Nuclear Magnetic Shielding Constants with the Polarizable Density Embedding Model

We extend the polarizable density embedding (PDE) model
to support
the calculation of nuclear magnetic resonance (NMR) shielding constants
using gauge-including atomic orbitals (GIAOs) within a density functional
theory (DFT) framework. The PDE model divides the total system into
fragments, describing some by quantum mechanics (QM) and the others
through an embedding model. The PDE model uses anisotropic polarizabilities,
inter-fragment two-electron Coulomb integrals, and a non-local repulsion
operator to emulate the QM effects. The terms involving Coulomb integrals
are straightforwardly extended with GIAOs. In contrast, we consider
two approaches to handle the gauge dependency of the non-local operator,
employing either simple symmetrization or a gauge transformation.
We find the latter approach to be most stable with respect to increasing
the basis set size of the QM region. We examine the accuracy of the
PDE model for calculating NMR shielding constants on several solutes
in a water solution. The performance is compared with the classical
polarizable embedding (PE) model in addition to supermolecular reference
calculations. Based on these systems, we address the basis set convergence
characteristics and the QM region size requirements. Furthermore,
we investigate the performance of the PDE model for a system with
significant electron spill-out. In many cases, we find that the PDE
model outperforms the PE model, especially regarding the accuracy
of nuclear shielding constants when using small QM region sizes and
in systems with significant electron spill-out.