Weighted Holistic Invariant Molecular

WHIM descriptors Weighted Holistic Invariant Molecular descriptors) are discussed in detail in the Handbook, Chapter XIII, Section 2 [48, 49]. 

Molecular-Surface Weighted Holistic Invariant Molecular... 

Grid-Weighted Holistic Invariant Molecular descriptors G-WHIM descriptors... 

Todeschini, R., Gramatica, R, Marengo, E. and Provenzani, R. (1995). Weighted Holistic Invariant Molecular Descriptors. Part 2. Theory Development and Applications on Modeling Physico-Chemical Properties of Poly Aromatic Hydrocarbons (PAH). Chemom.IntelLLab.Syst., 27, 221-229. 

Todeschini, R., Moro, G., Boggia, R., Bonati, L., Cosentino, U., Lasagni, M. and Pitea, D. (1997a). Modeling and Prediction of Molecular Properties. Theory of Grid-Weighted Holistic Invariant Molecular (G-WHIM) Descriptors. Chemom.Intell.Lab.Syst., 36,65-73. 

WHIM Weighted holistic invariant molecular descriptors... 

The 3D descriptors described in this section are the weighted holistic invariant molecular (WHIM) descriptors, the Jurs descriptors, and the GRID-based VolSurf and Almond descriptors, as well as pharmacophore fingerprints. 

Further commonly used molecular descriptors are for example, eigenvalue-based descriptors including 3D information, such as BCUT descriptors (Burden, CAS, University of Texas eigenvalues), EVA, and WHIM descriptors (weighted holistic invariant molecular descriptors). For more information about molecular descriptors, the reader is referred to a handbook by Todeschini and Consonni and a recent review by Xue and Bajorath. ... 

Weighted Holistic Invariant Molecular (WHIM) indices [77] represent a different 3D approach to overcome the molecular 3D alignment problem, as they are invariant to molecular rotations and translations. These indices encapsulate information about the molecular 3D structure in terms of size, shape, symmetry and atom distribution, solely derived from Cartesian coordinates. 

Other whole molecule descriptors that do not require alignment include the Weighted Holistic Invariant Molecular (WHIM) indices developed by Todeschini et al. [70]. These indices are calculated from the 3D coordinates, which are weighted and centered to make them invariant to translation principal component analysis (PCA) is applied to obtain three principal components. These are used to produce new coordinates, which can be analyzed to obtain a series of 10 descriptors based on eigenvalues and the third-order and fourth-order moments of the three score column vectors. These descriptors are related to molecular size, shape, symmetry, and atom distribution and density. 

Alignment independent descriptors can be derived from the molecular formula, from the 2D molecular graph, or from a 3D conformation. They cover global molecular properties, but also 3D chemical information at the molecular surface as provided, for instance, by the Molecular Surface Weighted Holistic Invariant Molecular descriptors (MS-WHIM) [52,53]. The class of alignment independent descriptors includes also properties which are obtained from QM calculations, such as dipole moment or orbital energies. 

Weighted holistic invariant molecular (WHIM) descriptors (Todeschini et al. 1994) are sophisticated geometrical descriptors based on statistical indices calculated using the elements Sj, of matrix S. 

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