Nuclei-selected atomic-orbital response-theory formulation for the calculation of NMR shielding tensors using density-fitting

An atomic orbital density matrix based response formulation of the nuclei-selected approach of Beer, Kussmann, and Ochsenfeld [J. Chem. Phys. 134, 074102 (2011)] to calculate nuclear magnetic resonance (NMR) shielding tensors has been developed and implemented into LSDalton allowing for a simultaneous solution of the response equations, which significantly improves the performance. The response formulation to calculate nuclei-selected NMR shielding tensors can be used together with the density-fitting approximation that allows efficient calculation of Coulomb integrals. It is shown that using density-fitting does not lead to a significant loss in accuracy for both the nuclei-selected and the conventional ways to calculate NMR shielding constants and should thus be used for applications with LSDalton.