A bivariate view of Kohn-Sham iteration and the case for potential\n mixing

2018/07/16 by Paul E. Lammert, Lammert, Paul E.
Chemistry · Materials Science · Physics and Astronomy · #Advanced Chemical Physics Studies #Advanced Condensed Matter Physics #Advanced NMR Techniques and Applications #Crystal Structures and Properties #FOS: Physical sciences #Machine Learning in Materials Science #Materials Science (cond-mat.mtrl-sci)

paper · pdf · doi:10.48550/arxiv.1807.06125

openalex publication_date 2018/07/16 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28

Abstract

A bivariate perspective on Kohn-Sham density functional theory is proposed,\ntreating potential and density as simultaneous independent variables, and used\nto make fruitful connection between Lieb's rigorous foundational framework and\npractical Kohn-Sham computation. Support is found for potential-mixing schemes,\nbut not for more standard density-mixing. Under presumably-generic conditions,\ntotal energy can be lowered from one iteration to the next. Density, intrinsic\nand total energy are analytic functions of the noninteracting potential on the\nopen set of potentials having a single isolated ground spin-multiplet.\n

Related

• Kohn-Sham computation and the bivariate view of density functional theory
• Exact density-functional theory as parallel ensemble variational hierarchies: from Lieb's formulation to Kohn-Sham theory
• On the Kohn-Sham Approach to Time-Dependent Problems in a Density-Functional Framework
• Unconstrained Variational Determination of the Kohn-Sham Potential
• On the Analysis of the Discretized Kohn-Sham Density Functional Theory