Molecular orbital calculations dissociation energy

An alkyl radical and a nitroxide radical exist in an equlibrium with the corresponding alkoxyamine as their coupling product (Eq. 57). Moad and Rizzardo [213] and Kazmaier et al. [214] independently estimated the effects of the structure of the alkyl group and the nitroxide on the dissociation energy of various alkoxyamines into the radicals by semiempirical molecular orbital calculations. The bond dissociation energies determined are summarized in Table 5 ... 

Co2(CO)q system, reveals that the reactions proceed through mononuclear transition states and intermediates, many of which have established precedents. The major pathway requires neither radical intermediates nor free formaldehyde. The observed rate laws, product distributions, kinetic isotope effects, solvent effects, and thermochemical parameters are accounted for by the proposed mechanistic scheme. Significant support of the proposed scheme at every crucial step is provided by a new type of semi-empirical molecular-orbital calculation which is parameterized via known bond-dissociation energies. The results may serve as a starting point for more detailed calculations. Generalization to other transition-metal catalyzed systems is not yet possible. 

In addition to this type of empirical approach, there are several other approaches that are related more directly to specific properties of the organic, such as the C-H bond dissociation enthalpies (Heicklen, 1981 Jolly et a.L, 1985), ionization energy (Gaffney and Levine, 1979), or NMR shifts (Hodson, 1988). In addition, molecular orbital calculations (Klamt, 1993) and transition state theory (Cohen and Benson, 1987) have been applied. 

Bonds become weaker as we move down the Periodic Table. Compare C O and C S, or the carbon-halogen bonds C—F, C—Cl, C—Br, C—1. This is a consequence of the first generalization, since bond distances must increase as we go down the periodic table because the number of inner electrons increases. However, it is noted that high-level ab initio molecular-orbital calculations confirm that the effect of alkyl substituents on R—X bond dissociation energies varies according to the nature of X (the stabilizing... 

S+ 211,(2), 2nu(2), 411,(2), 4nu(2), and 2A 2AU, 4A 4AU [39], In 1981 H. H. Michels presented curves for these states and calculated dissociation energies and Ea for the bound states of 02( ) from —1.5 eV to —3.7 eV [40]. Assigning the experimental and theoretical Ea and VEa, we obtain 12 M and 12 D HIMPEC for the 24 states [5, 41 -43. The relative bond orders of the ground state agree with simple molecular orbital predictions. The bond orders for the excited states are reasonable compared to the predicted values. Two anion curves for S2, Se2, and Te2 have been constructed from experimental data [44-47]. 

Molecular orbital calculations on molecules with three or more electrons are based on Slater-determinant wavefunctions. If the basis sets are sufficiently large, such Hartree-Fock or HF calculations are generally found to reproduce experimental bond distances to within 3 or 4 pm, and experimental valence angles to within 3 or 4 degrees. The dissociation energies obtained by such calculations are, however, too inaccurate to be useful. 

The structures shown above the dotted line illustrate the implications of these criteria and suggest more stable structures. In addition although the stmcture shown for N2O2 is consistent with the Lewis formalism, the weak N-N single bond means that the structure is only observed at low temperatures. The dissociation energy of the NO dimer is only 8.3 kJ moP and it represents an example of a molecule which is not adequately represented by Hartree-Fock molecular orbital calculations [76]. The structures below the dotted line are disfavoured because of they are dipolar or have identical charges on adjacent atoms. 

The continuous development and implementation of molecular orbital theory ab initio methods have enlarged the applications to this area too. Indeed, the impact of theoretical calculations in thermochemistry is substantial. Experimental groups often use calculations as a supplement to the interpretation of their results. In this section we will mention a few recent and representative studies that are directly associated with the bond dissociation energies of silanes. Early theoretical investigations of the Si—H bond strength in silanes have been summarized [13]. 

Why does an electron-pair bond calculated by the MO method not dissociate properly We have seen that half of the time both electrons in the low-energy molecular orbital are in the vicinity of just one of the nuclei. But as the nuclei move far apart, this corresponds to a far greater energy than having only one electron in the vicinity of each nucleus, as the VB method suggests. 

Improvement of the MO method involves better orbitals, better account of interelectronic repulsion, and introduction of mixing of different electron configurations in the molecular orbitals ( configuration interaction ). Improved MO calculations give much more accurate energies at the minimum of a plot such as Figure 21-11, but the bonds still do not dissociate properly, for the same reason as with the simple MO method. 

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