A General Algorithm for Minimal Uncoupled Stress--Strain Calculations of Elastic Constant

Abstract

We have developed a general algorithm for constructing the minimum number of strain configurations required to extract second-order elastic constants from first-principles stress-strain calculations without algebraic coupling between the constants targeted for extraction. The method operates on the sparsity structure of the symmetry-reduced elastic stiffness matrix, represented by an auxiliary binary matrix, and generates admissible strain patterns algorithmically rather than prescribing separate strain sets for individual crystal symmetries. Each independent elastic constant is obtained from a single stress component, while additional stress relations generated by the same deformation provide internal consistency checks. Because the six-dimensional strain space contains only 2^6-1=63 non-empty strain patterns, the minimality of the resulting sets can be verified exactly for every elastic-symmetry type considered. The construction reproduces established high-efficiency strain sets in cases where they are minimal and yields improved sets for symmetry classes in which previously tabulated schemes require additional configurations. Because the formulation is based on stress-strain derivatives, it can also be readily extended to finite temperatures using consistently sampled ensemble-averaged thermodynamic stresses. Explicit strain sets are derived for all elastic-symmetry types spanning the 230 crystallographic space groups, and their accuracy and computational efficiency are benchmarked against established approaches.