In search of density functional approximations for accurate evaluation of NMR shielding constants for main-group nuclei: Analytic derivatives, benchmarking, and insights from density-corrected density functional theory

Abstract

Predicting nuclear magnetic resonance (NMR) chemical shielding constants (CSCs) remains a great challenge. Being second-order response properties, NMR CSCs impose stringent demands on the accuracy and approximations of theoretical methods, as they are highly sensitive to subtle changes in the electronic structure. In this work, we develop and implement analytic derivatives for gauge-including atomic orbital shielding tensors within a density-corrected density functional theory (DC-DFT) Lagrangian/Z-vector framework. We benchmark the results against the comprehensive NS372 set of main-group CSCs and analyze the method errors in view of density-driven and functional-driven components within the DC-DFT framework, thereby rationalizing when and why substituting the electron density improves NMR shielding predictions. We find that the commonly employed HF-density strategy yields only modest and highly nuclear-dependent improvements in CSC accuracy. In contrast, combining MN15-L electron density with the SCAN0 energy functional can lead to a substantial error cancellation, reducing the overall mean absolute deviation to 5.02 ppm, approaching the accuracy of state-of-the-art double-hybrid functionals while avoiding the computational cost of perturbative correlation treatments. Our results establish DC-DFT as a practical and interpretable strategy for enhancing NMR shielding predictions with lower-rung functionals and offer clear guidance for selecting beneficial density/energy functional pairings for magnetic response properties.