Multi-Center Decomposition of Molecular Densities: A Mathematical Perspective

Explore a mathematical perspective on multi-center decomposition of molecular densities in this 52-minute lecture. Delve into existing schemes for partitioning molecular density into atomic contributions, with a focus on Iterative Stockholder Atom (ISA) methods. Discover a unified mathematical framework for ISA methods and learn about a new scheme called L-ISA (linear approximation of ISA). Examine important mathematical properties of ISA and L-ISA minimization problems, including the revelation that ISA algorithms can be viewed as alternating minimization schemes. Investigate specific mathematical properties of ISA decomposition for diatomic systems. Compare different numerical schemes applied to various molecules, and evaluate the advantages and drawbacks of each approach.