Convergence of Electronic Structure with the Size of the QM Region: Example of QM/MM NMR Shieldings

The influence of the chemical environment on NMR shifts of a central molecular region is studied for several biomolecular and supramolecular systems. To investigate the long-range effects, we systematically increase the QM region until the changes of the NMR shielding tensor are negligible for the considered nuclei; that is, convergence with the selected QM size is reached. To reach size convergence, QM regions with up to about 1500 atoms and 15 000 basis functions are treated by our density matrix-based linear-scaling coupled perturbed self-consistent field methods. The results also provide insights into the locality and convergence of the electronic structure. Furthermore, we demonstrate to what extent the inclusion of the chemical environment as partial point charges within a hybrid QM/MM approach improves the convergence behavior. In addition, some benchmark data on NMR accuracies are provided using various ab initio methods.