Deformation density chemical

In the chemical deformation densities introduced by Schwarz and collaborators, the density and the orientation of the atoms is quantitatively defined by variation of the atomic orientation and orbital population such as to minimize the space integral over the squared deformation density (Schwarz et al. 1989, Mensching et al. 1989). 

For HF, the F atom in the oriented reference state of the chemical deformation density has 1.414 e (rather than 5/3 = 1.67 e in the spherical atom, or 1 e in the oriented atom) in the pa orbital, and 1.793 e (rather than 1.67 e in the spherical atom, or 2 e in the oriented atom) in each of the pn orbitals. As in Fig. 5.4(b) and (c), the trough along the bond axis of the total deformation density disappears, and the overlap density becomes evident. 

The most likely cause of such discrepancy is an unsuitable atomic scattering factor. That means, some factor that affects the chemical behaviour of an atom may, for instance, not be properly accounted for in the calculated electronic structure from which scattering factors are derived. The use of oriented non-spherical atomic ground-states has been proposed [182] as a possible remedy. On this basis theoretically acceptable chemical deformation densities have been obtained. Such usage has led to the development of aspherical-atom, or multipole refinement of crystallographic structures in charge-density studies. 

In the next section we will see how the theory of AIM enables us to obtain chemical insight directly from the experimental density as determined by experiment or by calculation, thereby avoiding the need for deformation densities. 

G. Will, Electron Deformation Density in Titanium Diboride Chemical Bonding in TiB2, Jour. Sol. St. Chem., 177, 628 (2004). 

The multipole formalism described by Stewart (1976) deviates from Eq. (3.35) in several respects. It is a deformation density formalism in which the deformation from the IAM density is described by multipole functions with Slater-type radial dependence, without the K-type expansion and contraction of the valence shell. While Eq. (3.35) is commonly applied using local atomic coordinate systems to facilitate the introduction of chemical constraints (chapter 4), Stewart s formalism has been encoded using a single crystal-coordinate system. 

To examine the reliability of X-ray charge densities at a time of rapid development of new methods, the Commission on Charge, Spin and Momentum Densities of the lUCr organized a project under which a single substance, a-oxalic acid dihydrate, was studied in a number of laboratories using X-ray, neutron, and theoretical methods. The report by Coppens on the study, published in 1984, established unequivocally the qualitative reproducibility of chemically significant features in deformation density maps, which had not been generally accepted. 

Molecular geometry, namely, each atomic position ry in the unit cell, is conventionally determined by the least-squares fitting method based on the residue between IF qI and FC. A simple least-squares technique used in the conventional crystal structure analysis gives a slightly biased atomic position, because of the aspherical electron-density distribution caused by the chemical environment (15, 18). To obtain the unbiased deformation density, the atomic positions are commonly de-... 

If we wish to discuss the chemical properties derived from the observed deformation densities, it is obviously essential that the experimental errors should be estimated. This subject has been discussed in detail in a number of publications (13, 17, 26, 27, 51, 61, 73). Thus, only the main sources and magnitudes of the experimental errors necessary for proper assessments of the results will be described here. Experimental errors may be divided into systematic and statistical errors, and statistical errors will be treated first. As discussed in the previous section, the deformation density is defined as... 

The redistribution of the valence electron density due to chemical bonding may be obtained from summing the multipole populations or Fourier transforming appropriately calculated structure factors, having removed the contribution from neutral spherical atoms, to produce a so-called deformation density map [2], This function was introduced by Roux et al. [23] and has been widely used since then. The deformation electron density represents the difference between the electron density of the system, p(r), and the electron... 

However, due to chemical bonding and to the molecule-molecule interactions, the electron density is not spherical and the deformation density ... 

Because electron density is a local property, electron density studies of the peptide-like molecules show that the nonspherical part of the deformation density (i.e the P]m parameters of Eq. 8) remain essentially the same for a given atom in the same environment (the peptide residue, a phenyl ring, a methyl group...) [29], The same observation was made for porphyrin ligands [30] and by Brock, Dunitz, and Hirshfeld [37] for naphthalene and anthracene type molecules. All these observations suggest that the multipole parameters are highly transferrable from one atom to a chemically similar atom in different molecules and crystals. A key question is is it possible to determine for each chemical type of a given atom a small set of pseudoatom multipole parameters, and can such parameters be used to calculate electrostatic properties of new molecules To answer this question [29], two accurate but low resolution X-ray data sets (sin 0/Xmax = 0.65 A-1) were... 

In addition, deformation densities provide further guidance on how to recognize the presence of chemical bonds and lone pairs as special features of the total density. Significant early suggestions on how to achieve a chemically meaningful partitioning were proposed by Berlin [183] and by Daudel [184]. 

Figure 2. Deformation density in the plane through the iron atom and the pyrrole ring in bis(tetrahydrofurane)(mesotetraphenylporphinato)iron(II) after averaging over the molecular mmm symmetry. Contours at 0.5 eA (Reproduced from ref. 8. Copyright 1986 American Chemical Society.)...

FIGURE 4. Experimental deformation density curve for a [3.1.1]propellane derivative. The C(l)-C(3) bond is the central bond. Note the bent C(l)—C(2) and C(2)—C(3) bonds. Taken from Ref. 24 with permission of the American Chemical Society... 

FIGURE 9.17. Examples of deformation density maps, (a) Chemical formula of letrafluoroterephthalonitrrile. 

Deformation density maps give some indications of the deformation from sphericity (or ellipticity) of the electrons of the atoms in the model as a result of chemical bonding or the existence of lone-pair electrons. They should, however, be interpreted with caution, especially with respect to the resolution of the electron-density map obtained from them. The maximum value of sin 0/A should be much higher than normally used, generally requiring short-wavelength X rays and low temperatures of measurement. 

The difference Ag(X) = p(X) - Pm(X) between the actual density and the pro-molecule density is known as the deformation density and can be interpreted as the electron density reorganization that occurs when a collection of independent, isolated, spherically symmetric atoms is combined to form a molecule in a crystal. Since Aq is only a very small fraction of total Q in the region of the atoms, it is very susceptible to experimental error in the X-ray measurements and to inadequacies in the model, namely errors in the assumed atomic positions, atomic scattering factors, and ADPs. In one approximation, a deformation density map is obtained by direct subtraction of the two densities. The density map obtained in this way is smeared by vibrational motion of the atoms, but its peaks and troughs can often be interpreted in terms of some model of chemical bonding, e.g., peaks between bonded atoms being identified with bonding density and so on. A difference density map for tetrafluoroterephthalodinitrile [27] is shown in Fig. 3. 

Figure 10 (a) Molecular structure of 118 shown with displacement ellipsoids of 50% probability (b) deformation density plot (positive contours as solid lines, negative contours dashed lines contour interval 0.05 eA (c) total electron density (exponential contours) with Co-C, Fe-C, and C-0 bond paths shown (d) Laplacian of the electron density, V, (exponential contours negative contours as solid lines, positive contours as dashed lines). Reproduced from Macchi, P. Garlaschelli, L. Sironi, A. J. Am. Chem. Soc. 2002, 124, 14173-14184 with permission of the American Chemical Society. 

With decreasing ability of PEU and PBU to be deformed because of increase in its chemical network density, curves of dependences of 8 and plasticizer volume fraction, < ), become concave. The critical strain is heavily reduced already by a small content of a polar plasticizer. The data demonstrate a strong influence of chemical network on the critical strain of elastomer on swelling. 

In addition to Mulliken charge analysis, ADF calculates several atomic charges that do not share the flaws of Mulliken (strong basis set dependence). These charge analysis methods ( Voronoy deformation density and Hirshfeld provide atomic charges that agree well with chemical intuition. 

Some of the carbyne complexes are particularly suitable for a precise determination of the chemical bonds. Their molecular and crystal structures possess high symmetry [1,2]. The molecules themselves are placed on high symmetrical sites in the crystal. In addition, big single crystals of some complexes can be obtained. These conditions are very favorable for electron deformation density studies and for other physical techniques such as polarised Raman spectroscopy in order to understand the nature of the chemical bonds existing in this class of compounds. It is also possible to compare these experimental results with ab iniV/o calculations. This paper relates some results of these studies, essentially focused on the conjugation effect of carbynes. 

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