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We study the effects of atomic vibrations on the solid-state chemicalshielding tensor using first principles density functional theory calculations.At the harmonic level, we use a Monte Carlo method and a perturbativeexpansion. The Monte Carlo method is accurate but computationally expensive,while the perturbative method is computationally more efficient, butapproximate. We find excellent agreement between the two methods for both theisotropic shift and the shielding anisotropy. The effects of zero-point quantummechanical nuclear motion are important up to relatively high temperatures: at500 K they still represent about half of the overall vibrational contribution.We also investigate the effects of anharmonic vibrations, finding that theircontribution to the zero-point correction to the chemical shielding tensor issmall. We exemplify these ideas using magnesium oxide and the molecularcrystals L-alanine and beta-aspartyl-L-alanine. We therefore propose as themethod of choice to incorporate the effects of temperature in solid statechemical shielding tensor calculations the perturbative expansion within theharmonic approximation. This approach is accurate and requires a computationaleffort that is about an order of magnitude smaller than that of dynamical orMonte Carlo approaches, so these effects might be routinely accounted for.

Temperature effects in first-principles solid state calculations of the chemical shielding tensor made simple