Quantify the sources of large ZFS errors for Sc, Y, and La

Determine and quantify the sources of the large errors observed when predicting the zero-field splitting in the 2D ground term of Sc, Y, and La using the BP2-QDNEVPT2 and DKH2-QDNEVPT2 methods, explicitly assessing the contributions of high-order dynamic correlation effects (such as triple and higher excitations outside the active space) and their interplay with spin–orbit coupling, as suggested by the performance of variational X2C-MRCISD for Sc and La.

Background

In the transition-metal benchmark (Sc, Y, La; 2D ground term), the authors report that both BP2- and DKH2-QDNEVPT2 significantly deviate from experimental zero-field splittings, and that even variational X2C-MRCISD shows large errors for Sc and La. This points to unresolved methodological issues impacting accuracy.

While the authors hypothesize that high-order dynamic correlation effects beyond doubles (e.g., triples in non-active orbitals) and their interaction with spin–orbit coupling likely contribute, they explicitly state that they cannot quantify the source of these errors. A clear determination and quantification of these effects is needed to guide methodological improvements and benchmarking across these challenging systems.