P3_Reaction Energies

For example comparison of isobutene and cis and

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Unformatted text preview: ns, for example, that between 1-butyne and 2-butyne mentioned above, formally fit this category, as do all comparisons of regio and stereoisomers. For example, comparison of isobutene and cis and trans2-butene. The latter two are stereoisomers and both are regioisomers of isobutene. 11 H3 C H C H3 C H3C C CH3 C H H H3 C C H C H H C CH3 Also of note are reactions that compare the energies of protonation (proton affinities) of closely-related molecules, for example, that compare the proton affinities of ammonia and trimethylamine. This is a quantity that can be accurately measured although not necessarily directly (see previous discussion). (CH3)3NH+ + NH3 → (CH3)3N + NH4+ In all of these cases, comparisons are between molecules with the same number of each kind of chemical bond and of each kind of electron pair. Only the local environment changes. It might be expected that these kinds of reaction would benefit from error cancellation to a greater extent than the previous types of reactions. The obvious suspicion is that it will be “easier” to calculate relative quantites, for example, the relative proton affinities of ammonia and methylamine, than it is to calculate absolute quantities, for example, the absolute proton affinity of ammonia. This will be tested in the next section. At the outset it should be pointed out that while absolute energies will certainly be required in some instances, in many others relative energies will suffice. 12 Limiting Behavior of Hartree-Fock, Density Functional and MP2 Models for Reaction Energies We first set out to establish or at least to estimate the limiting behavior of Hartree-Fock, B3LYP and MP2 models with regard to reaction energies using examples of each of the types processes discussed in the previous section. This will allow us to separate the effects of the LCAO approximation from effects arising from replacement of the exact manyelectron wavefunction by an approximate Hartree-Fock, density functional or MP2 wavefunction. As commented in the introduction to this chapter and in Chapter P2, it is not possible to actually reach the limit for either Hartree-Fock and B3LYP models, nor is it possible to establish the MP2 limit. However, it should be possible to use a sufficiently large basis set such that the addition of further functions to the basis set will have only a small effect on calculated reaction energy. As for geometry comparisons, the ccpVQZ basis set will be employed. This should be sufficiently large to be able to reflect the properties of the limit, but small enough to be applied to the molecules in the comparisons provided. Of more practical concern, ccpVQZ is about as large a basis set that can be applied to the molecules used in the comparisons that follow. The results provided in this section based on use of the cc-pVQZ basis set will be paralleled by those obtained using the slightly smaller cc-pVTZ basis set. This will allow us to quantify the extent to which reactions energies based on the cc-pVQZ basis set actually approach limiting values. The first comparison involves AH bond energies in molecular hydrogen and in one-heavy-atom hydrides and AB bond energies in two-heavy-atom hydrides. AH A +H AB A +B Reference bond energies have been obtained from the G3(MP2) recipe (see discussion later in this chapter) rather than from experiment. This provides a more uniform baseline and allows comparisons to be extended to molecules where experimental bond energies are not accurately known (if known at all). G3(MP2) heats of formation have already been corrected for zero-point vibrational energy and for finite temperature (298 K). That is, they correspond to the experimental data most commonly found in the chemical literature (including that in the NIST database). 13 These corrections are based on vibrational frequencies obtained from the HF/6-31G* model scaled by 0.9 to take account of a known systematic error in these frequencies. This means that energies from the Hartree-Fock, B3LYP and MP2 calculations also need to be corrected. Signed differences between B3LYP/cc-pVQZ and MP2/cc-pVQZ and G3(MP2) AH bond energies are shown in Figure P3-1 and between G3(MP2) AB bond energies are shown in Figure P3-2. Excel spreadsheets containing AH and AB bond dissociation energies discussed in this section (including Hartree-Fock bond energies) are provided on the CD-ROM accompanying this text (limiting AH bond energies and limiting AB bond energies, respectively). The Hartree-Fock cc-pVQZ model provides a very poor account of both AH and AB bond energies and individual errors have not been included in the figures. As expected, Hartree-Fock bond energies are much larger than G3(MP2) values, with mean absolute deviations of 125 and 160 kJ/mol for AH and AB bond energies, respectively. Bond energies calculated using the smaller cc-pVTZ basis set (not provided in the figures but available in the Excel spreadsheet) are nearly identical with those, confirming that the...
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