The Separability Problem in Molecular Quantum Systems: Information‐Theoretic Framework for Atoms in Molecules

• Published in: Chemphyschem Vol. 25; no. 14; pp. e202400030 - n/a
• Main Authors: Esquivel, Rodolfo O., Carrera, Edmundo
• Format: Journal Article
• Language: English
• Published: Germany Wiley Subscription Services, Inc 15.07.2024
• Subjects: Atoms in Molecules; Constituents; Crystallography; Euclidean geometry; Euclidean space; Fisher entropy; Fisher information; Hilbert space; Information Theory; Molecular structure; Partitioning; QTAIM; Quantum Information; Relative entropy; Rigid structures; Stockholder partition; Topology; Wave functions; Quantum Information; Information Theory; Relative entropy; Fisher entropy; Atoms in Molecules; Stockholder partition; QTAIM
• ISSN: 1439-4235; 1439-7641; 1439-7641
• DOI: 10.1002/cphc.202400030

Even though molecules are fundamentally quantum entities, the concept of a molecule retains certain classical attributes concerning its constituents. This includes the empirical separability of a molecule into its three‐dimensional, rigid structure in Euclidean space, a framework often obtained through experimental methods like X‐Ray crystallography. In this work, we delve into the mathematical implications of partitioning a molecule into its constituent parts using the widely recognized Atoms‐In‐Molecules (AIM) schemes, aiming to establish their validity within the framework of Information Theory concepts. We have uncovered information‐theoretical justifications for employing some of the most prevalent AIM schemes in the field of Chemistry, including Hirshfeld (stockholder partitioning), Bader's (topological dissection), and the quantum approach (Hilbert's space definition). In the first approach we have applied the generalized principle of minimum relative entropy derived from the Sharma‐Mittal two‐parameter functional, avoiding the need for an arbitrary selection of reference promolecular atoms. Within the ambit of topological‐information partitioning, we have demonstrated that the Fisher information of Bader's atoms conform to a comprehensive theory based on the Principle of Extreme Physical Information avoiding the need of employing the Schwinger's principle, which has been proven to be problematic. For the quantum approach we have presented information‐theoretic justifications for conducting Löwdin symmetric transformations on the density matrix to form atomic Hilbert spaces generating orthonormal atomic orbitals with maximum occupancy for a given wavefunction. We explore the mathematical underpinnings of partitioning a molecule into its constituent atoms through the Atoms‐in‐Molecules (AIM) approach, validating its applicability through concepts from Information Theory. We present information‐theoretic justifications for employing some of the most widely utilized AIM partitioning schemes in chemistry, such as the disjoint electron density partitioning (Hirshfeld), the fuzzy domains (Bader's basins) and the density matrix partitioning (Hilbert space).