P3_Reaction Energies

Mean absolute errors are 8 and 17 kjmol for ah and ab

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Unformatted text preview: problem is the Hartree-Fock approximation and not the use of a finite basis set. The B3LYP/cc-pVQZ model provides a far better account. Mean absolute errors are 8 and 17 kJ/mol for AH and AB bond energies, respectively. Individual bond energies are always smaller than G3(MP2) values, and usually within 10 kJ/mol of G3(MP2) values for AH bond energies and 20 kJ/mol for AB bond energies. The B3LYP/cc-pVTZ model yields bond energies that differ from the corresponding cc-pVQZ values by only 1-2 kJ/mol, although the difference is 6 kJ/mol for the OH bond energy in water and 3-4 kJ/mol for some bonds involving two heteroatoms. This suggests that B3LYP models are more sensitive to basis set than Hartree-Fock models. Still, most of the discrepancy between B3LYP and G3(MP2) bond energies does not appear to be due to limitations in the basis set. Individual bond energies from the MP2/cc-pVQZ model show much wider variation from G3(MP2) values than those from the corresponding B3LYP model, although mean absolute errors are virtually identical (9 kJ/mol for AH bond energies and 17 kJ/mol for AB bond energies). These range from 25 kJ/mol too large for the bond energy in hydrogen, to 35 kJ/mol too small 14 Figure P3-1: Signed Deviations Between B3LYP/cc-pVQZ (left) and MP2/cc-pvQZ (right) and G3(MP2) AH Bond Energies (kJ/mol) Figure P3-2: Signed Deviations Between B3LYP/cc-pVQZ (left) and MP2/cc-pvQZ (right) and G3(MP2) AB Bond Energies (kJ/mol) 15 for the OO bond energy in hydrogen peroxide. In part, the problem may reside with the basis set. Bond energies from the MP2/cc-pVQZ model differ by as much as 18 kJ/mol (in Cl2) from those obtained from the corresponding cc-pVTZ model, and differences on the order of 10 kJ/mol are common. This result, while disturbing, is not unexpected. MP2 models (unlike Hartree-Fock and density functional models) directly use “excited-state” wavefunctions which involve both higher-order and more diffuse component than required in the ground state. In summary, “limiting” Hartree-Fock models fail to provide an acceptable account of bond dissociation energies. The corresponding B3LYP and MP2 models perform much better, although sizable deviations are noted for individual molecules, in particular, for MP2 models. Bond energies obtained from both Hartree-Fock and B3LYP models do not change significantly in moving from the cc-pVQZ to the smaller cc-pVTZ basis set. On the other hand, large changes are noted for some molecules between the corresponding MP2 models. The second comparison (Table P3-1) involves energy differences among structural isomers. Here, the total number of electron pairs is conserved but the numbers of individual bond types are not maintained. Both experimental data and data from the G3(MP2) thermochemical recipe have been used as references. “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. Both the mean absolute error of Hartree-Fock isomer energies from experimental enthalpies and the mean absolute deviation from G3(MP2) values are 11 kJ/mol, much less than the errors seen previously for bond energy comparisons. Note, however, that differences in isomer energies are much smaller than bond energies. The largest individual error from experiment is 33 kJ/mol, and involves comparison of 1,3-butadiene with its highly strained isomer, bicyclo[1.1.0]butane. The corresponding deviation from G3(MP2) is 21 kJ/mol. Other large errors (from experiment) involve comparisons of propyne and cyclopropene and 1,3-butadiene and cyclobutene (both 20 kJ/mol). Other large deviations (from G(MP2)) involve comparisons of acetaldehyde and oxirane (17 kJ/mol) and acetonitrile and methyl isocyanide (16/kJ/mol) and methyl ethyl ketone and 2,3-dihydrofuran (16 kJ/mol). As with bond dissociation energies, isomer energy differences 16 from Hartree-Fock calculations with the cc-pVTZ basis set (not provided in the table) are nearly identical to those with the cc-pVQZ basis set. Table P3-1: Errors in “Limiting” Hartree-Fock, B3LYP and MP2 Energies of Structural Isomers (kJ/mol) HF reference propyne B3LYP MP2 G3(MP2) Expt. isomer allene 7 -9 18 1 7 cyclopropene 113 99 99 100 93 cyclopropane 43 40 19 38 29 2-butyne 32 37 21 39 36 cyclobutene 68 67 40 56 48 bicyclo[1.1.0]butane 141 131 90 120 108 cyclobutane 54 53 35 47 46 1,4-pentadiene 55 56 83 67 70 methyl isocyanide 84 99 113 100 88 vinyl alcohol 52 43 44 41 43 oxirane 132 121 110 115 118 ethanol dimethyl ether 44 44 54 50 51 acetic acid methyl formate 70 68 75 70 75 methyl vinyl ketone cyclobutanone 32 27 11 22 23 2-hydroxy-1,3-butadiene 52 41 38 38 2,3-dihydrofuran 51 45 35 43 divinyl ether 104 91 105 95 102 mean absolute error 11 9 (10) 5 - mean absolute deviation from G3(MP2) 11 5 (12) - 5 propene 1,3-butadiene isobutene cyclopentene acetonitrile acetaldehyde 17 An Excel spreadsheet containing structural isomer energies for Hartree-Fock, B3LYP and M...
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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 Berkeley.

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