Descriptors electron density derived

Breneman, C., Bennett, Bi, J., Song, M., and Embrechts, M. (2002) New electron density-derived descriptors and machine learning techniques for computational ADME and molecular design. MidAtlantic Computational Chemistry Meeting, Princeton University, Princeton, NJ. 

Other pharmacological activities have also been correlated with quantum-chemically derived descriptors. For instance, the quantitative structure-activity relationship developed for the antibacterial activity of a series of monocyclic (i-lactam antibiotics included the atomic charges, the bond orders, the dipole moment, and the first excitation energy of the compound [103]. The fungicidal activity of A3-l,2,4-thiadiazolines has been correlated with an index of frontier orbital electron density derived from semi-empirical PM3 molecular orbital calculations [104],... 

Figure 16 WCDs are generated as illustrated for each electron density-derived property. The property distribution is deconstructed using the DWT (pyramid algorithm), allowing the isolation of the lowest frequency and coarsest approximation coefficients (ay and dy). These few coefficients are sufficient to reconstruct most of the original signal (via the inverse DWT) and contain the vital molecular property information needed for modeling. The WCDs replace the original TAE histogram descriptors and are orthogonal, consistent, and representative.

MolSurf parameters [33] are descriptors derived from quantum mechanical calculations. These descriptors are computed at a surface of constant electron density, with which a very fine description of the properties of a molecule at the Van der Waals surface can be obtained. They describe various electrostatic properties such as hydrogen-bonding strengths and polarizability, as well as Lewis base and acid strengths. MolSurf parameters are computed using the following protocol. 

For the second derivative of the electronic density with respect to the number of electrons, the dual descriptor, one can proceed as in the case of the energy. That is, the Fukui function using the Heaviside function [25] is written as... 

The effect of external field on reactivity descriptors has been of recent interest. Since the basic reactivity descriptors are derivatives of energy and electron density with respect to the number of electrons, the effect of external field on these descriptors can be understood by the perturbative analysis of energy and electron density with respect to number of electrons and external field. Such an analysis has been done by Senet [22] and Fuentealba [23]. Senet discussed perturbation of these quantities with respect to general local external potential. It can be shown that since p(r) = 8E/8vexl, Fukui function can be seen either as a derivative of chemical potential... 

The molecular volume descriptor, V, can be recognized as an important descriptor once one realizes that the free energy of solution is related in part to the size of the cavity that must be carved out of the solvent bath by the solute molecule during the solvation process. The surface area, A, of a molecule or a fragment of a molecule may be construed as a measure of the region available for interaction with another molecule. For computing V and A, one could use a particular electron density contour or a non-QM-derived measure of atomic size such as the van der Waals radii available from standard tables in physical chemistry textbooks. 

The descriptors developed to characterize the substrate chemotypes are obtained from a mixture of molecular orbital calculations and GRID probe-pharmacophore recognition. Molecular orbital calculations to compute the substrate s electron density distribution are the first to be performed. All atom charges are determined using the AMI Hamiltonian. Then the computed charges are used to derive a 3D pharmacophore based on the molecular electrostatic potential (MEP) around the substrate molecules. 

Many quantum-chemical descriptors are derived from the charge distribution in a molecule or the electron density of specified atoms or molecular regions, and from conformational energy values such as the Joshi electronic descriptors. Moreover, several -> charge descriptors and -> electric polarization descriptors are obtained from atomic charge estimations. 

We have used transferable atom equivalent (TAE) descriptors [116,117] that encode the distributions of electron density based molecular properties, such as kinetic energy densities, local average ionization potentials, Fukui functions, electron density gradients, and second derivatives as well as the density itself. In addition autocorrelation descriptors (RAD) were used and represent the molecular geometry characteristics of the molecules, while they are also canonical and independent of 3D coordinates. The 2D descriptors alone or in combination with the latter 3D descriptors were calculated for 26 data sets collated by us from numerous publications. These data sets encompass various ADME/TOX-related enzymes, transporters, and ion channels as... 

Several different kinds of quantum-chemical descriptors have been defined and these can be broadly divided into energy-based descriptors, orbital energies descriptors, local quantum-chemical properties, descriptors based on the analysis of the wave function, frontier orbital electron densities, superdelocalizability indices, polarizabilities, and derived from the Density Functional Theory [Cartier and Rivail, 1987 Bergmarm and Hinze, 1996 Karelson, Lobanov et al., 1996]. 

In closing, we should also include the molecular graphs introduced by Bader and co-workers.These graphs are derived from the entire electron density function p(r, K) and not from one molecular contour surface. In this sense, these are 2D descriptors of molecular 3D models. 

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