Ab initio and DFT studies of the spin–orbit and spin–spin contributions to the zero-field splitting tensors of triplet nitrenes with aryl scaffolds

Abstract

Spin–orbit and spin–spin contributions to the zero-field splitting (ZFS) tensors (D tensors) of spin-triplet phenyl-, naphthyl-, and anthryl-nitrenes in their ground state are investigated by quantum chemical calculations, focusing on the effects of the ring size and substituted position of nitrene on the D tensor. A hybrid CASSCF/MRMP2 approach to the spin–orbit term of the D tensor (D^SO tensor), which was recently proposed by us, has shown that the spin–orbit contribution to the entire D value, termed the ZFS parameter or fine-structure constant, is about 10% in all the arylnitrenes under study and less depends on the size and connectivity of the aryl groups. Order of the absolute values for D^SO can be explained by the perturbation on the energy level and spatial distributions of π-SOMO through the orbital interaction between SOMO of the nitrene moiety and frontier orbitals of the aryl scaffolds. Spin–spin contribution to the D tensor (D^SS tensor) has been calculated in terms of the McWeeny–Mizuno equation with the DFT/EPR-II spin densities. The D^SS value calculated with the RO-B3LYP spin density agrees well with the D(Exptl) − D^SO reference value in phenylnitrene, but agreement with the reference value gradually becomes worse as the D value decreases. Exchange–correlation functional dependence on the D^SS tensor has been explored with standard 23 exchange–correlation functionals in both RO- and U-DFT methodologies, and the RO-HCTH/407 method gives the best agreement with the D(Exptl) − D^SO reference value. Significant exchange–correlation functional dependence is observed in spin-delocalized systems such as 9-anthrylnitrene (6). By employing the hybrid CASSCF/MRMP2 approach and the McWeeny–Mizuno equation combined with the RO-HCTH/407/EPR-II//U-HCTH/407/6-31G* spin densities for D^SO and D^SS, respectively, a quantitative agreement with the experiment is achieved with errors less than 10% in all the arylnitrenes under study. Guidelines to the putative approaches to D^SS tensor calculations are given.