The electron pair density, in conjunction with the definition of an atom in a molecule, enables one to determine the average number of electron pairs that are localized to each atom and the number that are formed between any given pair of atoms. Thus, it is through the pair density that the Lewis model of electronic structure finds physical expression. The pairing of electrons is a consequence of the Pauli principle whose effect is made manifest through the creation of the Fermi hole. The density describing the spatial distribution of the Fermi hole for an electron of given spin determines how the density of that electron is spread out in space, excluding an equivalent amount of same-spin density. The averaging of the Fermi density over single atoms or pairs of atoms determines the corresponding contributions to the total Fermi correlation. It is these terms that yield the localization and delocalization indices that determine the intra- and interatomic distribution of electron pairs that enables one to compare the pairing predicted by theory with that of a Lewis structure. The agreement is best at the Hartree−Fock level, where the Fermi hole is the sole source of correlation between the electrons. The introduction of the remaining correlation, the Coulomb correlation, disrupts the sharing of electron pairs between the atoms, and its effect is therefore, most pronounced for shared interactions. For example, Coulomb correlation reduces the number of shared pairs in N2 from the Hartree−Fock value of three to just above two. In ionic systems, the electrons are strongly localized within each atomic basin and the effect of Coulomb correlation on the atomic pairing is minimal, approaching zero over each of the atomic basins, as it does for the total molecule.

This work introduces a new local aromaticity measure, defined as the mean of Bader's electron delocalization index (DI) of para-related carbon atoms in six-membered rings. This new electronic criterion of aromaticity is based on the fact that aromaticity is related to the cyclic delocalized distribution of pi-electrons. We have found that this DI and the harmonic oscillator model of aromaticity (HOMA) index are strongly correlated for a series of six-membered rings in eleven planar polycyclic aromatic hydrocarbons. The correlation between the DI and the nucleus-independent chemical shift (NICS) values is less remarkable, although in general six-membered rings with larger DI values also have more negative NICS indices. We have shown that this index can also be applied, with some modifications, to study of the aromaticity in five-membered rings.

In this work we quantify the local aromaticity of six-membered rings in a series of planar and bowl-shaped polycyclic aromatic hydrocarbons (PAHs) and fullerenes. The evaluation of local aromaticity has been carried out through the use of structurally (HOMA) and magnetically (NICS) based measures, as well as by the use of a new electronically based indicator of aromaticity, the para delocalization index (PDI), which is defined as the average of all the Bader delocalization indices between para-related carbon atoms in six-membered rings. The series of PAHs selected includes C(10)H(8), C(12)H(8), C(14)H(8), C(20)H(10), C(26)H(12), and C(30)H(12), with benzene and C(60) taken as references. The change in the local aromaticity of the six-membered rings on going from benzene to C(60) is analyzed. Finally, we also compare the aromaticity of C(60) with that of C(70), open [5,6]- and closed [6,6]-C(60)NH systems, and C(60)F(18).

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A similarity‐driven approach to flexible ligand docking is presented. Given a reference ligand or a pharmacophore positioned in the protein active site, the method allows inclusion of a similarity term during docking. Two different algorithms have been implemented, namely, a similarity‐penalized docking (SP‐DOCK) and a similarity‐guided docking (SG‐DOCK). The basic idea is to maximally exploit the structural information about the ligand binding mode present in cases where ligand‐bound protein structures are available, information that is usually ignored in standard docking procedures. SP‐DOCK and SG‐DOCK have been derived as modified versions of the program DOCK 4.0, where the similarity program MIMIC acts as a module for the calculation of similarity indices that correct docking energy scores at certain steps of the calculation. SP‐DOCK applies similarity corrections to the set of ligand orientations at the end of the ligand incremental construction process, penalizing the docking energy and, thus, having only an effect on the relative ordering of the final solutions. SG‐DOCK applies similarity corrections throughout the entire ligand incremental construction process, thus affecting not only the relative ordering of solutions but also actively guiding the ligand docking. The performance of SP‐DOCK and SG‐DOCK for binding mode assessment and molecular database screening is discussed. When applied to a set of 32 thrombin ligands for which crystal structures are available, SG‐DOCK improves the average RMSD by ca. 1 Å when compared with DOCK. When those 32 thrombin ligands are included into a set of 1,000 diverse molecules from the ACD, DIV, and WDI databases, SP‐DOCK significantly improves the retrieval of thrombin ligands within the first 10% of each of the three databases with respect to DOCK, with minimal additional computational cost. In all cases, comparison of SP‐DOCK and SG‐DOCK results with those obtained by DOCK and MIMIC is performed. Proteins 2000;40:623–636. © 2000 Wiley‐Liss, Inc.

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