Electron density in molecules

J. R. Van Wazer and I. Abser, Electron Densities in Molecules and Molecular Orbitals, Academic Press, New York, 1975. 

At this point it would be well to differentiate clearly between spin densities, p s, which arc obtained experimentally from contact interaction constants, and electron densities in molecules. If a simple Iluckel LCAO MO calculation is carried out on the allyl radical, the computed distribution of the single unpaired electron is as shown below... 

That molecules do have definite bonds, and that these tend to correspond in direction and number to the conventional bonds of simple valence theory, is indicated by the quantum theory of atoms-in-molecules (AIM, or QTAIM) [2], This is based on an analysis of the variation of electron density in molecules. 

How extensively parametrized a pseudoatom multipole model is necessary for reproducing crystallographic informations of the electron density in molecules containing first, second-row elements, and first-row transition metals ... 

Localized Models of Electron Density in Molecules.—Based on the linear response equation (122), applied however to periodic monatomic crystals, Jones and March57 have argued that in discussion of vibrational properties the correct tool... 

For a review of the existing methods of apportioning the electron density in molecules see K. Jug and Z.B. Maksic, in Theoretical Models of Chemical Bonding, Vol.3, Z.B. Maksic (ed.), Springer Verlag, Berlin-Heidelberg, 1991, p. 235. 

X-rays are scattered predominantly by electrons rather than atomic nuclei. To determine atomic coordinates, electron densities are therefore assumed to be concentrated spherically around individual nuclei. This assumption ignores all possible effects that chemical bonding may have on electronic density in molecules. Such a hypothetical array of spherical atoms located at the nuclear positions of an actual molecule in a crystal is known as a promolecule. Molecular structures determined by routine crystallographic methods are invariably the structures of promolecules. 

Synthetic zeolites of various types differ in the number of cations in their voids which are accessible for direct interaction with the molecules adsorbed. Table I lists, for typical examples of zeolites, the numbers of accessible cations Na per zeolite void and their number Z in mmole/ gram for dehydrated zeolites. When passing from zeolite NaA to zeolite L, the number of accessible cations Z—i.e., the number of adsorption centers in the void—decreases almost by a factor of 10. Therefore, in the case of zeolite L, the relative role of interactions among cations and molecules adsorbed, conventionally called electrostatic, will be approximately one order lower than for zeolite NaA. In adsorption on this zeolite of substances with slightly pronounced nonuniformity of distribution of electron density in molecules— for instance, saturated hydrocarbons— one may expect that electrostatic interactions will not play the decisive role. As a result, we obtain the limiting case of adsorption on zeolites like zeolite L and erionite with a weak electrostatic interaction. 

As with other schemes of partitioning the electron density in molecules, Mulliken population analysis is arbitrary and is strongly dependent on the particular basis set employed. However, the comparison of population analyses for a series of molecules is useful for a quantitative description of intramolecular interactions, chemical reactivity and structural information. In another approach, the Lowdin population analysis, the atomic orbitals are first transformed to an orthogonal set, as are the molecular orbital coefficients [Lowdin, 1970]. 

Spectroscopic evidence for bent bonds in cyclopropanes has been provided b carefol, low-temperature X-ray studies, which are able to map the electron density in molecules. As shown in Figure 4.10, the electron density in a cyclopropane bond is strongly displaced outward from the internuclear axis. 

There is no immediate need to abandon the conventional use of structural formulae as graphical models of molecular shape, provided it carries no connotation of electron pairs or hybrid orbitals. The extensive use of LCAO methods to simulate electron densities in molecules may be even harder to give up, but is also more misleading than the naive model of localized Lewis pairs. 

The distance parameter, da. is the distance between the centers of electronic distribution in the donor and the acceptor orbitals, not a distance based on molecular geometry. Since electron density in molecules is highly polarizable. Equation (22) often has only qualitative value in assessing electronic coupling. 

Recent theoretical studies and accurate experimental determinations of electron densities in molecules have confirmed that the majority of electrons do indeed form a concentrated core near the nucleus which appears very atomic like [120]. The electTOTi density is very monotonic as the radial distance from the nucleus increases. Chemists sometimes wrongly consider that the electron density in the cores of atoms has outer maxima corresponding to the shell structures. The inner electron cores are almost transferable entities and cmisequently endorse the valence-care partition proposed by Lewis and Kossel, and this property is utilised in frozen core approximations [138]... 

In fact, information about the three-dimensional electron densities in molecules can be obtained more directly from the experimental intensity functions. Results for the Roux function (the difference between the molecular electron density and the sum of the electron densities of unperturbed atoms) have been given for diatomic molecules by Kohl and Bartell. ... 

Atomic populations are obtained by integration of /OA(r)), which can be either computed with variational calculus or approximated by sums of Gaussian or Slater-type basis functions. At the HF/6-311-1—l-G level of theory, the last method produces chaiges of 0.778 and 0.878 for the Li atoms in LiH and LiF, and of —0.578 and 0.043 for the carbons in CH4 and CO, respectively. The main objection to Stewart partitioning is the unrealistic assumption of the sphericity of atomic electron densities in molecules. Approaches to fitting of p(r) that do not employ spherically symmetric atoms are... 

The development of the new techniques for the computation of charge, the efficient calculation of long range electrostatic interactions by fast multipole and Particle Mesh Ewald techniques, and for the increased efficiency of integration by the multiple time step methods (RESPA) lead to a spirit of optimism in the computational chemistry community, Improvements in force fields, such as the incorporation of polarizability and a more accurate representation of the electron density in molecules should lead to even better agreement with experiment,... 

Trivially extending the well-known formula for electron densities in molecules, where Dpq is an element of the density matrix between orbitals p and q,... 

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