Half-arrow method

Fig. 9 Different descriptions of the metal-metal bond orders in some dinuclear complexes with bridging hydride ligands according to the electron-counting method. The half-electron method does not explicitly take into account the 3-center-2-electron nature of the M-H-M interaction and thus results in a greater M-M bond order than would be predicted theoretictilly. In contrast, the half-arrow method treats the 3-center-2-electron nature of the M-H-M interactions explicitly and thereby predicts an M-M bond order which is in accord with theory...

Table 4 Comparison of calculated bond orders for a series of dinuclear molybdenum compounds with those predicted by two alternative electron-counting methods. In each case, the bond order predicted by the [p.-LX] half-arrow method corresponds exactly to that derived by consideration of the orbital occupations, whereas the half-electron method fails for compounds with bridging hydride and methyl ligands. Data ttiken from reference 6...

Mo Mo /A Mayer bond index M Mo-Mo configuration and calculated bond order electron count bond order [p-LX] half-arrow method electron count bond order half-electron method... 

Consideration of both the Mayer bond order analysis and the molecular orbital analysis indicates that the Mo-Mo bond order predicted by the p,-LX half-arrow method for [CpMo(p,-02CH)]2(p,-PH2)(p,-H) is much more in accord with the theoretical calculations than is the bond order of two predicted by the half-electron method. A variety of other studies support the use of the p,-LX half-arrow electron-counting method for predicting M-M bond orders in dinuclear compounds [52-59]. In particular, Hoffmann and Albright have used MO theory to analyze the... 

CO)sM]2 (p,-H) (M = Cr, Mo, W) [11] represents a classic series of complexes with single 3-center-2-electron M-H-M interactions for which the half-electron method predicts an M-M single bond, whereas the p,-LX half-arrow method... 

JI.-LX "Half-Arrow" Method "Half-Electron" Method... 

An analysis of the bonding in compounds with bridging hydrogen ligands demonstrates that, for every 3-center-2-electron M-H-M interaction, the half-electron method over counts the M-M bond order by one from the value predicted by the p,-LX half-arrow method. At one level, this is not really an issue once it... 

In contrast, the p,-LX half-arrow method requires one to consider the structure of the molecule prior to determining the M-M bond order. The p,-LX half-arrow method thus provides a more complete picture of the bonding by clearly distinguishing between (1) the number of 3-center-2-electron M-H-M interactions and (2) the number of direct 2-center-2-electron M-M interactions. A significant advantage of the p,-LX half-arrow method is that, by not forcing an 18-electron count on... 

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