G3/05 test set

An extensive evaluation has been done by Curtiss et al., who tested a number of density functionals on the G3/05 test set. This set includes 454 energies, all of which have experimental uncertainties less than 1 kcalmoH The computed results are based on single-point B3LYP/6-311- -G(3df,2p) energies at second-order M0ller-Plesset perturbation theory (MP2)/6-31G(d) geometries with scaled (0.89) Hartree-Fock (HF)/... 

The Gaussian-4 theory was tested on the G3/05 test set [55] including 454 energies. The overall average absolute deviation for these energies was found to be about 3.5 kJ/mol. 

Curtiss LA, Redfem PC, Raghavachari K (2005) Assessment of Gaussian-3 and density functional theories on the G3/05 test set of experimental energies. J Chem Phys 123 124107-1/12... 

The G4 method is an improvement on G3 and differs from G3 as follows G4 uses an extrapolation procedure [Eq. (15.23)] to estimate the Hartree-Fock energy in the complete-basis-set limit uses a larger basis set replaces the QCISD(T) calculation by a CCSD(T) calculation uses B3LYP/6-31G(2df,p) to find the equilibrium geometry and the zero-point energy and includes two additional empirical parameters in the higher-level correction [L. A. Curtiss et al., J. Chem. Phys., 126, 084108 (2007)]. For the G3/05 test set, G4 has a mean absolute error of 0.83 kcal/mol, compared with 1.13 kcal/mol for G3. Relative computation times for benzene are 2 for G2, 1 for G3, and 3 for G4. 

Summaries of G3X(MP3) and G3X(MP2) mean absolute deviations from experiment for the G3/99 test set of 376 energies are given in Table 3.4. The overall mean absolute deviations for G3X(MP3) and G3X(MP2) theories are 1.13 and 1.19 kcal/mol, respectively. These are improvements over G3(MP3) and G3(MP2), which have mean absolute deviations of 127 and 131 kcal/mol, respectively, for the same set of energies. For enthalpies of formation, the mean absolute deviations decrease from 1.29 to 1.07 kcal/mol [G3X(MP3)] and from 1.22 to 1.05 kcal/mol [G3X(MP2)]. Much of the improvement in enthalpies is due to non-hydrogen molecules, although other types of species also improve slightly or stay the same. The G3X(MP3) and G3X(MP2) methods save considerable computational time and have a reasonable accuracy. The ratio of the computational costs for G3X, G3X(MP3), and G3X(MP2) theories is approximately 52 1 for a molecule such as benzene. 

G3X theory gives significantly better agreement with experiment for the G3/99 test set of 376 energies (Table 27.3). Overall, the mean absolute deviation from experiment decreases from 1.07 kcal/mol (G3) to 0.95 kcal/mol (G3X). Thus the mean absolute deviation in G3X not only beats our target accuracy of 2 kcal/mol but also meets the more rigorous definition of chemical accuracy (1 kcal/mol). Even more impressively, the mean absolute deviation for the 222 enthalpies of formation decreases from 1.05 kcal/mol (G3) to 0.88 kcal/mol (G3X). This is clearly due to the improvement for non-hydrogen systems where the mean absolute deviation decreases from 2.11 to 1.49 kcal/mol. 

These new ccCA schemes were then tested on the entire G3/05 set of 454 energetic properties, and the ccCA-PS3 method had a MAD of 1.01 kcal moP. While these modifications do not represent an overwhelming improvement over the previous ccCA methodology, this does not suggest that the changes were merely cosmetic. On the contrary, they are indicative of the substantial reliability of ccCA over a broad range of molecular species. 

Due to statistical noise derived from experimental uncertainties in a large number of molecules within the G3/05 set, as well as the accuracy limits of an MP2-based composite method, 1.00 kcal moP may well be near the threshold of error for ccCA when applied toward the Gn test sets. In order to substantially improve the accuracy of ccCA for these test sets, changes to the basis set size or level of theory used in the additive corrections would likely be necessary, which will in turn greatly increase the computational requirements for ccCA energies. However, since ccCA does not include parameterizations, further improvements can easily be identified. 

Pople and coworkers [47] have first realized the benefit of evaluating quantum chemical methods by benchmarking them against accurate experimental measurements. Their work mainly focused on atomization energies, which were used to calculate the heats of formation for around 150 molecules having weU-estabUshed enthalpies of formation at 298K and were summarized in the so-called G2/97 benchmark test set [48] and later enhanced to the benchmark versions G3/99 [49] and G3/05 [50], where electron and proton affinities and ionization potentials of small molecules played an additional minor role. 

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