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Hartree‐Fock difference approach to chemical valence: Three‐electron indices in UHF approximation
Author(s) -
Nalewajski Roman F.,
Mrozek Janusz
Publication year - 1996
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1996)57:3<377::aid-qua11>3.0.co;2-1
Subject(s) - ionic bonding , valence (chemistry) , chemistry , quadratic equation , valence electron , electron , atomic physics , covalent bond , density matrix , basis set , hartree–fock method , diagonal , quantum mechanics , physics , computational chemistry , ion , density functional theory , mathematics , geometry , quantum
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 O Q 2 ( Q = 1,0, −1) and O 2 (bond)H + systems. Preliminary results for B 2 H 6 are also given. © 1996 John Wiley & Sons, Inc.