Valence bond structures, weights

More elaborate definitions of atomic orbital charges, bond-orders and valence-bond structural weights are needed when atomic orbital overlap integrals are included in normalization constants and orthogonality relationships. These are not required for the considerations of this book. 

Benzene has already been mentioned as a prime example of the inadequacy of a connection table description, as it cannot adequately be represented by a single valence bond structure. Consequently, whenever some property of an arbitrary molecule is accessed which is influenced by conjugation, the other possible resonance structures have to be at least generated and weighted. Attempts have already been made to derive adequate representations of r-electron systems [84, 85]. 

Graphical modeling can also be useful in representing the elements of the transfer matrix, J], adopted by Klein et ah, [13] Fig 3 shows the five Kekule valence-bond structures of enanthrene and their local states In this case one needs a directed graph with weighted edges and loops ... 

The retention volume of several aliphatic, phenolic, heterocyclic, amine and aromatic compounds in THF and toluene have been reported elsewhere ( ). It is clear that aromatic compounds, as expected from their valence bond structures, have smaller linear molecular sizes compared to n-alkanes of similar molecular weight It is expected that most of the con-... 

From the experimental values of dipole moments it is possible, in a number of cases, to make a semi-quantitative evaluation of the weights of the various valence bond structures contributing to a bond (see Chapter 18). These calculations must be regarded as only approximate since the bond is described in terms of the Heider-London theory with the superposition of ionic states. The results cannot, therefore, be more precise than is permitted by the Heitler-London approximation. Nevertheless, the calculations are of significance since they permit an assessment to be made of the more important structures contributing to the bond and thus assist in predicting and explaining the reactivity of bonds. 

The vector addition of dipole moments is only permissible if the weights of the ionic states in the various bonds does not alter significantly in the various compounds, such as would be produced if molecular resonance occurred in these cases only is it possible to assign definite values for the contributions of the various valence bond structures. The data for the bonds OH, OR, NH, NR and SH are given in Table... 

Calculation of the relative weights of the structures of the halogen derivatives of the acetylenes shows that the contribution of the valence bond structure III is not very great [Table XCIII) nevertheless, this small contribution is sufficient to affect the resultant dipole moment as the structures... 

Table XCIII. Relative Weights of Valence Bond Structures in Halogen Derivatives of Acetylene...

Equation 18.198 may be used to calculate and and by this means the weights of the different valence bond structures may be determined. 

Two different bonding indiees will be used in this book, namely bond-number and bond-order. The bond number refers to the number of pairs of electrons that form a covalent bond. It may be calculated from the weights of the valence-bond structures that are used to describe the electronic structure of the molecule, as is demonstrated above for N2O. The bond-order is a molecular orbital index of bonding. For the purpose of qualitative discussion of diatomic bonding, we shall define the bond-order to be /4 (No. of bonding electrons) - (No. of antibonding electrons). Another definition of bond-order will be introduced in Chapter 14. 

The r-delocalisation in the parent phospholide anion I (Fig. 3, R =R =H) can be expressed in the valence bond picture by resonance between the canonical structures lA-IC (and their mirror images). Phosphonio-sub-stituents (R =R =PH3 ) increase the weight of the 1,2-dipolaric canonical structure IB and induce thus, in essence, a partial r-bond localisation and a shift of r-electron density from the phosphorus to the adjacent carbon atoms [16]. Consequences of this effect are the decrease in delocalisation energy for reaction (1) depicted in Fig. 4, and lower C2-C3/C4-C5 and higher C3-C4 bond orders which are reproduced in concomitant variations of computed bond distances [16]. 

We focus in this Section on particular aspects relating to the direct interpretation of valence bond wavefunctions. Important features of a description in terms of modern valence bond concepts include the orbital shapes (including their overlap integrals) and estimates of the relative importance of the different structures (and modes of spin coupling) in the VB wavefunction. We address here the particular question of defining nonorthogonal weights, as well as certain aspects of spin correlation analysis. 

In the valence-bond method, a wave equation is written for each of various possible electronic structures that a molecule may have (each of these is called a canonical form), and the total is obtained by summation of as many of these as seem plausible, each with its weighting factor ... 

The two chief general methods of approximately solving the wave equation, discussed in Chapter 1, are also used for compounds containing delocalized bonds.2 In the valence-bond method, several possible Lewis structures (called canonical forms) are drawn and the molecule is taken to be a weighted average of them. Each in Eq. (3), Chapter 1,... 

STRUCTURAL COEFFICIENTS AND WEIGHTS OF VALENCE BOND WAVE FUNCTIONS... 

Polymers differ from other substances by the size of their molecules which, appropriately enough, are referred to as macromolecules, since they consist of thousands or tens of thousands of atoms (molecular weight up to 106 or more) and have a macroscopic rectilinear length (up to 10 4 cm). The atoms of a macromolecule are firmly held together by valence bonds, forming a single entity. In polymeric substances, the weaker van der Waals forces have an effect on the components of the macromolecules which form the system. The structure of polymeric systems is more complicated than that of low-molecular solids or liquids, but there are some common features the atoms within a given macromolecule are ordered, but the centres of mass of the individual macromolecules and parts of them are distributed randomly. Remarkably, the mechanical response of polymeric systems combines the elasticity of a solid with the fluidity of a liquid. Indeed, their behaviour is described as viscoelastic, which is closely connected with slow (relaxation time to 1 sec or more) relaxation processes in systems. 

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