Analysis of the Electron Density Distribution

While a qualitative understanding of the structures and stabilities of Ng molecules was achieved by the donor-acceptor model, the quantitative analysis of the binding properties was provided by the analysis of the electron density distribution. 

The electron denstiy distribution p(r) of an atom or molecule is an observable property that can be measured by a combination of X-ray and neutron diffraction experiments [22]. Also, it is easy to calculate p(r) once the MOs and the wave function of a molecule have been determined. The distribution p(r) is invariant with regard to any unitary transformation of the MOs. It has been shown by Hohenberg and Kohn that the energy of a molecule in its (nondegenerate) ground state is a unique functional of p(r) [23]. In other words, the physical and chemical properties of a molecule can be related to p(r). Thus, p(r) represents the best starting point for an analysis of chemical bonding. 

Bader and coworkers have shown that properties of the electron density distribution p(r) can be used to partition the molecular space into subspaces in a unique way [24]. This has been used by Cremer and Kraka (CK) to establish a model of the chemical bond that it easy to use, that allows a simple distinction between bonding and nonbonding situations, and that helps to characterize covalent bonds [19]. Therefore, the CK model has been applied when quantitatively describing chemical bonding in molecules containing light noble gas elements. In the following, we will briefly review the essentials of the Bader analysis and the CK bond model [25]. 

Analysis of the electron density distribution p(r) of numerous molecules [27-30] has revealed that there exists a one to one relation between MED paths and saddle points Fq on the one side and chemical bonds on the other side. 

This relation is the basis for a definition of a chemical bond [19, 27] Two atoms will be bonded if and only if there exists a MED path linking them (necessary condition). 

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In the following chapter we show how the topology of an important function of p, the Laplacian, enables us to obtain additional information from the analysis of the electron density distribution. 

Analysis of the electron density distribution p (r) of numerous molecules has revealed that there exists a one-to-one relation between MED paths, saddle points p and interatomic surfaces on the one side and chemical bonds on the other27,81,82. However, low-density MED paths can also be found in the case of non-bonding interactions between two molecules in a van der Waals complex82. To distinguish covalent bonding fron non-bonded or van der Waals interactions, Cremer and Kraka have given two conditions for the existence of a covalent bond between two atoms A and B8. 

In 46, the Si+ interacts with two H atoms of the adjacent methyl groups at distances of 1.925 A. [44] This interaction is also revealed by a lengthening of the C-H bonds of the interacting H atoms. An analysis of the electron density distribution in the Si—H region suggests that weak covalent bonds are formed (Table 7). 

Analysis of the electron density distribution confirms that Ng,C bonding in HeCCHe " is due to s-electron donation from He while in NeCCNe and ArCCAr it is due to pcr-electron donation from Ng. Again, this is nicely reflected by the calculated Laplace concentrations (Fig. 19). 

In contrast to the natural bond orbital [159] picture, a detailed analysis of the electron density distribution and its associated Laplace field suggests that bonding in HeBeO, NeBeO and ArBeO is caused by strong charge induced... 

An analysis of the electronic density distribution (Mulliken analysis of the valence orbital population [147]) has shown the bonding in the 6d element compounds to be dominated by a large participation of both the 6d3/2 and 6dsn orbitals (e.g., 70% in DbCls) and is typical of d-element compounds [148]. The 7s, as well as both the 6pi/2 and 6ps/2 orbitals, each contribute about 15 % to the bonding. The most important conclusion for the chemical experiment was, therefore, that the 6d elements are close homologs of the 5d elements and should exhibit similar chemical properties. 

For example, consider the Nephelauxetie Effeet. Analysis of the interelectron repulsion parameters derived from analyzing the d-d speetrum invariably leads to lower values than in the free ion. The interpretation is that, in the eomplex, the d eleetrons are, on average, further apart which is consistent with expanded rf-funetions in the eomplex and/or with d electron delocalization onto the ligands. Analysis of the electron density distribution from X-ray diffraction in trans-[Ni(NH3)4(N02)2] yields a rf-orbital radius larger than that for free Ni. However, the unpaired electron density derived from polarized neutron diffraction (PND) data yields a if-orbital radius less than for free Ni " prompting Figgis to propose an anti-Nephelauxetic effect. DFT calculations support LFT in that the d-orbitals expand upon complex formation but also provide an explanation of the diffraction data. 

The spectroscopic properties of M-SiO and M-(SiO)2 (1-1 and 1-2 complexes with M = Cu, Ag, or An) have been theoretically studied. It has been shown that both M-SiO and M-(SiO)2 compounds in their ground state are bent with a metal-Si bonded structure. The calculated M(ns) spin density agrees well with the ESR experimental data. iFrom a topological analysis of the electron density distribution it has been found that the M-Si bond enei correlates with the electron density located at the M-Sl bond path (bond critical point). Audenies fortuna juvat... 

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