G2 molecule set

Model Chemistry Range of MAD /Max. Error Applicability on G2 Molecule Set [ heavy atoms] Relative Cost... 

However, it is also important to recognize the weaknesses of the G2 molecule set when interpreting and extrapolating from the results for any particular model chemistry, ... 

We are now in a position to examine the relative accuracies of a variety of different model chemistries by considering their performance on the G2 molecule set. The following table lists the mean absolute deviation from experiment, the standard deviation and the largest positive and negative deviations from experiment for each model chemistry. The table is divided into two parts the first section lists results for single model chemistries, and the remaining sections present results derived from... 

The following table summarizes the accuracy of the various methods we have considered for the G2 molecule set ... 

Here are the overall results for the CBS and G2 model chemistries we have considered on the G2 molecule set, as well as some sample relative performance data ... 

Calculation of thertnochetnical quantities like those we have just considered are a widely-used method for evaluating the accuracy of theoretical methods and models. In this section, we will look at the Gaussian-2 molecule set and then consider how well a variety of model chemistries perform on it. Note that our consideration of the G2 method itself will come later in this chapter. 

One should also keep in mind that the G2 paper s authors never intended the molecule set to be a definitive test suite, and so they should not be held responsible for its shortcomings as one. 

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. 

Here we propose a new reduced-cost variant of W1 theory which we shall denote Wlc (for cheap ), with Wlch theory being derived analogously from Wlh theory. Specifically, the core correlation and scalar relativistic steps are replaced by the approximations outlined in the previous two sections, i.e. the MSFT bond additivity model for inner-shell correlation and scaled B3LYP/cc-pVTZuc+l Darwin and mass-velocity corrections. Representative results (for the W2-1 set) can be seen in Table 2.1 complete data for the molecules in the G2-1 and G2-2 sets are available through the World Wide Web as supplementary material [63] to the present paper. 

In a study of 110 G1 and G2 molecules composed of G, H, O, and F, the average BAG-MP4 unsigned error in predicted heat of formation was 2.1 kcal mol (Zachariah etal. 1996). As the MP4 calculation uses a relatively modest basis set size, the BAG procedure is quite fast by comparison to some of the multilevel methods described above. On the other hand, as with any method relying on pairwise parameterization, extension to a large number of atoms requires a great deal of parameterization data, and this is a potential limitation of the BAG method when applied to systems containing atoms not already parameterized. 

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. 

The benchmark calculations of ionization potentials and electron affinities of the atoms and molecules in the G2 data set" calculated using the hybrid functional (B97) show that this functional is adequate. The average absolute deviation from experimental data amounts to 0.055 eV and 0.056 eV for ionization potential and electron affinity, respectively.51... 

Mean absolute errors (mae s) and maximum error for the bond lengths and harmonic vibrational frequencies of the molecules belonging to the reduced G2 data set. All values have... 

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