Relationship with bond-order calculations

To illustrate the importance of vicinal connectivity of conjugating units, we consider two dienes in non-vicinal relationships 1,5-hexadiene, 9, and allene, 10. As shown in Table 3.19, the direct diene conjugations are negligible in both species, on account of spatial separation in 9 and symmetry-imposed orthogonality of the two pi planes in 10. Consistently with the essential absence of conjugation, the unsaturated C—C bonds of 9 and 10 have calculated bond orders characteristic of ethylene or other unconjugated systems and the ficc NLMOs have essentially localized character ... 

The most optimistic response to this situation is to claim that the force constant — t-bond order relationship is still valid, but that the reference points need to be changed V(CO)e itself is then a possible reference compound (76). The relationship can then only be quantified by using calculated orbital populations for the reference species, and can only be tested by more extended comparisons between calculated bond order and observed force constant. Precisely this test has been apphed to a whole group of substituted and unsubstituted octahedral carbonyls of groups VI and VII, the substituents in every case being hahde (77). The data used in fact were not force constants, but Cotton-Krainhanzel parameters this does not actually matter, since no reference molecules were used at all. Excellent agreement was found with an expression. 

The aromaticity obtained by means of the DE values and their differences in the single pseudoazulene systems are also the result of calculations of the bond orders (Fig. 1). The calculated bond alternations46 57-77-79-82-117118-129 are in line with the heteroaromaticity of the systems. Similar relationships were calculated for azulene.219 The extent of the bond alternation, however, differs from one system to the other (see Fig. 1). In indeno[2.1-f>]-l-benzo-pyran (44a) the bond lengths of the central cyclo[fo]pyran system indicate pronounced bond alternation, and in the opinion of the authors, the systems have little aromatic character.129 Calculations with 1 //-pyrindines (26) and 2//-pyrindines (29) show that 26 is more stable than 29, but both are less aromatic than indole.63 A comparison of SCF calculations for pseudoazulenes 26 and 29 with their aza analogs 68 and 69-73, which contain a pyrrole-type nitrogen, shows only minor perturbations of carbon-carbon bond lengths on replacing a =CH— moiety by =N—.66... 

The iterative method is incorporated into the HMO method as follows starting with certain values of and atomic charges and bond orders are calculated. From these values new values of and arc obtained by using certain relationships (empirical or semi-empirical) between and a, and The secular deter-... 

Similar results are also obtained for the octahedral clusters as shown in Fig. 14. Thus, the present result is independent of the clusters used for the calculation. Once A and B elements are chosen, the A/B compositional ratio is determined following a relationship with the bond order ratio shown in Fig. 13 or Fig. 14. 

In the same way, Abraham has calculated, from partition coefficients, an effective or summation hydrogen-bonding acidity scale, half - However, while sot is obtained from one reference partition system (octanol/chloroform), with the hypothesis that a number of solute parameters acting on log P cancel out, Abraham determines the haf values by a back calculation procedure over numerous sets of partition systems, and uses linear solvation energy relationships with a more complete set of solute parameters. Table 7 shows that Ea > ea and af values do not differ much for simple mono hydrogen-bond donors. It is also important to note that the order of acidity ... 

Other pharmacological activities have also been correlated with quantum-chemically derived descriptors. For instance, the quantitative structure-activity relationship developed for the antibacterial activity of a series of monocyclic (i-lactam antibiotics included the atomic charges, the bond orders, the dipole moment, and the first excitation energy of the compound [103]. The fungicidal activity of A3-l,2,4-thiadiazolines has been correlated with an index of frontier orbital electron density derived from semi-empirical PM3 molecular orbital calculations [104],... 

Furthermore, Gunther et al (14) found a result similar to Sojka s (15) when correlating coumarin shifts with n charge densities calculated by the Hiickel MO method (63). This, however, fails for methoxylated coumarins (14) demonstrating that simple charge density - shift relationships are not generally applicable reliably. Ernst (20) reported a linear relationship between fi-methyl substituent effects in unhindered methylated coumarins and the it bond order, P , of the C-a—C-f) bond calculated by the INDO MO method (64) ... 

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