2016/03/24 by Michelle Fritz, Marivi Fernandez-Serra, Marivi Fernández-Serra +2 · 1 citation
Materials Science · Physics and Astronomy · #Advanced Chemical Physics Studies #Bayes' theorem #Density functional theory #Energy functional #Hybrid functional #Liquid water #Machine Learning in Materials Science #Parameter space #Projection (relational algebra) #Space (punctuation) #Spectroscopy and Quantum Chemical Studies #Variety (cybernetics) #cond-mat.other #physics.chem-ph #physics.comp-ph
paper · pdf · doi:10.1063/1.4953081
10 pages, 10 figures
arxiv created 2016/03/24 · openalex publication_date 2016/06/09 · openalex created_date 2016/06/24 · arxiv updated 2016/06/29 · openalex updated_date 2026/08/05
We describe a method, that we call data projection onto parameter space (DPPS), to optimize an energy functional of the electron density, so that it reproduces a dataset of experimental magnitudes. Our scheme, based on Bayes theorem, constrains the optimized functional not to depart unphysically from existing ab initio functionals. The resulting functional maximizes the probability of being the "correct" parameterization of a given functional form, in the sense of Bayes theory. The application of DPPS to water sheds new light on why density functional theory has performed rather poorly for liquid water, on what improvements are needed, and on the intrinsic limitations of the generalized gradient approximation to electron exchange and correlation. Finally, we present tests of our water-optimized functional, that we call vdW-DF-w, showing that it performs very well for a variety of condensed water systems.