In search of the appropriate theoretically justified mixing coefficient in parameter-free hybrid functionals for computing the NMR parameters

Abstract

The methods of density functional theory have long been known to play imperative roles in predicting the parameters of nuclear magnetic resonance (NMR) spectroscopy. In the present work, we propose the parameter-free hybrid functionals based on non-empirical exchange and correlation approximations of Perdew, Ernzerhof, and Burke (PBE) and Tao, Perdew, Staroverov, and Scuseria (TPSS) with a single theoretically justified coefficient controlling the amount of exact exchange for predicting the NMR parameters. The considered benchmark sets consist of experimental data on the spin–spin coupling constants (SSCCs) and chemical shifts in diverse sets of compounds containing phosphorus–hydrogen (P–H) and carbon–hydrogen (C–H) bonds. Our numerical results on P–H SSCCs suggest that a hybrid based on the PBE functional with the mixing coefficient of 1/3 has a significant improvement over other coefficients and previously reported high performance functionals. In the case of C–H SSCCs and calculations of chemical shifts based on linear regression analysis approach, generally good performances are revealed using all mixing coefficients. Moreover, comparing the results in greater detail, we find that the TPSS-based hybrids containing kinetic energy density and a correlation component free of self-interaction do not represent superiority with respect to hybrid functionals based on PBE. Overall, this study stimulates the use of theoretically justified mixing parameters for density functionals to achieve increased accuracy.