Bond order partial

Fractional Bond Orders Partial bonding, as in resonance hybrids, often leads to fractional bond orders. For the oxygen-oxygen bonds in O3, we have... 

Geometrical descriptors are derived from the three-dimensional representations and include the principal moments of inertia, molecular volume, solvent-accessible surface area, and cross-sectional areas. Since conformational analysis (see Conformational Analysis 1 Conformational Analysis 2 and Conformational Analysis 3) often requires calculation of atomic charges, these routines can also produce electronic descriptors. Electronic descriptors characterize the molecular structures with such quantities as LUMO and HOMO energies, bond orders, partial atoim c charges, etc. Hybrid descriptors combine aspects of several of these descriptor types. The design and implementation of new descriptors is one important aspect of on-going research in the area of QSPR. 

The molecular orbital description of the bonding in NO is similar to that in N2 or CO (p. 927) but with an extra electron in one of the tt antibonding orbitals. This effectively reduces the bond order from 3 to 2.5 and accounts for the fact that the interatomic N 0 distance (115 pm) is intermediate between that in the triple-bonded NO+ (106 pm) and values typical of double-bonded NO species ( 120 pm). It also interprets the very low ionization energy of the molecule (9.25 eV, compared with 15.6 eV for N2, 14.0 eV for CO, and 12.1 eV for O2). Similarly, the notable reluctance of NO to dimerize can be related both to the geometrical distribution of the unpaired electron over the entire molecule and to the fact that dimerization to 0=N—N=0 leaves the total bond order unchanged (2 x 2.5 = 5). When NO condenses to a liquid, partial dimerization occurs, the cis-form being more stable than the trans-. The pure liquid is colourless, not blue as sometimes stated blue samples owe their colour to traces of the intensely coloured N2O3.6O ) Crystalline nitric oxide is also colourless (not blue) when pure, ° and X-ray diffraction data are best interpreted in terms of weak association into... 

The essence of the resonance concept is partial (non-integer) bond order, intermediate between, e.g., the idealized single- and double-bond patterns in (5.28a). 

Because the resonance-type interactions (5.28b) and (5.28c) that lead to partial bond order between molecular species are essentially similar to those within... 

Thus, by virtue of the continuity of the bond-order-bond-length relationship across the entire proton-transfer region, the interpretation of the H-bonded complexes in terms of partial proton transfer (with associated charge and covalent-bond transfer) can hardly be avoided. (Additional discussion of the properties of transition-state species in relation to the associated reactant and product species will be presented in Section 5.4.)... 

Figure 10.7 During the adsorption of molecular nitrogen onto iron metal, the two nitrogen atoms donate an increment of charge to adjacent atoms of iron on the metal surface, as depicted by the vertical arrows. The N=N triple bond cleaves partially, with a resultant bond order of about 1.5...

A final useful index of sigma nonbonded interactions between lone pairs is the partial bond order p (Xm, Yn) which is evaluated over the MO s which result from the interaction of the lone pair group MO s with the sigma HOMO and vacant MO s of the coupling unit. This index is intimately connected with the type of analysis employed in this work. In our survey of a variety of problems of molecular structure we shall provide computational results pertinent to the analysis outlined, i e. all or some of the following indices will be provided ... 

Good quality ab initio calculations have not yet been carried out in order to test whether lone pair nonbonded attraction obtains in 1,2-difluoroethane. Results of INDO calculations shown below indicate the presence of a nonbonded attractive interaction on the basis of the partial bond order p (F2px, F2px). By contrast, the presence of a nonbonded repulsive interaction favoring the anti conformation is indicated on the basis of the bond order p(F2px, F2px). 

A. Partial Derivatives and Polarizability Coefficients Expansion of (8) yields a polynomial, the characteristic or secular polynomial, whose roots are determined by the values of the parameters , vw- The ground state energy (12) is likewise a function of the (a,j3) parameter values, as are all quantities such as AO coefficients in the MO s, charges q bond orders p t, etc. It is possible, therefore, to specify the h partial derivative with respect to any or at an arbitrary point defined by a set of values (a,j8) in the parameter space, and to make expansions such as... 

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]. 

---