Determination of Three-Center Bond Indices from Population Analyses: A Fuzzy Atom Treatment

Bond order analysis based on the Laplacian of electron density in fuzzy overlap space

Bond order is an important concept for understanding the nature of a chemical bond. In this work, we propose a novel definition of bond order, called the Laplacian bond order (LBO), which is defined as a scaled integral of negative parts of the Laplacian of electron density in fuzzy overlap space. Many remarkable features of LBO are exemplified by numerous structurally diverse molecules. It is shown that LBO has a direct correlation with the bond polarity, the bond dissociation energy, and the bond vibrational frequency. The dissociation behavior of LBO of the N-N bond in N2 has been studied. Effects of the basis sets, theoretic methods, and geometrical conformations on LBO have also been investigated. Through comparisons, we discussed in details similarities and discrepancies among LBO, Mayer bond order, natural localized molecular orbital bond order, fuzzy overlap population, and electron density at bond critical points.

Laplacian Field of the Effectively Unpaired Electron Density: Determination of Many-Body Effects on Electron Distributions

This work carries out the study of the Laplacian field function of the electron density L(r) = -nabla2rho(r) splitted in two contributions rho(r) = rho(p)(r) + rho(u)(r), which correspond to the effectively paired and effectively unpaired electron densities, respectively. The visualization of the concentration and depletion of these fields and their spatial localization show no contribution of the effectively unpaired electrons to the conventional bonding among two centers, but the field -nabla2rho(u)(r) provides an interesting structure. We also study the reliability of the information contained in the partitioning of this electron density field function for describing nonclassical bondings as the three-center two-electron ones.

An orbital localization criterion based on the theory of “fuzzy” atoms

This work proposes a new procedure for localizing molecular and natural orbitals. The localization criterion presented here is based on the partitioning of the overlap matrix into atomic contributions within the theory of "fuzzy" atoms. Our approach has several advantages over other schemes: it is computationally inexpensive, preserves the sigma/pi-separability in planar systems and provides a straightforward interpretation of the resulting orbitals in terms of their localization indices and atomic occupancies. The corresponding algorithm has been implemented and its efficiency tested on selected molecular systems.

QTAIMn-center delocalization indices as descriptors of aromaticity in mono and poly heterocycles

The implementation of the n-center electron delocalization indices, n-DIs, and n-order electron localization indices, n-LIs, within the framework of the quantum theory of atoms in molecules, QTAIM, is performed. n-DIs are shown to be very useful to study the local aromaticity in monocyclic and polycyclic compounds. Total and pi n-DIs from n=4 to 7 were computed for a series of typical 4, 5, 6, and 7-center aromatic and antiaromatic rings. For n>or=5 the pi n-DI accounts for the 95% of the total n-DI and can be employed alone to measure the aromaticity. A scaling factor on the n-DIs is required in order to compare the aromaticity of [5c-6e] and [6c-6e] rings, the same correction allows to estimate the relative aromatic stabilization of polycyclic compounds using the sum of its values for individual rings. This is called Effective Scaled Electron Delocalization, ESED. The comparison with other aromaticity indices reflects a good correlation between ESED and both resonance energies, and HOMA indices. The most important differences between scaled pi n-DIs and NICS(0) indices are found for compounds that contain rings with different number of centers or pi electrons.