3D autocorrelation

In the calculation of a 3D autocorrelation vector the spatial distance is used as given by Eq. (20). 

In contrast to the topological autocorrelation vector, it is possible to distinguish between different conformations of a molecule using 3D autocorrelation vectors. 

The 3D autocorrelation vector of the three xylene isomers in Figure 8-4 differ only with respect to the component relating to the two methyl groups. For o-xylene it is... 

Figure 8-4. Comparison of 3D autocorrelation vectors of o-, m-, and j-xylene (without hydrogen atoms) Atomic property p = 1.

Topological descriptors and 3D descriptors calculated in distance space", such as 3D autocorrelation, surface autocorrelation, and radial distribution function... 

ADRIANA.code Global physicochemical descriptors, size and shape descriptors, atom property-weighted 2D and 3D autocorrelations and RDF, surface property-weighted autocorrelations 1,244... 

Sadowski etal. [49] have described the use of 3D autocorrelation vectors that are based on the electrostatic potential measured on the molecular surface of a molecule. The electrostatic potential was measured over 12 different distances giving 12 autocorrelation coefficients per molecule. The vectors were calculated for the molecules in two different combinatorial libraries a xanthene library and a cubane library. The compounds were then used to train a Kohonen network. The network was successfully able to separate the libraries. 

Autocorrelation descriptors can also be calculated for 3D-spatial molecular geometry. In this case, the distribution of a molecular property can be a mathematical function /(x, y, z), x, y, and z being the spatial coordinates, defined either for each point of molecular space (i.e. a continuous property such as electronic density or molecular interaction energy) or only for points occupied by atoms (i.e. atomic properties). An example of 3D autocorrelation descriptors are the - spectral weighted invariant molecular descriptors defined by - SWM signals. 

D autocorrelation, 3D MoRSE code, and radial distribution function code... 

In contrast to the topological autocorrelation vectors in the 3D autocorrelation vector, the spatial distance between atoms is used for calculation. Flence, using 3D autocorrelation vectors, it is possible to distinguish between different conformations of a molecule. The calculation of autocorrelation vectors of surface properties is similar to equation (10.2) ... 

D and 3D autocorrelation vectors [70] represent intramolecular 2D topologies or 3D distances within particular molecules. An autocorrelation coefficient is a sum over all atom pair properties separated by a predefined number of bonds (2D) or distance (3D), while the entire vector represents a series of coefficients for all topological or Cartesian distances. Atomic properties involve hydrophobicity [71], partial atomic charges, hydrogen bonding potential and others. Again, a PCA is often used to reduce the number of variables. 3D autocorrelation vectors of properties based on distances calculated from 3D molecular surfaces [72] have also been applied to visually assess the diversity of different libraries [73]. 

For a 3D-QSAR autocorrelation matrix, the distances are calculated from the 3D structures of the molecules. Both points on a CoMFA-like lattice and points on the molecular surface have been used for these distance calcula-tions.2 7 208 Similarly, the 3D autocorrelation properties are based on properties at these points (e.g., electrostatic or hydrophobic potential). Wagener et al. used a point density of 10 points/A on the van der Waals surface for the property calculation for the autocorrelation matrix, they considered distances from 1 to 13 A and a distance interval of 1 A to produce an autocorrelation vector of length 12.2° These 12 properties were then analyzed by principal components analysis, a Kohonen map, and a feed-forward multilayer neural... 

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