Topological analysis of the

Most of the relevant features of the charge density distribution can be elegantly elucidated by means of the topological analysis of the total electron density [43] nevertheless, electron density deformation maps are still a very effective tool in charge density studies. This is especially true for all densities that are not specified via a multipole model and whose topological analysis has to be performed from numerical values on a grid. 

A topological analysis of the total static density has been carried out. The analysis is not complete, and will not be discussed in any great detail in the present context. It is worth mentioning however that similar results as found for benzoylacetone were obtained. The values of pb and V2pbat the 0(1)-H(X) and 0(3)-H(X) bond critical... 

Petlyuk FB, Kievskii VY and Serafimov LA (1975) Thermodynamic and Topological Analysis of the Phase Diagrams of Polyazeotropic Mixtures II. Algorithm for Construction of Structural Graphs for Azeotropic Ternary Mixtures, Russ J Phys Chem, 49 1836. 

For over a decade, the topological analysis of the ELF has been extensively used for the analysis of chemical bonding and chemical reactivity. Indeed, the Lewis pair concept can be interpreted using the Pauli Exclusion Principle which introduces an effective repulsion between same spin electrons in the wavefunction. Consequently, bonds and lone pairs correspond to area of space where the electron density generated by valence electrons is associated to a weak Pauli repulsion. Such a property was noticed by Becke and Edgecombe [28] who proposed an expression of ELF based on the laplacian of conditional probability of finding one electron of spin a at t2, knowing that another reference same spin electron is present at ri. Such a function... 

The ELF was proposed by Becke and Edgecombe [7] in 1990 and very soon extensively applied to a variety of systems ranging from atoms to inorganic and organic molecules to solids [9]. In 1994, a topological analysis of the ELF was... 

Such analysis sufficiently supplements with topological analysis of the electron density proposed earlier by Bader, where the condition... 

The modem state of EDSA in combination with topological analysis of the ESP and electron density allows to obtain reliable and quantitative information about chemical bonding and properties. 

Bond critical points represent extremes of electronic density. For this reason, these points are located in space where the gradient vector V p vanishes. Then the two gradient paths, each of which starts at the bond critical point and ends at a nucleus, will be the atomic interaction line. When all the forces on all the nuclei vanish, the atomic interaction line represents a bond path. In practice, this line connects two nuclei which can consequently be called bonded [5]. In terms of topological analysis of the electron density, these critical points and paths of maximum electron density (atomic interaction lines) yield a molecular graph, which is a good representation of the bonding interactions. 

Figures 5.20 illustrates the equilibrium and transition-state structures obtained for these complexes. As shown, the L1H-H20 complex in equilibrium state 1 shows an intramolecular dihydrogen bond with a very short H- H distance of 1.580 A calculated at the MP2/6-311++G(2d,2p) level. The topological analysis of the electron density on the H- H direction has resulted in the small pc and positive V pc values (0.0388 and 0.0453 an, respectively) typical of dihydrogen bonding. In contrast, no dihydrogen bonding was observed in the LiH-H2S molecule (3), where the corresponding hydrogen atoms are strongly remote.

A topological analysis of the electron density in the framework of AIM theory, performed for the systems in Figure 6.2, has completely confirmed their formulation as dihydrogen-bonded complexes. In accord with the AIM criteria, the pc and V pc parameters at the bond critical points found in the H- - -H directions are typical of dihydrogen bonds 0.042 and 0.057 au for complex LiH HF and 0.046 and 0.048 au for complex NaH- - -HF, respectively. The presence of the bond critical points can be well illustrated by the molecular graph in Figure 6.3, obtained for the HCCH H-Li complex by Grabowski and co-workers [8]. 

For comparison, the authors have probed a complex formed by the same proton-donor molecule and molecular hydrogen. In this very weak complex, HCCH- - (H2), the H- - (H2) distance has been calculated as 2.606 A (i.e., significantly larger than the sum of the van der Waals radii of H). It is extremely interesting that a topological analysis of the electron density also leads to the appearance of the bond critical point in the H- - (H2) direction. However, the Pc and V pc values are very small (0.0033 and 0.0115 au, respectively) compared with those in the HCCH- - -HLi complex (0.0112 and 0.0254 au, respectively). The most important conclusion of this comparison is There is no evident borderline between the dihydrogen-bonded complexes and the van der Waals systems. 

NH4-CH4]+ complex in the gas phase [36]. Topological analysis of the electron density performed in the framework of AIM theory shows the bond critical points on the H- H directions with pc values of 0.013 an. It is interesting that the electron density in this complex is larger than that obtained for the BH4 - CH4 dihydrogen-bonded system (pc = 0.007 an), the CH4 molecule of which acts as a proton donor. In accordance with the electronic density, the H- H distances in the BH4 - H4C complex were remarkably longer than 2.4 A (2.797, 2.929,... 

AIM topological analysis of the electron density performed for two complexes and for isolated components is shown in Table 6.15. The bond critical points found in the H H directions are characterized by the small electronic density with Pc = 0.002 and 0.009 au in the CILj- HF and SilLj- HF systems, respectively. The Laplacian, V pc, is also small but takes positive values in accordance with the AIM criteria for dihydrogen bonding. 

Space Partitioning and Topological Analysis of the Total Charge Density... 

The topological analysis of the total density, developed by Bader and coworkers, leads to a scheme of natural partitioning into atomic basins which each obey the virial theorem. The sum of the energies of the individual atoms defined in this way equals the total energy of the system. While the Bader partitioning was initially developed for the analysis of theoretical densities, it is equally applicable to model densities based on the experimental data. The density obtained from the Fourier transform of the structure factors is generally not suitable for this purpose, because of experimental noise, truncation effects, and thermal smearing. 

The topological analysis of the density leads to a powerful classification of bonding based on the electron density. It is discussed in the final sections of this chapter. 

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