## 2 Accuracy of Predictive Methods and What Is Required
### Why do Methods often not Perform up to the Required Level of Accuracy and Reliability?
As we focus on accurate and reliable methods, with numerical requirements set, the effects of erroneous data are expected a problem. Actually, data curation should _always_ be considered necessary [37] and a procedure needs to be in place to ensure that the data set does contain any erroneous data. The larger issue here will be that the experimental data must have at least the accuracy and reliability we require from the method to be developed. For log K\({}_{\text{ow}}\), related to the octanol-water partition coefficient and a parameter of importance in various domains including toxicity, it has been discussed that experimental values can differ by an order of magnitude [38]. For the AMES test (mutagenicity), it is known that this test has about 85% agreement with true real-life mutagenicity tests. As the AMES test is easy and cheap to apply, the results are often taken to establish a method to predict mutagenicity. But also for parameters like heat of formation and boiling point one finds inaccurate or even wrong data in literature, even in some well-known databases. Our experience, on a larger variety of data sets, is that erroneous data can often be easily detected by the following approach. Establish a method based on neural networks using a large number of nodes and several layers. The consequence will normally be that one arrives at a method showing overfitting and therefore not good as a predictive tool. However, as the neural network framework can fit any proper data set to any level of accuracy, it turned out in practice that all data points that were off-line an almost perfect correlation model value - experimental value turned out, after careful check, as erroneous input data. Ad (iv)Regarding _neglecting of the physics of involved_, what is sometimes missing in building models is the discussion on the physics and /or specific interactions involved. Without doing this one builds models based purely on mathematical tools which is some cases do but in other cases do not represent the real-life behaviour and therefore erroneous predictions start popping up when making predictions for systems that were not involved whilst establishing the method. This can be illustrated with the example of free energies of formation, more specifically the entropy part. Group contribution methods but similarly molecular descriptor like methods, can be applied to molecular enthalpy prediction. For large molecules, the number of atomic connectivity can become very large. However, as in organic chemistry many (but not all) properties have a high degree of additivity of individual molecular group contributions, one still needs to fit relatively few parameters only. Higher order terms are introduced if necessary, as mentioned in the above. If a property depends on the _integral structure of the molecule_, this picture breaks down. This is the case for the vibrational contribution to the molecular entropy, which can be obtained from  
\[S_{\text{\emph{vibration}}}=R\sum_{i}\big{[}\frac{(hvi/kT)\exp(-hvi/kT)}{[1- \exp(-hvi/kT)}-\ln[1-\exp(-hvi/kT)]\big{]}. \tag{5}\]  
with R the gas constant, T absolute temperature, h Planck's constant and \(\
u_{i}\) the vibrational frequency associated with the \(i\)th normal mode and \(\sigma\) the symmetry number [39]. This expression indicates that the low-lying molecular vibrations count most and in practice these are by far dominating. In a not very small organic molecule these vibrations extend over a large part, if not all, of the molecule. This in turn make a group contribution method, which tries to work with a minimum number of neighbours (third order groups as currently the maximum), unsuitable for describing the entropy term and therewith the Gibbs free energy. There are, however, semi-empirical quantum mechanics methods that very quickly provide the low-lying frequencies with high accuracy thereby leading to accuracy and reliable molecular entropies [7,8].