Sublinear scaling method for indirect spin–spin coupling constant calculations at Hartree–Fock and density functional theory level

Abstract

The spin–spin coupling (SSC) phenomenon in nuclear magnetic resonance (NMR) spectroscopy is useful for determining the structures of unknown compounds. The SSC constants (SSCCs) can be obtained via quantum chemistry simulations. However, conventional analytical algorithms for simulating SSCCs are not applicable to large molecules due to their high computational costs. Building on recent advances in sublinear scaling (O(1)) methods, including the O(1) SSCC method developed by Luenser et al., J. Chem. Phys. 145, 124103 (2016), and the O(1) NMR shielding method by Yuan et al., J. Chem. Phys. 150, 154113 (2019), we have developed a sublinear scaling method to compute the SSCCs of molecules with hundreds of atoms. The accuracy of the O(1) method has been calibrated using the SSCCs of organic molecules, recovering ∼99.9% of the canonical one-bond SSCC results. In the present work, SSCCs in peptides, including those involving hydrogen bonds, have been computed and analyzed using the new O(1) method as well. The new O(1) method is able to address systems with more than ten thousand basis functions.