Expansion of pair and multibody interactions in a truncated compact basis
|Date/Time:||Thursday, 10 Apr 2014 from 4:10 pm to 5:00 pm|
|Location:||A401 Zaffarano Hall|
We present a generic mathematical machinery for dealing with basis expansions of physical data. A physical potential can be expanded in one of many possible basis sets. A complete basis allows to precisely reproduce the expanded potential, hence all complete basis expansions are equivalent. However, a complete basis is typically an infinite sum, which becomes practical only after truncation. We define compactness and local completeness of a truncated basis, and generalize these concepts for a basis including multibody interactions. We discuss the truncation errors and their minimization techniques. We present the optimal truncation algorithm for minimizing predictive errors. As examples, we consider potentials that decay faster than 1/r, and their expansions in various truncated basis sets.