2D autocorrelation vectors

Z eb index, Wiener index. Balaban J index, connectivity indices chi (x), kappa (k) shape indices, molecular walk counts, BCUT descriptors, 2D autocorrelation vector... 

The following section gives an overview of feature trees and 2D autocorrelation vectors, the two most important graph-based topological descriptors used for virtual screening. 

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]. 

The original 2D autocorrelation analysis calculates a vector based on the distances between all atoms of a structure and any property of these atoms.205>206 For each pair of atoms, the distance between the atoms (number of bonds between them) and the product of the properties is noted. Each element of the autocorrelation vertor is the sum of these products for one particular distance. A separate autocorrelation vector is calculated for each property of interest—typically, volume, electronegativity, hydrogen bonding character, hydrophobicity. As a final step a principal components analysis reduces the number of variables to consider. 

This function is a measure of the reorientation of the component of the velocity vector parallel to the surface It is calculated by choosing a molecule and following its motion as a function of time for a specified time period, averaging the velocity autocorrelation function (the dot product of the 2D vector velocity at the time t, with the velocity at a later time in the... 

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