Bond Order between Centers A and

Strictly speaking, there should be no electron population between pairs of atoms in SHMO since orbitals are assumed not to overlap. However, it is conventional to set all overlap integrals to unity for the purpose of defining a bond order. The bond order, BAb, between centers A and is defined as 

Exercise 3.3. Show that the maximum value for the bond order due to a single bond is 1 and that it occurs when na — 2 and cA = cB = l/ /2. 

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The off-diagonal terms of the P S matrix betv een pairs of atomic orbitals centered on different atoms can be used to define the Mulliken bond order between atom A and atom B Bab) -... 

This is apparently the situation that exists in the triplet state. The triplet state has a high bond order between C(2) and C(3) and resists rotation at the center, but the barrier to rotation at either of the terminal carbons is low. In contrast, it... 

Generally, this tendency is in line with the changes in the M—NO bond lengths and the bond orders (Tables 2.4 and 2.5). However, there is a remarkable variance for the d5 configuration and between the Fe11 and Fe111 centers, already noted elsewhere [68], The energy of the formation of the dinitrosyl complexes (i.e., adsorption of the second NO molecule) is with the exception of Cr+ distinctly smaller (5 20 kcal/mol) that those... 

An A-B diblock copolymer is a polymer consisting of a sequence of A-type monomers chemically joined to a sequence of B-type monomers. Even a small amount of incompatibility (difference in interactions) between monomers A and monomers B can induce phase transitions. However, A-homopolymer and B-homopolymer are chemically joined in a diblock therefore a system of diblocks cannot undergo a macroscopic phase separation. Instead a number of order-disorder phase transitions take place in the system between the isotropic phase and spatially ordered phases in which A-rich and B-rich domains, of the size of a diblock copolymer, are periodically arranged in lamellar, hexagonal, body-centered cubic (bcc), and the double gyroid structures. The covalent bond joining the blocks rests at the interface between A-rich and B-rich domains. 

A second 7r interaction between that it orbital of the organic group and a molecular orbital of a symmetry centered on the metal fragment (Fig. 11), although of less energy than the former tt interaction, results in a calculated bond order between M and Ca of between 2 and 3 and, more importantly, indicates that rotation of the vinylidene unit about the M-Ca bond should be facile. This prediction is easily deduced from the lone pair... 

Then the computations on the 2,5-cyclohexadienones were used to obtain 3, 3-bond orders of the five electronic states listed in Scheme 1.5. As noted above, such bond orders between nonconjugated centers are equivalent to a perturbation computation and provide information on tendencies of the two centers to bond. There are positive bond orders for three of these states. However, it is known that the Type A rearrangement occurs selectively from a triplet, and only the n-x triplet has a positive bond order, thus providing theoretical support for the reaction mechanism. 

In MO theory, the Mulliken population analysis [149], where the population of the MOs is decomposed into atomic populations and diatomic overlap populations, considerably influenced the formulation of bonding concepts, although it does not describe a bond order per se. On the basis of the Mulliken population analysis, Mayer introduced a popular definition of the number of bonds between two centers A and B originally formulated for one-determinant wave functions [142-144, 150],... 

Bond Order and Bond Lengths—Single, double, and triple covalent bonds are said to have a bond order of 1, 2, and 3, respectively. Bond length is the distance between the centers of two atoms joined by a covalent bond. The greater the bond order, the shorter the bond length (Table 10.2). 

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