Revisiting the foundations of the quantum theory of atoms in molecules: Some open problems

Abstract

In a series of papers in the last 10 years, various aspects of the mathematical foundations of the quantum theory of atoms in molecules have been considered by this author and his coworkers in some details. Although these considerations answered part of the questions raised by some critics on the mathematical foundations of the quantum theory of atoms in molecules, however, new mathematical problems also emerged during these studies that were reviewed elsewhere [Sh. Shahbazian Int. J. Quantum Chem. 2011, 111, 4497.]. Beyond mathematical subtleties of the formalism that were the original motivation for initial exchanges and disputes, the questions raised by critics had a constructive effect and prompted the author to propose a novel extension of the theory, now called the multi-component quantum theory of atoms in molecules [M. Goli, Sh. Shahbazian Theor. Chem. Acc. 2013, 132, 1365.]. Taking this background into account, in this paper a new set of open problems is put forward that the author believes proper answers to these questions, may open new doors for future theoretical developments of the quantum theory of atoms in molecules. Accordingly, rather than emphasizing on the rigorous mathematical formulation, the practical motivations behind proposing these questions are discussed in detail and the relevant literature are reviewed while when possible, evidence and routes to answers are also provided. The author hopes that proposing these open questions as a compact package may motivate more mathematically oriented people to participate in future developments of the quantum theory of atoms in molecules and its multi-component version. K E Y W O R D S holographic principle, quantum theory of atoms in molecules, subsystem quantum mechanics, topological atom, virial partitioning

Electrostatic Potential Topology for Probing Molecular Structure, Bonding and Reactivity

“…Non-nuclear maxima have been noted especially in metals, semiconductors and at the positions of defects in crystals. The universal bond path criterion to determine whether two atoms are bonded has been a matter of detailed scrutiny [ 17 , 18 , 19 , 20 , 21 ]. However, Bader [ 6 , 22 ] underlined that bond paths, being a measurable property of the system, should be used as a topological proof of the bonding of atoms but not be taken as the presence of a chemical bond.…”

New charge-transfer complexes of 1,2,5-chalcogenadiazoles with tetrathiafulvalenes

“…They are lower than E b of 102–328 kJ mol −1 in the anionic complexes of 7 and 8 featuring E⋯X − (E = Se, Te; X = PhS − , F − , I − ) chalcogen bonding. 21,80,99,100 The QTAIM 101,102 analysis reveals bond critical points 103 (BCPs) between D and A moieties in all complexes (Fig. 5) characterized by low values of electron density ρ b and its Laplacian ∇ 2 ρ b (Table 2).…”

Tuning Molecular Electron Affinities against Atomic Electronegativities by Spatial Expansion of a π‐System

“…The formation of [ E / R ]⋅ − is ultimate manifestation of the EAA of E / R , and [ E / R ]⋅ − worth in‐depth consideration. DFT‐calculated Mulliken [44] and QTAIM [45,46] distributions of atomic charges and spin densities in [ E / R ]⋅ − confirm that a whole molecule participates in charge/spin delocalization despite Mulliken and QTAIM patterns are quite different (ESI) [47] . The QTAIM and ELI‐D [48,49] analyses disclose important stereoelectronic changes on going from E / R to [ E / R ]⋅ − (Figure 2; ESI).…”