Conservation of bond order

There have been a number of investigations of the formulation of the problem of electron transfer accompanied by atom transfer particularly with regard to the simultaneous movement of the proton (which, in view of its small mass, may in fact be an atypical case). A possible model for such processes would assume a conservation of bond order along the reaction coordinates (Johnston, 1960). It is of interest that the results of such calculations are similar to those for electron transfer for weak coupling, although the interpretation of the process and parameters (such as a) are different. 

An effort is underway in our laboratory to determine transition state structures for phosphoryl transfer reactions by the use of secondary 0 isotope effects measured by the remote label method. The hypothesis is that an associative mechanism would have single bonds from phosphorus to the nonbridge oxygens in the transition state, whereas a dissociative mechanism would have enhanced bond order. So far we have determined the secondary 0 isotope effects on glucose-6-P hydrolysis at pH 4.5, 100°C (112), and by alkaline phosphatase (128). The chemical hydrolysis showed no isotope effect on P-O bond cleavage, which is consistent with a largely dissociative transition state without total conservation of bond order to phosphorus (i.e., a partial positive change exists on phosphorus). 

Conservation of bond order gives n = — Wj, and this assumption plus Pauling s rule immediately determines the reaction path. The reaction path of methyl radical plus hydrogen is given by the curved line in Fig. 1, and the reaction path for methyl radical plus ethane or acetone, for example, is given in Fig. 2. 

Finally, one should mention that some version of bond-order conservation, known as the bond-energy/bond-order (BEBO) method, has been applied to chemisorption bonding and surface reactivity by Weinberg and... 

The conservation of the sum of bond orders the following chemical equations... 

The effect of decreased coordination of surface metal atoms compared to the bulk leads to small decreases in the bond distances with atoms in the subsurface layer. Because of bond order conservation, discussed in Section 10.3.5, this increased bonding of metal atoms in the subsurface layer to those in the surface layer will weaken bonds with metal atoms in the next subsurface layers. The result is a decaying alternating strengthening and weakening of the interaction energies between atoms in layers perpendicular to the surface layer. 

H. Sellers,/. Phys. Chem., 98,968 (1994). Relationship Among Force Constants Implied by the Principle of Bond-Order Conservation in Chemisorbed Systems. 

Figure 3.54. Schematic illustration of the use of Bond Order Conservation to predict attractive or repulsive interaction between adsorbates, (a) Adsorbates which bond to the same surface metal atom are weakened by the presence of one another as the result of competition for electron density from the same metal atom. These interactions are repulsive, (b) Adsorbates that are bound to metal atoms which are neighbors have an effective attractive interaction, because of the weakening of the metal—metal bond due to their coadsorption. Bond order conservation indicates that attractive and repulsive interactions alternate through bonds. Binding to a next-nearest metal atom neighbor such as K" versus A has a weaker interaction and, hence, this through-surface interaction is repulsive.

The bond orders obtained from Mayer s formula often seem intuitively reasonable, as illustrated in Table 2.6 for some simple molecules. The method has also been used to compute the bond orders for intermediate structures in reactions of the form H -1- XH HX -1- H and X I- XH -H H (X = F, Cl, Br). The results suggested that bond orders were a useful way to describe the similarity of the transition structure to the reactants or to the products. Moreover, the bond orders were approximately conserved along the reaction pathway. 

The dependence on electron locahzation energy can also be illustrated by the use of the bond order conservation principle. This principle gives an approximate recipe to estimate changes in bond strength when coordination of a surface atom or adsorbate attachment changes [5, 15]. 

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