Electron deformation density

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. 

Mezey, P.G. (1996) Molecular similarity measures of conformational changes and electron density deformations. In Advances in Molecular Similarity, Vol. 1, p. 89. 

Since difference electron densities, deformation densities or valence electron densities are not observable quantities, and since the Hohenberg-Kohn theorem64 applies only to the total electron density, much work has concentrated on the analysis of p(r). The accepted analysis method today is the virial partitioning method by Bader and coworkers67, which is based on a quantum mechanically well-founded partitioning of the molecular... 

J. Gu et al., H-bonding patterns in the platinated guanine-cytosine base pair and guanine-cytosine-guanine-cytosine base tetrad An electron density deformation analysis and aim study. J. Am. Chem. Soc. 126, 12651-12660 (2004)... 

P.G. Mezey, "Molecular Similarity Measures of Conformational Changes and Electron Density Deformations", Advances in Molecular Similarity, 1, 89 (1996). 

As the resolution of the Bragg reflection data is improved, it becomes possible to obtain information on the more minute details of electron density in a molecule. At high enough resolution information can be obtained on the redistribution of electron density (deformation density) around atoms when they combine to form a molecule. Electrons in molecules ma -form bonds or exist as lone pairs, thereby distorting the electron density around each atom and requiring a more complicated function to describe this overall electron density than normally used, in which it is treated as if it were spherically symmetrical (deformed to an ellipsoid in order to account for anisotropic displacements). This assumption is inherent in the use of spherically-symmetrical scattering factors although the elec-... 

A detailed study of the X-ray and neutron diffraction data for trans C5HsFe(CO)2]2 at 78 K and a subsequent X-N calculation of electronic density deformation maps has yielded an accurate picture of the... 

F. Baert and A. Laamyen, CJi.Seances Acad.Sci., 1990,311,1417 (electron density deformation). 

The approximate transferability of fuzzy fragment density matrices, and the associated technical, computational aspects of the idempotency constraints of assembled density matrices, as well as the conditions for adjustability and additivity of fragment density matrices are discussed in Section 4, whereas in Section 5, an algorithm for small deformations of electron densities are reviewed. The Summary in Section 6 is followed by an extensive list of relevant references. 

Small deformations of electron densities, adjustability and additivity conditions for fragment density matrices... 

According to the aspherical-atom formalism proposed by Stewart [12], the one-electron density function is represented by an expansion in terms of rigid pseudoatoms, each formed by a core-invariant part and a deformable valence part. Spherical surface harmonics (multipoles) are employed to describe the directional properties of the deformable part. Our model consisted of two monopole (three for the sulfur atom), three dipole, five quadrupole, and seven octopole functions for each non-H atom. The generalised scattering factors (GSF) for the monopoles of these species were computed from the Hartree-Fockatomic functions tabulated by Clementi [14]. 

Stuckenschmidt, E., Joswig, W. and Baur, W.H. (1994) Natrolite, Part II determination of deformation electron densities by X-XMethod, Phys. Chem. Minerals, 21, 309- 316. 

Figure 6.7 shows the calculated electron density distributions for the H2 and N2 molecules in their equilibrium geometry together with the standard deformation densities. There is clearly a buildup of electron density in the bonding region in both molecules. In the N2 molecule there is also an increase in the electron density in the lone pair region and a de-... 

Clearly the form of a deformation density depends crucially on the definition of the reference state used in its calculation. A deformation density is therefore meaningful only in terms of its reference state, which must be taken into account in its interpretation. As we will see shortly, the theory of AIM provides information on bonding directly from the total molecular electron density, thereby avoiding a reference density and its associated problems. But first we discuss experimentally obtained electron densities. 

In the Kohn-Sham Hamiltonian, the SVWN exchange-correlation functional was used. Equation 4.12 was applied to calculate the electron density of folate, dihydrofolate, and NADPH (reduced nicotinamide adenine dinucleotide phosphate) bound to the enzyme— dihydrofolate reductase. For each investigated molecule, the electron density was compared with that of the isolated molecule (i.e., with VcKt = 0). A very strong polarizing effect of the enzyme electric field was seen. The largest deformations of the bound molecule s electron density were localized. The calculations for folate and dihydrofolate helped to rationalize the role of some ionizable groups in the catalytic activity of this enzyme. The results are,... 

---