Virial inversion and density functionals

Jansen, S. ORCID: https://orcid.org/0000-0002-9611-0356, Kuna, T. ORCID: https://orcid.org/0000-0002-3933-5903 and Tsagkarogiannis, D. ORCID: https://orcid.org/0000-0001-5780-9095 (2023) Virial inversion and density functionals. Journal of Functional Analysis, 284 (1). 109731. ISSN 0022-1236 doi: 10.1016/j.jfa.2022.109731

Abstract/Summary

We prove a novel inversion theorem for functionals given as power series in infinite-dimensional spaces. This provides a rigorous framework to prove convergence of density functionals for inhomogeneous systems with applications in classical density function theory, liquid crystals, molecules with various shapes or other internal degrees of freedom. The key technical tool is the representation of the inverse via a fixed point equation and a combinatorial identity for trees, which allows us to obtain convergence estimates in situations where Banach inversion fails.