecular systems has been hindered by unfavorable computational scaling. In this work, we introduce an 𝒪  (1) scaling algorithm for SSCC calculations at the SOPPA level based on localized molecular orbitals. By leveraging the spatial decay of SSCC, our approach achieves constant computational cost with increasing system size. With the default settings, the 𝒪 (1) SOPPA method achieves 99.9% accuracy in reproducing canonical results, enabling efficient computations for systems involving over 3000 basis functions, such as large peptides and host–guest complexes. This advancement extends high-accuracy SSCC predictions to large-scale biological and chemical systems.