AxolotE: Automated Generation of Overlap Distribution Coefficients for Solid Harmonics GTFs in the McMurchie-Davidson Framework

Gaussian Type Functions (GTFs) are widely used as basis sets in electronic structure calculations. In many situations, it is advantageous to transform them into Real Solid Harmonic (RSH) GTFs, which reduces the size of the basis set and facilitates the interpretation of results. A variation of the McMurchie-Davidson method makes direct use of RSH GTFs; in this procedure, the coefficients defining the linear combination of functions must be computed. Here, we introduce the first open-source automated tool for generating code to evaluate these coefficients. The implementation, written in Mathematica and Python, is publicly available and designed to facilitate reproducibility and integration into existing electronic structure codes. Benchmark tests show that the choice of symbolic algebra engine affects both generated code and computational performance.