Descriptors nature

A linear descriptor naturally contains an ordering of its elements, which makes it very easy to compare them. In a tree structure however, it is not clear which parts should be mapped onto each other. Different mappings will result in different similarity values ... 

Similarity Metrics Should take Descriptor Nature into Account... 

Molecular dipole moments are often used as descriptors in QPSR models. They are calculated reliably by most quantum mechanical techniques, not least because they are part of the parameterization data for semi-empirical MO techniques. Higher multipole moments are especially easily available from semi-empirical calculations using the natural atomic orbital-point charge (NAO-PC) technique [40], but can also be calculated rehably using ab-initio or DFT methods. They have been used for some QSPR models. 

If the descriptors are on different scales then those which naturally occupy a larger scale may be given more weight in the subsequent analysis, simply because of their natura units. In autoscaling the descriptors are scaled to zero mean and a standard deviatior of 1. 

Pet food purchases are based on the satisfaction of the owner, and pet food proliferation is enormous with accompanying advertising descriptors including natural, Hte, low calorie, high calorie, low protein, and high protein. New therapeutic series, sizes, densities, colors, and attractive packaging have also added to the proliferation. 

Odor perception and description are highly subjective in nature. Nevertheless, there is a generally agreed-upon odor vocabulary that is used to characterize individual ingredients and finished fragrances. Table 1 shows some commonly used odor descriptors grouped into five general classifications. 

Many classes of natural product possess heterocyclic components (e.g. alkaloids, carbohydrates). However, their structures are often complex, and although structure-based names derived by using the principles outlined in the foregoing sections can be devised, such names tend to be impossibly cumbersome. Furthermore, the properties of complex natural product structures are often closely bound up with their stereochemistry, and for a molecule containing a number of asymmetric elements the specification of a particular stereoisomer by using the fundamental descriptors (R/S, EjZ) is a job few chemists relish. 

Campbell [campj82], in his Grammatical Man Information, Entropy, Language and Life, was one of the first to assert the importance of adding information to our short list of fundamental descriptors of nature ... 

The retention depends on the nature of both the stationary phase and the organic modifier in the mobile phase. Therefore CHI values obtained using different systems show different sensitivities towards solute characteristics. This has been studied systematically and used for the quantitative calculation of solute molecular descriptors (H-bond donor capacity, H-bond acceptor capacity and dipolarity/polarizability) for application in a general solvation equation [21]. 

Pd The percent delocalized effect. It too is a descriptor of the nature of the electrical effect. It is represented in subscripts as k . 

Table 3.1 compares key bonding and ionicity descriptors for the NBO Lewis-structure representations of the five AF diatomic fluorides in this series. From this table it can be seen that the single-term natural Lewis-structure description is practically exact for all species (with %p 99.9% for A = F, Cl, Br, H, and only a... 

Table 3.29. The NBO descriptors of XYZ triatomic anions (see Table 3.28), showing natural atomic charges (Q), percentage polarization of oxy and ayz NBOs toward terminal atoms, second-order nz— oxy and nx->OYZ stabilizations (A/s(2)), and occupancies of valence antibonds (oxy and ayz ) and extra-valent Rydberg orbitals (ry ) parenthesized values refer to Lewis structure of lower accuracy...

The aptness of the idealized sd/J Lewis-like model is also confirmed by the quantitative NBO descriptors, as summarized inTable4.5. This table displays the overall accuracy of the Lewis-like description (in terms of %pl, the percentage accuracy of the natural Lewis-like wavefunction for both valence-shell and total electron density) as well as the metal hybridization (hM), bond polarity toward M (100cm2), and... 

Table 4.26. Geometrical (Rxy) and NBO descriptors ofXYn ligands (NH3, PH3, and CO), illustrating natural atomic charges (Qy) and NBO occupancy (Occ ), polarity (%pol = lOOcx2), and orbital energy (e ) of Unh, apn or rtco acceptor orbitals in the free ligands...

Table 4.36. The NBO descriptors o/ M2H2 species (see Fig. 4.57) namely the accuracy of the natural Lewis structure (%/+). metal charge (Qu), metal hybrid (hM), percentage polarization toward metal (%m), and occupancies (Occ.) of two-center bonds and antibonds...

Secondly, information is obtained on the nature of the nuclei in the molecule from the cusp condition [11]. Thirdly, the Hohenberg-Kohn theorem points out that, besides determining the number of electrons, the density also determines the external potential that is present in the molecular Hamiltonian [15]. Once the number of electrons is known from Equation 16.1 and the external potential is determined by the electron density, the Hamiltonian is completely determined. Once the electronic Hamiltonian is determined, one can solve Schrodinger s equation for the wave function, subsequently determining all observable properties of the system. In fact, one can replace the whole set of molecular descriptors by the electron density, because, according to quantum mechanics, all information offered by these descriptors is also available from the electron density. 

Details on the numerical evaluation of the descriptors will be given in the individual cases but in most cases a computational DFT approach is used, with a hybrid functional of the B3LYP type [32]. Condensation of f(r) or sir) is done with conventional population analysis techniques (Mulliken [33], Natural Population Analysis (NPA) [34]) or with the Hirshfeld technique [35], often used by our group [36]. 

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