## 2 Accuracy of Predictive Methods and What Is Required
### QSPR Methods using Molecular Descriptors  
After molecular descriptors (see Section 1.2 for the introduction of these) have been evaluated for a series of molecules for which experimental property data are available, for example boiling, points, heats of formation, toxicity data or any other property, statistical or artificial intelligence methods are applied to build a method between descriptors and physicochemical property. Subsequently, for a new molecule for which the property value is unknown, the molecular descriptors are calculated and inserted in the model, leading to a prediction for the physicochemical property. The methods applied are generically of two different types: classical statistical methods and artificial intelligence. The former include the regularly used linear regression and, if not sufficient, polynomial regression and other ways to fit a given mathematical function of relatively simple form. We have seen, however, that current methods are mostly not sufficiently accurate and predictive for the experimental chemist and engineer, the environmental scientist or the toxicologist. The classical methods allow for limited flexibility and  
Figure 5: The boiling points of alkanes as a function of chain length. there is no reason to assume that properties exhibit a linear or any other fixed mathematical form. Practice (literature) has shown the accuracy and reliability remain limited. Neural networks are more generic and can model any complex relationship to any desired accuracy (see, for example, Reference [11]). Surprisingly, although [PERSON] and [PERSON] pointed out the capabilities of neural networks as early as 1993 [45], still many use classical statistical methods. Still, meanwhile neural networks and other artificial intelligence methods are gaining exposure, not only for physicochemical properties but in a much wider area including describing the relation between (chemical plant) process parameters like catalyst type, catalyst concentration, flow, feed characteristics and so forth. Boiling points of organics were modelled using neural networks using 17,768 pure chemical compounds as available input data for constructing the model [16]. The average absolute relative deviations of the predicted properties from existing literature values: 3.2% and squared correlation coefficient R\({}^{2}\) was 0.94. Another study compared various publicly available methods using over 2000 experimental data points [15]. Also the more difficult to predict melting points were reported [46], as well as pKa neural network methods [47]. Very recently a neural network based approach was reported for the calculation of molecular energies, claiming less than 3 kJ/mole (0.6 kcal/mole) difference between DFT results and the neural network method [48]. The molecular descriptor based approach can equally well be applied to organometallics. Reports date more than a decade ago, for example on the catalytic efficiency in the Heck reaction [49], More than a decade ago. The method was applied to other classes of homogeneous catalysts [18] and to the heat of formation of organometallics [50]. There are two excellent reviews available from [PERSON] [51; 52]. A critical issue in modelling using molecular descriptors is how many should be used. As we have indicated tools are available to readily evaluate thousands of parameters. Obviously, when we have only hundreds or even a few thousands of experimental data as input during the construction of the method, we easily have more parameters that can be fitted compared to the number of experimental data. This leads to a phenomenon known as overfitting. Overfitting and ways to deal with this has been discussed by, for example, [PERSON] et al. [53]. Having too many fitting parameters results in multiple methods with different parameter values describing the experimental data set equally well but which is the correct method? As these methods are often produced as black boxes, albeit for a good reason, they will be less predictive.