Relative Performance of Gaussian theories
1) Relative computational effort and accuracy:
L. A. Curtiss, P. C. Redfern, K. Raghavachari, V. Rassolov, J. A. Pople,
"Gaussian-3 theory using reduced Møller-Plesset order"
J. Chem. Phys. 1999, 110, 4703 - 4709.
| Method | Rel. CPUa | MAD(1)b | MAD(2)c |
|---|---|---|---|
| G3(MP2) | 1.0 | 4.94 | 5.44 |
| G2(MP2) | 2.9 | 8.49 | 7.91 |
| G3 | 7.8 | 3.93 | 4.23 |
| G2 | 14.7 | 6.53 | 6.19 |
a Relative CPU time for benzene (D6h)
b Mean absolute deviation for the extended G2 neutral set (148 energies, kJ/mol)
c Mean absolute deviation for all energies in the extended G2 set (299 energies, kJ/mol)
It is clear from these results that G3 theory is the most accurate method for a broad range of molecular and atomic systems, while G3(MP2) theory is the most economical method. It must also be noted that G3(MP2) is more accurate than G2 theory!
2) B3LYP vs. MP2 geometries:
A. G. Baboul, L. A. Curtiss, P. C. Redfern, K. Raghavachari,
"Gaussian-3 theory using density functional geometries and zero-point energies"
J. Chem. Phys. 1999, 110, 7650 - 7657.
| Method | MAD(1)a | MAD(2)b |
|---|---|---|
| G3 | 3.93 | 4.26 |
| G3B3 | 3.89 | 4.14 |
| G3(MP2) | 4.94 | 5.44 |
| G3(MP2)B3 | 4.73 | 5.23 |
a Mean absolute deviation for the extended G2 neutral set (148 energies, kJ/mol)
b Mean absolute deviation for the full G2/97 test set (299 energies, kJ/mol)
The use of B3LYP or MP2 geometries does not lead to dramatically different MADs for both test sets. Especially for large systems, the use of the more economical B3LYP method for geometry optimization appears to be advisable.
3) Performance in treating open shell systems:
D. J. Henry, M. B. Sullivan, L. Radom,
"G3-RAD and G3X-RAD: Modified Gaussian-3 (G3) and Gaussian-3X (G3X) procedures for radical thermochemistry"
J. Chem. Phys. 2003, 118, 4849 - 4860.
| Method | MADa | LDb | MADc |
|---|---|---|---|
| G3(MP2) | 5.15 | +11.72 | 5.44 |
| G3(MP2)-RAD | 5.10 | +13.39 | 5.17 |
| G3(MP2)B3 | 4.94 | +13.39 | 5.23 |
| G3 | 3.51 | -7.94 | 4.26 |
| G3-RAD | 3.19 | +12.86 | 3.96 |
| G3B3 | 3.18 | +10.04 | 4.14 |
| G3X | 3.18 | -8.79 | 4.02 |
| G3X-RAD(5d) | 3.14 | +9.14 | 3.85 |
| G3-RAD | 2.59 | +11.01 | 3.96 |
| G3X-RAD | 2.50 | +8.16 | 3.65 |
a Mean absolute deviation for 29 radicals in the G2/97 test set (kJ/mol)
b Largest deviation for 29 radicals in the G2/97 test set (kJ/mol)
c Mean absolute deviation for the full G2/97 test set (kJ/mol)
The differences between the "RAD"-modified procedures and the corresponding references methods (G3(MP2)-RAD vs. G3(MP2)B3; G3-RAD vs. G3B3; G3X-RAD vs. G3X) are not very large in general. This may, however, be different for systems involving large, strongly delocalized radicals.
4) G3 theories vs. DFT methods:
L. A. Curtiss, P. C. Redfern, K. Raghavachari,
"Assessment of Gaussian-3 and density-functional theories on the G3/05 test set of experimental energies"
J. Chem. Phys. 2005, 123, 124107.
| Method | MADa |
|---|---|
| G3 | 4.73 |
| G3X | 4.22 |
| B98 | 13.93 |
| B3LYP | 17.32 |
a Mean absolute deviation for the G3/05 data set incuding 454 energies (in kJ/mol)
The difference between DFT and G3 results is significantly larger for the G3/05 dataset due to the additional consideration of data for larger molecular systems.
5) G3 theories vs. DFT methods II:
S. Grimme,
"Semiempirical hybrid density functional with perturbative second-order correlation"
J. Chem. Phys. 2006, 124, 034108.
| Method | MADa |
|---|---|
| G3 | 3.8 |
| G2 | 6.7 |
| B2-PLYP | 7.5 |
| B3-LYP | 13.0 |
| PBE0 | 20.1 |
| B-LYP | 30.5 |
a Mean absolute deviation for heats of formation in the G2/97 test set (148 energies, kJ/mol)
The mixture of DFT and PT2 correlation energies leads to improved performance in the prediction of thermodynamic data.
6) DFT vs. double-hybrid DFT vs. Gaussian-X theories:
B. Chan, L. Radom,
"BDE261: A Comprehensive Set of High-Level Theoretical Bond Dissociation Enthalpies"
J. Phys. Chem. A 2012, 116, 4975 - 4986.
| Method | MADa | LDb |
|---|---|---|
| CBS-QB3 | 2.2 | +7.2 |
| G4 | 3.6 | -7.9 |
| G3X(MP2)-RAD | 4.4 | -14.5 |
| G4(MP2) | 5.9 | -15.4 |
| RO-B2PLYP | 4.4 | -14.5 |
| B2-PLYP | 12.6 | -24.8 |
| B3-LYP-D3 | 22.2 | -38.8 |
| M06-2X | 6.5 | -23.4 |
| B3LYP | 26.7 | -51.9 |
a Mean absolute deviation for heats of formation in the BDE261 test set (relative to W1w, in kJ/mol)
b Largest deviation for heats of formation in the BDE261 test set (relative to W1w, in kJ/mol)
M06-2X performs best among hybrid DFT methods. ROB2-PLYP is quite competitive with some of the more expensive compound schemes when used in combination with quadruple-zeta quality basis sets. The performance of G4 is better than that of other Gaussian-X schemes, but still not as good as CBS-QB3.