Bond Energy Approach

The bond energy approach is typically not directly aimed at the determination of standard enthalpies of formation for individual molecules although there are several exceptions.162 The bond energy technique is still worth discussing in the context of this chapter, however, since many researchers use it routinely to estimate reaction enthalpies. 

AHr = X (energy of bonds broken) - X (energy of bonds formed) [17] 

A more useful approach that deals with partial bond contributions to the gas phase enthalpy of formation at 298.15 K is that of Benson.162 Basically the bond contributions can be added together to predict either the enthalpy of formation of a molecule or the reaction enthalpy directly. 

A simple example of how the bond energy approach may be used is illustrated in the following trivial example. Suppose one needed to determine the reaction enthalpy for the following hypothetical reaction  

For the purposes of an engineering design at an early stage, the reaction enthalpy may be needed to an accuracy of only, say, 8 kcal/mol. Without resorting to a single bond energy table, one can predict that this reaction will be close to thermoneutral because the bonds broken and formed are so similar  

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The bond energy approach may not always be adequate because it is the free energy change, AG, that is related to equilibrium constants, and the free energy is given by... 

Theoretical considerations of the enthalpy of the reactions represented by the intersystem constants based on the bond-energy approach show that the values of AH assuming only cx-bond contributions differ considerably from the AH values that were calculated from the intersystem constant according to Eq. (13). These differences are attributable to 7r-bonding effects which, therefore, appear to be the major driving force for the nonrandom equilibrations described by the data in Table VIII. 

Empirical methods26 use known experimental enthalpy data to estimate enthalpies and bond energies for unknown compounds. Among the methods in this group are the bond energy approach and Benson s rules. The empirical methodologies still hold an important place in the tool box of the scientist simply because these methods are so easy to use and are of proven reliability. The empirical methods require little in the way of computer resources and can handle very large molecules. These methods can be reasonably accurate for molecules that have standard bond types. 

A natural extension of the bond energy approach is to account for interactions close to the chemical bond in question (which certainly affect the stability, and hence the thermodynamic properties). Based on this concept, a number of group contribution methods have been developed over the years, and many of these methods have been reviewed in Ref. 171. Benson s second-order group contribution method, probably the most successful and widely embraced method, was developed some 30 years ago as an improvement to bond energy (or bond contribution) methods for the prediction of thermochemical properties.167 This improvement was accomplished by accounting for ... 

The alternative bond energy approach, as modified by adding to it the steric energy terms calculated by molecular mechanics, has been used by Schleyer s group (Engler et al., 1973) and by ourselves, with a moderate degree of success. In order for such a bond energy scheme to work, it must be possible to include in the calculation, in... 

This method was used in early force fields in the 1970s. It worked pretty well, better than any previously existing method. There are, however, some better approximations that can be applied to this type of procedure. The Benson type of method, or the bond energy approach, assumes the additivity of bond energies over a sizable range. But bond energies are made up of component pieces, and, in principle at least, such a broad assumption may not be the best way to proceed. Let us look at this in a little more detail. 

The flash lamp teclmology first used to photolyse samples has since been superseded by successive generations of increasingly faster pulsed laser teclmologies, leading to a time resolution for optical perturbation metliods tliat now extends to femtoseconds. This time scale approaches tlie ultimate limit on time resolution (At) available to flash photolysis studies, tlie limit imposed by chemical bond energies (AA) tlirough tlie uncertainty principle, AAAt > 2/j. 

The simplest arithmetic approach subtracts the C—C cr bond energy of ethane (368 kj/mol 88 kcal/mol) from the C=C bond energy of ethylene (605 kJ/mol 144.5 kcal/mol). This gives a value of 237 kJ/mol (56.5 kcal/mol) for the tt bond energy. 

Formula for the chemical potentials have been derived in terms of the formation energy of the four point defects. In the process the conceptual basis for calculating point defect energies in ordered alloys and the dependence of point defect concentrations on them has been clarified. The statistical physics of point defects in ordered alloys has been well described before [13], but the present work represents a generalisation in the sense that it is not dependent on any particular model, such as the Bragg-Williams approach with nearest neighbour bond energies. It is hoped that the results will be of use to theoreticians as well as... 

Ideally one would wish to remove the need for statistics by directly and reproduce-ably measuring a single bond only. One problem with the measurement of specific individual bond energies is that it is extremely difficult, even with a tip of small radius, to isolate a single bond species between the tip and the sample. To form a single bond in a controlled way requires the cantilever to be stiffer than the maximum force gradient experienced during the approach, but stiffer levers exhibit less sensitivity. If multiple bonds are formed, then it can be difficult to make an independent calculation of the contact area and hence the number of bonds involved. 

A free-electron metal only possesses a broad sp band. Upon approach, the electron levels of the adsorbate broaden and shift down in energy, implying that the adsorbate becomes more stable when adsorbed on the metal. The interaction results in a bonding energy of typically 5 eV for atomic adsorbates on metals. The situation is illustrated in Fig. 6.23. 

Ziegler, T, Baerends, E.J., Snijders, J.G., Ravenek, W. and Tschinke, V. (1989) Calculation of bond energies in compounds of heavy elements by quasi-relativistic approach. The Journal of Physical Chemistry, 93, 3050-3056. 

It was an approach that enabled bond energies of chemisorbed states Z)M-h to be estimated [eqn (2)] provided that the heat of chemisorption AH was known, with/) [2the H2 bond energy ... 

While the general features of halogen bonding are now well known, it has proven challenging to develop models with sufficient accuracy to predict spectroscopic features and bond energies. This is particularly problematic with iodine, where high quality basis sets are not readily available and are computationally expensive. There have been numerous approaches taken to address this issue during the past decade, many of which are discussed below. 

Figure 5.7 The variation of the potential energy as two non-bonded atoms approach each other curve a, the hard sphere model curve b, a potential of the form V = C/r12.

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