Density functional models local

Halls, M. D., Schlegel, H. B., 1998, Comparison of the Performance of Local, Gradient-Corrected, and Hybrid Density Functional Models in Predicting Infrared Intensities , J. Chem. Phys., 109, 10587. 

Calculated equilibrium geometries for hydrogen and main-group hydrides containing one and two heavy (non-hydrogen) atoms are provided in Appendix A5 (Tables A5-1 and A5-10 for molecular mechanics models, A5-2 and A5-11 for Hartree-Fock models, A5-3 and A5-12 for local density models, A5-4 to A5-7 and A5-13 to A5-16 for BP, BLYP, EDFl and B3LYP density functional models, A5-8 and A5-17 for MP2 models and A5-9 and A5-18 for MNDO, AMI and PM3 semi-empirical models). Mean absolute errors in bond lengths are provided in Tables 5-1 and 5-2 for one and two-heavy-atom systems, respectively. 

Calculated heavy-atom bond distances in molecules with three or more first and/or second-row atoms are tabulated in Appendix A5 molecular mechanics models (Table A5-21), Hartree-Fock models (Table A5-22), local density models (Table A5-23), BP, BLYP, EDFl and B3LYP density functional models (Tables A5-24 to A5-27), MP2 models (Table A5-28), and MNDO, AMI and PM3 semi-empirical models (Table A5-29). Results for STO-3G, 3-21G, 6-31G and 6-311+G basis sets are provided for Hartree-Fock models, but as in previous comparisons, only 6-3IG and 6-311+G basis sets are employed for local density, density functional and MP2 models. 

None of the semi-empirical models perform as well as Hartree-Fock models (except STO-3G), local density models, density functional models or MP2 models. PM3 provides the best overall description, although on the basis of mean absolute errors alone, all three models perform to an acceptable standard. Given the large difference in cost of application, semi-empirical models clearly have a role to play in structure determination. 

Results from local density models and BP, BLYP and EDF 1 density functional models are, broadly speaking, comparable to those from 6-3IG models, consistent with similarity in mean absolute errors. As with bond length comparisons, BLYP models stand out as inferior to the other non-local models. Both B3LYP/6-31G and MP2/6-31G models provide superior results, and either would appear to be a suitable choice where improved quality is required. 

Consistent with earlier remarks made for bond length comparisons, little if any improvement results in moving from the 6-3IG to the 6-311+G basis set for Hartree-Fock, local density and density functional models, but significant improvement results for MP2 models. 

Comparative data for heavy-atom bond lengths and skeletal bond angles for molecules incorporating one or more third or fourth-row, main-group elements are provided in Appendix A5 Table A5-39 for Hartree-Fock models with STO-3G, 3-2IG and 6-3IG basis sets. Table A5-40 for the local density model, BP, BLYP, EDFl andB3LYP density functional models and the MP2 model, all with the 6-3IG basis set, and in Table A5-41 for MNDO, AMI and PM3 semi-empirical models. 6-31G, local density, density functional and MP2 calculations have been restricted to molecules with third-row elements only. Also, molecular mechanics models have been excluded from the comparison. A summary of errors in bond distances is provided in Table 5-8. 

All density functional models (including the local density model) and the MP2/6-31G model perform admirably in describing the structures of these compounds. In terms of mean absolute errors, the local density model fares best and the BLYP model fares worse. The former observation is consistent with the favorable performance of Hartree-Fock models for these systems and of the previously noted parallels in structural results for Hartree-Fock and local density models. Figures 5-32 to 5-37 provide an overview. 

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... 

As with metal-carbon monoxide bonds, the MP2/6-3IG model does not lead to results of the same calibre as those from density functional models (except local density models). The model actually shows the opposite behavior as 6-3IG, in that bond lengths are consistently shorter than experimental values, sometimes significantly so. In view of its poor performance and the considerable cost of MP2 models (relative to density functional models), there seems little reason to employ them for structural investigations on organometallics. 

Comparative data for a few particularly interesting systems is provided in Table 5-15. STO-3G, 3-21G and 6-3IG Hartree-Fock models, local density models, BP, BLYP, EDFl and B3LYP density functional models all with the 6-3IG basis set, the MP2/6-31G model and MNDO,AMl andPM3 semi-empirical models have been examined. 

Triplet methylene is known to be bent with a bond angle of approximately 136°. This is closely reproduced by all Hartree-Fock models (except for STO-3G which yields a bond angle approximately 10° too small), as well as local density models, BP, BLYP, EDFl and B3LYP density functional models and MP2 models. Semi-empirical models also suggest a bent structure, but with an HCH angle which is much too large. 

There is a very wide variation in the quality of results from the different models. MNDO and AMI semi-empirical models, the ST0-3G model and both local density models are completely unsatisfactory. The 3-2IG model, all density functional models with the 6-3IG basis set and the PM3 model fare better, while 6-3IG ... 

Density functional models and MP2 models show more consistent behavior. With the 6-311+G basis set, calculated basicities are generally very close to experimental values. The corresponding results with the 6-3IG basis set are generally not as good, although the differences are not that great. In terms of mean absolute errors, local density models perform the worst, and B3LYP/6-311+G and MP2/ 6-311+G models perform the best. 

Data are provided in Table 6-10, with the same calculation models previously examined for hydrogenation reactions. As might be expected from the experience with hydrogenation reactions, Hartree-Fock models with 6-3IG and 6-311+G basis sets perform relatively well. In fact, they turn in the lowest mean absolute errors of any of the models examined. The performance of density functional models (excluding local density models) and MP2 models with both 6-3IG and 6-311+G basis sets is not much worse. On the other hand, local density models yield very poor results in all cases showing reactions which are too exothermic. The reason is unclear. Semi-empirical models yield completely unacceptable results, consistent with their performance for hydrogenation reactions. 

The comparison between propyne and allene warrants additional comment. Experimentally, propyne is the more stable by approximately 2 kcal/mol, an observation which is reproduced by Hartree-Fock models but is somewhat exaggerated by MP2 models. Note, however, that all density functional models (including local density models) show the reverse order of isomer stabilities with allene being more stable than propyne. This is another instance where the behavior of B3LYP and MP2 models do not mimic each other. 

BP, BLYP, EDFl and B3LYP density functional models all lead to significant improvements over both Hartree-Fock and local density models, at least in terms of mean absolute deviations. While most reactions are better described, there are exceptions. Most notable among these is the bond separation reaction for tetrachloromethane. All four models show a highly exothermic reaction in contrast with both G3 and experimental results which show a nearly thermoneutral reaction. Similar, but somewhat smaller, effects are seen for isobutane and trimethylamine. As was the case with Hartree-Fock calculations. 

With the exception of semi-empirical models, all models provide very good descriptions of relative nitrogen basicities. Even STO-3G performs acceptably compounds are properly ordered and individual errors rarely exceed 1 -2 kcal/mol. One unexpected result is that neither Hartree-Fock nor any of the density functional models improve on moving from the 6-3IG to the 6-311+G basis set (local density models are an exception). Some individual comparisons improve, but mean absolute errors increase significantly. The reason is unclear. The best overall description is provided by MP2 models. Unlike bond separation energy comparisons (see Table 6-11), these show little sensitivity to underlying basis set and results from the MP2/6-3IG model are as good as those from the MP2/6-311+G model. 

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. 

Hartree-Fock, local density and MP2 models all yield barrier heights which are slightly larger than those from density functional models, and are outside the experimental range. Additionally, the energies of the twist-boat intermediate and boat transition state (relative to the chair conformer) are also slightly higher. 

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