Electrons cloud

In 1930, London [1,2] showed the existence of an additional type of electromagnetic force between atoms having the required characteristics. This is known as the dispersion or London-van der Waals force. It is always attractive and arises from the fluctuating electron clouds in all atoms that appear as oscillating dipoles created by the positive nucleus and negative electrons. The derivation is described in detail in several books [1,3] and we will outline it briefly here. 

Such attractive forces are relatively weak in comparison to chemisorption energies, and it appears that in chemisorption, repulsion effects may be more important. These can be of two kinds. First, there may be a short-range repulsion affecting nearest-neighbor molecules only, as if the spacing between sites is uncomfortably small for the adsorbate species. A repulsion between the electron clouds of adjacent adsorbed molecules would then give rise to a short-range repulsion, usually represented by an exponential term of the type employed... 

The result is that, to a very good approxunation, as treated elsewhere in this Encyclopedia, the nuclei move in a mechanical potential created by the much more rapid motion of the electrons. The electron cloud itself is described by the quantum mechanical theory of electronic structure. Since the electronic and nuclear motion are approximately separable, the electron cloud can be described mathematically by the quantum mechanical theory of electronic structure, in a framework where the nuclei are fixed. The resulting Bom-Oppenlieimer potential energy surface (PES) created by the electrons is the mechanical potential in which the nuclei move. Wlien we speak of the internal motion of molecules, we therefore mean essentially the motion of the nuclei, which contain most of the mass, on the molecular potential energy surface, with the electron cloud rapidly adjusting to the relatively slow nuclear motion. 

There can be subtle but important non-adiabatic effects [14, ll], due to the non-exactness of the separability of the nuclei and electrons. These are treated elsewhere in this Encyclopedia.) The potential fiinction V(R) is detennined by repeatedly solving the quantum mechanical electronic problem at different values of R. Physically, the variation of V(R) is due to the fact that the electronic cloud adjusts to different values of the intemuclear separation in a subtle interplay of mutual particle attractions and repulsions electron-electron repulsions, nuclear-nuclear repulsions and electron-nuclear attractions. 

These results do not agree with experimental results. At room temperature, while the translational motion of diatomic molecules may be treated classically, the rotation and vibration have quantum attributes. In addition, quantum mechanically one should also consider the electronic degrees of freedom. However, typical electronic excitation energies are very large compared to k T (they are of the order of a few electronvolts, and 1 eV corresponds to 10 000 K). Such internal degrees of freedom are considered frozen, and an electronic cloud in a diatomic molecule is assumed to be in its ground state f with degeneracy g. The two nuclei A and... 

Electronic spectra are almost always treated within the framework of the Bom-Oppenlieimer approxunation [8] which states that the total wavefiinction of a molecule can be expressed as a product of electronic, vibrational, and rotational wavefiinctions (plus, of course, the translation of the centre of mass which can always be treated separately from the internal coordinates). The physical reason for the separation is that the nuclei are much heavier than the electrons and move much more slowly, so the electron cloud nonnally follows the instantaneous position of the nuclei quite well. The integral of equation (BE 1.1) is over all internal coordinates, both electronic and nuclear. Integration over the rotational wavefiinctions gives rotational selection rules which detemiine the fine structure and band shapes of electronic transitions in gaseous molecules. Rotational selection rules will be discussed below. For molecules in condensed phases the rotational motion is suppressed and replaced by oscillatory and diflfiisional motions. 

The atomic scattering factor for electrons is somewhat more complicated. It is again a Fourier transfonn of a density of scattering matter, but, because the electron is a charged particle, it interacts with the nucleus as well as with the electron cloud. Thus p(r) in equation (B1.8.2h) is replaced by (p(r), the electrostatic potential of an electron situated at radius r from the nucleus. Under a range of conditions the electron scattering factor, y (0, can be represented in temis... 

One can see tliat tlie Dexter exchange mechanism is exponentially dependent on tlie distance between tlie donor and acceptor, and as such it begins to play a visible role only at very short distances when tlie electron clouds begin to... 

Hence we have two molecular orbitals, one along the line of centres, the other as two sausage-like clouds, called the n orbital or n bond (and the two electrons in it, the n electrons). The double bond is shorter than a single C—C bond because of the double overlap but the n electron cloud is easily attacked by other atoms, hence the reactivity of ethene compared with methane or ethane. 

The space filling model developed by Corey, Pauling, and Koltun is also known as the CPK model, or scale model [197], It shows the relative volume (size) of different elements or of different parts of a molecule (Figure 2-123d). The model is based on spheres that represent the "electron cloud . These atomic spheres can be determined from the van der Waals radii (see Section 2.10.1), which indicate the most stable distance between two atoms (non-bonded nuclei). Since the spheres are all drawn to the same scale, the relative size of the overlapping electron clouds of the atoms becomes evident. The connectivities between atoms, the bonds, are not visualized because they are located beneath the atom spheres and are not visible in a non-transparent display (see Section 2.10). In contrast to other models, the CPK model makes it possible to visualize a first impression of the extent of a molecule. 

Equation (3.40) is the DFT equivalent of the Schrbdinger equation. The subscript Vext indicates that this is under conditions of constant external potential (i.e. fixed nuclear po.-,ilions). It is interesting to note that the Lagrange multiplier, p, can be identified with (lu chemical potential of an electron cloud for its nuclei, which in turn is related to the... 

The three particles that make up atoms are protons, neutrons, and electrons. Protons and neutrons are heavier than electrons and reside in the "nucleus," which is the center of the atom. Protons have a positive electrical charge, and neutrons have no electrical charge. Electrons are extremely lightweight and are negatively charged. They exist in a cloud that surrounds the atom. The electron cloud has a radius 10,000 times greater than the nucleus. 

The ball and wire display is used for model building Although it is convenient for this purpose other model displays show three dimensional molecular structure more clearly and may be preferred The space filling display is unique m that it portrays a molecule as a set of atom centered spheres The individual sphere radii are taken from experi mental data and roughly correspond to the size of atomic electron clouds Thus the space filling display attempts to show how much space a molecule takes up... 

An expression for the short-range repulsive force (which arises from the interpenetration of the electron clouds of the two atoms) can also be derived from quantum-mechanical considerations" as... 

The nonbonding electron clouds of the attached fluorine atoms tend to repel the oncoming fluorine molecules as they approach the carbon skeleton. This reduces the number of effective coUisions, making it possible to increase the total number of coUisions and stiU not accelerate the reaction rate as the reaction proceeds toward completion. This protective sheath of fluorine atoms provides the inertness of Teflon and other fluorocarbons. It also explains the fact that greater success in direct fluorination processes has been reported when the hydrocarbon to be fluorinated had already been partiaUy fluorinated by some other process or was prechlorinated, ie, the protective sheath of halogens reduced the number of reactive coUisions and aUowed reactions to occur without excessive cleavage of carbon—carbon bonds or mnaway exothermic processes. 

When plastic deformation occurs, crystallographic planes sHp past each other. SHp is fackitated by the unique atomic stmcture of metals, which consists of an electron cloud surrounding positive nuclei. This stmcture permits shifting of atomic position without separation of atomic planes and resultant fracture. The stress requked to sHp an atomic plane past an adjacent plane is extremely high if the entire plane moves at the same time. Therefore, the plane moves locally, which gives rise to line defects called dislocations. These dislocations explain strain hardening and many other phenomena. 

For any nucHde that decays only by this electron capture process, if one were to produce an atom in which all of the electrons were removed, the effective X would become infinite. An interesting example of this involves the decay of Mn in interstellar space. For its normal electron cloud, Mn decays with a half-life of 312 d and this decay is by electron capture over 99.99% of the time. The remaining decays are less than 0.0000006% by j3 -decay and a possible branch of less than 0.0003% by /5 -decay. In interstellar space some Mn atoms have all of their electrons stripped off so they can only decay by these particle emissions, and therefore their effective half-life is greater than 3 x 10 yr. 

The dielectric constant is a measure of the ease with which charged species in a material can be displaced to form dipoles. There are four primary mechanisms of polarization in glasses (13) electronic, atomic, orientational, and interfacial polarization. Electronic polarization arises from the displacement of electron clouds and is important at optical (ultraviolet) frequencies. At optical frequencies, the dielectric constant of a glass is related to the refractive index k =. Atomic polarization occurs at infrared frequencies and involves the displacement of positive and negative ions. 

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