Determination of the error bar on ab initio calculated electric-field gradients

L.A. ERRICO; K. LEJAEGHERE; J. RUNCO; V. FERNÁNDEZ; J.J. MELO QUINTERO; G. N. DARRIBA; A.V GIL REBAZA; S.N. MISHRA; M. RENTERÍA; S. COTTENIER

Leuven

Conferencia; HYPERFINE 2016 - International Conference on Hyperfine Interactions and their Applications,; 2016

HFI & NQI Executive Committee

** Invited Plenary Talk **Density Functional Theory (DFT) is nowadays the most popular method to predict from first principles the properties of crystalline solids. Although DFT is an exact method in principle, practical implementations require approximations that limit the agreement between theory and experiment. For several decades, the lack of sufficient computing resources forced the community of DFT-users to besatisfied with only a hand-waving assessment of those error bars. In the bestcase, this led to "common knowledge" statements as, for instance: "It is well-known that the LDA- functional underestimate the equilibrium volume of crystals by afew percent". For more specific properties, such as the Electric-Field Gradient(EFG), the error bar information is essentially unknown. Only during the past few years, computing resources have come to the level that allows computing properties of benchmarks sets that are sufficiently large for obtaining statistically justified error bars. In the present work we deal with the error bar determination of ab initio predicted EFG tensors. When using computing EFG tensors for interpreting complex experimental data, it is obviously important to know how large the error bar on the computed values can be. So far, one usually resorts to the "10 % rule": the first digit to the computed EFG isprobably right, the second digit is unsure by 1 to 5 units. There is no formal justification for this "rule", it roughly captures the experience or feeling ofthe early researches in this field. In this work we present the results of DFT-based EFG calculations for different isotopes routinely used in experimental EFG studies, and for which a reliable nuclear quadrupole moment is known. For each isotope, we performed calculations in crystals hosts for which sufficiently accurate structural parameters and experimental EFG values are available in the literature (preferably at low temperature). An even distribution over metals and insulators was attempted, and EFG values should cover evenly the entire relevant window of values. Both the APW+lo method (WIEN2k code) and GIPAW method (Quantum Expresso code) were used. Based on these data, we will address the following questions: "how close to the experimental values can one expect a DFTY-predicted EFG tensor to be ?" (*accuracy* of DFT for EFG calculations) and "how wood is the agreement between EFG predictions by two different implementations of DFT ?" (*precision* of DFT codes for EFG calculations).