Energy bonds

Bond energies for commonly occurring diatomic molecules range from 135 kcal per mole for HF to 36 kcal per mole for I2. Similar measurements on No and O2 set the energy of the NssN triple bond at 170 kcal per mole and the energy of the system of one single bond plus two three-electron bonds in oxygen (Chap, 4) as 158 kcal per mole. 

The O—H bond energy thus calculated (110 kcal) is an average value  

The heats of formation of hydrocarbons from the atoms (and from them, the values of the C—H, C—C, 0=0, and CssC bond energies) are often determined by combining heats of combustion of the hydrocarbons with the known heats of combustion of carbon and hydrogen thus for methane, CH  

The average value for the C—H bond energy, 99 k al, is thus one fourth the energy released in the reaction C + 4H — CH, that is, the formation of methane from the free atoms in the gaseous state. 

Of the energies above, the heat of atomization of graphite to gaseous 

Bond energies are of obvious importance in chemistry. For simple molecules, they can be derived from spectroscopic measurements but, in general, experimental bond energies are obtained from thermochemical data. 

Another point to note is whether the M-L bond energy was measured relative to the dissociation of a single ligand or to the decomposition of the entire complex. The two cases imply different computational procedures. 

The latter essentially estimates the M-L bond energy in the complex prior to dissociation. This cannot be measured directly since, in practice, the dissociation process will always be accompanied by relaxation. Thus, if the relaxation of the products lowers their energies, then the in-complex value will be higher than experimentally observed, and vice versa. However, the concept of an in-complex bond energy is useful in Transition State theory. For example, in a dissociative process, the initial slope of the reaction profile will be dominated by the energy of the bond being broken which would be better represented by the in-complex value than by the (dissociated) bond energy. 

Ziegler has developed a procedure for analyzing in-complex bond energies within the Density Functional Theory (DFT) formalism [14]. Somewhat confusingly, he labels this the transition-state procedure but this is more in deference to Slater s Multiple Scattering Xa (MSXa) transition-state method [15] (see Sect. 2.5.2) for estimating ionisation and excitation energies and should not be confused with PE surface Transition States. 

The orbital mixing can be further sub-divided in terms of the local MO symmetry. For favourably aligned systems, therefore, it is possible to separate the bonding energies into their constituent cr, n and 5 parts thereby giving a more detailed picture of the nature of the M-L bonding. 

The bond energies of neutral and cationic GeH and SiH species exhibit a zig-zag pattern as a function of n114 (Table 3). For example, the Ge—H bond energy decreases 

TABLE 3. Stepwise bond dissociation energies (BDE, kcal mol 1) for MI I  

TABLE 4. Calculated reaction energies (AE) and activation energies (Ea) for equation 5 at various levels of theory  

Perturbation theory (PT). eDirac-Hartree-Fock (DHF). f Pseudopotentials by Hay and Wadt90. 

Miriam Kami, Yitzhak Apeloig, JUrgen Kapp and Paul von R. Schleyer 

We can think of bond-dissociation energy as an enthalpy change or a heat of reaction, as discussed in Chapter 7. For example. 

It is not hard to picture the meaning of bond energy for a diatomic molecule, because there is only one bond in the molecule. It is also not difficult to see that the bond-dissociation energy of a diatomic molecule can be expressed rather precisely, as is that of H2(g)- With a polyatomic molecule, such as H2O, the situation is different (Fig. 10-17). The energy needed to dissociate one mole of H atoms by breaking one O—H bond per H2O molecule, 

As you can see from Table 10.3, double bonds have higher bond energies than do single bonds between the same atoms, but they are not twice as large. Triple bonds are stronger still, but their bond energies are not three times as 

The same quantity of energy, 435.93 Id mol is required to break all H — H bonds. In H2O, more energy is required to break the first bond (498.7 Id mol ) than to break the second (428.0 kJ mol ). The second bond broken is that in the OH radical. The O—H bond energy in H2O is the average of the two values 463.4 kJ mol  

Bond Bond Energy, kJ mol Bond Bond Energy, kJ mol- Bond Bond Energy, kJ mo -  

The dissociation energies quoted are generally 1 or 2 kcal/mole. 

As would be expected, organometallic compounds containing metal ions generally are formed by the most electropositive elements. The formation of ionic compounds is especially favoured when the hydrocarbon anion may be stabilized, for example where the negative charge may be delocalized 

If Sab smaller than (Sa + Sg), then AEbond will be negative, a result that implies that the strength of the bond between A and B increases when the hardness increases. 

the bond energy given by Eq. (36) depends on the parameters associated with the isolated species A and B, and on the softness of the system AB in the equilibrium position Sab- would be interesting to express the latter also in terms of the isolated species parameters to obtain an expression for the bond energy just in terms of the properties of the interacting molecules. It has been shown [16] that this may be achieved by making use of the arithmetic average principle for molecular softness [41], that establishes that the softness of a 

This approximation establishes that the harder the species that interact, the stronger the bonds that they may form. 

This approximation establishes that the strongest bond in a molecule is the one formed by the adjacent atoms with the smallest values of the condensed fukui function, and that the weakest bond is the one formed by the adjacent atoms with the largest values of the condensed fukui function. Note that since the condensed fukui functions are different for nucleophilic, electrophilic, and free radical attacks, the weakest bond in a molecule, which may be associated with the most reactive site (this one may be either of the two atoms forming the bond or the bond itself), may be a different one, depending on the type of attack, in agreement 

It is important to mention that if one makes use of the experimental values of I and A in Eq. (11), to determine the hardnesses in Eq. (39), and one makes use of molecular orbital theory to determine the values of the condensed fukui function, then, if one sets Ng = 1, one finds that this expression provides the correct trends, and reasonable estimates of the bond energies of a wide variety of molecular systems [16]. 

It is important to bear in mind that the exact properties of a specific kind of bond will be determined in part by the nature of the other bonds in the molecule thus the energy and length of the C-H bond will be somewhat dependent on what other atoms are connected to the carbon atom. Similarly, the C-H bond length can vary by as much a 4 percent between different molecules. For this reason, the values listed in tables of bond energy and bond length are usually averages taken over a variety of environments for a specific atom pair. 

In some cases, such as C—O and C—C, the variations can be much greater, approaching 20 percent. In these cases, the values fall into groups which we interpret as representative of single- and multiple bonds double, and triple. 

The bond energy is the amount of work that must be done to pull two atoms completely apart in other words, it is the same as the depth of the well in the potential energy curve in Fig. 1. This is almost, but not quite the same as the bond dissociation energy actually required to break the chemical bond the difference is the very small zero-point energy as explained inFig. 3. 

Bond energies are usually determined indirectly from thermodynamic data, but there are two main experimental ways of measuring them directly  

Although this method is simple in principle, it is not easy to carry out experimentally. The highly reactive components must be prepared in high purity and in a stream of moving gas. 

On the other hand, one should know the bond energies of the reacting atoms with the catalyst. Here also, in the first approximation, the knowledge of the mean values of the bond energies is sufficient. 

In the next approximation one should take into account the effect exerted upon the bond energy by substituents in the molecule and by atoms adjacent to the active center of the catalyst (see Sections II,E II,G). 

In the future, corresponding tables of bond energies or formulas should be developed, or such information should be stored in the memory of electronic computers. Such information should be used when applying the principle of energy correspondence. At present this information is very scanty, nevertheless, its application is highly encouraging, as is shown, in particular, in Section II,D. 

To apply the equations of the multiplet theory one should know the bond energies with the catalysts, Qak The bond energies may be found experimentally by thermochemical, comparative, and kinetic methods. 

Again we can take as a basis for our considerations the original suggestion of Pauling, to express the dissociation energy of a bond between atoms A and B as 

The correlation obtained between experimentally determined dissociation energies[50] and the relation, eq. (7.6), is displayed in Fig. 2, and the parameters we obtained in this regression are presented in Table 3. The resulting correlation coefficient was r =. 987 and the standard error 7 = 5 kcal/mol. Even though the correlation obtained is already quite satisfactory, we do hope to improve on it in the future, using a much larger data base to be derived from heats of formation. 

Standing on the shoulders of scientific giants like Pauling, provided one can climb up, opens great new vistas. 

Acknowledgment The authors are grateful for the financial support of this work due to the Fonds der Chemischen Industrie . 

Pauling s Legacy Modem Modelling of the Chemical Bond 213 

Although standard enthalpies of formation provide information about the net stability of molecules and their transformations, they do not always indicate stability of individual bonds. This analysis normally involves parameters, loosely called bond energies, that reflect the amount of energy required to cleave chemical bonds. 

In the rest of this section we review the corrections due to relativistic effects in the electronic structure. We go into some detail because these effects are usually of negligible size in studies of main-row elements, which are the most commonly found in the literature. We finish with examples of application of several computational methods to calculations of bond dissociation energies in actinide-containing molecules. 

To illustrate the magnimde of this term, recall that for a hydrogen-like model this correetion is of order (Za). Hence, in the heavy elements, where Z is comparable to the inverse of the fine structure constant, l/oc = 137, this term cannot be ignored. Because this term in the Hamiltonian is an operator on the spatial wavefunction of the eleetron, it is referred as a scalar relativistic effect, to distinguish it from the vector terms that depend on more than one component of the spin states, as we discuss below. 

The second relativistic contribution of scalar nature is the one-electron Darwin term, Wd. This term derives from the non-relativistic expansion of Dirac s equation, in powers of (v/c), and results in a non-local interaction between the electron and the nucleus. The interaction extends over a region in space of size roughly that of the Compton wavelength of the electron. The order of magnimde of this term in the Hamiltonian is also (Za) making it non-negligible for heavy elements. [12] These scalar relativistic terms have significant effects on the radial extent of the inner core orbitals. 

We should point out that these magnitudes are estimated for the most extreme relativistic situations, those associated with the Is orbital. For higher shells the magnitude of these terms are much smaller. After all, the valence elecfions are bound by energies of the order 

We will address this issue further in Chapter 10, where the polar effects of the substituents on both the c and n electrons will be considered. For the case of electrophilic aromatic substitution, where the energetics of interaction of an approaching electrophile with the 7t system determines both the rate of reaction and position of substitution, simple resonance arguments are extremely useful. 

Bond Energy, Polarity, and Polarizability 1.2.1. Bond Energies 

Of the various geometric parameters associated with molecular shape, the one most nearly constant from molecule to molecule and most nearly independent of substituent effects is bond length. Bond lengths to carbon depend strongly on the hybridization of the carbon involved but are little influenced by other factors. Table 1.2 lists the interatomic distances for some of the most common bonds in organic molecules. The near constancy of bond lengths from molecule to molecule reflects the fact that the properties of individual bonds are, to a good approximation, independent of the remainder of the molecule. 

A similar explanation lies behind the diminished strength of the sp —sp carbon-carbon bond in ethylbenzene. The general trend toward weaker C—C bonds with increased substitution that can be recognized in Table 1.3 reflects the increased stability of substituted radicals relative to primary radicals. 

Part A of Table 1.5 shows all the acyclic C4-C6 and some of the Cg hydrocarbons. A general trend is discernible in the data. Branched-chain hydrocarbons are more stable than straight-chain hydrocarbons. For example, A/fj for -octane is —49.82 kcal/mol, whereas the most highly branched isomer possible, 2,2,3,3-tetramethylbutane, is the most stable of the octanes, with of —53.99 kcal/mol. Similar trends are observed in the other series. 

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B = Average bond energy of P-CI bond. From the cycle it follows that ... 

Born-Haber cycle A thermodynamic cycle derived by application of Hess s law. Commonly used to calculate lattice energies of ionic solids and average bond energies of covalent compounds. E.g. NaCl ... 

Metals A and B form an alloy or solid solution. To take a hypothetical case, suppose that the structure is simple cubic, so that each interior atom has six nearest neighbors and each surface atom has five. A particular alloy has a bulk mole fraction XA = 0.50, the side of the unit cell is 4.0 A, and the energies of vaporization Ea and Eb are 30 and 35 kcal/mol for the respective pure metals. The A—A bond energy is aa and the B—B bond energy is bb assume that ab = j( aa + bb)- Calculate the surface energy as a function of surface composition. What should the surface composition be at 0 K In what direction should it change on heaf)pg, and why ... 

The adsorption of nonelectrolytes at the solid-solution interface may be viewed in terms of two somewhat different physical pictures. In the first, the adsorption is confined to a monolayer next to the surface, with the implication that succeeding layers are virtually normal bulk solution. The picture is similar to that for the chemisorption of gases (see Chapter XVIII) and arises under the assumption that solute-solid interactions decay very rapidly with distance. Unlike the chemisorption of gases, however, the heat of adsorption from solution is usually small it is more comparable with heats of solution than with chemical bond energies. 

Vibrational energy states are too well separated to contribute much to the entropy or the energy of small molecules at ordinary temperatures, but for higher temperatures this may not be so, and both internal entropy and energy changes may occur due to changes in vibrational levels on adsoiption. From a somewhat different point of view, it is clear that even in physical adsorption, adsorbate molecules should be polarized on the surface (see Section VI-8), and in chemisorption more drastic perturbations should occur. Thus internal bond energies of adsorbed molecules may be affected. 

The W—W bond energy should be about one-sixth of the sublimation energy (note Section III-IB), and there are various schemes for estimating electronegativities, of which Mulliken s [151,152] is perhaps the most fundamental. 

K has been identified as CFl200I-I from its chemistry the reaction mechanism is insertion [115], Collision-induced dissociation (in a SIFT apparatus, a triple-quadnipole apparatus, a guided-ion beam apparatus, an ICR or a beam-gas collision apparatus) may be used to detemiine ligand-bond energies, isomeric fomis of ions and gas-phase acidities. 

Vibrational frequencies and bond-energy considerations imply that r CNaCr) > (NaCl). Therefore,... 

Watson L R, Thiem T L, Dressier R A, Salter R FI and Murad E 1993 Fligh temperature mass speotrometrio studies of the bond energies of gas-phase ZnO, NIG, and CuO J. Phys. Chem. 97 5577-80... 

Berkowitz J, Ellison G B and Gutman D 1994 Three methods to measure RFI bond energies J. Phys. Chem. 98 2744-65... 

As a scientific tool, ab initio quantum chemistry is not yet as accurate as modem laser spectroscopic measurements, for example. Moreover, it is difficult to estimate the accuracies with which various methods predict bond energies and lengths, excitation energies and the like. In the opinion of tlie author, chemists who... 

Lain L, Su C X and Armentrout P B 1992 Collision-induced dissociation ofTi (n = 2-22) with Xe bond energies, geometric structures, and dissociation pathways J. Chem. Rhys. 97 4084... 

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. 

For many purposes, for example the estimation of approximate heats of formation (p. 63), it is sufficient to have an average value. This average of the bond dissociation energies is called the average thermochemical bond energy or (more commonly) simply the bond energy. ... 

Bond energy values can be obtained from thermochemical calculations (p. 72) and a number are included in Table 2.70 together with the compound used in the calculation. 

Strictly, these values are bond enthalpies, but the term energies is commonly used. Other descriptions are average standard bond energies, mean bond energies . 

Bond In compound Average thermochemical bond energy (kJ mol" )... 

While bond energies increase in. for example, the sequence C—C. C=C. 

A/i the dissociation or bond energy of hydrogen (it is also, by definition, twice the enthalpy of atomisation two gram atoms being produced). 

A/13 twice the bond energy of hydrogen chloride (twice since two moles of hydrogen chloride are produced). 

A/14 the enthalpy of reaction, which is in this case twice the enthalpy of formation of hydrogen chloride. Clearly A/14 is the difference between the total bond energies of the products and the total bond energies ol the reactants, lhat is... 

For a reaction to be exothermic the sum of the bond energies of the products must exceed those of the reactants. 

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