Bond dissociation energy in methane

The bond dissociation energy in methane, Z)o(CH3 H), is the minimum energy to achieve reaction (5). The results from several ab initio computations are compiled in Table 3. Vibrational zero-point energies (see Section 7) are included, and were computed using unsealed B3LYP/ 6-31G(d) frequencies. Geometries were also computed at the B3LYP/6-31G(d) level. 

There is weaker dependence on basis set than in the previous example because the spatial extent of the orbitals does not change as much in reaction (5) as in reaction (4). Including electron correlation is important because the number of electron pairs changes. The best calculation in 

Bond dissociation energy in methane, Z o(CH3-H) (in kJ mol ), computed using a va-riety of theories and basis sets [geometries and ZPEs from B3LYP/6-31G(d)] 

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The radical stabilization energy (RSE) of a substituted methyl radical CH2X is generally defined as the difference between the C-H bond dissociation energy in methane and the C-H BDE in the substituted methane CH3X ... 

Alternatively, the BDE values may be reported relative to the C-H bond dissociation energy in methane (3) as the reference. This is quantitatively described in Equation 5.3 as a formal hydrogen transfer process between methane (3) and a substituted carbon-centered radical 2. The reaction enthalpy for this process is often interpreted as the stabilizing influence of substituents Rj, R2, and R3 on the radical center and thus referred to as the radical stabihzation energy (RSE). When defined as in Equation 5.3, positive values imply a stabilizing influence of the substituents on the radical center. The RSE energies are connected to the BDE values in Equations 5.land 5.2 as described in Equation 5.4. 

As the table indicates, C—H bond dissociation energies in alkanes are approximately 375 to 435 kJ/mol (90-105 kcal/mol). Homolysis of the H—CH3 bond in methane gives methyl radical and requires 435 kJ/mol (104 kcal/mol). The dissociation energy of the H—CH2CH3 bond in 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. 

It is clear that proper description of the energetics of homolytic bond dissociation requires models that account for electron correlation. Are correlated models also needed for accurate descriptions of relative homolytic bond dissociation energies where the relevant reactions are expressed as isodesmic processes A single example suggests that they may not be. Table 6-15 compares calculated and measured CH bond dissociation energies in hydrocarbons, R-H, relative to the CH bond energy in methane as a standard ... 

Table 6-15 CH Bond Dissociation Energies in Hydrocarbons Relative to Methane... 

In principle, one might try to study the ionic dissociation of an acid (equation 7.3) directly in the gas phase, but AH for dissociation of a neutral species to a proton and an anion is usually quite large without solvent stabilization of the ions. For example, the AH for the gas phase dissociation of methane to methyl anion and a proton (AH° jj) was calculated to be - -417kcal/mol. This is much greater than the homolytic C—H bond dissociation energy of methane (-I-104 kcal/mol), so thermolysis of methane in the gas phase leads to radicals instead of ions. The pKg value of an acid can be determined indirectly, however, by measuring the equilibrium for proton transfer from the acid to a base with a known pKg. With a series of measurements, a scale of gas phase acidity values can be established by referencing one compound to another. 

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

From this value and known C—H bond dissociation energies, pK values can be calculated. Early application of these methods gave estimates of the p/Ts of toluene and propene of about 45 and 48, respectively. Methane was estimated to have a pAT in the range of 52-62. Electrochemical measurements in DMF have given the results shown in Table 7.3. These measurements put the pK of methane at about 48, with benzylic and allylic stabilization leading to values of 39 and 38 for toluene and propene, respectively. The electrochemical values overlap with the pATdmso scale for compounds such as diphenyl-methane and triphenylmethane. 

Caibon has eight electrons in its valence shell in both methane and carbon tetrafluoride. By forming covalent bonds to four other atoms, carbon achieves a stable electron configuration analogous to neon. Each covalent bond in methane and carbon tetrafluoride is quite strong—comparable to the bond between hydrogens in Fl2 in bond dissociation energy. 

The functionalization reaction as shown in Scheme 1(A) clearly requires the breaking of a C-H bond at some point in the reaction sequence. This step is most difficult to achieve for R = alkyl as both the heterolytic and homolytic C-H bond dissociation energies are high. For example, the pKa of methane is estimated to be ca. 48 (6,7). Bond heterolysis, thus, hardly appears feasible. C-H bond homolysis also appears difficult, since the C-H bonds of alkanes are among the strongest single bonds in nature. This is particularly true for primary carbons and for methane, where the radicals which would result from homolysis are not stabilized. The bond energy (homolytic dissociation enthalpy at 25 °C) of methane is 105 kcal/mol (8). 

The reaction enthalpy and thus the RSE will be negative for all radicals, which are more stable than the methyl radical. Equation 1 describes nothing else but the difference in the bond dissociation energies (BDE) of CH3 - H and R - H, but avoids most of the technical complications involved in the determination of absolute BDEs. It can thus be expected that even moderately accurate theoretical methods give reasonable RSE values, while this is not so for the prediction of absolute BDEs. In principle, the isodesmic reaction described in Eq. 1 lends itself to all types of carbon-centered radicals. However, the error compensation responsible for the success of isodesmic equations becomes less effective with increasingly different electronic characteristics of the C - H bond in methane and the R - H bond. As a consequence the stability of a-radicals located at sp2 hybridized carbon atoms may best be described relative to the vinyl radical 3 and ethylene 4 ... 

Bond dissociation energies (BDEs) provide a measure of both the reactivity of a compound (with respect to homolytic bond rupture) and the stability of the corresponding radical. There have been many theoretical investigations of BDEs for a wide variety of species [36], In particular, the C-H BDE for a substituted methane is given by the enthalpy change for the reaction ... 

Bond dissociation energies for a selection of substituted methanes, calculated at a range of levels [23], are compared with experimental values [37] in Tables 6.9 and 6.10. Also listed are mean absolute deviations (MADs) and mean deviations (MDs) from experimental values [e.g. MAD(Exp.)] and from CBS-RAD [e.g. MD(CBS-RAD)]. 

The determination of thermodynamic stability of a radical from C—H bond-dissociation energies (BDE) in suitable precursors has a long tradition. As in other schemes, stabilization has to be determined with respect to a reference system and cannot be given on an absolute basis. The reference BDE used first and still used is that in methane (Szwarc, 1948). Another more refined approach for the evaluation of substituent effects by this procedure uses more than one reference compound. The C—H BDE under study is approximated by a C—H bond in an unsubstituted molecule which resembles most closely the substituted system (Benson, 1965). Thus, distinctions are made between primary, secondary and tertiary C—H bonds. It is important to be aware of the different reference systems if stabilization energies are to be compared. 

A very useful thermodynamic cycle links three important physical properties homolytic bond dissociation energies (BDE), electron affinities (EA), and acidities. It has been used in the gas phase and solution to determine, sometimes with high accuracy, carbon acidities (Scheme 3.6). " For example, the BDE of methane has been established as 104.9 0.1 kcahmol " " and the EA of the methyl radical, 1.8 0.7 kcal/mol, has been determined with high accuracy by photoelectron spectroscopy (PES) on the methyl anion (i.e., electron binding energy measurements). Of course, the ionization potential of the hydrogen atom is well established, 313.6 kcal/ mol, and as a result, a gas-phase acidity (A//acid) of 416.7 0.7 kcal/mol has been... 

Simple MO pictures also explain the differences in the bond dissociation energies (BDE) of methane and ammonia, and explain different triplet carbene and nitrene reactivities toward hydrogen atom donors. 

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