Atom counts, molecular descriptor

A particular case of walk counts, self-returning walk counts are atomic and molecular descriptors obtained from an - H-depleted molecular graph Q, based on graph walks starting and ending at the same vertex, i.e. self-returning walks (SRWs) [Harary, 1969a],... 

Rucker, G. and Rucker, C. (1993). Counts of All Walks as Atomic and Molecular Descriptors. JChem.Inf.Comput.ScL, 33, 683-695. 

Ruecker G, Ruecker C. Counts of all walks as atomic and molecular descriptors. J Chem Inf Comput Sci 1993 33 683-695. 

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]. 

These descriptors can vary in complexity from simple atom counts to electronic properties derived from high-level ab initio calculations. Available molecular descriptors fall into three broad categories (1) Two-dimensional, encoding the topology of a molecule. (2) Three-dimensional, based on the 3D structure of a molecule. (3) Physicochemical (and electronic) representing whole molecule properties. 

Other topological matrices are derived from the adjacency matrix, such as -> atom connectivity matrices, -> Laplacian matrix and the powers of the adjacency matrix used to obtain walk counts and the corresponding - molecular descriptors. 

Average molecular weight and -> relative atom-type count are simple molecular descriptors that encode information on atomic composition. Other important descriptors of the atomic composition are based on the -> total information content and the - mean information content, defined as ... 

These are simple molecular descriptors based on counting the defined elements of a compound. The most common chemical count descriptors are atom number A, bond number B, cyclomatic number C, -> hydrogen-bond acceptor number and -> hydrogen-bond donor number, -> distance-counting descriptors, -> path counts, walk counts. 

Molecular descriptors related to the dimensions of the molecule and often calculated from the - molecular geometry. Combined with molecular shape information, they are closely related to - steric descriptors. The simplest size descriptors are atom count, -> bond count, -> molecular weight, and some among the -> volume descriptors such as van der Waals volume. Other size descriptors are - Sterimol parameters and - WHIM size descriptors. 

Atom-type topological indices are used to describe a molecule by information related to different atom types in the molecule. An atom-type index is usually derived from some properties of all the atoms of the same type and their structural environment. Atom-type Estate indices of Kier and Hall, perturbation connectivity indices, atom-type path counts, and atom-type autocorrelation descriptors are examples of these molecular descriptors. 

The intrinsic state of an atom can be simply thought of as the ratio of it and lone-pair electrons over the count of the g bonds in the molecular graph for the atom considered. Therefore, the intrinsic state reflects the possible partitioning of non-0 electron s influence along the paths starting from the considered atom the less partitioning of the electron influence, the more available are the valence electrons for intermolecular interactions. The sum of the intrinsic states of all of the atoms is a molecular descriptor called intrinsic state sum moreover, from the intrinsic state sum the —> Q polarity index was derived. 

From the atomic VEM counts, two molecular descriptors are derived ... 

This representation is independent of any knowledge concerning the molecular structure, and hence molecular descriptors obtained from the chemical formula can be called OD descriptors. Examples are the atom number A, molecular weight MW, atom-type count Nx, and, in general, constitutional descriptors and any function of the atomic... 

Chemical Shift Sum (CSS) was proposed as single molecular descriptor derived from spectra as the sum of the chemical shifts of the carbon atoms from C-NMR spectroscopy [Randic, 1980a]. It was shown that at least for alkanes, the chemical shift sum varies regularly with some physico-chemical properties of alkanes. QSAR models for CSS, based on artificial neural networks, were proposed by using the first four path counts [Ivanciuc, Rabine et al., 1997]. 

The —> walk connectivity indices are molecular descriptors defined by analogy with the —> Randic connectivity index by using the atomic walk counts in place of the vertex degrees [Razinger, 1986]. 

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