Electron density distribution in molecules

L.-C. Wang and R. J. Boyd, /. Chem. Phys., 90, 1083 (1989). The Effect of Electron Correlation on the Electron Density Distributions in Molecules Comparison of Perturbation and Configuration Interaction Methods. 

Before showing more complex DOS, we will first concentrate on how to characterize the electron density distribution in molecules and solids because that is where we started this is also needed to further decompose the density-of-states and characterize the electronic structures in terms of bonding properties. Recalling the LCAO ansatz for the molecular orbital (MO) of the H2 molecule as given in Equation (2.11), we may square-integrate the MO over all space and yield... 

Electron densities and their relations to experimentally observable effects play an important role in the discussions of molecular properties. Electron density distributions in molecules may be related to dipole moments (47), that is, observables. However, the most widely used concept of charges attributed to atoms in a molecule associates the electron density distributions to a set of (theoretically determined) indices characteristic for the atoms in the molecule. 

Electron density distributions in molecules are often used to discuss qualitatively chemical reactivities. In particular, electron densities may be used as indications of a proton to attack a molecule at different sites. For instance, the electron density distribution in ketene (43) with its pronounced negative charges at the terminal carbon and oxygen atoms, respectively, is expected to allow C protonation (43b) as well as O protonation (43a). 

Molecular art appears in various formats to serve different needs. Molecular models help to visualize the three-dimensional arrangement of atoms in a molecule. Electrostatic potential maps illustrate the electron density distribution in molecules. Finally, there is the macroscopic-to-microscopic art, helping students understand processes at the molecular level. 

Primary goal of our study was to provide objective criteria to predict theoretically, at least qualitatively, photoelectrochemical properties of the molecules by their structure. In our opinion, the most important factor in the selection process is the electron density distribution in molecules. 

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... 

If the electronegativity of the ligands X is much less than the electronegativity of the central atom A, the electrons in the valence shell of A are not well localized into pairs and therefore have a small or zero effect on the geometry. In such molecules the bonds are very ionic in the sense A X+, and the central atom A is essentially an anion with a spherical electron density distribution. In this case the VSEPR model is not valid, and the geometry of the molecule is determined by ligand-ligand repulsions. 

The Hellmann-Feynman theorem demonstrates the central role of p, the electron density distribution, in understanding forces in molecules and therefore chemical bonding. The main appeal and usefulness of this important theorem is that it shows that the effective force acting on a nucleus in a molecule can be calculated by simple electrostatics once p is known. The theorem can be stated as follows ... 

In the framework of AIM theory, which well be used extensively to describe dihydrogen bonds, the situation above corresponds to the electron density distribution in the H2 molecule, where the pc parameter takes the very large value 1.857 au and the Laplacian, V pc, is strongly negative ( —34.15 au). These data have been obtained by ab initio calculations at the MP2/6-31G level [4],... 

At the conclusion of a geometric optimization calculation, we have the equilibrium positions of all the atomic nuclei, as well as the overall electron density distributed in space (x, y, z). Many important properties, especially for an isolated single molecule at absolute zero temperature, can be obtained by solving the quantum mechanical or the molecular mechanical equations. Only the former method can produce electronic properties, such as electron distributions and dipole moments, but both methods can produce structural and energy properties. 

Aromatic substitution reactions are often complicated and multistep processes. A correlation, however, in many cases can be found between the charged attacking species and the electron density distribution in the molecule attacked during electrophilic and nucleoph c substitution. No such correlation is expected in radical substitution where the attacking particles are neutral, rather a correlation between the reactivities of separate bonds and a free valency index of the bond order. This allows the prediction of the most reactive bonds. Such an approach has been used by researchers who applied quantum calculations to estimate the reactivities of the isomeric thienothiophenes and to compare them with thiophene or naphthalene. " Until recently quantum methods for studying reactivities of aromatics and heteroaromatics were developed mainly in the r-electron approximation (see, for example, Streitwieser and Zahradnik ). The M orbitals of a sulfur atom were shown not to contribute substantially to calculations of dipole moments, polarographic reduction potentials, spin-density distribution, ... 

Fig. 5.42 Contour lines for p, the electron density distribution, in a homonuclear diatomic molecule X2. The lines originating at infinity and terminating at the nuclei and at the bond critical point C are trajectories of the gradient vector field (the lines of steepest increase in p two trajectories also originate at C). The line S represents the dividing surface between the two atoms (the line is where the plane of the paper cuts this surface). S passes through the bond critical point and is not crossed by any trajectories...

Electron density distribution in the molecules presides over spin preservation preventing the redistribution of spin to other electrons in the system in form of polarization. 

Although X-ray crystallography has mainly been used for structure determination in the past, the diffraction data, especially if measured carefully and to high orders, contain information about the total electron density distribution in the crystal. This may be analyzed to provide essential information about the chemical properties of molecules, in particular the characterization of covalent and hydrogen bonds, both from the point of view of the valence electron density, the Laplacian of the density and derived energy density distribution. In addition, calculation of the molecular electrostatic potential indicates direction of chemical attack as well as how molecules can interact with their environment. 

The analysis of quantum-chemical calculations of electron density distribution in the molecules of 2-nitro-, 4-nitro-, and 5-nitrothiazole allows a conclusion that the nature of all three bands is related to tt—electron transfers [1166],... 

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