Bryan Sundahl

TL;DR: The features and capabilities of MADNESS are described and some current applications in chemistry and several areas of physics are discussed.

TL;DR: The MADNESS (multiresolution adaptive numerical environment for scientific simulation) as mentioned in this paper is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods with guaranteed precision that are based on multiresolution analysis and separated representations.

TL;DR: Overall data suggest that QD coverage density on the DWNTs varies, based upon the different ligand pendant groups used, and that the presence of a π-conjugated carbon framework within the ligands themselves coupled with the electron affinity of their pendants groups collectively play important roles in the resulting charge transfer from QDs to the underlying CNTs.

TL;DR: The new constructions proceed via least-squares projection onto smooth bases and provide substantially improved numerical properties as well as permitting direct construction of high-order derivative operators for smooth functions represented via discontinuous multiwavelet bases.

TL;DR: The approach uses an adaptive basis of multiwavelet functions to solve the full four-component Dirac-Coulomb equation to a user-specified accuracy and applicability to molecules is shown via ground state calculations of some simple molecules.