Four-component relativistic density functional theory with the polarisable continuum model: application to EPR parameters and paramagnetic NMR shifts

Abstract

The description of chemical phenomena in solution is as challenging as it is im- portant for the accurate calculation of molecular properties. Here, we present the implementation of the polarizable continuum model (PCM) in the four-component Dirac–Kohn–Sham density functional theory framework, o ↵ ering a cost-e ↵ ective way to concurrently model solvent and relativistic e ↵ ects. The implementation is based on the matrix representation of the Dirac–Coulomb Hamiltonian in the basis of restricted kinetically balanced Gaussian-type functions, exploiting a non-collinear Kramers unrestricted formalism implemented in the program ReSpect ,andthein- tegral equation formalism of the PCM (IEF-PCM) available through the standalone library PCMSolver . Calculations of EPR parameters ( g -tensors and hyperfine cou- pling A -tensors), as well as of the temperature-dependent contribution to paramag- netic NMR (pNMR) shifts, are presented to validate the model and to demonstrate the importance of taking both relativistic and solvent e ↵ ects into account for mag- netic properties. As shown for selected Ru and Os complexes, the solvent shifts may amount to as much as 25% of the gas-phase values for g -tensor components and even more for pNMR shifts in some extreme cases.