To Be or Not to Be: Demystifying the 2nd-Quantized Picture of Complex Electronic Configuration Patterns in Chemistry with Natural Poly-Electron Population Analysis.

We provide a didactic introduction to 2nd-quantized representation of complex electron-hole (e/h) excitation patterns in general configuration interaction wave functions built from orthonormal local orbitals of natural atomic orbital or natural bond orbital (NBO) type. Such local excitation patterns of chemically oriented basis functions can be related to the resonance concepts of valence bond theory, and quantitative evaluation of the associated excitation probabilities then provides an alternative assessment of resonance "weighting" that may be compared with those of NBO-based natural resonance theory. We illustrate the usefulness of anticommutation relations in deriving Pauli-compliant expressions for allowed excitation patterns, showing how the exciton-like promotions φλ → φν (creating an e/h excitation with h in φλ and e in φν ) impose strict constraints on associated e/h-probabilities (requiring, e.g., that the e-probability for an electron "to be" or "not to be" in φν must be rigorously linked to the complementary h-probabilities in φλ ). Specific examples are presented of the quantum Boolean logic for four or six local spin-orbitals, with emphasis on Natural Poly-Electron Population Analysis (NPEPA) evaluation of VB-type covalent and ionic contributions in conventional 2-center bonding, resonance weightings in 3-center hydrogen bonding, and general characteristics of higher-order m-center bonding motifs for m > 3. Numerical results are presented for methylamine, acrolein, and water dimer to illustrate current NPEPA implementation in the NBO program. © 2019 Wiley Periodicals, Inc.

Study of Electron Delocalization in 1,2-, 1,3-, and 1,4-Azaborines Based on the Canonical Molecular Orbital Contributions to the Induced Magnetic Field and Polyelectron Population Analysis.

The electron delocalization in 1,2-azaborine, 1,3-azaborine, and 1,4-azaborine is studied using canonical molecular orbital contributions to the induced magnetic field (CMO-IMF) method and polyelectron population analysis (PEPA). Contour maps of the out-of-plane component of the induced magnetic field (Bz(ind)) of the π system show that the three azaborines, in contrast with borazine, sustain much of benzene's π-aromatic character. Among them, 1,3-azaborine exhibits the strongest π delocalization, while 1,4-azaborine is the weakest. Contour maps of Bz(ind) for individual π orbitals reveal that the differentiation of the magnetic response among the three isomers originates from the π-HOMO orbitals, whose magnetic response is governed by rotational allowed transitions to unoccupied orbitals. The low symmetry of azaborines enables a paratropic response from HOMO to unoccupied orbitals excitations, with their magnitude depending on the shape of interacting orbitals. 1,3-Azaborine presents negligible paratropic contributions to Bz(ind) from HOMO to unoccupied orbitals transitions, where 1,2- and 1,4-azaborine present substantial paratropic contributions, which lead to reduced diatropic response. Natural bond orbital (NBO) analysis employing PEPA shows that only the 1,3-azaborine contains π-electron fully delocalized resonance structures.