Delving into theoretical and computational considerations for accurate calculation of chemical shifts in paramagnetic transition metal systems using quantum chemical methods

Abstract

The chemical shielding tensor for a paramagnetic system has been derived from the macroscopically observed magnetization using the perturbation theory. An approach to calculate the paramagnetic chemical shifts in transition metal systems based on the spin-only magnetic susceptibility directly evaluated from the ab initio Hilbert space of the electronic Zeeman Hamiltonian has been discussed. Computationally, several advantages are associated with this approach: (a) it includes the state-specific paramagnetic Curie (first-order) and Van Vleck (second-order) contributions of the paramagnetic ion to the paramagnetic chemical shifts; (b) thus it avoids the system-specific modeling and evaluating effectively in terms of the electron paramagnetic resonance (EPR) spin Hamiltonian parameters of the magnetic moment of the paramagnetic ion formulated previously; (c) it can be utilized both in the point-dipole (PD) approximation (in the long-range) and with the quantum chemical (QC) method based the hyperfine tensors (in the short-range). Additionally, we have examined the predictive performance of various density functional theory (DFT) functionals of different families and commonly used core-augmented basis sets for nuclear magnetic resonance (NMR) chemical shifts. A selection of transition metal ion complexes with and without first-order orbital contributions, namely the [M(AcPyOx)₃(BPh)]⁺ complexes of M = Mn²⁺, Ni²⁺ and Co²⁺ ions and CoTp₂ complex and their reported NMR chemical shifts are studied from QC methods for illustration.