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Unformatted text preview: P2 models with both cc-pVQZ and cc-pVTZ basis sets is provided on the CD-ROM
accompanying this text (limiting structural isomer energies). The B3LYP model offers some improvement over the corresponding
Hartree-Fock model. The mean absolute error from experiment is reduced to
9 kJ/mol and the mean absolute deviation from G3(MP2) is reduced to 5
kJ/mol. The largest individual deviation error from experiment is reduced to
9 kJ/mol (for comparison of 1,3-butadiene and bicyclo[1.1.0]butane). The
largest individual deviations from G3(MP2) are 11 kJ/mol (for ). Consistent
with previous results for bond energies, isomer energies change only slightly
in moving to the smaller cc-pVTZ basis set (data are not provided in the
The “limiting” MP2 model shows a mean absolute error with experimental
results of 10 kJ/mol, similar to that for the corresponding B3LYP and MP2
models. However, the largest individual error (comparison of 1,3-butadiene
and bicycle[1.1.0] butane) is larger (30 kJ/mol). The mean absolute
deviation with G3(MP2) is 12 kJ/mol, somewhat greater than that for the
other two models.
The final comparison (Table P3-2) involves regio and stereoisomers and
exemplifes reactions in which both the total number of electron pairs and the
numbers of individual bond types are conserved. As with the previous
comparisons, the reference is to G3(MP2) energy differences, and the
“limiting” Hartree-Fock, B3LYP and MP2 isomer energies have been
corrected for zero-point energy and finite temperature in the same way as
G3(MP2) energy differences.
An Excel spreadsheet containing region and stereoisomer energies for Hartree-Fock,
B3LYP and MP2 models with both cc-pVQZ and cc-pVTZ basis sets is provided on the
CD-ROM accompanying this text (limiting regio and stereoisomer energies). The “limiting” Hartree-Fock model provides a good account of differences
in isomer energies. The mean deviation from G3(MP2) energy differences is
5 kJ/mol, and with a single exception (comparison of cyclobutene and
methylenecyclopropane) individual deviations are 7 kJ/mol or less. This is
not unexpected. Regio and stereoisomers are more closely related to each
other than structural isomers, and energy comparisons should benefit from 18 and cancellation of errors. Results from Hartree-Fock calculations with the
smaller cc-pVTZ basis set (not provided in the table) are nearly the same.
Table P3-2: Errors in “Limiting” Hartree-Fock, B3LYP and MP2 Energies of Regio and
1,3-butadiene B3LYP MP2 G3(MP2) Expt. isomer
1,2-butadiene 55 44 51 51 53 1-butyne 24 27 21 19 20 methylenecyclopropane 26 19 33 40 44 trans-2-butene 2 1 6 6 7 cis-2-butene 9 7 11 11 10 1-butene 13 15 18 16 17 methylenecyclobutane 87 80 90 87 86 1,4-pentadiene 21 29 31 30 30 1,1-dimethylallene 53 44 52 53 53 1,3-dimethylallene 55 45 58 57 1,2-pentadiene 62 55 66 65 65 2-methyl-2-propenal 7 4 1 3 9 trans-2-butenal 13 10 13 6 5 mean absolute error 4 8 (3) 2 - mean absolute deviation from G3(MP2) 4 7 (3) - 2 2-butyne
2-methyl-1,3-butadiene methyl vinyl ketone 19 In terms of mean absolute deviation from G3, the B3LYP/cc-pVQZ model is
slightly inferior to the corresponding Hartree-Fock model for region and
stereoisomer energy comparisons, although the difference is not large. This
suggests that errors inherent to Hartree-Fock theory in large part cancel
where reactants and products have the same number of bonds and electron
pairs, and differ only in detailed environment.
MP2 20 Practical Hartree-Fock and Density Functional Models for Reaction
Except for very small molecules, Hartree-Fock, B3LYP and especially MP2
models with very large basis sets such as cc-pVTZ and cc-pVQZ are not
practical for calculation of the energies for any but reactions involving very
small molecules. While this will slowly change with improvements in
computer speed and storage capabilities, at the present time these basis sets
are primarily of value in judging the limits and ultimately the quality of the
underlying (Hartree-Fock and B3LYP and MP2) models. Here we examine
the performance of two smaller basis sets, 6-31G* and 6-311+G**, both of
which are presently easily applicable to much larger molecules (with
molecular weights approaching 500 amu). The primary focus will be to
establish the ability of the models to reproduce G3(MP2) relative energies to
“chemical accuracy” that is, within 8 kJ/mol.
A summary of mean absolute errors for collections of AH and AB bond
dissociation energies are provided in Table P3-3. These include HartreeFock, B3LYP and MP2 models with the 6-31G* and 6-311+G** basis sets
as well as with the cc-pVTZ and cc-pVQZ basis sets previously examined.
An Excel spreadsheet containing AH and AB bond dissociation energies for HartreeFock, B3LYP and MP2 models with 6-31G*, 6-311+G**, cc-pVQZ and cc-pVTZ basis
sets is provided on the CD-ROM accompanying this text (AH and AB bond dissociation
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This note was uploaded on 02/22/2010 for the course CHEM N/A taught by Professor Head-gordon during the Spring '09 term at University of California, Berkeley.
- Spring '09