Mean absolute deviations, transition metal

Several points should be mentioned in this context. First, while we use QCISD(T) in our basic dehnition of G2 and G3 theories, analogous methods have been defined where the CCSD(T) method replaces QCISD(T). Both variations seem to yield very similar mean absolute deviations in most cases. However, in our most recent work on transition metal systems [78], it appears that CCSD(T) has a clear advantage over QCISD(T) and will thus become the preferred method. For the first- and second-row molecules, however, there is no clear preference. The key point to note is that the accuracy and predictive capability of these methods comes from the inherent accuracy of QCISD(T) or CCSD(T). Finally, this is one of the steps in the calculation and is likely to be rate-limiting if carried out with very large basis sets. Indeed, it is the bottleneck in CCSD(T) calculations with large correlation-consistent basis sets. In G2 theory, QCISD(T) calculations are carried out with a polarized valence triple-zeta basis set. This is a very modest basis set and this makes it possible to carry out G2 calculations on molecules of the size of naphthalene on small workstations. In our later work on G3 theory, we use even smaller 6-31G(d) calculations that makes these methods applicable for even larger molecules. 

The idea of benchmarking quantum chemical methods by introducing databases covering a wide variety of different properties, for example, atomization energies, spectroscopic properties, barrier heights and reaction energies of diverse reactions, proton affinities, interaction energies of noncovalent bond systems, transition metal systems, and catalytic processes, was extended by Truhlar and coworkers [51]. They were the first to carry out overall statistical analyses of combinations of different test sets to obtain an overall mean absolute deviation (MAD) number for each tested quantum chemical method, which made a comparison with other approaches more feasible. 

For the G3/99 test set the mean absolute deviations from experiment are 0.96 and 0.97 kcal/mol for the versions ccCA-P and ccCA-S4 (which differ in the extrapolation formulas used), compared with 1.16 and 0.95 kcal/mol for G3 and G3X, respectively. About 20 versions of ccCA exist, including a version for transition metal compounds, a multireference version, and RI versions. 

As mentioned above, the PCI-X method was originally designed for the treatment of transition metal system. Therefore this procedure has to be tested for this kind of system too. The first test of the PQ-80 scheme on transition metal systems is performed on the atomic spectra, which is the only set of very accurate experimental data available. The s s° excitation was calculated for the neutral second row transition metal atoms and the first row transition metal cations, The s -> s excitation was calculated for both the first and the second row neutral transition metal atoms. In Table 3 we summarize the mean absolute deviation from experimental data on these excitations at the MCPF and the PCI-80 levels. A few technical comments on the results in Table 3 should be made. The first comment concerns the s states. As already noted above for first row atoms, valence excitations from s to p introduce additional problems. To avoid this problem for the s states of the transition metal atoms, the correlation energy associated with these two electrons is excluded from the extrapolation procedure. This somewhat awkward procedure was used to obtain the results in Table 3. but is entirely restricted to these atomic calculations. To avoid this problem for the molecular bond strengths, the calculated s asymptote should be used and experimental excitation energies should be used to obtain the final bond strengths. This has been done for most of the molecular results given below. Second, in... 

Table 3 Mean Absolute Deviations from Experimental Results in kcal mol" for Atomic Excitation Energies for First and Second Row Transition Metal Atoms and Cations...

Wilson and coworkers assessed the performance of 13 hybrid-GGA, hybrid-meta-GGA, and double-hybrid DFT functionals on the cc-CA-TM/11 dataset [83]. The hybrid B97-1 [42, 84] functional and the double-hybrid functional mPW2-PLYP [85] were found to give the best performance over experimental results with mean absolute deviations of 7.2 and 7.3 kcal mol . The dataset (cc-CA-TM/11) is rather diverse and consists of AyH of 193 3d transition metal molecules (Sc(C5H5)3 and (Cr03)3, halides, oxides, and heavy chalcogenides, hydrides, nitrides, small clusters, metal carbonyls, and other coordination complexes) [86]. 

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