Symbols of Molecular Descriptors

The most common elementary symbols used for molecular descriptors are reported in the following tables the first table collects normal symbols, the second Greek symbols. Symbols denoting molecular descriptors by more complex combinations of elementary symbols are not reported in the tables. 

Symbols, Definitions and Classification of Calculated Molecular Descriptors... 

Global SMILES attributes were defined as (%,0,l,2,3)-code of six symbols si, s2, s3, s4, s5, and s6. The first symbol (si) is % . This symbol indicates this SMILES attribute is global. The s2 is descriptor of a presence of fluorine 0 means F symbol is absent in the SMILES 1 means there is one F symbol 2 means there are two F symbols finally 3 means that there are three or more F symbols in the SMILES the s3, s4, s5 are the same descriptors for Cl , Br , and O , respectively the s6 is the descriptor for the ( symbol in the SMILES. The brackets are tools to reflect the branching of molecular skeleton (Weininger, 1988, 1990 Weininger et al., 1989). Thus, ( and ) are indicators of the same phenomenon These SMILES attributes (i.e., brackets) have common correlation weight. 

Because of convention, the symbols for the chemical potential, used in Equation 6.44 and Equation 6.45, and the dipole moment are the same. Further evaluation of Equation 6.48 proceeds through introduction of the LCAO-MO expansion (Equation 6.18) and, dependent on the level of theory, consideration of relevant approximations such as the NDDO formalism (Equation 6.31) in the case of semiempirical MNDO-type methods. Because the calculation of the dipole moment is usually considered a somewhat demanding test of the quality of the wavefunctions employed in the quantum chemical model, this property is included in the comparative statistical analysis of various methods to calculate molecular descriptors as presented in Section V. 

The symbols of the molecular descriptors derived from the most common expanded distance matrices are collected in the Table E-8. 

Molecular descriptors are formally mathematical representations of a molecule obtained by a well-specified algorithm applied to a defined molecular representation or a well-specified experimental procedure the molecular descriptor is the final result of a logical and mathematical procedure which transforms chemical information encoded within a symbolic representation of a molecule into a useful number or the result of some standardized experiment. 

By the definition given above, molecular descriptors are divided into two main classes -+ experimental measurements, such as - logP, - molar refractivity, - dipole moment, -> polarizability, and theoretical molecular descriptors, which are derived from a symbolic representation of the molecule and can be further classified according to the different types of molecular representation. 

A fundamental task is how to predict and understand experimental facts, i.e. physico-chemical properties, biological activities, and environmental behaviour, from symbolic representations of real objects such as molecules by molecular descriptors. 

Deconinck et al. (53) used CART in a quantitative structure-activity relationship context on an intestinal absorption data set of 141 drug-hke molecules. Many theoretical molecular descriptors were calculated and used as explanatory variables (X matrix). The considered response (y) was the percentage human intestinal absorption of the compounds. The total sum of squares of the response values about the mean of the node was applied as impurity measure. From all descriptors, only two were chosen to describe and predict the intestinal absorption, and this resulted in three terminal nodes. However, the tree thus obtained did not allow dehning classes with a limited absorption range, and therefore more complex trees were evaluated. Finally, a tree with 11 terminal nodes was selected. The absorption of the molecules was divided into five (absorption) classes. Each terminal node was labeled with one or two class symbols. From an external test set, three out of 27 molecules were wrongly classified (11.1%). 

The representation of molecular structure can be looked upon as a hierarchical process similar to the Russian doll, which contains a series of dolls hidden inside it. At the very elementary level, the structure of the model of an assembled entity, e.g., a molecule comprising atoms, can be represented by a graph G = (V, E), where y represents a non-empty set and is a binary relation defined on the set V. When V represents a set of atoms and E symbolizes the set of covalent (or any other) bonds, we have the simplest representation of molecular structure [13,18]. Invariants derived from such graphs or matrices derived from them are the simplest structural descriptors of molecules. 

Table 2 Symbols, definitions, and classification of calculated molecular descriptors...

As previously mentioned, the acronym QSAR stands for the quantitative structure-activity relationship. However, there may be some ambiguity associated with the attribute quantitative. It does not necessarily follows that results expressed or having numerical representation are necessarily quantitative. Qualitative results can equally be numerically represented. Strictly speaking, we define and view QSAR models as quantitative only when the numerically expressed models allow meaningful interpretation of the numerical results obtained for the structure-activity relationship within the basic concepts of the particular model. This means that the physicochemical models should allow quantitative interpretation of the numerical physicochemical descriptors used and that the structure-mathematical models should allow quantitative interpretation of the numerical structure-mathematical descriptors used. We will use the symbol qsar and QSAR as the abbreviation for qualitative structure-activity relationship. Such are the relationships that are non-numerical and the relationships that may be numerical but the variables used are interrelated and thus do not allow unique interpretation of the MRA equations. Because all molecular descriptors hitherto used in QSAR, whether they are based on physicochemical properties, quantum mechanical calculations, or molecular graphs, are all interrelated, it follows that all such hitherto reported results, without further elaboration, remain essentially qualitative, being qsar rather than QSAR. 

A simple description of the magnetic state can be given by term symbols, which provide a compact way to summarize the spin and angular momentum of a given orbital occupancy of an atom this also forms the foundation for similar descriptors of molecular electronic states. 

The symbol V is often associated with the electrical potential in the literature, but U is employed here so as not to conflict with the volume descriptor. Another aspect of chemical reactivity involves the molecular electrostatic potential (MEP). The MEP is the interaction energy between a unit point charge and the molecular charge distribution produced by the electrons and nuclei. The electrostatic potential, U r), at a point, r, is defined by Eq. [13]. 

Let SAd and SAa be the solvent accessible surface areas of hydrogen-bonding donors (d) and acceptors (a), respectively, and Qa the corresponding partial atomic charges, SASA the molecular solvent-accessible surface area the HB-CPSA descriptors are then defined as follows (note that the two different symbols encountered in the literature for some are considered as synonymous). 

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