Mayer/-bonds

Coulomb potential multiplied by -p. The graphical representation of the virial coefficients in temis of Mayer/ -bonds can now be replaced by an expansion in temis ofy bonds and Coulomb bonds ). 

Table 2.6 Bond order obtained from the Mayer bond order scheme [Mayer 1983].

The calculation of Mayer bond orders and valence indices is straightforward using the codes that Mayer has made available on the Internet [14]. The formulas have been built into several electronic structure codes, like HONDO [15], Gaussian 03 [16] (note that in Gaussian only the closed-shell formulas have been coded), ADF [17], and some versions of GAMESS [18]. 

Preliminary cluster studies [129] on the electronic structure of the trigonal V203(0001) surface substantiate the above concepts. As an example. Table 3, lists atom charges from Mulliken populations and Mayer bond orders for the substrate cluster VnOssHss, see Fig. 12b. The data are obtained from DFT calculations [129] using the RPBE functional [124, 125]. Here positive vanadium ions closest to the surface are described as and the negative oxygen as... 

Table 17 Bond lengths and Mayer bond orders of the C = 0 bond in the...

Table 19. Mulliken Charge and Mayer Bond Order Analysis of V10O31H12 Clusters...

Atom Mulliken charge, e Bond Mayer bond order... 

Many methods have been proposed to calculate bond orders from SCF MO wave functions. One useful definition is due to Mayer [1. Mayer, Chem. Phys. Lett., 97,270 (1983)]. For a closed-shell molecule whose occupied MOs are i= 2 the Mayer bond order Bcd between atoms C and D is defined as... 

That interaction was also supported by the Mayer bond order of 0.41, and Mulliken charges, calculated to be 4-1.02 for scandium and —0.04 for iron, which indicated that the interaction between scandium and iron was mainly electrostatic, with iron serving as a donor and scandium being the acceptor. Similar results were obtained from DFT calculations carried out on Sc2 anth. 

A variety of protocols exist for evaluating bond orders in molecules [48] and the bonding in [Cp Mo(p,-02CMe)]2(P -PMe2)(p.-Me) and [CpMo(p.-02CH)]2-(p,-PH2)(p.-X) was assessed using the Mayer bond order [49], that has also been used in other inorganic systems [50, 51]. The Mayer bond orders for a series of dimolybdenum compounds are summarized in Table 4, which provide several important comparisons. Firstly, the Mayer bond order of 0.72 for [Cp Mo-... 

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... 

Wiberg-Mayer Bond Orders Between Atoms (See Chem. Phys. Letters, v97, p270 (1983)... 

Basis Set C-N Wiberg-Mayer Bond C=0 Wiberg-Mayer Bond Dipole Moment (D)... 

Figure 8 Evolution of the forming bromide charge and Mayer bond orders B (C-C (bold line), Br-C (single line) and Br-Br (dotted line)) along a standard reactive trajectory (from Ref 32)...

There have been many attempts to build a link between modern electronic structure calculations and various intuitive models of chemical bonding. Among the concepts that proved to be especially useful in this respect is the idea of bond order and/or the bond index as a theoretical counterpart of the classical concept of bond multiplicity that reflects the number of shared electron pairs involved according to Lewis model in the bonding between the given pair of atoms. There is a plethora of various definitions of bond order but of speeial relevance for our purposes is the so-called Wiberg-Mayer bond order defined by eqn (l)... 

In the case of Hartree-Fock and formally also Kohn-Sham approximation and integer orbital occupations the above formula reduces to the following equation, which also shows the close link of the hole analysis to the 2-center Wiberg-Mayer bond indices ... 

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