Evolution of nuclear magnetic shielding theory: from molecule in the gas phase to large molecular systems

The paper considers the current state of the theory and non-empirical methods of nuclear magnetic shielding constants calculation for molecules in the gas phase and in condensed media (solutions and solids), i.e. discrete supermolecular model, continuum models in different approaches, mixed models, methods of quantum mechanics/molecular mechanics combined with the methods of molecular dynamics. The results of calculations of magnetic shielding constants of phosphorous nuclei in trimethylbetaine molecules in acetone and dimethylsulfoxide solvents using QM/MM, ONIOM and molecular dynamics methods are given as an example.