Effect of molecular size on the parity-non-conserving contributions to the nuclear magnetic resonance shielding constant

We present density-functional theory studies on the effects of molecular size on the parity-violating contribution to the nuclear magnetic shielding constant. We focus on models with different backbone and side chain lengths, as well as the details of geometry optimization for certain helical polysilylenes and investigate the parity-violating contribution to the shielding constant of the ²⁹Si nucleus of the backbone. Our calculations show that the molecular geometry has a large influence on the magnitude of the parity-violating shielding contribution, a result that is in line with the previous studies on much smaller molecules. In addition, we find convergence in the magnitude of the PV effect with respect to system size, when using geometries that preserve the helical Si backbone structure optimized for the largest of the present systems. This can be interpreted in terms of the non-size-extensive nature of the parity-violating operator influencing the leading-order effect on nuclear magnetic shielding, as opposed to the size-extensive interaction affecting the energy difference between enantiomers. Our molecules are truncated models of large polysilylene systems, for which a difference in the ²⁹Si chemical shift between enantiomers has been observed to be 0.06 ppm (Fujiki in Macromol Rapid Commun 22, 669–674, 2001). As expected based on earlier first principles studies of small molecules, we do not find support for the difference to be of the parity-violating origin. Instead, the predicted parity-violation-induced splitting of the ²⁹Si resonance is found to converge at values around 10^?8 ppm with increasingly large Si backbone.