Bond Orbital Optimization

The NBOs are an optimized set of localized bonding, antibonding, and lone pair orbitals. The bond orbitals typically have occupancies of 1.98e in molecules with one simple Lewis structure. In C2H6, Weinhold and coworkers36 have shown that the barrier height V3 = 1025 cm-1 can be understood in the NBO terms in the form of aCH — donor-acceptor interactions. When the corresponding off-diagonal... 

TABLE 3. Hybridizations of bonding orbitals for cr-bonds from NBO (Natural Bond Orbital) analyses based on MP2/6-31G(d,p) optimized structures... 

In this model, one considers the acetals to be composed of polarizable dipolar moieties that can be stabilized by electron transfer from an electron-rich moiety (non-bonding electron on oxygen low ionisation energy) to adjacent polar and polarizable moieties (high electron affinity). A strong overlap between n(O) and cr c 0 orbitals optimizes this electronic transfer. As these orbitals are not spherical, n(0)/ct c o overlap depends on... 

Such a spin-coupled wavefunction is optimized with respect to the core wavefunction (if applicable), as well as to the nonorthogonal valence bond orbitals,... 

As is the case for standard orthogonal-orbital MCSCF calculations, the optimization of VB wavefimctions can be a complicated task, and a program such as CASVB should therefore not be treated as a black box . This is true, to a greater or lesser extent, for most procedures that involve orbital optimization (and, hence, non-linear optimization problems), but these difficulties are compounded in valence bond theory by the... 

Two additional points that are self-evident are discussed below for the sake of completeness. The coordination number of a metal ion counting all ligands other than the adjacent metal involved in multiple metal bonding is less than the maximum coordination number possible for that metal center. Furthermore, the number of d-electrons on the metal is nearly equal to the number of metal valence orbitals not involved in metal-ligand bonding to optimize metal-metal bond formation by filled bonding MOs. 

It seems that the repulsive steric interactions play a more dominant role in regioselectivity of aryne reactions than is sometimes realized. In fact, it has been argued that in nucleophilic addition to arynes, the transition state is reached early, while the incipient bond is still very much extended. Consequently, steric effects were considered not to be of great importance.80 81 It should, however, be noted that the dehydro bond orbitals are so oriented that the optimal approach trajectory for the nucleophile lies in the... 

The key geometric features of the optimized Pd-Cl bridging structures were found to nicely match those determined experimentally, and the presence of rather strong Cl-B interactions was substantiated by Natural Bond Orbital (NBO) analyses. For both complexes, rotation around the P— Pd bond allowed the location of another minimum devoid of any Cl-B interaction (B-pendant form, coordination mode E) (Figure 27). The two forms lie very close in energy (AG298 = 3-5 kcal), in agreement with the coexistence of the two coordination modes in solution. 

All the VB methods that deal with semilocalized orbitals use a generalization of the Coulson—Fischer idea (12), whereby a bond is described as a singlet coupling between two electrons in nonorthogonal orbitals that possess small delocalization tails resulting from the variational orbital optimization. Albeit formally covalent, this description implicitly involves some optimal contributions of ionic terms, as a decomposition of the wave function in terms of pure AO determinants would show (see Eqs. 3.5 and 3.6). For a polyatomic... 

The generalized valence bond (GVB) method was the earliest important generalization of the Coulson—Fischer idea to polyatomic molecules (13,14). The method uses OEOs that are free to delocalize over the whole molecule during orbital optimization. Despite its general formulation, the GVB method is usually used in its restricted form, referred to as GVB SOPP, which introduces two simplifications. The first one is the perfect-pairing (PP) approximation, in which only one VB structure is generated in the calculation. The wave function may then be expressed in the simple form of Equation 9.1, as a product of so-called geminal two-electron functions ... 

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