Mathematical aspects of mean-field theories

Theoretical bases of continuum models including their mathematical formulation and numerical implementation have already been discussed in the previous chapter of this book. We have therefore restricted our review to the environment effects on the NMR observables, without going into the theory of continuum models. This contribution is divided into five sections. After the Introduction, the definitions of the NMR parameters are recalled in the second section. The third section is focused on methodological aspects of the calculation of the NMR parameters in continuum models. The fourth section reviews calculations of the solvent effects on the nuclear magnetic shielding constants and spin-spin coupling constants by means of continuum models, and the final section presents a survey on the perspectives of this field. 

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