0-0 bond dissociation energy

9 Bond Dissociation Energy D(HP-H) in kcal/mol (if not otherwise stated) 

Estimates of 79 [5] (see also [7 to 9]) or 67 kcal/mol [6] were based on thermochemical data of minor quality. 

Dq or De values from ab initio MO and semiempirical calculations are partially in remarkable agreement with the most recent experimental result (for abbreviations used for the theoretical methods, see the remarks)  

An ab initio MO calculation without any electron correlation correction yielded De=1.92 eV for the ground state X and Dq=1.72 eV for the excited state A a [9]. 

Bond breaking can be quantified using the bond dissociation energy. 

The superscript (°) means that vaiues are determined under standard conditions (pure compounds in their most stabie state at 25 °C and 1 atm pressure). 

Additionai bond dissociation energies for C - C muitiple bonds are given in Tabie 1.3. 

The energy absorbed or released in any reaction, symbolized by AH°, is called the enthalpy change or heat of reaction. 

A bond dissociation energy is the AH° for a specific kind of reaction— the homolysis of a covalent bond to form two radicals. Because bond breaking requires eneigy, bond dissociation energies are always positive numbers, and homolysis is always endothermic. Conversely, bond formation always releases energy, so this reaction is always exothermic. The H-H bond requires +104 kcal/mol to cleave and releases -104 kcal/mol when formed. Table 6.2 contains a representative list of bond dissociation energies for many common bonds. 

By assuming atomic radii to be specified by ionization radii, r0, the diatomic curves could, in principle, be used to calculate the dissociation energy of any covalent bond, irrespective of bond order, only from its interatomic distance. This promise is largely fulfilled, but the calculated energies are proportionately too low in virtually all cases. The obvious reason for this is that the calculation makes no allowance for steric interactions that occur in molecular environments. Because of this effect the (experimentally measured) interatomic distances used in the calculation do not refer to the strain-free situation modelled by ionization radii. 

The problem is avoided by modification of the characteristic atomic radii to match the condition of strain that exists in molecules. As a typical example the variation of calculated dissociation energy with characteristic radius is shown in the table below for the C-C bonds in ethane, ethene and acetylene. The discrepancy approaches experimental uncertainty for all three bonds at the same value of rc = 1.85 A, which also models diatomic C2 correctly. 

Starting from ionization radii, r o, and using experimentally measured values of dissociation energy and interatomic distance for homonuclear diatomic molecules, a self-consistent set of characteristic radii, suitable for the point-charge calculation of bonding parameters, of both homonuclear and 

The comparison between ionization radii and characteristic radii is informative. All of the traditional non-metals have rx ro- A number of 

In order to test the point-charge method experimentally measured dissociation energy and interatomic distance are required for each chemical bond. Dissociation energies for most homonuclear diatomic molecules have been measured spectroscopically and/or thermochemically. Interatomic distances for a large number of these are also known. However, for a large number of, especially metallic diatomic molecules, equilibrium interatomic distances have not been measured spectroscopically. In order to include these elements in the sample it is noted that for those metals with measured re, it is found to be related, on average, to 5, the distance of closest approach in the metal, by re = 0.78(5. On this assumption reference values of interatomic distance (d) become available for virtually all elements, as shown in the data appendix. In some special cases well-characterized dimetal bond lengths have also been taken into account for final assessment of interatomic distance. 

Sample Problem 6.1 Use full-headed or half-headed curved arrows to show the movement of electrons In each equation. 

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The energy required to break the bond between two covalently bonded atoms is called the bond dissociation energy . In polyatomic molecules this quantity varies with environment. For example, ammonia has three N—H bond dissociation energies ... 

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. ... 

The heats of formation of the gaseous atoms, 4, are not very different clearly, it is the change in the bond dissociation energy of HX, which falls steadily from HF to HI, which is mainly res ponsible for the changes in the heats of formation. 6. We shall see later that it is the very high H—F bond energy and thus the less easy dissoeiation of H—F into ions in water which makes HF in water a weak aeid in comparison to other hydrogen halides. 

The bond dissociation energy of the hydrogen-fluorine bond in HF is so great that the above equilibrium lies to the left and hydrogen fluoride is a weak acid in dilute aqueous solution. In more concentrated solution, however, a second equilibrium reaction becomes important with the fluoride ion forming the complex ion HFJ. The relevant equilibria are ... 

Emphasis was put on providing a sound physicochemical basis for the modeling of the effects determining a reaction mechanism. Thus, methods were developed for the estimation of pXj-vahies, bond dissociation energies, heats of formation, frontier molecular orbital energies and coefficients, and stcric hindrance. 

The knowledge base is essentially two-fold on one hand it consists of a series of procedures for calculating all-important physicochemical effects such as heats of reaction, bond dissociation energies, charge distribution, inductive, resonance, and polarizability effects (.see Section 7.1). The other part of the knowledge base defines the reaction types on which the EROS system can work. 

A more useful quantity for comparison with experiment is the heat of formation, which is defined as the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. The heat of formation can thus be calculated by subtracting the heats of atomisation of the elements and the atomic ionisation energies from the total energy. Unfortunately, ab initio calculations that do not include electron correlation (which we will discuss in Chapter 3) provide uniformly poor estimates of heats of formation w ith errors in bond dissociation energies of 25-40 kcal/mol, even at the Hartree-Fock limit for diatomic molecules. 

These harmonic-oscillator solutions predict evenly spaced energy levels (i.e., no anharmonicity) that persist for all v. It is, of course, known that molecular vibrations display anharmonicity (i.e., the energy levels move closer together as one moves to higher v) and that quantized vibrational motion ceases once the bond dissociation energy is reached. 

The Morse oscillator model is often used to go beyond the harmonic oscillator approximation. In this model, the potential Ej(R) is expressed in terms of the bond dissociation energy Dg and a parameter a related to the second derivative k of Ej(R) at Rg k = ( d2Ej/dR2) = 2a2Dg as follows ... 

Even within a particular approximation, total energy values relative to the method s zero of energy are often very inaccurate. It is quite common to find that this inaccuracy is almost always the result of systematic error. As such, the most accurate values are often relative energies obtained by subtracting total energies from separate calculations. This is why the difference in energy between conformers and bond dissociation energies can be computed extremely accurately. 

In this section you have seen how heats of com bustion can be used to determine relative stabilities of isomeric alkanes In later sections we shall expand our scope to include the experimentally determined heats of certain other reactions such as bond dissociation energies (Section 4 16) and heats of hydrogenation (Section 6 2) to see how AH° values from various sources can aid our understanding of structure and reactivity... 

The energy required for homolytic bond cleavage is called the bond dissociation energy (BDE) A list of some bond dissociation energies is given m Table 4 3... 

As the table indicates C—H bond dissociation energies m alkanes are approxi mately 375 to 435 kJ/mol (90-105 kcal/mol) Homolysis of the H—CH3 bond m methane gives methyl radical and requires 435 kJ/mol (104 kcal/mol) The dissociation energy of the H—CH2CH3 bond m ethane which gives a primary radical is somewhat less (410 kJ/mol or 98 kcal/mol) and is consistent with the notion that ethyl radical (primary) is more stable than methyl... 

Bond Dissociation Energies of Some Representative Compounds ... 

Bond Bond dissociation energy Bond Bond dissociation energy... 

Bond dissociation energies refer to bond indicated in structural formula for each substance... 

Because the starting material (propane) and one of the products (H ) are the same m both processes the difference m bond dissociation energies is equal to the energy dif ference between an n propyl radical (primary) and an isopropyl radical (secondary) As depicted m Figure 4 20 the secondary radical is 13 kJ/mol (3 kcal/mol) more stable than the primary radical... 

Similarly by comparing the bond dissociation energies of the two different types of C—H bonds m 2 methylpropane we see that a tertiary radical is 30 kJ/mol (7 kcal/ mol) more stable than a primary radical... 

Carbon-carbon bond dissociation energies have been measured... 

Cleavage of the carbon-carbon bond in ethane yields two methyl radicals whereas propane yields an ethyl radical and one methyl radical Ethyl radical is more stable than methyl and so less energy is required to break the carbon-carbon bond in propane than in ethane The measured carbon-carbon bond dissociation energy in ethane is 368 kJ/mol (88 kcal/mol) and that in propane is 355 kJ/mol (85 kcal/mol)... 

The bond dissociation energy of the other reactant methane is much higher It IS 435 kj/mol (104 kcal/mol)... 

You have seen that measurements of heats of reaction such as heats of combustion can pro vide quantitative information concerning the relative stability of constitutional isomers (Section 2 18) and stereoisomers (Section 3 11) The box in Section 2 18 described how heats of reaction can be manipulated arithmetically to generate heats of formation (AH ) for many molecules The following material shows how two different sources of thermo chemical information heats of formation and bond dissociation energies (see Table 4 3) can reveal whether a particular reaction is exothermic or en dothermic and by how much... 

The same conclusion is reached using bond dis sociation energies The following equation shows the bond dissociation energies of the reactants and prod ucts taken from Table 4 3... 

Compare chlorination of methane with lodina tion The relevant bond dissociation energies are given in the equation... 

Bromination of methane is exothermic but less exothermic than chlorination The value calculated from bond dissociation energies is AH° = -30 kJ Al though bromination of methane is energetically fa vorable economic considerations cause most of the methyl bromide prepared commercially to be made from methanol by reaction with hydrogen bromide... 

Basing your answers on the bond dissociation energies in Table 4 3 calculate which of the following reactions are endothermic and which are exothermic... 

The degree to which allylic radicals are stabilized by delocalization of the unpaired electron causes reactions that generate them to proceed more readily than those that give simple alkyl radicals Compare for example the bond dissociation energies of the pri mary C—H bonds of propane and propene... 

The benzyhc position m alkylbenzenes is analogous to the allyhc position m alkenes Thus a benzyhc C—H bond like an allyhc one is weaker than a C—H bond of an alkane as the bond dissociation energies of toluene propene and 2 methylpropane attest... 

We attributed the decreased bond dissociation energy in propene to stabilization of allyl radical by electron delocalization Similarly electron delocalization stabilizes benzyl rad ical and weakens the benzylic C—H bond... 

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