Bond order approximation

The infrared spectra of several of these complexes confirm that the olefin exists, with its double bond, in the complex (35, 177, 178), but that the double bond is weakened by complex formation, as shown by the decrease of some 140 cm-1 in the C C stretching frequency (35). The total platinum-olefin bond order is approximately 4/3 (35), and the C C bond order approximately 5/3 (126). 

Bonding of a nitrile to an electron acceptor through the lone pair in general increases 427, 460), although examples, such as CoH(RCN) (PPh3)j 351), have been cited for which decreases 50 cm 128, 218). Two schools of thought exist to explain the general increase in i cn-one the free nitrile is considered to have a bond order approximately intermediate between 2 and 3 because of mesomerism 145, 184, 224) ... 

This will be called the bond order approximation. It might be noted that this approximation is at the heart of the Hiickel MO method. Using this approximation ... 

A better estimate of the bond energy from the ionization energies is obtained from a more complete understanding of the nature of the bond. Theoretical models represent the bond in the hydrogen molecule with a 94% contribution of a covalent term and a 6% contribution of ionic terms.(lO) The bond order approximation applies only to the covalent portion. As we will show again later, the contribution of the ionic portion to the bond energy is essentially lost with ionization. Equation 2 can be generalized as follows ... 

The relationship between force constant and bond order can also be seen in the series of homonuclear diatomics N2, O2, and F2. For this series, the bond orders (approximate indicators of the bond strength) are 3, 2, and 1, respectively. The corresponding force constants are 2290, 1180, and 440Nm CO and NO, which also have bond orders of 3, have force constants of 1900Nm and... 

If S is a single atom or a group of atoms with the bonds attached to the same atom (such as a CHi group), then we have the additivity of bond properties, liie first-order approximation, as given by Eq. (3). 

The next higher order of approximation, the first-order approximation, is obtained by estimating molecular properties by the additivity of bond contributions. In the following, we will concentrate on thermochemical properties only. 

The bond orders obtained from Mayer s formula often seem intuitively reasonable, as illustrated in Table 2.6 for some simple molecules. The method has also been used to compute the bond orders for intermediate structures in reactions of the form H -1- XH HX -1- H and X I- XH -H H (X = F, Cl, Br). The results suggested that bond orders were a useful way to describe the similarity of the transition structure to the reactants or to the products. Moreover, the bond orders were approximately conserved along the reaction pathway. 

The simplest molecular orbital method to use, and the one involving the most drastic approximations and assumptions, is the Huckel method. One str ength of the Huckel method is that it provides a semiquantitative theoretical treatment of ground-state energies, bond orders, electron densities, and free valences that appeals to the pictorial sense of molecular structure and reactive affinity that most chemists use in their everyday work. Although one rarely sees Huckel calculations in the resear ch literature anymore, they introduce the reader to many of the concepts and much of the nomenclature used in more rigorous molecular orbital calculations. 

Table I-l lists the various theoretical treatments published on the thiazole molecule for each the type of approximation, the mode of parametrization. and, eventually, the geometry employed are given net charges and bond orders for various theoretical calculations are listed in Tables 1-2 and 1-3.

Defining ethane, ethylene and acetylene to have bond orders of 1, 2 and 3, the constant a-is found to have a value of approximately 0.3 A. For bond orders less than 1 (i.e. breaking and fonning single bonds) it appears that 0.6 A is a more appropriate proportionality constant. A Mulliken style measure of the bond strength between atoms A and B can be defined from the density matrix as (note that this involves the elements of the product of the D and S matrices). 

A criterion for the position of the extent of the mesomerism of type 9 is given by the bond order of the CO bond, a first approximation to W hich can be obtained from the infrared spectrum (v C=0). Unfortunately, relatively little is known of the infrared spectra of amide anions. How-ever, it can be assumed that the mesomeric relationships in the anions 9 can also be deduced from the infrared spectra of the free amides (4), although, of course, the absolute participation of the canonical forms a and b in structures 4 and 9 is different. If Table I is considered from this point of view, the intimate relationship betw-een the position of the amide band 1 (v C=0) and the orientation (0 or N) of methylation of lactams by diazomethane is unmistakeable. Thus the behavior of a lactam tow ard diazomethane can be deduced from the acidity (velocity of reaction) and the C=0 stretching frequency (orientation of methylation). Three major regions can be differentiated (1) 1620-1680 cm h 0-methylation (2) 1680-1720 cm i, O- and A -methylation, w ith kinetic dependence and (3) 1730-1800 em , A -methylation, The factual material in Table I is... 

The dependence on electron locahzation energy can also be illustrated by the use of the bond order conservation principle. This principle gives an approximate recipe to estimate changes in bond strength when coordination of a surface atom or adsorbate attachment changes [5, 15]. 

Electrical discharges through samples of helium gas generate He cations, some of which bond with He atoms to form Hc2 cations. These fall apart as soon as they capture electrons, but they last long enough to be studied spectroscopically. The bond dissociation energy is 250 kJ/mol, approximately 60% as strong as the bond in the H2 molecule, whose bond order is 1. 

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