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

Abstract

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.