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

TL;DR

This paper compares Monte Carlo and perturbative methods for including temperature effects in first-principles calculations of the chemical shielding tensor, finding the perturbative approach efficient and sufficiently accurate for routine use.

Contribution

It introduces a computationally efficient perturbative method within the harmonic approximation to incorporate temperature effects in solid-state chemical shielding tensor calculations.

Findings

Excellent agreement between Monte Carlo and perturbative methods.

Zero-point motion significantly affects shielding up to 500 K.

Anharmonic vibrations have a small impact on zero-point corrections.

Abstract

We study the effects of atomic vibrations on the solid-state chemical shielding tensor using first principles density functional theory calculations. At the harmonic level, we use a Monte Carlo method and a perturbative expansion. The Monte Carlo method is accurate but computationally expensive, while the perturbative method is computationally more efficient, but approximate. We find excellent agreement between the two methods for both the isotropic shift and the shielding anisotropy. The effects of zero-point quantum mechanical nuclear motion are important up to relatively high temperatures: at 500 K they still represent about half of the overall vibrational contribution. We also investigate the effects of anharmonic vibrations, finding that their contribution to the zero-point correction to the chemical shielding tensor is small. We exemplify these ideas using magnesium oxide and the molecular crystals L-alanine and beta-aspartyl-L-alanine. We therefore propose as the method of choice to incorporate the effects of temperature in solid state chemical shielding tensor calculations the perturbative expansion within the harmonic approximation. This approach is accurate and requires a computational effort that is about an order of magnitude smaller than that of dynamical or Monte Carlo approaches, so these effects might be routinely accounted for.