Mean absolute scaled error

Mean absolute scaled error (MASE) To overcome the drawbacks of existing measures, Hyndman and Koehler (2006) proposed MASE as the standard measure for comparing forecast accuracy across multiple time series after comparing various accuracy measures for univariate time-series forecasting. MASE is expressed as follows ... 

If we use B3LYP/VTZ+1 harmonics scaled by 0.985 for the Ezpv rather than the actual anharmonic values, mean absolute error at the W1 level deteriorates from 0.37 to 0.40 kcal/mol, which most users would regard as insignificant. At the W2 level, however, we see a somewhat more noticeable degradation from 0.23 to 0.30 kcal/mol - if kJ/mol accuracy is required, literally every little bit counts . If one is primarily concerned with keeping the maximum absolute error down, rather than getting sub-kJ/mol accuracy for individual molecules, the use of B3LYP/VTZ+1 harmonic values of Ezpv scaled by 0.985 is an acceptable fallback solution . The same would appear to be true for thermochemical properties to which the Ezpv contribution is smaller than for the TAE (e.g. ionization potentials, electron affinities, proton affinities, and the like). 

The best scale factor in the least-squares sense is 0.788 while the mean absolute error of 0.04 kcal/mol is more than acceptable, the maximum absolute error of 0.20 kcal/mol (for SO2) is somewhat disappointing. Representative results (for the W2-1 set) can be found in Table... 

This equation is quite accurate in comparison with group contributing methods [40] or other predictive LSER methods [41]. For compounds where the solvatochromic parameters are known, the mean absolute error in log Dy is about 0.16. It is usually less than 0.3 if solvatochromic parameters of the solute and solvent must be estimated according to empirical rules [42], In contrast to the prediction of gas-liquid distribution coefficients, which is usually easier, the LSER method allows a robust estimation of liquid-liquid distribution coefficients. However, these equations always involve empirical terms, despite their being physico-chemically founded thermodynamic models. However, this is considered due to the fundamental character of the solvatochromic scales. 

G3 theory and the other variants discussed thus far include a HLC term to correct for the remaining deficiencies in the computed energies. The HLC term in G3 theory consists of four molecule-independent additive parameters that depend only on the number of paired and unpaired electrons in the system. While basis set deficiencies are the biggest source of errors in the computed energies, the HLC parameters can also correct for any other systematic errors (such as those from zero-point energies or from relativistic effects). Such an approach will work if such deficiencies are systematic and scale as the number of electrons. While it may make it difficult to identify the source of systematic errors, this approach is indeed successful as indicated by the overall mean absolute deviation of < 1 kcal/mol for the G3X method with the large G3/99 test set. 

Mean Absolute Deviations A (kcal/mol) Obtained After Scaling the Correlation Error Using Various Basis Sets and Methods for the First-Row Benchmark Test... 

For example. East and Radom devised a procedure they call El, which calculates from the MP2/6-31G geometry (MP2 calculations are (Uscussed in Section 15.18) and Svib from HF/6-31G scaled vibrational frequencies and the harmonic-oscillator approximation, except that internal rotations with barriers less than 1.4R7 are treated as free rotations [A. L. L. East and L. Radom,/. Chem. Phys., 106,6655 (1997)]. For 19 small molecules with no internal rotors, their El procedure gave gas-phase 5S,298 values with a mean absolute deviation from experiment of only 0.2 J/mol-K and a maximum deviation of 0.6 J/mol-K. The El procedure was in error by up to Ij J/mol-K for molecules with one internal rotor and by up to 2 J/mol-K for molecules with two rotors. An improved procedure called E2 replaces the harmonic-osdllator potential for internal rotors by a cosine potential calculated using the MP2 method and a large basis set, and reduces the error to 1 J/mol-K for one-rotor molecules. 

This error can be considerably reduced, at very little cost, by employing B3LYP density functional theory instead of SCF. The scale factor, 0.896, is much closer to unity, and both mean and maximum absolute errors are cut in half compared to the scaled SCF level corrections. (The largest errors in the 120-molecule data set are 0.10 kcal/mol for P2 and 0.09 kcal/mol for BeO.) It could in fact be argued that the remaining discrepancy between the scaled B3LYP/cc-pVTZuc+1 values is on the same order of magnitude as the uncertainty in the ACPF/MTsmall values themselves. 

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