Quantum mechanical valence study of a bond‐breaking–bond‐forming process in triatomic systems

Abstract

The recently introduced set of the quadratic, two-electron covalent and ionic valence indices is used to investigate the bond-breaking-bond-forming (BB-BF) process in an atom exchange reaction between H2 and X (X = H, F-I) as well as in the 0 2 -H system. Valence changes accompanying selected charge reorganizations are examined within the three-orbital model and valence diagrams for symmetric transition states (TSS) are given. The UHF valence data for Liz0 and C02 and the H-H-X, 0-0-H, and 0-H-0 (ABC) TSS (collinear and angular) are reported and compared to valence data in the separated fragments limits (SFL), AB and BC. The overall valence, v ( A B C ) , and the total (ionic plus covalent) diatomic valences, and v~c, are used as measures of the overall bond-order in a concerted BE-BF reaction, to test the postulate of the bond-energy-bond-order (BEBO) model. In collinear TSS of H2X, 7 / = -I , i.e., one bonding electron pair, is found to be roughly preserved, whereas in the angular H2X and in collinear 0-H-0 TSS, the effect of increased valence at the saddle-point is observed, relative to that of diatomic fragments (reactants or products). For the angular 0-0-H TS, a similar increase in I v ( A B C ) J relative to both 0 2 and OH s n s is detected; smaller changes relative to the 0 2 data are found in the collinear TS. This observation is in agreement with earlier predictions from the intersecting-state model. The relative diatomic valences, v: ; / v: F and %'$/-viF, are shown to conserve the overall relative bond multiplicity around 1 in both collinear and angular TSS of the H2-X systems. 0 1994 John Wiley & Sons, Inc. qo = {PEP (p} = qo.ff + qO'P. These reference occupations and the associated atodion electron populations, no = {I: 4:) (the summation is over all OAOS of atom A), define the respective occupatiodpopulation displacements: AqP = P -0 , P 9 q . ( 3 ) 0 An = nno, The explicit expressions for the QVIS are defined as follows [l]:Aq = qq , Aq" = qff -qo3",

On the asymmetry in molybdenum–oxygen bonding in the MoO3 structure: ETS–NOCV analysis

“…The NOCV have been derived from the NalewajskiMrozek valence theory [40][41][42][43][44][45] as eigenvectors that diagonalize the deformation density matrix. It was shown that the pairs of the natural orbitals for chemical valence (w -k , w k , corresponding to eigenvalues -v k and v k ) decompose the differential density Dq into NOCV-contributions (Dq k ):…”

Chemical bonds from through-bridge orbital communications in prototype molecular systems

“…A similar description follows [1][2][3] from the Wiberg-type bond-multiplicities formulated in the MO theory [4,[14][15][16][17][18][19][20][21][22][23]. In MO description the chemical interaction between, say, two (valence) AO or general basis functions originating from different atoms is strongly influenced by their direct overlap and interaction, which both condition the bonding effect experienced by electrons occupying their bonding combination in the molecule, compared to the non-bonding reference of electrons on separated AO.…”

Communications in molecules: local and multi-configuration channels and their entropic descriptors of bond multiplicity and composition

“…It vanishes for the lone-pair configurations, when P = (0 or 1), This simple model thus properly accounts for the competition between the bond covalency and ionicity, while preserving the single bond-order measure reflected by the conserved single IT multiplicity of the chemical bond. Similar effects transpire from the quadratic bond indices formulated in the MO theory [87][88][89][90][91][92][93][94][95][96][97]. For example, the plot of Wiberg bond-order [87] for this model (see Fig.…”

“…= S, i.e., the overall conditional entropy of the average AO channel in the CI MO-ensemble [Eq. (93)], now stands for the overall entropic measure of the bond multiplicity.…”