Positively charged nuclei

Two factors affect the stability of this orbital. The first is the stabilizing influence of the positively charged nuclei at the center of the AOs. This factor requires that the center of the AO be as close as possible to the nucleus. The other factor is the stabilizing overlap between the two constituent AOs, which requires that they approach each other as closely as possible. The best compromise is probably to shift the center of each AO slightly away from its own nucleus towards the other atom, as shown in figure 7-23a. However, these slightly shifted positions are only correct for this particular MO. Others may require a slight shift in the opposite direction. 

Tire total energy equals the sum of the nuclear energy (the electrostatic repulsion between the positively charged nuclei) and the electronic energy. The electronic energy comprises... 

An electric dipole consists of two equal and opposite charges separated by a distance. AH molecules contain atoms composed of positively charged nuclei and negatively charged electrons. When a molecule is placed in an electric field between two charged plates, the field attracts the positive nuclei toward the negative plate and the electrons toward the positive plate. This electrical distortion, or polarization of the molecule, creates an electric dipole. When the field is removed, the distortion disappears, and the molecule reverts to its original condition. This electrical distortion of the molecule is caHed induced polarization the dipole formed is an induced dipole. 

Early in the twentieth century physicists established that molecules are composed of positively charged nuclei and negatively charged electrons. Given their tiny size and nonclassical behavior, exemplified by the Heisenberg uncertainty principle, it is remarkable (at least to me) that Eq. (1) can be considered exact as a description of the electrostatic forces acting between the atomic nuclei and electrons making up molecules and molecular systems. Eor those readers who are skeptical, and perhaps you should be skeptical of such a claim, I recommend the very readable introduction to Jackson s electrodynamics book [1]. 

Electron Density Surfaces. An alternative technique for portraying molecular size and shape relies on the molecule s own electron cloud. Atoms and molecules are made up of positively-charged nuclei surrounded by a negatively-charged electron cloud, and it is the size and shape of the electron cloud that defines the size and shape of an atom or molecule. Quantum mechanics provides the mathematical recipe for determining the size and shape of the electron cloud, and computer programs can carry out the necessary calculations. 

If we apply an external electrostatic field E then the protons and electrons each experience a force. This force tends to cause charge separation in the dielectric. The positively charged nuclei move in the direction of the applied field, the negatively charged electrons move in the opposite direction. I have illustrated this behaviour in Figure 15.3. 

A molecule may be considered as a number of electrons surrounding a set of positively charged nuclei. The Coulombie attraetion between these two types of paitiele forms the basis for atoms and moleeules. The potential between two partieles with charges qt and qj separated by a distance is (in suitable units) given by... 

Nuclei suitable for fusion must come near each other, where near means something like the nuclear radius of 10" cm. For positively charged nuclei to make such a close approach it requires large head-on velocities, and therefore multimillion-degree Celsius temperature. In contrast, fission can occur at normal temperatures, either spontaneously or triggered by a particle, particularly an uncharged neutron, coming near a fissionable nucleus. 

Net molecular polarity is measured by a quantity called the dipole moment and can bethought of in the following way assume that there is a center of mass of all positive charges (nuclei) in a molecule and a center of mass of all negative charges (electrons). If these two centers don t coincide, then the molecule has a net polarity. 

How large is an atom We cannot answer this question for an isolated atom. We can, however, devise experiments in which we can find how closely the nucleus of one atom can approach the nucleus of another atom. As atoms approach, they are held apart by the repulsion of the positively charged nuclei. The electrons of the two atoms also repel one another but they are attracted by the nuclei. The closeness of approach of two nuclei will depend upon a balance between the repulsive and attractive forces. It also depends upon the energy of motion of the atoms as they approach one another. If we think of atoms as spheres, we find that their diameters vary from 0.000 000 01 to 0.000 000 05 cm (from 1 X 10-8 to 5 X 10 8 cm). Nuclei are much smaller. A typical nuclear diameter is 10, s cm, about 1/100,000 the atom diameter. 

Chemists also need to know the distribution of electric charge in a molecule, because that distribution affects its physical and chemical properties. To do so, they sometimes use an electrostatic potential surface (an elpot surface), in which the net electric potential is calculated at each point of the density isosurface and depicted by different colors, as in Fig. C.2f. A blue tint at a point indicates that the positive potential at that point due to the positively charged nuclei outweighs the negative potential due to the negatively charged electrons a red tint indicates the opposite. 

The bonding orbital in a hydrogen molecule has a high electron density between the two positively charged nuclei. This mediates... 

A molecule is composed of positively charged nuclei surrounded by electrons. The stability of a molecule is due to a balance among the mutual repulsions of nuclear pairs, attractions of nuclear-electron pairs, and repulsions of electron pairs as modified by the interactions of their spins. Both the nuclei and the electrons are in constant motion relative to the center of mass of the molecule. However, the nuclear masses are much greater than the electronic mass and, as a result, the nuclei move much more slowly than the electrons. Thus, the basic molecular structure is a stable framework of nuclei undergoing rotational and vibrational motions surrounded by a cloud of electrons described by the electronic probability density. 

We begin with a presentation of the ideas of the electronic structure of metals. A liquid or solid metal of course consists of positively charged nuclei and electrons. However, since most of the electrons are tightly bound to individual nuclei, one can treat a system of positive ions or ion cores (nuclei plus core electrons) and free electrons, bound to the metal as a whole. In a simple metal, the electrons of the latter type, which are treated explicitly, are the conduction electrons, whose parentage is the valence electrons of the metal atoms all others are considered as part of the cores. In some metals, such as the transition elements, the distinction between core and conduction electrons is not as sharp. 

In metals, an attraction is formed between the negatively charged electrons and the positively charged nuclei of the atoms. 

Metals are solid at room temperature, except for mercury. This tells us that the attractive forces between metal atoms are strong. The valence electrons of metal atoms can easily move from the free orbitals of one atom to another. These electrons that can move freely between atoms form an electron sea . An attractive force occurs between the negatively charged sea of electrons and the positively charged nuclei. Metal atoms are held together because of this attractive force. This is called the metallic bond. 

For condensed phases of bulk metals, the binding energy can be divided into repulsions between nuclei (see above) and the interaction of the positively charged nuclei with an electron gas. Within this breakdown, the motion of the nuclei can be determined by pair-additive forces with the addition of volume-dependent terms arising from the pressure of the electron gas . While computer simulations based on these types of interactions have been carried out , volume-dependent interactions are difficult to define unambiguously for surfaces. 

Like 18th-eentury dynamieal atomism, modem atomism also recognizes the importanee of short-range interparticle forces—now interpreted in terms of electrical forces of attraction and repulsion between negatively charged electrons and positively charged nuclei. 

For slow neutron-induced reactions that do not involve resonances, we know (Chapter 10) that ct ( ) °c 1 /vn so that (ctv) is a constant. For charged particle reactions, one must overcome the repulsive Coulomb force between the positively charged nuclei. For the simplest reaction, p + p, the Coulomb barrier is 550 keV. But, in a typical star such as the sun, kT is 1.3 keV, that is, the nuclear reactions that occur are subbarrier, and the resulting reactions are the result of barrier penetration. (At a proton-proton center-of-mass energy of 1 keV, the barrier penetration probability is 2 x 10-10). At these extreme subbarrier energies, the barrier penetration factor can be approximated as ... 

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