Molecular complexity indices

Molecular - OD-descriptors with high degeneracy, derived from the chemical formula of compounds and defined as - information indices of the elemental composition of the molecule, can be considered -> molecular complexity indices that take account of molecular diversity in terms of different atom types. 

Entropy Descriptors (SHED), graph entropy, and some descriptors among the molecular complexity indices and the GETAWAY descriptors. 

Basak, S.C. (1987) Use of molecular complexity indices in predictive pharmacology and toxicology a QSAR approach. Med. Sci Res., 15, 605-609. 

It is sometimes helpful to distinguish between the complexity of objects and that of processes. If one seeks to compare different objects to one another in terms of their complexity that is object complexity theory. The objects might be molecules, people, social structures, poems, toxins, etc... An enormous literature exists with much of the chemical focus being on molecular complexity indices that attempt to order molecular graphs according to some measure of their complexity. While not yet directly concerned with complexity, much environmental focus has been on the relative toxicity of pollutants partially ordered by their effects on different things. 

S. Basak. Use of molecular complexity indices in predictive pharmacology and toxicology ... 

S. Nikolid, N. Trinajstid, I.M. Tolid, G. Rucker, and C. Rucker, On molecular complexity indices, in Complexity in chemistry—Introduction and fundamentals, ed. D. Bonchev and D.H. Rouvray, Taylor and Francis, London, 2003b, pp. 29-76. 

Extensive experimental and theoretical studies for small molecular complexes indicate that multipolar term is the most specific and aniso-... 

As the number of connections is sensitive to different features of molecular structure such as size, branching, cyclicity and multiple bonds it was used by Bertz to define its -> molecular complexity index. 

A molecular complexity index defined as a linear combination of five single information indices ... 

A general form of a molecular complexity index Icpx is... 

Thus, H is directly related to the size of the molecule considered, whatever the structure of the skeleton, which is numerically characterized by the index S which includes all the elements of structure. It is also useful to consider the S/H ratio, which is termed the specific molecular complexity index (Pietra, 2002). 

Bertz, S.H. (1981) The First General Index of Molecular Complexity. Journal of the American... 

On the basis of graph theory and information theory, Bertz [30] has proposed, in the past few years, the first general index of molecular complexity (T ), so introducing a quantitative concept of "molecular complexity" which may be applied to synthetic analysis. 

Molecular complexity" is a rather subjective concept. Although the structural features which contribute to the complexity of a molecule have been pointed out by different authors [1] [2] [3] [4], only recently Bertz has defined a quantitative and unified index embracing the size, symmetry, branching, unsaturation, and heteroatoms chatracteristic of a complex molecule [ 5] [6]. 

Nevertheless, it was decided to make the measurements of density and of refractive index for specimens after different times of curing. Since the molecular weight of the polymerized silane was not known, the molecular refractivity could not be calculated but only the ratio of this to the molecular weight. Nevertheless, interesting results were obtained with a linear relationship between the cure time and refractive index up to 18 h. The relationship between the cure time and the ratio of molecular refractivity to molecular weight is shown in Fig. 3 and indicates a steady increase in molecular complexity up to 24 h, when it approaches a constant value suggesting a final state of crosslinking. 

TTie structural features are represented by molecular descriptors, which are numeric quantities related directly to the molecular structure rather than physicochemical properties. Examples of such descriptors include molecular weight, molecular connectivity indexes, molecular complexity (degree of substitution), atom counts and valencies, charge, molecular polarizability, moments of inertia, and surface area and volume. Once a set of descriptors has been developed and tested to remove interdependent/collinear variables, a linear regression equation is developed to correlate these variables with the retention parameter of interest, e.g., retention index, retention volume, or partition coefficient The final equation includes only those descriptors that ate statistically significant and provide the best fit to the data. For more details on QSRR and the development and use of molecular descriptors, the reader is referred to the literature [188,195,198,200-202 and references therein]. 

Bertz-Herndon relative complexity index -> molecular complexity... 

Other information indices are - atomic composition indices, - information bond index, -> Morowitz information index, information index on size, information index on molecular symmetry, - information index on amino acid composition, -> information index on molecular conformations, -> Bertz complexity index, - Dos-morov complexity index, - Bonchev complexity index, -> atomic information indices, and electropy index. 

Minoli complexity index molecular complexity mixed CoMFA approach - comparative molecular field analysis mixed CoMFA model -> comparative molecular field analysis MmPS topological index detour/Wiener index -> detour matrix model complexity (cpx)... 

The most well-known complexity indices are listed below. Other molecular descriptors which give information about molecular complexity are the indices of neighbourhood symmetry and the - total adjacency index. The latter was proposed by Bonchev and Polansky [Bonchev and Polansky, 1987] as a simple measure of topological complexity, being a measure of the degree of connectedness of molecular graph. 

The most popular complexity index was introduced by Bertz [Bertz, 1981 Bertz, 1983a Bertz, 1983b], tal g into account both the variety of kinds of bond connectivities and atom types of a - H-depleted molecular graph. 

A molecular descriptor defined in analogy with the Dosmorov complexity index, also accounting for electronic properties of molecules [Bonchev, 1983] ... 

This index was proposed as a measure of -> molecular complexity together with some other information indices derived from the distance matrix [Raychaudhury et ai, 1984]. 

The molecular walk count is related to - moleeular branehing and size, and in general to the - molecular complexity of the graph. In fact, it was found that mwe is directly related to the Lovasz-Pelikan index, i.e. the largest eigenvalue of the adjacency matrix [Cvetkovic and Gutman, 1977]... 

It may be tempting to assimilate molecular complexity (complexity of structure) with synthetic complexity (complexity of the synthetic process). However, indices of molecular complexity, even ones such as that described by Bertz, are not equally good as indices of synthetic difficulty. For one thing, there are features such as thermodynamic stability that cannot easily be incorporated into such an index. Also, because each individual feature of structure places constraints on the specific chemical reactions and conditions that may be applied during the time it is present in the synthetic sequence, and because synthetic difficulties may arise through the synergy of certain structural elements, complexity increases nonlinearly with the accumulation of structural elements. In other words, specific combinations of the same structural features can... 

Bertz, Steven H. 1981. "The First General Index of Molecular Complexity." Journal of the American Chemical Society, 103 3599-3601. 

Bertz branching index molecular complexity (0 molecular branching)... 

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