MADNESS (Multiresolution Adaptive Numerical Environment for Scientific Simulation) is a general purpose numerical framework for fast computation with guaranteed precision in many dimensions. Initially motivated by applications in chemistry (molecular electronic structure) it has been successfully applied in nuclear physics, molecular and atomic physics, and other fields. We review the basic elements of this computational approach and contrast it with the mainstream approach that employs atom-centered Gaussian basis sets. The errors and computational costs are also compared and, for the non-relativistic models initially tested, MADNESS proves both faster and more accurate. Finally, we discuss the initial application of this approach to both quasi-relativistic (Douglass-Kroll) and relativisitic (Dirac-Fock-Coulomb) approaches for which it provides the first fully-numerical results for general polyatomic systems.

Eliminating basis-set incompleteness error in relativistic chemical computations

255th National Meeting (2018)

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