Nonmodel-based methods

Nonmodel-based methods use large sets of descriptors and, often, complex methods for regression analysis. The equations from regression analysis have been labeled by Bakken and Jurs as type 1 equations.The equations are similar in form to those used with small descriptor sets. Type 1 equations rely on QM and other theoretical descriptors. 

The interpretation of Eq. [44] is suggested by the negative DPSA term. Decreased DPSA values mean decreased positively charged surface atom area as compared to negatively charged surface atom area. This could be associated with smaller (weaker) intermolecular surface electrostatic interactions which 

Katritsky, Lobanov, and Karelson correlated the boiling point, (K), for a set of 584 compounds with a very large set ( 800) descriptors of various types, including many of those employed by Jurs and colleagues. Equation [47] regresses on eight descriptors. As before, QM descriptors were calculated with the AMI Hamiltonian and other calculations were done with CODESSA. 

Following a similar approach but using a smaller data set of 369 compounds, Ivanciuc et al. correlated their liquid viscosity (10 Pa s) at 298 K with a mixed set of descriptors to obtain Eq. [48]. This involves three QM descriptors, one topological, and one constitutional descriptor. The QM descriptors were calculated with the AMI Hamiltonian in AMPAC, and CODESSA was used to calculate the descriptors and perform the statistical analyses. The HDCA2 parameter is the same HBD charged surface area used in Eq. [46]. The maximum electrophilic reactivity index, Ep, for a carbon atom is defined by X/ lumo,/A lumo+ 10), with the summation over the valence AOs on a carbon atom in the LUMO. The maximum AO electronic population, Y, models the molecular nucleophilicity and is defined by 

2J2) cj, where the sum runs over the occupied MOs for a single AO. The molecular mass is represented by M, and is the Randic connectivity index of order 3. 

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Table 3 Some QM Descriptors Developed for Nonmodel-Based Methods ...

Nonmodel-based controllers, such as the least mean square (LMS) and artificial neural network back-propagation adaptive controllers, employ iterative approaches to update control parameters in real time [14-17]. However, those methods may encounter difficulties of numerical divergence and local optimiza-... 

The examples presented here help us to address the question of whether to use a model-based (small sets of simply interpreted descriptors) or nonmodel-based QSAR/QSPR method (large sets of descriptors). The model-based equations (which includes LFERs) can be used to fairly readily predict the result of changing molecular structure on a property. This is because these equations can often be easily interpreted from a chemical viewpoint. The nonmodel-based equations are frequently not so easily interpreted... 

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