Calculation of Magnetic Shielding Constants with meta-GGA Functionals Employing the Multipole-Accelerated Resolution of the Identity: Implementation and Assessment of Accuracy and Efficiency

We present a highly efficient implementation for density functional calculations of chemical shielding constants. It employs the multipole-accelerated resolution of the identity for the calculation of the Coulomb part, which complements the usage of low order scaling routines for the evaluation of the exchange-correlation part and the Hartree–Fock exchange part. Introduced errors for shifts of chemical shielding constants of H, C, F, and P are evaluated for respective test sets of molecules and are related to the accuracy of shifts obtained with hybrid and nonhybrid functionals of the generalized gradient approximation type as well as for meta-GGA functionals themselves. Efficiency is demonstrated for α-d-glucose chains with more than 2500 atoms on a single CPU as well as with an OpenMP parallelized version.