G2/97 test set

The G2 extrapolation scheme - which is a prescription to extrapolate the quality of QCISD(T)/ 6-311++G(3df,2p) calculations - actually reaches chemical accuracy for the G2 test set of species, but only with an empirical correction, depending on the number of electron pairs in a molecule in order to better account for these effects. 

Schmider, H. L., Becke, A. D., 1998a, Optimized Density Functionals from the Extended G2 Test Set , J. Chem. 

This sequence of calculations was applied to neutral and ionic molecular species from the G2 test set. Experimental adiabatic electron affinities and ionization energies were taken from Refs. 53 - 74. 

With respect to absolute accuracy, Table 9.2 provides the mean unsigned errors in harmonic vibrational frequencies for a number of levels of theory over the 32 molecules in the reduced G2 test set. HF theory shows the poorest performance (AMI and PM3 are in general somewhat worse than HF with a moderate basis set, however data are not available for this particular test set). MP2 shows significant improvement over HF, but substantial... 

Deviation = experiment - theory. The 148 enthalpies of formation in this table are from the G2/97 test set (Refs. 3 and 30). The G2-1 subset molecules are ones from the original G2 test set (Ref. 29), and the G2-2 subset are new ones added to the G2/97 test set. fcSee Ref. 3 for experimental references. 

To test the accuracy of the G2 method, Pople and co-workers used a set of very accurate experimental data consisting of 55 atomization energies, 38 ionization energies, 25 electron affinities, and 7 proton affinities of small molecules. Later, these workers also proposed an extended G2 test set of 148 gas-phase heats of formation. For this extended set of data, the average absolute errors for G2 and G3 are 6.7 and 3.8 kJ mol-1, respectively. Furthermore, it is noted that G3 is actually less expensive than G2, which shows the importance of designing a basis set judiciously. Experience indicates that, for systems of up to 10 nonhydrogen atoms, the expected absolute uncertainty for G2/G3 is about 10 to 15 kJ mol-1. 

In the W3 and W4 methodologies, connected triple and quadruple correlations are incorporated in order to correct the imperfection of the CCSD(T) wavefunction. As a result, the very sophisticated W3 and W4 methods are only applicable to molecular systems with no more than three non-hydrogen atoms. For the extended G2 test set, the uncertainty for W1 is 1.98 kJ mol-1. On the other hand, for the original G2 test set, the absolute errors for the W2 and W3 methods are 1.50 and 0.89 kJ mol-1, respectively. Tested with a very small test data set consisting of 19 atomization energies, the respective absolute errors for the W2, W3, W4a, and W4b methods are 0.96, 0.64, 0.60, and 0.71 kJ mol-1, where W4a and W4b are two variants of the W4 method. 

Salomon O, Reiher M, Hess BA (2002) Assertion and validation of the performance of the B3LYP functional for the first transition metal row and the G2 test set. J. Chem. Phys. 117 4729-4737... 

Ideally, one would apply these high-accuracy methods as a routine for thermochemistry and kinetics studies. However, these methods can be very expensive for even a moderate system. For example, a G2(MP2) calculation on a octane molecule exceeds 100 cpu hours on a CRAY-YMP supercomputer. Petersson (1998) did extensive benchmark study and his conclusion is that most of the CBS and G2 methods are not practical for systems that have more than a half dozen non-hydrogen atoms. Table 2 shows the summary of error measurements for the G2 test set of 125 reactions. Most of these reactions involve very small gas molecules. 

Table 2. Summary of error measurements for the G2 test set of 125 reactions.

Pople s approach has indeed led to energy predictions of impressive accuracy for a test set of 148 small molecules (the so-called G2 test set). ° Especially... 

Figure 1 Average absolute deviations of atomization energies (AEs), ionization potentials (IPs), electron affinities (EAs), and proton affinities (PAs) calculated from G2, G2(MP2), and G2(MP2,SVP) theories for the 125 reaction energies in the G2 test set...

Several empirical corrections are added to the resulting energies in the CBS methods to remove the systematic errors in the calculations. The CBS-Q method contains a two-electron correction term similar in spirit to the higher-level correction used in G2 theory, a spin correction term to account for errors resulting from spin contamination in UHF wavefunctions for open shell systems, and a correction to the Na atom to account for core-valence correlation effects. The CBS-4 and CBS-q methods also contain a one-electron correction term to improve the computed ionization energies and electron affinities. The mean absolute deviation for the 125 energies in the G2 test set is 2.0 kcal mol (CBS-4), 1.7 kcal mol (CBS-q), and 1.0 kcal mol (CBS-Q), respectively. These methods have not yet been tested for the 148 molecules in the enlarged G2 test set. 

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