Bond enthalpy scheme

Incorporation of sterically demanding aryl substituents allows isolation of bis(arene)zirconium and hafnium complexes. The bond enthalpies of (7]6-(l,3,5-tBu)3C6H3)2M (M = Ti, 1 Zr, 2 Hf, 3) have been measured by iodinolytic bath calorimetry and values of 49(1), 64(3), and 67(4) kcal mol-1 have been determined for the respective metal-arene bond enthalpies (Scheme l).4 Computational studies establish that the major metal-arene bonding interaction is a 5-backbond formed from the overlap of metal dxz-yz and orbitals with the appropriate linear combination of arene p-orbitals. The observed increase in metal-arene bond strength is consistent with increased backbonding down the... 

Various schemes have been proposed to calculate heats of formation. Traditionally heats of formation have been calculated by increment addition method. In molecular mechanics, the method can be applied by either using bond energy schemes with the vibrational energies being absorbed in the bond energy increments, or using bond enthalpy schemes ... 

The more proper calculation of the heats of formation with a full statistical mechanical treatment in molecular mechanics is referred to as a bond enthalpy scheme, and this method can also be applied to quantum mechanical calculations discussed later. This scheme was first used by Lifson and Warshel and by Boyd. However, they calculated the heats of formation of only a small number of sample molecules, and so the abilities of these force fields in this respect cannot be judged. Extensive studies were carried out by Wertz, who developed a force field that was capable of calculating geometries, vibrational frequencies, and then heats of formation by the complete statistical mechanical method, including an explicit evaluation of the vibrational eneigy. Wertz s force field was simpler and more limited than the one in the molecular mechanics programs such as MM3, but the resulting calculated heats... 

Figure 1 Total energy content of a molecule in its ground state the bond enthalpy scheme in MM4...

The difference between an MM calculation of the enthalpy of formation and a bond energy scheme comes in the steric energy, which was shown in Eile 4-3. The sum of compression, bending, etc. energies is the steric energy, E = 2.60 kcal mol in Eile 4-3. This is added to BE, as is the partition function energy contribution (see below), PCE = 2.40 kcal moP, to yield... 

The so-called Laidler scheme was developed as a tool to estimate standard enthalpies of formation of organic compounds [90], It relies on the bond-additivity concept, that is, it assumes that the standard enthalpy of atomization of a given molecule in the gas phase (Aat//°, defined as the standard enthalpy of the reaction where all the chemical bonds are cleaved, yielding the gaseous ground-state atoms) can be evaluated by adding the relevant bond enthalpy terms. For instance, in the case of phenol, its standard enthalpy of atomization, or simply its enthalpy of atomization, refers to reaction 5.28 at 298.15 K ... 

This coherent reaction network clearly demonstrates the in ortance of the 30-40 kJ mole selectivity limit. When it is exceeded, as is the case with propane oxidation to acrolein, selectivity declines drastically. Similarly the accnmmulated data for propane and propene ammoxidation [27,28] to acrylonitrile indicate selectivities at 30% conversion of 50% and 85% respectively. These data are consistent with the 41 kJ mole difference in bond enthalpies shown in scheme 2 for propane and propene. 

Table 5 shows that the enthalpies and entropies of these octanes, while not identical, differ by only 4kcalmor and 5.3 eu, respectively, from smallest to largest. In general, bond additivity schemes for thermochemical properties can provide order-of-magnitude... 

In contrast to the FVP synthesis of indenocorannulene (98) from phenyl-corannulene, the fluoro-substituted analogue 29 (X=F) turns out to be very efficient [126] (Scheme 28). Catalytic cyclization is initiated by reaction of a silyl cation with an aryl fluoride to generate a phenyl cation and, subsequently, Friedel-Crafts reaction to an intramolecular aryl coupling, flowed by deprotonation, to give 98, The enabling feature of this reaction is the exchange of carbon-fluorine for sihcon-fluoiine bond enthalpies. 

The energetics of the C—H activation process have been of concern since its discovery. Calorimetric, equilibrium constant and kinetic information have been used to obtain estimates of the M—C and M—H bond energies. In general, these bonds have been found to be stronger than originally anticipated. Nolan et al. used a combination of calorimetric and kinetic data to estimate these bond enthalpies from the reactions in the following Scheme ... 

Ultimately, of course, it may be expected that all quantum mechanical calculations will yield thermodynamic quantities, e.g. enthalpies of formation. However, this stage has not yet been reached, but, at present, relations between classical chemical structures and thermodynamic quantities are being established. For example, Cox and Pilcher s book devotes some 70 pages to bond energy terms, bond energy schemes, steric effects, destabilization energies, and related matters. 

The procedure used in MM4 is basically similar to those described earlier in the bond energy scheme, but replaces steric energies with enthalpies. MM4 starts with the fundamental concept of heats of atomization (A//a the work required to dissociate one mole of the substance into the constituent atoms in their ground states) to calculate heats of formation. Few the A/fa can be calculated on the basis of the following thermochemical relationship ... 

Equation (10) contains almost the same energy terms as those defined in equation (9), except for the inclusion of an additional energy correction term, PFC, which was discussed in Section 2. Some terms in equation (10) have the same meaning as the terms defined in the bond energy scheme, such as the contributions from the formation of bonds (BE), the structural features increments (SE), and the statistical mechanical energy corrections (POP and TOR) that are included in the PFC term of equation (10). The effects of strain are represented by enthalpy in MM4 instead of by steric energy Ps. MH, the molar heat content or enthalpy of the compound, includes the terms as described in equation (9). T/R (Pt(av) + Pr(av>), die translational/rotational contribution in MM3, is considered as part of the MH term in MM4. 

Something additional will be needed to calculate heats of formation for compounds that contain delocalized electronic systems, particularly aromatic compounds, and related substances. Tlie problem with the methods previously described when applied to these systems is that one cannot expect to have constant bond energy or bond enthalpy units, because conjugated bonds come with various kinds of bond orders essentially from zero to one in the jr-bond component (or up to two if acetylenes are included), and these different bond orders correspond to different bond lengths and to different bond energies. Somehow this all has to be taken into account if one is to apply the calculation schemes described previously to these conjugated systems. 

In addition, several organoactinide complexes also catalyze the regioselective hydrothiolation of alkynes with various thiols (Scheme 14) [46,47]. Bond enthalpy considerations for the unexplored reaction predict net exothermicity for RSH addition to alk5mes, aUenes, and alkenes mediated by organoactinide complexes. While alkyne insertion into the An-S bmid (step ii) is predicted to be exothermic. 

The predictions of the reactivities by the geminal bond participation have been confirmed by the bond model analysis [103-105] of the transition states and the calculations of the enthalpies of activation AH of the Diels-Alder reaction [94], the Cope rearrangement [95], the sigmatropic rearrangement [96], the Alder ene reaction [100], and the aldol reaction [101] as are illustrated by the reactions of the methyl silyl derivatives in Scheme 38 [102], The bond is more electron donating than the bond. A silyl group at the Z-position enhances the reactivity. 

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