Wiberg indexes

FIGURE 22. Partial CS d) Wiberg indexes characterizing d-orbital participation plotted against the experimentally determined S—C bond lengths in some sulfonyl derivatives70. ... 

The bond index By (also called Wiberg index) was proposed to measure the multiplicity of bonds between two atoms [Wiberg, 1968 Trindle, 1969]. It is defined between two bonded atoms i and j as the square of the off-diagonal elements P v of the charge density matrix between atomic orbitals p on the ith atom and v on the jth atom, summed over all such distinct orbitals ... 

Wiberg index = bond index —> quantum-chemical descriptors... 

Using the charges on the appropriate hydrogens and Wiberg indexes W 6 from the ETSA of the active, weakly active, and inactive compound sets obtained above, we can suggest the following regression equation for the inhibitory activity. These relate to the ease of the above tautomeric transformation. 

Hydrochloric acid is able to react with a hydroxyl-free silica surface without a barrier, with formation of hydroxyl groups and weakly bonded chlorine (Fig. 5( 1)). The distance between chlorine and silicon for the system under study is 2.417 A, compared to the experimental value of 2.017 A and calculated value 2.054 A for SiCU. The formal charge on chlorine for the system under study is -0.754 e, compared with -0.354 e for SiCU- The Wiberg index (bond order) for the chlorine-silicon bond for the system under study is 0.3231, compared to a value of 0.8468 for SiCU- A similar phenomenon is presented for systems like water and hydrochloric acid/water (Fig. 5(2)). These data show that the chlorine atom is bonded to the silica cluster mainly as an ion, and it is possible to understand the system under study as an ion-pair, which may dissociate into ions. As a result the chatted particles will be repelled electrostatically. 

With respect to the metal-adsorbate interaction it is of interest, for comparison with the experimental results, to develop theoretical calculations based on molecular models that involve the adsorbate molecules and a metal cluster. The INDO/1 semiempirical method has been proved to be very useful in the stmc-ture optimization and in the evaluation of the bond characteristics throughout the Wiberg index - ° The interaction of azamacrocycle complexes with simulated copper surfaces studied by the same method was performed -... 

Theoretical data supported quite well the vibrational IR and RAIRS data and allowed an interpretation of the energetic process of the complex-surface interaction. The variation observed in the Wiberg index values for the metal-ligand coordination bond suggests an important tc electronic redistribution around the cation by surface effect Table 14.7. 

Table 14.7. Selected Wiberg index values for different interactions...

The most relevant data of the adsorbate-substrate interaction, listed in Table 14.8, indicate that the Ni complex-colloidal Ag interaction is the most stable in the series. The Wiberg index values of the free complexes and the adsorbate-substrate adduct in Table 14.9, point to an electronic energy redistribution by interaction effect, being the most influenced bonds those directly involved in the metal coordination site. 

Table 14.9. INDO/1 Wiberg index values for selected bonds of the free complexes and the adsorbate-suhsirate adducts.(See Figure 14.10)...

The most relevant Wiberg index values for the isolated and the macrocycle-cluster interaction systems are displayed in Table 14.11. 

The off-diagonal conditional probability of 7th AO output given ith AO input is thus proportional to the squared element of the CBO matrix linking the two AO, 7/, = Yv thus being also proportional to the corresponding AO contribution M J = ylj to the Wiberg index [77] of the chemical bond order between two atoms A and B in the molecule... 

The Wiberg index has thus been recovered as the overall IT descriptor of the chemical bond in the 2-AO model, with its covalent (Sab) and ionic (/ ) contributions being established at the same time. It follows from Figure 8.17 that these IT covalency/ionicity components compete with one another while conserving the Wiberg bond order as the overall information measure of chemical bond multiplicity... 

Subsequent theoretical calculations confirmed the important role of the Si-<—N interaction in the formation of the silatrane structure. A significant Si- —N bond order was determined at the CNDO/2 level using the experimental solid state geometries of silatranes Thus, the Wiberg indexes of this bond in the crystalline a, and y... 

To get a more quantitative measurement of synchroni-city/asynchronicity, Wiberg indexes [111] and NBO bond orders (B,) were calculated. B, were computed using the NBO program as implemented in Gaussian 03, and the synchronicity (S, ) was estimated using the concept proposed by Moyano et al. [112-114] (for more details, see section V in the Supporting information). 

Calculating Wiberg indexes B, for reactant complexes, TS, and products complexes allows locating the position of the TS between reactant and product (Table 2). For simplicity, only results for NHC = ADC H, IH, and IMes are shown in Table 2 as these are representative of the entire set of species studied (See Supporting material. Table S5-S7). 

Bond indexes were, once more, calculated to give a more quantitative analysis of the transition-state asynchronicity. For this analysis, Cu-H, Cu-O, 7t(C-0), and C-H bonds were considered. Calculated Wiberg indexes for NHC = ADC H, IH, and IMes are reported in Table 4. 

Density differences (Fig. 7) once more qualitatively show an asynchronous transition state with the Cu-O bond breaking/O-Si bond formation being more advanced compared to the hydrogen transfer toward the Cu atom. Wiberg indexes (Table 7) confirm this asynchronicity, although it being less pronounced compared to the previous steps (Sy = 0.90-0.95). At the TS, the Si-H and Cu-O bonds are broken at approximately 75 and 85 %, while almost 85 % of the Si-O bond has been formed. The Cu-H bond has only been formed up to about 60-65 %. SB ay... 

We have thus recovered the Wiberg index as the overall IT descriptor of the chemical bond in the 2-AO model, Vab° = 4 a,b> at the same time establishing... 

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