Origin of heteroatom substitution effects on hyperfine coupling in muoniated radicals: A path-integral molecular dynamics study

Muonium (Mu) represents a powerful probe of radical electronic structure owing to its hyperfine coupling constant (HFCC). In this study, we investigate the influence of heteroatom substitution on the HFCC of Mu through ab initio path integral molecular dynamics simulations on muoniated xanthene-9-thione (μ-XT) and thioxanthene-9-thione (μ-TXT). The simulations reproduce the experimental trend that μ-XT exhibits a larger HFCC than μ-TXT, highlighting the crucial influence of nuclear quantum effects on the local structure around Mu. The Mu-S bond exhibits nearly identical behavior in both molecules and, therefore, does not explain the observed difference in the HFCC. In contrast, the dihedral angle between the S-Mu bond and the molecular framework considerably affects the HFCC. In particular, when the S-Mu bond is oriented perpendicular to the molecular framework, the HFCC difference between μ-XT and μ-TXT is maximized. Natural bond orbital analyses reveal that oxygen substitution enhances electron delocalization across the π-system, thereby stabilizing the C1 p-orbital and intensifying the hyperconjugative interaction. Overall, the reduced HFCC in μ-TXT originates from diminished hyperconjugation caused by the weaker electronic delocalization associated with the longer C-S bond. These results provide fundamental insights into substituent effects on Mu-labeled radicals.