Hartree-Fock difference approach to chemical valence: Three-electron indices inUHF approximation

1996/02/05 by Roman F. Nalewajski, Janusz Mrozek · 53 citations
Chemistry · Materials Science · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Atomic physics #Basis set #Chemistry #Computational chemistry #Covalent bond #Crystallography and molecular interactions #Density functional theory #Density matrix #Diagonal #Electron #Geometry #Hartree–Fock method #Ion #Ionic bonding #Mathematics #Physics #Quadratic equation #Quantum mechanics #Thermal and Kinetic Analysis #Valence (chemistry) #Valence electron

paper · doi:10.1002/(sici)1097-461x(1996)57:3<377::aid-qua11>3.0.co;2-1

published in International Journal of Quantum Chemistry 57(3), 377-389 (Wiley)

openalex publication_date 1996/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/26

Abstract

The recently introduced set of quadratic ionic and covalent valence indices from changes in the pair-diagonal part of the molecular (Hartree-Fock) two-electron density matrix, ΔΓ(2)(a, b) (orthogonal atomic orbital [OAO] basis set), relative to separated atoms limit (SAL), is extended to cubic valence numbers; they are calculated from the corresponding changes in the three-electron density matrix, ΔΓ(3)(a,b,c). The two- and three-electron indices are given by the corresponding contributions to ΔΓ(2), and ΔΓ(3), which are quadratic and cubic in terms of relevant changes in the one-electron density matrix. The new valence measures are partitioned into one-, two-, and three-center contributions comprising purely ionic (covalent) and mixed ionic-covalent terms. For integral OAO occupations in the SAL, the sum of all three-electron contributions vanishes exactly in the UHF approximation; for fractional occupations, they give rise to a rather small correction to the overall two-electron valence index. The properties of cubic valence numbers are tested on a model three-orbital description of a symmetric (ABA), collinear transition state and on the OQ2 (Q = 1,0, −1) and O2(bond)H+ systems. Preliminary results for B2H6 are also given. © 1996 John Wiley & Sons, Inc.

Citations

• Modified valence indices from the two‐particle density matrix
• Charge, bond order and valence in the AB initio SCF theory
• Quantum mechanical valence study of a bond‐breaking–bond‐forming process in triatomic systems
• Covalent Bond Orders and Atomic Valence Indices in the Topological Theory of Atoms in Molecules

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• ETS-NOCV description of chemical bonding: from covalent bonds to non-covalent interactions. [europepmc]

Related

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• Two-electron valence indices from the Kohn-Sham orbitals
• Modified valence indices from the two‐particle density matrix
• Bond order and valence indices: A personal account
• Quantum mechanical valence study of a bond‐breaking–bond‐forming process in triatomic systems