DFT-GIPAW ²⁷Al NMR Simulations for Intermetallics: Accuracy Issues and Magnetic Screening Mechanisms

Abstract

This study reports first-principles simulations of 27Al solid-state nuclear magnetic resonance (ssNMR) shifts (δiso exp) carried out for a set of seven Al-containing intermetallic compounds. With the aim of assessing accuracy issues in such calculations using the gauge-including projector augmented waves method, the referred set was sought to cover the wide range of experimental 27Al δiso exp shifts reported in the literature for this type of compound in a representative way (from about −200 to 1600 ppm). From a technical/computational perspective, the findings allowed the detection of critical sources of inaccuracy and they were addressed to different approximations inherent in the computational methods. Among those, it is possible to highlight the formulation of the exchange-correlation energy functional in density functional theory, which at least for the 27Al nuclide has proved to be more critical than the frozen-core approximation, especially in the case of weakly magnetic aluminides. From a practical point of view, particularly regarding a possible use of such simulations for a more efficient interpretation of experimental ssNMR spectra, key physical insights into the magnetic screening mechanisms underlying the 27Al δiso exp shifts are reported, in which theory supports that in addition to the contributions of closed orbitals, those coming from unpaired electronic spins arise from two main competing hyperfine interactions: the first one with local magnetic moments at specific sites, resulting in a shielding effect and even negative shifts, and the second mechanism in which large Knight shifts to downfield gradually dominate in those compounds having a rather metallic character.

Formation of the Sub-oxide Sc4Au2O1–x and the Drastically Negative 27Al NMR Shift in Sc2Al

“…DFT calculations on binary intermetallic aluminum compounds showed that, for example, in VAl 3 and TiAl, the orbital contribution gets surpassed by the spin contribution, leading to an overall negative NMR shift. In CuAl 2 , for example, both contributions point in the same direction . It is interesting to note that metal–organic Al­(I) compounds like Cp*Al (δ = −150 ppm), (C 5 H 2 (SiMe 3 ) 3 )Al (δ = −165 ppm), or (C 5 H 3 (SiMe 3 ) 2 )Al (δ = −168 ppm) reported by Schnöckel and co-workers also show negative chemical shifts .…”

“…In CuAl 2 , for example, both contributions point in the same direction. 118 It is interesting to note that metal−organic Al(I) compounds like Cp*Al (δ = −150 ppm), (C 5 H 2 (SiMe 3 ) 3 )Al (δ = −165 ppm), or (C 5 H 3 (SiMe 3 ) 2 )Al (δ = −168 ppm) reported by Schnockel and co-workers also show negative chemical shifts. 119 This extreme shielding was explained by significant π-bonding interactions between the Al and the ligand and therefore an energetic separation between the HOMO and LUMO.…”

GIPAW Pseudopotentials of d Elements for Solid-State NMR

“…Thus, in the framework of planewaves DFT, a gauge including the projected augmented wave [2,3] (GIPAW) method was introduced to calculate nuclear resonance magnetic (NMR) parameters in solids, avoiding all-electron calculations. In the GIPAW approach [4,5], a uniform magnetic field is applied using boundary conditions, a periodic magnetic field with a finite wavelength r G is the gauge origin and is subsequently extrapolated in the limit r G → 0 to compute the chemical shielding. This formalism was seen to manage the numerical instabilities associated with the summation of two divergent terms and with the generalized gradient approximation exchange-correlation functional (the method of choice for condensed-matter simulations) to perform accurate results [6][7][8][9][10][11][12][13][14][15].…”