Precisely and efficiently computing phonons via irreducible derivatives: characterizing soft modes*

Computing phonons from first-principles is typically considered a solved

problem, yet inadequacies in existing techniques continue to yield deficient

results in systems with sensitive phonons, like those with soft modes.

Here we circumvent this issue via the lone irreducible derivative (LID) and

bundled irreducible derivative (BID) approaches to computing phonons via finite

displacements, where the former optimizes precision and the latter, efficiency.

The strategy behind the irreducible approaches is to convert gains

in efficiency into enhanced accuracy. We illustrate our approach on two

prominent charge density wave systems, the shape memory alloy AuZn and the

vanadium based kagome metal KV₃Sb₅; in addition to metallic lithium.

LID is executed using energy and force derivatives, and practical guidelines

are developed. For BID, a bundled basis is derived guaranteeing minimal

propagation of error and maximal efficiency, and demonstrating that BID

faithfully reproduces the LID results. Comparing our resulting phonons in the

aforementioned crystals to the literature reveals nontrivial

inaccuracies in all cases. Our approaches' unbiased execution can be fully

automated, making it well suited for both niche systems of interest and big

data approaches.