A comparison of methods for the calculation of NMR chemical shifts

A theory (MPL) to compute the NMR chemical shifts in condensed matter syste ms using periodic boundary conditions was presented by F. Mauri, B. Pfromme r, and S. G. Louie [Phys. Rev. Lett. 77, 5300 (1996)]. The MPL method has b een implemented so far within a pseudopotential formulation in which the wa ve functions are expanded in plane waves. In this paper, we compare analyti cally the MPL approach within the density functional theory to existing met hods for the calculation of the chemical shifts such as GIAO (gauge-includi ng atomic orbitals), CSGT (continuous set of gauge transformations), and IG AIM (individual gauges for atoms in molecules). To this end we apply the MP L approach to molecules since the latter methods are conceived only for fin ite systems. We show theoretically the equivalence between a variant of the CSGT and the MPL method applied to finite systems. Moreover, we analyze nu merically the efficiency of the different methods when atomic orbital basis sets are employed, by comparing the basis-set convergence properties. We f ind that the CSGT and IGAIM approaches have the same convergence properties as GIAO, whereas their computational time is significantly smaller. In the MPL method, the contribution of the valence electrons to the chemical shif t converges rapidly with respect to the size of the basis set, whereas the convergence properties of the core contribution are poor. We improve the co nvergence by separating the core and the valence contributions in a gauge-i nvariant manner, by applying the MPL method only to the valence contributio n, and by treating the core contribution with IGAIM. The performances of th e resulting approach compare favorably with those of the other methods. Fin ally we find that the core contribution to the chemical shift is independen t of the chemical environment, in contrast to what is sometimes found in th e literature. In conclusion, our results indicate that, to compute the chem ical shifts in both molecules and solids, using atomic orbital basis sets, one could use the MPL method to evaluate the valence contribution and add t o it a rigid core contribution as obtained, for instance, from an atomic ca lculation. (C) 1999 American Institute of Physics. [S0021-9606(99)30129-X].