Shell structure of atoms

Politzer P, Murray JS, Grice ME (1993) Charge Capacities and Shell Structures of Atoms. 80 101-114... 

As a second example of the use of the orbital idea in many-electron atoms, we consider briefly the spectra from inner-shell electrons. One very direct way of measuring the energies of these is by photoelectron spectra, as discussed in Section 1.3 (see Fig. 1.11). Table 5.1 shows the binding (ionization) energies of electrons in the occupied orbitals of Na+ and Cl-, which can be obtained from the photoelectron spectrum of solid NaCl. These data illustrate the fact that the 10 electrons in Na+ occupy the If, 2j, and 2p orbitals, and the 18 in Cl- occupy If, 2s, 2p, 3s, and 3p. Remembering that there am three different p orbitals for each n, we can see that these ions have five and nine occupied orbitals, respectively. Observations such as this provide strong evidence for the shell structure of atoms, and the principle that no more than two electrons can occupy each individual orbital. 

Secondary atomic properties as those, which require, in addition to the experimentally determined quantities for the free atoms, theoretical concepts of the quantum mechanical characerisation of the electronic structure of the atoms. These are orbitals, the shell structure of atoms with emphasis of the valence shell as well as concepts like hybridisation, the definition of the valence state and the valence state promotion energy in its relation to the spectroscopic term values of the free atoms. 

Despite its importance of principle, one should not overstate the role of chaos in the spectroscopy of highly excited atoms although favourable circumstances can arise, they are rare. There are two fundamental reasons for this. The first is the Pauli principle as noted in chapter 1, the shell structure of atoms restores spherical symmetry to the many-electron atom at each new row of the periodic table, and spherical symmetry, which helps the independent particle model, inhibits chaos. Secondly, as the excitation energy is increased, autoionisation and the Auger effect also become obstacles to the emergence of chaos, because the lifetimes are so short that instabilities in the underlying classical dynamics do not have time to develop. 

The application of this principle to the periodic system leads to the conception of the shell structure of atoms (see also 29, p. 176). The first period, consisting of the elements H and He, represents the structure of the innermost shells. The system of two electrons of the inert gas He must therefore be a very stable arrangement. 

The atomic orbitals chosen for this work are derived from the MIDI Gaussian sets of Huzinaga preserving the n I m shell structure of atoms. They are split valence bases whose last components are left free, increased by two p and one d diffuse functions for the transition atom whose exponents are the values recommended in ref [32]. Writing the Gaussians in the s/p/d descending order, they are expressed as follows ... 

There is a continuing interest in exploring possible relationships between the shell structures of atoms and their electronic density distributions [31-39]. In this respect, considerable attention has focused upon the radial density function, D(r) = 4nr p(r), which goes through a series of maxima and minima with increasing radial distance from the nucleus [6,31-36,40], [p(r) is the electronic density function since atomic charge distributions are spherically symmetric... 

Lewis and Kossel s proposals coincided with the shell structure of atoms which resulted firom the hybrid classical/quantum model for the hydrogen atom developed by Bohr [37, 38] and subsequently extended by Sommerfeld [39 1] to other atoms. They did not fully appreciate the physical imphcations of a quantum model. Specifically Lewis based his model on the following postulates ... 

The periodicity of chemical elements discovered by Mendeleev is another fundamental idea of chemistry. It has its source in the shell structure of atoms. Following on, we can say that the compounds of sulphur with hydrogen should be... 

The functionals considered in Section 1.3 are all semilocal the local kinetic energy at the point r depends only on the electron density and its derivatives at the point r. Improved models for the kinetic energy require considering how the electron density at other points r affects the local kinetic energy at the point r. Without including these effects, the oscillations in electron density that are essential for modeling the shell structure of atoms and differentiating between core and valence electrons in molecules cannot be recovered. 

Pauli, Wolfgang (1900-58) Austrian-born Swiss theoretical physicist. Pauli is best known for his enunciation of the Pauli exclusion principle in 1925. This enabled the electronic structure of atoms to be understood, particularly how the shell structure of atoms, and hence the periodic table of the elements, comes about. Pauli won the 1945 Nobel Prize for physics for this work. Pauli made many other important contributions to physics including his prediction of the neutrino in beta decay, the incorporation of spin into quantum mechanics, and the explanation of paramagnetism in metals. He also wrote several classic books and reviews on quantum mechanics. 

For EPLF close to zero, the average distances between spin-like and spin-unUke electrons are similar. The minimal EPLF value of —1 is reached in regions where the opposite-spin electrons are much closer than the same-spin ones (and vice versa for the maximal EPLF value of 1). EPLF reveals the shell structure of atoms. It was used to describe the bonding situation in molecules. As stated by Amador-Bedolla et al. [70], EPLF is a relative measure in the sense that it depends only on the ratio daddas and not on the actual average distance between the electrons. 

Pacios LF, G6mez PC (1998) Radial behavior of gradient expansion approximation to atomic Fukui function and shell structure of atoms. J Comput Chem 19(5) 488-503... 

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