Topological density

Experimental determination of the electron density topology in a non-centrosymmetric transition metal complex [Ni(H3L)] N03][PF6] [H3L = N, N, N"-tris(2-hydroxy-3-... 

The B network derived from the electron density topology links all atoms that share faces. Although the B links are all topologically equivalent, only those... 

It is well known that there are numerous factors that influence the gel collapse (charge density, topological structure of a network, medium composition, etc.). The same factors are effective in the case under study as well (see... 

Cubero E, Orozco M, Hobza P, Luque FJ (1999) Hydrogen bond versus anti-hydrogen bond A comparative analysis based on the electron density topology. J Phys Chem A 103 6394-6401... 

Once the multipole analysis of the X-ray data is done, it provides an analytical description of the electron density that can be used to calculate electrostatic properties (static model density, topology of the density, dipole moments, electrostatic potential, net charges, d orbital populations, etc.). It also allows the calculation of accurate structure factors phases which enables the calculation of experimental dynamic deformation density maps [16] ... 

The first objective of this review (Section II) is to give a first answer to all these questions it will be shown that all the answers are positive. Then, it allows the second part of this review to be devoted to the applications of charge density research like electron density topology, electrostatic properties, study of hydrogen bonds, and metal-ligand interactions. 

Then, analyzing the electron density topology requires the calculation of Vp and of the hessian matrix. After diagonalization one can find the critical points in a covalent bond characterized by a (3, -1) critical point, the positive curvature X3 is associated with the direction joining the two atoms covalently bonded, and the X2, curvatures characterize the ellipticity of the bond by ... 

R. A. Klein, Electron density topological analysis of hydrogen bonding in glucopyranose and hydrated glucopyranose,/. Am. Chem. Soc., 124 (2002) 13931-13937. 

E. Cubero, M. Orozco, and F. J. Luque, Electron density topological analysis of the C—H O anti-hydrogen bond in the fluoroform-oxirane complex, Chem. Phys. Lett. 310, 445-450 (1990). 

C. Gatti, P. Fantucd, G. Pacchioni. Charge density topological study of bonding in lithium clusters. Part I Planar Li n clusters (n=4, 5, 6). Theor. Chem. Acc. (Formerly, Theoret. Chim. 

Figures commonly discussed as recently as a decade ago included internal coordinates in conjunction with the location and height of deformation density peaks [12]. Most recent studies [13], on the other hand, analyze correlations between density-topological indices that require precise parameter estimates of ED models fitted to high quality and resolution intensity data. Significant improvements of experimental conditions over the past few years have resulted in an unprecedented flow of reliable XRD data. Charge-coupled devices (CCD)...

For an excellent review on the density topology in the crystalline state and for a detailed discussion on the interpretation of topological features introduced by the periodicity, symmetry, and cooperative field effects, we refer to a recent work by Gatti [30]. Only two important aspects of the topological approach to solid-state chemical interactions highlighted in that work are re-emphasized here. 

A third classifying quantity relates to the surface structure of silicas, which is characterized by the coordination of surface silicon atoms the resulting functional groups their density, topology, and distribution the degree of hydroxylation the hydration-dehydration behavior the acidic... 

Tables 1 and 2 summarize the obtained total energy, dipolar moments and geometrical parameters, respectively. Tables 3-5 list the electron density topological analysis results. 

A third classifying quantity relates to the surface structure of silicas, which is characterized by the coordination of surface silicon atoms the resulting functional groups their density, topology, and distribution the degree of hydroxylation the hydration-dehydration behavior the acidic and basic properties of surface functional groups and their adsorption behavior and chemical reactivity. The pattern of the surface structure in terms of these properties is discussed in the section Current View of the Silica Surface. The following section reviews the methods by which reliable information on these properties is obtained. 

Many reviews analyzed the structures [4, 5, 8-10], spectra [6, 11], and electron density topologies [12] of bridging carbonyls. However, no systematic review about theoretical and molecular orbital analysis of the bridging carbonyls is currently available. A selection of about ten systems covering different types of bridging carbonyls is presented here with full analysis of their molecular orbitals to help connect the theoretical descriptions of chemical bonds and electronic structures to the observable molecular structures. 

A further example of an alkyl lithium compound with ambiguous chemical bonding that was resolved on the basis of electron density topology considerations is given in the on-line supplementary section for chapter 10. 

There are many other types of contact or weak bonding interaction that cannot always be decided on by distance criteria alone. These include weak dispersive interactions between heavy elements, interactions between aromatic units and hydrogen bonding. Other sources of information from spectroscopy, electron density topology or quantum mechanical calculations have to be used jointly to give a satisfactory chemical explanation. This should always be remembered when you see a crystal structure with a simple line drawn between two atoms. 

In this section we put aU of this into practice with some examples to demonstrate what we can learn from electron density topology studies, but also to show what some of its limitations are. T vo further examples can also be found in case histories 12.10 and 12.12, where the charge density studies are placed into a wider context together with results from other methods. Charge density studies on various chemical topics are reviewed in [49]. 

How are the concepts of Lewis acidity and Lewis basicity reflected in features of electron density topology and its assoeiated parameters ... 

Calculated electron density topologies for adamantane encapsulating a helium atom show four bond paths between the carbon cage and the noble gas, and 60 for the system He C6o- Use these data to discuss the difference in the concepts of chemical bonding in the conventional sense, and within the framework of AIM theory. 

If such a transfer of electron density takes place, we should be able to see this in the region between the Si and N atoms as a local valence charge accumulation. The electron density topologies (Section 10.10) of... 

---