B3LYP density functionals

We win run this job on methane at the Hartree-Fock level using the 6-31G(d) basis our molecule specification is the result of a geometry optimization using the B3LYP Density Functional Theory method with the same basis set. This combination is cited... 

Perform a low-level geometry optimization with a medium-sized basis set, for example, a Hartree-Fock or B3LYP Density Functional Theory calculation with the 6-31G(d) basis set. (For very large systems, a smaller basis set might be necessary.)... 

The keyword for a given density-functional method is formed by concatenating the symbols for its exchange and correlation functionals. For example, combining the Becke three-term (B3) exchange functional with the Lee-Yang-Parr (LYP) correlation functional leads to the popular B3LYP density functional method. 

Baik and Friesner used an SCRF procedure in conjunction with B3LYP density functional calculations to obtain electrode potentials for groups of aromatic molecules, metallocenes and transition metal complexes in four different solvents 132 the average absolute deviation was about 0.15 volts for a range of values of 3.82 volts. Saracino et al. computed pKa for a series of carboxylic acids with an average absolute deviation of 0.41 for pKa between 1.23 and 5.03.133... 

This error can be considerably reduced, at very little cost, by employing B3LYP density functional theory instead of SCF. The scale factor, 0.896, is much closer to unity, and both mean and maximum absolute errors are cut in half compared to the scaled SCF level corrections. (The largest errors in the 120-molecule data set are 0.10 kcal/mol for P2 and 0.09 kcal/mol for BeO.) It could in fact be argued that the remaining discrepancy between the scaled B3LYP/cc-pVTZuc+1 values is on the same order of magnitude as the uncertainty in the ACPF/MTsmall values themselves. 

A complementary paper was reported soon after by Adam, Bach and coworkers where eight transition structures for the epoxidation of the chiral allylic alcohol (Z)-3-methyl-3-penten-2-ol with peroxyformic acid were computed by the B3LYP density functional method with 6-31G(d) and 6-31G(d,p) basis sets. The four lowest-energy transition structures and their respective prereaction clusters were fuUy re-optimized by employing 6-31H-G(d,p) and correlation-consistent polarized valence triple- cc-pZTV basis sets. 

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. 

B3LYP density functional models provide somewhat better bond length results than the other density functional models, generally very close to experimental distances and to those from MP2 calculations. As with the other density functional models, the errors are largest where one (or two) second-row elements are involved. This is apparent from Figure 5-4, which compares B3LYP/6-311+G and experimental bond distances. 

As with hydrocarbons, accurate descriptions of equilibrium structures for molecules with heteroatoms from density functional and MP2 models requires polarization basis sets. As shown in Table A5-20 (Appendix A5), bond distances in these compounds obtained from (EDF 1 and B3LYP) density functional models and from MP2 models... 

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. 

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. 

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. 

Individual activation energies from BP, BLYP, EDFl and B3LYP density functional models are similar (and different from those of Hartree-Fock and local density models). They are both smaller and larger than standard values, but typically deviate by only a few kcal/mol. The most conspicuous exception is for Diels-Alder cycloaddition of cyclopentadiene and ethylene. Density functional models show activation energies around 20 kcaPmol, consistent with the experimental estimate for the reaction but significantly larger than the 9 kcal/mol value obtained from MP2/6-311+G calculations. Overall, density functional models appear to provide an acceptable account of activation energies, and are recommended for use. Results from 6-3IG and 6-311+G basis sets are very similar, and it is difficult to justify use of the latter. 

Relative times for the MMFF molecular mechanics model, the AMI semi-empirical model, Hartree-Fock models with 3-2IG, 6-3IG and 6-311+G basis sets, EDFl and B3LYP density functional models and the MP2 model with 6-3IG and 6-311+G basis sets, for energy calculations, geometry optimizations and frequency evaluations, and the localized MP2 (LMP2) model with 6-3 IG and... 

Heats of formation obtained from bond separation reactions from Hartree-Fock, EDFl and B3LYP density functional and MP2 models all with 6-3IG and 6-311+G basis sets are compared to experimental values in Table 13-1. Errors in calculated quantities are exactly the same as those for the underlying bond separation reactions. ... 

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