- © The Mineralogical Society Of America
NMR provides one of the most effective ways of identifying and quantifying the species present in a geochemical system (Engelhardt and Michel 1987; Kirkpatrick 1988). NMR shifts and other properties (such as quadrupole coupling constants for nuclei with spin > 1/2) often show simple systematic dependence upon local structural parameters. Features in the NMR spectra of disordered systems, such as glasses and solutions, can often be identified with those seen in well-ordered crystalline materials, a “fingerprint” approach. However, for unusual species no such fingerprinting is possible and it is very desirable to be able to directly calculate their NMR properties from first principles. Calculations on crystalline systems or models for them are also desirable, both to test the quantum mechanical method and to provide a more fundamental understanding of the trends in properties. Recently it has become possible to calculate NMR shieldings and related properties for species in condensed phase systems with an accuracy great enough to help in the assignment of the species and the determination of the geometric and electronic structure of the material. The basics of molecular quantum mechanics are covered in several texts, such as Hehre et al. (1986), Jensen (1999) Sherman (this volume), and Xiao (this volume). Davidson (1990) has provided an illuminating discussion of the successes of molecular quantum mechanics and its remaining limitations, in terms of size of molecules treatable and accuracy and interpretability of results. Pople’s Nobel prize address (Pople 1999) also provides an excellent description of the present status of molecular quantum chemistry.
BASIC THEORY OF NMR SHIELDING
The basic equations for the NMR shielding were developed by Ramsey (1950), using quantum mechanical sum-over-states perturbation theory. The total shielding, σ, defined by the equation:
(where Bα is a component of the magnetic field vector and σαβ is a component …