Frontier bond characteristics

Apart from choosing the force field for the classical subsystem and the level for quantum computations, the only latitude left to the user is the choice of the frontier bond characteristics. These may be extracted from a computation on a model molecule containing the bond of interest. In such a case, only one orbital needs to be localized so that one can use a so-called external localization criterion which is based upon a property of the bond of interest. The Weinstein-Pauncz criterion, which maximizes the overlap population between the two atoms defining the bond, appears to be quite convenient for this purpose. This localized orbital usually contains minor contributions of atoms other than the X and Y atoms. In order to obtain a strictly localized orbital, these contributions are discarded and the orbital renormalized. If the reference frame is different from the frame used for the molecule on which the LSCF computation is being performed, a simple matrix transformation generates the SLO expression in the LSCF basis set and the contribution of the orbital to the Pl density matrix is straightforward. 

The ionization potential in a simple one-electron approximation measures the energy of the highest occupied molecular orbital (HOMO). This orbital is only one of an entire manifold of levels which contribute to the bonding characteristics and total stability of the cluster. Frontier fragment-orbital analysis in organometallic reactivity studies has provided a clear indication... 

Fig. 1.4), or indeed in ferrocene, Fe(C5H5)2. This is because such units as CH and Fe(CO)3 or MiiiCDf have very similar frontier orbital characteristics with which to bond to other units. Though not isoelectronic, they are isolobal/" " " Their frontier orbitals have similar energies, extensions in space, and lobal characteristics, which enables them to participate in the same types of bonding (Fig. 1.21). 

Two cluster fragments are isolobal if they possess the same frontier orbital characteristics same S5mmetry, same number of electrons available for cluster bonding, and approximately the same energy. 

Figure 10. Bonding characteristics of the frontier molecular orbitals for the bithienyl-bridged ferrocenyl complexes.

If the perturbations thus caused are relatively slight, the accepted perturbation theory can be used to interpret observed spectral changes (3,10,39). The spectral effect is calculated as the difference of the long-wavelength band positions for the perturbed and the initial dyes. In a general form, the band maximum shift, AX, can be derived from equation 4 analogous to the weU-known Hammett equation. Here p is a characteristic of an unperturbed molecule, eg, the electron density or bond order change on excitation or the difference between the frontier level and the level of the substitution. The other parameter. O, is an estimate of the perturbation. 

Each reaction species must have molecular orbitals available and with the correct symmetry to allow bonding. These will be called frontier orbitals composed of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). In addition to their involvement in bonding between species, these orbitals are of considerable interest in that they are largely responsible for many of the chemical and spectroscopic characteristics of molecules and species and are thus important in analytical procedures and spectroscopic methods of analysis [5-7],... 

A characteristic feature of [2 + 2] cycloaddition reactions is that the symmetry properties of the frontier orbitals of the reactants make them formally symmetry forbidden [4] through a symmetric pathway. As a result, the reactants must overcome an activation barrier which makes the process very slow for homogeneous reactants. In organic chemistry, photoexcitation can be used to change the nature of the frontier orbital occupation, breaking the 7r bond and hence facilitating the reaction, but otherwise high heat and other extreme conditions are required in order to make this type of reaction proceed. For reactions with silicon(lOO), chemisorption is observed to be facile for most alkenes even at room temperature [16], contrary to naive expectations based on the cycloaddition model. 

The extended Huckel calculations (45) start from an unbridged geometry where the OC—Mo—CO and Mo—Mo—C bond angles are both 90° while the Mo—Mo—Cp bond angle is set to 125.3°. This leads to a bond description including characteristic five below two frontier orbitals shown in Fig. 3. The five highest occupied molecular orbitals are 7r, 8, ir, 8, and a and allow a correlation with the triple bond assigned on the basis of the 18-electron rule. 

In the first three chapters, instances were noted where the number, symmetry characteristics and occupation numbers of the frontier orbitals of a transition-metal fragment were similar to those of a main-group fragment. Such fragments are said to be isolobal to emphasize similar bonding capabilities. Since its enunciation by Hoffmann and Mingos, the concept has been used effectively for the analysis of both organometallic and cluster problems. Let s explore the idea in a more systematic... 

A third approach notes the relationship between the anion [(q -CsHs) Fe(q5-C2B9Hii)]2 and the parent carborane from which it is derived, C2B10H12. An anionic [(q5-C5H5)Fe] unit in the former replaces a neutral BH unit in the latter. The capacities of these two units, [(CsHsjFe] and BH, to participate in cluster bonding are similar. Each can function as a source of two electrons, and three AOs, for use in skeletal bonding. Not only are the numbers of their frontier orbitals the same, but so are their lobal characteristics they are isolobal (Fig. 3.21).The metal unit can effectively supply a radially oriented Pzdz. hybrid orbital and two pd p.xL i,P-,d., ) hybrid orbitals to bond to the nido... 

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