B3LYP modelling

Density functional models provide a much better account. The local density model does the poorest and BP and B3LYP models do the best, but the differences are not great. As with metal-carbon (carbon monoxide) lengths, bond distances from all-electron 6-3IG calculations are usually (but not always) shorter than those obtained... 

It was this observation which gave rise to so-called hybrid derrsity ftmctional models, such as the B3LYP model. Here, the Hartree-Fock exchange energy is added to the exchange energy from a partictrlar density functional model with one or more adjustable parameters. 

With the exception of STO-3G and both MP2 models, all models (including semi-empirical models) provide a credible account of relative CH bond energies. In terms of mean absolute error, BP and B3LYP models with the 6-311+G basis set are best and Hartree-Fock 3-21G and 6-3IG models, local density 6-3IG models and semi-empirical models are worst. More careful scrutiny turns up sizeable individual errors which may in part be due to the experimental data. For example, the best of the models appear to converge on a CH bond dissociation for cycloheptatriene which is 35-37 kcal/mol less than that in methane (the reference compound) compared with the experimental estimate of 31 kcal/mol. It is quite possible that the latter is in error. The reason for the poor performance of MP2 models, with individual errors as large as 16 kcal/mol (for cycloheptatriene) is unclear. The reason behind the unexpected good performance of all three semi-empirical models is also unclear. 

In terms of both mean absolute error (in symmetric stretching frequencies) and of individual frequencies, density functional models perform significantly better than Hartree-Fock models. As with diatomic molecules, local density models appear to provide the best overall account, but the performance of the other models (except for B3LYP models) is not much different. B3LYP models and MP2 models do not appear to fare as well in their descriptions of frequencies in one-heavy-atom hydrides, and the performance of each appears to worsen in moving from the 6-3IG to the 6-311+G basis set. 

C=C stretching frequencies experimentally range from 1570 cm in cyclobutene to 1872 cm in tetrafluoroethylene (see appropriate tables in Appendix A7). All levels of calculation reproduce the basic trend in frequencies but, on the basis of mean absolute errors, show widely different performance (Table 7-5). Local density and MP2 models with the 6-311+G basis set perform best and semi-empirical models and density functional models (except the B3LYP model) with the 6-3IG basis set perform worst. Hartree-Fock models with the 3-2IG and larger basis sets also turn in good performance. 

The MP2/6-31G model provides a good account of relative activation energies in those systems (although it is no better than that provided by the corresponding Hartree-Fock model). This is another instance where the behavior of MP2 and B3LYP models diverge. 

Individual errors are typically quite small (on the order of a few tenths of a debye at most), and even highly polar and ionic molecules are reasonably well described. Comparison of results from 6-3IG and 6-311+G density functional models (Figure 10-5 vs. 10-6 for the EDFl model and Figure 10-7 vs. 10-8 for the B3LYP model) clearly reveals that the smaller basis set is not as effective, in particular with regard to dipole moments in highly polar and ionic molecules. Here, the models underestimate the experimental dipole moments, sometimes by 1 debye or more. 

B3LYP Model. A Hybrid Density Functional Model which improves on the Local Density Model by accounting explicitly for non-uniformity in electron distributions, and which also incorporates the Exchange Energy from the Hartree-Fock Model. The B3LYP model involves three adjustable parameters. 

Becke-Lee-Yang-Parr Model. See BLYP Model, B3LYP Model. 

B3LYP modelling of the reaction of lead tetraacetate with tricyclododec-10-enes indicated that the addition to the double bond is concerted.40... 

B3LYP model = both a hybrid density functional model and a non-local density functional model, it incorporates three adjustable parameters. 

Again, nonequilibrium calculations were performed using a DFT/B3LYP model, and employing for all systems (see below) experimental gas phase geometries and an aug-cc-pVDZ basis set. The linear response functions afso(0), aajg(—w to) and aa 8(—to to) were obtained analytically, whereas the higher order polarizabilities, Papy(—to to, 0) and 0), were determined via a finite electric field technique. The results published in ref. [30] are shown in Table 2.11. 

Assignment based on GIAO 30 values calculated from a BB-conformation DFT/B3LYP model. 7Cqllat or Cmethyi observed in 60 ps dipolar dephasing delay NQS spectrum. 

Check, C. E. Gilbert, T. M. Progressive systematic underestimation of reaction energies by the B3LYP model as the number of C-C bonds increases why organic chemists should use multiple DPT models for calculations involving polycarbon hydrocarbons, J. Org. Chem. 2005, 70, 9828-9834. 

It is quite apparent that the PBEO approach provides the most accurate results, even with respect to the B3LYP model. Note, furthermore, that conventional density functionals provide comparable hyperfine splittings for the hydrogen atom, but disappointing results for carbon [73]. 

In summary, the PBEO absolute shieldings for the carbon atoms are of remarkable quality for all the hybridizations and chemical enviroments considered here. In particular the mean absolute deviation for the PBEO model (4.6 ppm) is lower than that provided by the MP2 approach (6.0 ppm) and by the HF method (7.9 ppm). So, the PBEO functional represents an improvement over conventional quantum mechanical approaches, whereas the B3LYP model (and all the other current functionals) remains essentially at the same level as the HF method [82]. 

The CsC triple bonds of other alkynes closely follow the same pattern as ethyne including the effect of the extra QC methods. Since QC results have been collected for a significant number of compounds with C=C triple bonds and since they all show that MP2 calculations give rather poor bond lengths while the B3LYP model consistently gives bond lengths closer to experimental whether r, tq or even r, these results are presented in a different format in Table lOA for only a few combinations of method and basis set. 

A number of approaches have been proposed for the computation of NMR properties in the framework of DF approaches [86-91]. Here we will make explicit reference to the GIAO model, which appears particularly effective [92,93]. It has been recently pointed out that the MP2 method predicts chemical shifts which are closer to experiment than those obtained using DF approaches, including the B3LYP model [93]. It is so natural to include, as a stringent test, the computation of chemical shieldings. In particular, we have selected some examples in order to investigate the different possible hybridizations of carbon atoms. We have next added the ozone molecule, which is a particularly difficult test for NMR properties [90,92], The results are collected in table XIII. 

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