The Electron Distribution in Molecules

The one-electron spatial function P(r) describing the distribution of the electrons (the electron density) in the doubly occupied MO / (r)  

The electron density can be further analysed in terms of elementary contributions from the AOs, giving the so-called population analysis,n which shows how the electrons are distributed between the different atomic orbitals in the molecule. We obtain from Equation (1.81)  

In our model, an essential role will be assigned to the exchange-overlap densities (Magnasco and McWeeny, 1991 Magnasco, 2007,2008,2009a)  

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The dispersion (London) force is a quantum mechanieal phenomenon. At any instant the electronic distribution in molecule 1 may result in an instantaneous dipole moment, even if 1 is a spherieal nonpolar moleeule. This instantaneous dipole induces a moment in 2, which interacts with the moment in 1. For nonpolar spheres the induced dipole-induced dipole dispersion energy function is... 

Dispersion forces. These are weak attractions caused by instantaneous fluctuation of the electron distribution in molecules and even atoms. They were first posed by Fritz London whose focus was on helium liquefaction. Such London forces fall off with the sixth power of the distance of separation. Any individual fluctuation creates a +/— local charge and that instantaneous dipole can interact with other such instantaneous dipoles nearby. The important... 

Computer-Generated Images Show the Electron Distribution in Molecules As an aid to visualizing structure, we have used Spartan software to portray the distribution of electrons in many molecules. 

Valence shell electrons of the atoms in a molecule are either shared or unshared. The shared electrons are found in either o ox it bonds. Unshared electrons are found in AOs (usually hybrid AOs for first-row elements). Lewis structures provide a way to indicate the shared and unshared pairs of electrons in molecules. Sometimes, however, it is possible to indicate the electron distribution in molecules by more than one Lewis structure. For example, a car-boxylate anion can be represented by two equivalent but different Lewis structures. 

Inductive effects serve to alter the electron distributions in molecules, and con-sequendy they are very important influences on many types of reactions—not just acidity and basicity. To the extent that electronic changes occur during the conversion of reactants to products, inductive effects can facilitate or impede those electronic changes and thus change the rates of conversion. It is important then to keep them in mind when other examples of reactivity changes are discussed. 

Inductive and resonance effects described above can significantly alter the electron distributions in molecules and can influence not only acidity but many... 

The data on the electron distribution in molecules 117 were obtained with the use of H NMR (71AJC325 73RRC531) and 13C NMR [79JOM(181)329 81 JOM(212) 141 89H1007] studies. Some results are presented in Table IX. 

Deformation density maps have been used to examine the effects of hydrogen bonding on the electron distribution in molecules. In this method, the deformation density (or electrostatic potential) measured experimentally for the hydrogen-bonded molecule in the crystal is compared with that calculated theoretically for the isolated molecule. Since both the experiment and theory are concerned with small differences between large quantities, very high precision is necessary in both. In the case of the experiment, this requires very accurate diffraction intensity measurements at low temperature with good thermal motion corrections. In the case of theory, it requires a high level of ab-initio molecular orbital approximation, as discussed in Chapter 4. 

Even large multizeta basis sets will not provide sufficient mathematical flexibility to adequately describe the electron distribution in molecules. An example of this deficiency is the inability to describe bent bonds of small rings. Extending the basis... 

Because of the continuous variation of the electron distribution in molecules or crystals, the counting of electron charge is hopelessly dependent on the nature of the distribution function over which the integration is taken. Clearly, the charge of an atom in a molecule or crystal is not an observable it is arbitrary. 

The description and understanding of the nature of stereoelectronic effects is an appropriate held for the application of oiganic quantum chemistry. Molecular orbital (MO) methods " can describe the electron distribution in molecules, and the changes in internal rotation. In principle, they give the total potential energy of individual conformers completely, without the necessity to correct for various effects. Quantum chemical calculations offer a deeper insight into the orbital interactions in the molecule, and reveal the factors responsible for the stabilization of any conformation. 

In 1930 Fritz London demonstrated that he could account for a weak attractive force between any two molecules, whether polar or nonpolar. He postulated that the electron distribution in molecules is not fixed electrons are in continuous motion, relative to the nucleus. So, for a short time a nonpolar molecule could experience an instantaneous dipole, a short-lived polarity caused by a temporary dislocation of the electron cloud. These temporary dipoles could interact with other temporary dipoles, just as permanent dipoles interact in polar molecules. We now call these intermolecular forces London forces. 

Detailed information about the electron distribution in molecules is available from ab initio calculations or from very accurate X-ray diffraction experiments. In the latter case, the results are influenced by the surrounding crystal field. To achieve quantitative agreement between ab initio calculations and diffraction experiments, the influence of the nearest neighbors of the molecule in the crystal field has to be incorpo-... 

In this chapter, you will learn to recognize compounds that contain delocalized electrons and to draw structures that represent the electron distribution in molecules... 

Radiation interacts with matter through the effects of the electric field vector on the electron distributions in molecules. Absorption of radiation involves raising a system from one energy level to a higher level by the absorption of a quantum of energy (a photon). Elastic scattering of radiaLion involves no such quantum jumps and can be discussed in classical terms. ... 

The first two of the above conditions can be met by using what can only be called physically sensible basis functions functions which can be expected on general physical grounds to describe the electron distribution in molecules sensibly. Use of some form of approximate atomic orbitals as basis functions satisfy these requirements. 

Physically, the electron distribution in molecules is not so very different from the electron distribution in the component atoms and so the orbitals of the separate atoms is an obvious (to chemists) place to start the expansion of the molecular orbitals. 

SECTION 8.3 A covalent bond results from the diaring of electrons. We can represent the electron distribution in molecules by means of Lewis structures, which indicate how many talence electrons are involved in forming bonds and how many remain as unshared electron pairs. The octet rule helps determine how many bonds will be formed between two atoms. The sharing of one pair of electrons produces a single bond the sharing of two or three pairs of electrons between two atoms produces double or triple bonds, respectively. Double and triple... 

This approach allows numerical evaluations of the orbital electronegativity so by various approximations of the integrals used, as by a combination of the experimental data, for example, with die information which came from the X-ray analysis of the electronic distribution in molecule. 

The molecular orbital theory (MOT) is widely used by chemists. It includes both the covalent and ionic character of chemical bonds, although it does not specifically mention either. MOT treats the electron distribution in molecules in very much the same way that modem atomic theory treats the electron distribution in atoms. First, the positions of atomic nuclei are determined. Then orbitals aroimd nuclei are defined these molecular orbitals (MO s) locate the region in space in which an electron in a given orbital is most likely to be found. Rather than being localized arormd a single atom, these MO s extend over part or all of the molecule. 

In this chapter, you will learn how to recognize compounds that have delocalized electrons and how to draw structures that represent the electron distribution in molecules with delocalized electrons. You will also be introduced to some of the special characteristics of compounds that have delocalized electrons. You will then be able to understand... 

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