The alternatives to mathematical descriptors derived from molecular graphs or molecular geometry are the traditional QSAR (quantitative structure-activity relationship) descriptors and quantum chemically computed parameters. The former include the partition coefficient for oil/water (often octanol/water) (log P), the Hammet sigma value (

From that point of view, new mathematical descriptors of recent times are more likely than not to make many ad hoc descriptors of the past less relevant for QSAR than they appear today. [Pg.220]

The Wiener index for isopentane is 18. The Wiener index is used as a mathematical descriptor used in structure - property relationships. There are many other related descriptors for molecular graphs, including shape index, chirality index, Szeged index [12]. A comparison of the boiling points of alkanes against the different indices has been shown in the literature [13]. [Pg.549]

Describing a fact, property, or a situation this leads us to the topic of Mathematical Descriptors that are able to represent such information in a computer program. [Pg.7]

Basak SC, Mills D, Gute BD (2006) Predicting Bioactivity and Toxicity of Chemicals from Mathematical Descriptors A Chemical-cum-Biochemical Approach. In Klein DJ, Brandas E (eds) Advances in Quantum Chemistry, Elsevier, in press [Pg.80]

Basak, S. C., Mills, D., Gute, B. D. Predicting bioactivity and toxicity of chemicals from mathematical descriptors A chemical-cum-biochemical approach. In Advances in Quantum Chemistry, Klein, D. J., Brandas, E., Eds., Elsevier, Amsterdam, 2004, in press. [Pg.498]

Properties Cases are indexed by properties — typically one- or multidimensional experimental or mathematical descriptors. Descriptors allow a specific definition of the case according to the relevant features of a case. [Pg.23]

The development and application of molecular shape descriptors is an active area in computational chemistry and biology. The main goal of our work is to develop mathematical descriptors that can determine whether two molecules have comparable shapes. In this chapter we present a series of molecular shape descriptors developed oti the basis of molecular vdW space. The molecules are treated in the hard sphere approximation, as a body composed from a collection of atomic fused spheres. Each sphere is centered in the corresponding nucleus and it is characterized by its Cartesian coordinates and by its vdW radius, r. These molecular vdW shape descriptors depend only on the internal structure of the molecule, being invariants to any translation and rotation movement. Consequently, they may inform us that two molecules have comparable shapes, but since they carry no information about the absolute orientation or position of the molecule, they are not useful for computing molecular superposition. [Pg.339]

In the present work, we will use a relatively low level of theory to derive 32 weakly correlated molecular descriptors, each based on the subdivision and classification of the molecular surface area according to three fundamental properties contribution to ClogP, molar refractivity, and atomic partial charge. The resulting collection will be shown to have applicability in QSAR, QSPR, and compound classification. Moreover, the derived 32 descriptors linearly encode most of the information of a collection of traditional mathematical descriptors used in QSAR and QSPR. [Pg.262]

Throughout the realm of molecular modeling, the concept of molecular shape arises over and over in one form or another. Just what do scientists mean by a molecule s shape, and how can one use three-dimensional shape in modeling. In Chapter 5, Professor Gustavo A. Arteca examines these issues and delineates the hierarchical levels of molecular shape and shape descriptors. He explains molecular shape in terms of mathematical descriptors of nuclear geometry, connectivity, and molecular surfaces. Of special note are his comments on shape dynamics of flexible molecules and descriptors of relative shape. [Pg.303]

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