Computing Paramagnetic ¹³C NMR Chemical Shifts of Cobalt(II) Porphyrins with the eXtended ONIOM Method

Nuclear magnetic resonance (NMR) spectroscopy is a powerful tool for characterizing the structure and electronic properties of paramagnetic coordination compounds. However, accurate computation of paramagnetic NMR (pNMR) chemical shifts for large systems remains a major challenge due to the prohibitive cost of full first-principles calculations. Herein, we extend the eXtended ONIOM (XO) method to paramagnetic systems and develop an XO-pNMR approach for the efficient and precise calculation of ¹³C pNMR chemical shifts in large paramagnetic molecules. We validate the XO-pNMR method by investigating a series of cobalt(II) porphyrins, including cobalt(II) tetraphenylporphyrin (CoTPP) and its substituted derivatives, all of which possess a single unpaired electron. Benchmark calculations against experimental ¹³C chemical shifts at 308 K reveal that the CAM-B3LYP functional yields the closest agreement with experimental data in full-system calculations, whereas the PBE0-¹/₃ functional exhibits optimal performance in XO-pNMR calculations─achieving a mean absolute deviation of only 0.3 ppm relative to full calculations and demonstrating robust wave function stability that outperforms alternative functionals. Application of XO-pNMR to substituted Co(II) porphyrins further demonstrates that the method reliably captures substituent-induced variations in ¹³C chemical shifts, matching the predictive accuracy of full calculations. Collectively, our results establish XO-pNMR with the PBE0-¹/₃ functional as a cost-effective and reliable approach for calculating pNMR chemical shifts in large paramagnetic molecules featuring a single paramagnetic center with one unpaired electron.