Analysis of electron density

Maerker, C., Schleyer, P. v. R., Liedl, K. R., Ha, T. K., Quack, M., Suhm, M. A., 1997, A Critical Analysis of Electronic Density Functionals for Structural, Energetic, Dynamic, and Magnetic Properties of Hydrogen Fluoride Clusters , J. Comput. Chem., 18, 1695. 

Yamamoto, K., Takahashi, Y., Ohshima, K., Okamura, F.P. and Yukino, K. (1996) MEM analysis of electron-density distributions for silicon and diamond using short-wavelength X-rays (WKa, ), Acta Cryst., A52,606-613. 

The definition of the radius of an ion in a crystal as the distance along the bond to the point of minimum electron density is identical with the definition of the radius of an atom in a crystal or molecule that we discuss in the analysis of electron density distributions in Chapter 6. The radius defined in this way does not depend on any assumption about whether the bond is ionic or covalent and is therefore applicable to any atom in a molecule or crystal independently of the covalent or ionic nature of the bond, but it is not constant from one molecule or crystal to another. The almost perfectly circular form of the contours in Figure... 

Thus there are five bonding electrons giving a bond order of 2.5, consistent with the bond length of 115 pm, versus 121 pm for the four-electron bond in O2 and 110 pm for the six-electron bond in N2. For these and other related molecules, the double-quartet model is a convenient and useful alternative to the conventional molecular orbital model. Moreover, it shows that for a singly bonded terminal atom such as F or Cl there is a ring of six nonbonding electrons rather than three separate lone pairs. As we will see in Chapters 7 and 8, this conclusion is confirmed by the analysis of electron density distributions. 

This chapter is based on the VSEPR and LCP models described in Chapters 4 and 5 and on the analysis of electron density distributions by the AIM theory discussed in Chapters 6 and 7. As we have seen, AIM gives us a method for obtaining the properties of atoms in molecules. Throughout the history of chemistry, as we have discussed in earlier chapters, most attention has been focused on the bonds rather than on the atoms in a molecule. In this chapter we will see how we can relate the properties of bonds, such as length and strength, to the quantities we can obtain from AIM. 

Gillespie, R.J. (2000). Improving our understanding of molecular geometry and the VSEPR model through the ligand close-packing model and the analysis of electron density distributions. 

Chapters 8 and 9 are devoted to a discussion of applications of the VSEPR and LCP models, the analysis of electron density distributions to the understanding of the bonding and geometry of molecules of the main group elements, and on the relationship of these models and theories to orbital models. Chapter 8 deals with molecules of the elements of period 2 and Chapter 9 with the molecules of the main group elements of period 3 and beyond. 

C. Maerker, P. von Rague Schleyer, R. Liedl, T. K. Ha, M. Quack, and M. A. Suhm, A critical analysis of electronic density functionals for structural, energetic, dynamic and magnetic properties of hydrogen fluoride clusters. J. Comput. Chem. 18, 1695 1719 (1997). 

TABLE 2.1. Geometrical Parameters, Bonding Energies, and Topological Analysis of Electronic Density in the Framework of AIM Theory"... 

An approach to chemical bonding that is currently attracting attention is that based on an analysis of electron densities calculated from quantum mechanics or measured using X-ray diffraction. Since the electron density shows how the electrons are distributed, it gives a better physical picture of the nature of chemical bonding than other models. It has been admirably described by Bader (1990) and, for inorganic solids, by Pendas et al. (1997, 1998) and Luana et al. (1997), but it is only necessary here to give a brief account of the approach to show why it is difficult to relate its concepts to those of the bond valence model. 

A hybrid HF-DFT approach has been used to determine gas-phase acidities (AH values) for a range of aliphatic, cyclic, and polycyclic carbon acids and reference compounds. The results obtained have been discussed in terms of strain in three- and four-membered rings, carbon hybridization aromaticity and topological analysis of electron density.13... 

Careful analysis of electron-density maps usually reveals many ordered water molecules on the surface of crystalline proteins (Plate 4). Additional disordered water is presumed to occupy regions of low density between the ordered particles. The quantity of water varies among proteins and even among different crystal forms of the same protein. The number of detectable ordered water molecules averages about one per amino-acid residue in the protein. Both the ordered and disordered water are essential to crystal integrity, and drying destroys the crystal structure. For this reason, protein crystals are subjected to X-ray analysis in a very humid atmosphere or in a solution that will not dissolve them, such as the mother liquor. 

The atoms-in-molecules (AIM) analysis of electron density, using ab initio calculations, was considered in Section 5.5.4. A comparison of AIM analysis by DFT with that by ab initio calculations by Boyd et al. showed that results from DFT and ab initio methods were similar, but gradient-corrected methods were somewhat better than the SVWN method, using QCISD ab initio calculations as a standard. DFT shifts the CN, CO, and CF bond critical points of HCN, CO, and CH3F toward the carbon and increases the electron density in the bonding regions, compared to QCISD calculations [107]. 

T. Koritsanszky, S. Howard, P.R. Mallison, Z. Su, T. Ritcher and N.K. Hansen, XD, A computer Program Package for Multipole Refinement and Analysis of Electron Densities from Diffraction Data, User s Manual, University of Berlin, Germany (1995). 

The first section in this chapter focuses on HCN as an element in a chain of H-bonded units. The presence in this molecule of only one proton and one lone electron pair provides a simple testing ground for ideas about cooperativity. The linearity of the complex also simplifies analysis of electron density redistributions caused by multiple bonding. HCCH is similar in some ways, but its absence of a lone electron pair causes significant distinctions. 

In this review, we describe the basic steps in theoretical (molecular, nonperiodic) calculations to study the H-H bonding interactions. For the analysis of electron density obtained by high-resolution low-temperature X-ray diffraction experiments coupled with multipolar refinement [125], the reader is referred to the literature [65, 66]. 

Description of the method of analysis of electron density distributions... 

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