  In this study, we analyze various Iterative Stockholder Analysis (ISA)
methods for molecular density partitioning, focusing on the numerical
performance of the recently proposed Linear approximation of Iterative
Stockholder Analysis model (LISA) [J. Chem. Phys. 156, 164107 (2022)]. We first
provide a systematic derivation of various iterative solvers to find the unique
LISA solution. In a subsequent systematic numerical study, we evaluate their
performance on 48 organic and inorganic, neutral and charged molecules and also
compare LISA to two other well-known ISA variants: the Gaussian Iterative
Stockholder Analysis (GISA) and Minimum Basis Iterative Stockholder analysis
(MBIS). The study reveals that LISA-family methods can offer a numerically more
efficient approach with better accuracy compared to the two comparative
methods. Moreover, the well-known issue with the MBIS method, where atomic
charges obtained for negatively charged molecules are anomalously negative, is
not observed in LISA-family methods. Despite the fact that LISA occasionally
exhibits elevated entropy as a consequence of the absence of more diffuse basis
functions, this issue can be readily mitigated by incorporating additional or
integrating supplementary basis functions within the LISA framework. This
research provides the foundation for future studies on the efficiency and
chemical accuracy of molecular density partitioning schemes.
