Distribution of electrons in atoms

The magnetic forces between electrons are negligibly small compared to the electrostatic forces, and they are of no importance in determining the distribution of the electrons in a molecule and therefore in the formation of chemical bonds. The only forces that are important in determining the distribution of electrons in atoms and molecules, and therefore in determining their properties, are the electrostatic forces between electrons and nuclei. Nevertheless electron spin plays a very important role in chemical bonding through the Pauli principle, which we discuss next. It provides the fundamental reason why electrons in molecules appear to be found in pairs as Lewis realized but could not explain. 

Because the normally even distribution of electrons in atoms can momentarily become uneven, atoms can be attracted to one another by induced dipole-induced dipole attractions. 

The first quantitative atomic model appeared early in the previous century, based on the pioneering work of Lord Rutherford and the Danish physicist Niels Bohr. It was devised in simple analogy with Kepler s model of the solar system and, despite a number of known fatal defects, it has such intuitive appeal that, even today, scientists and non-scientists alike accept it as the most reasonable working model for understanding the distribution of electrons in atoms. Formulation of the model was guided by three important experimental observations which had no obvious explanation in terms of 19th century physics. 

Specific distribution of electrons in atomic orbitals of atoms or ions. 

As expected from our experience with a particle in a box, three quantum numbers are necessary to describe the spatial distribution of electrons in atoms. To describe an electron in an atom completely, a fourth quantum number, m called the spin quantum number must be specified. This is because every electron has associated with it a magnetic moment which is quantized in one of two possible orientations parallel with or opposed to an applied magnetic field. The magnitude of the magnetic moment is given by the expression... 

Be certain you understand these choices in each image you examine (or create ). These same issues appear in Chapter 5 when we discuss the wave functions for electrons in atoms, called atomic orbitals. Throughout this book, we have taken great care to generate accurate contour plots and isosurfaces for them from computer calculations to guide your thinking about the distribution of electrons in atoms and molecules. 

Let us now describe the distributions of electrons in atoms. For each neutral atom, we must account for a number of electrons equal to the number of protons in the nucleus, that is, the atomic number of the atom. Each electron is said to occupy an atomic orbital defined by a set of quantum numbers n, (, and m. In any atom, each orbital can hold a maximum of two electrons. Within each atom, these atomic orbitals, taken together, can be represented as a diffuse cloud of electrons (Figure 5-19). 

The values of n for elliptic orbits is assumed equal to that for circular orbits. There are, however, n6 values of n and n2 that agree exactly with the empirical values m = 3.63, 3.45 or 3.43. For Mi = 2 and n% = 5 we have n = 3.38. Other evidence of the distribution of electrons in atoms indicates that this arrangement is highly improbable. 

In the broadest sense, an electron configuration is any description of the complete distribution of electrons in atomic orbitals. Although this can mean either an orbital diagram or the shorthand notation, this text will follow the common convention of referring to only the shorthand notation as an electron configuration. For example,... 

The rules regarding n, I, and m can be derived in a more general way by the direct application of the Schrddinger wave equation to atoms of the same type as hydrogen. And by this method much additional information may be obtained about the actual distribution of electrons in atoms. 

The TF theory and electronic description is considered as the referential for the uniform distribution of electrons in atoms and molecules, respecting which the electronic accumulation in bonding is further described, usually as a perturbation - as in DFT when density gradient expansions are considered, or by general reformulation of the problem in terms of localization - in which case special quantum treatment as provided by stochastic Fokker-Planck modeling is needed these issues will be in next addressed and imfolded. 

A]ttention to the fact that the distribution of electrons in atoms characterized by the subgroupings 2 2,2,4 2,2,4,4,6 2,2,4,4,6,6,8 did not originate with Mr. E. Stoner, as within recent months various papers published in your journal have suggested. ... 

J.D. Main Smith,The Distribution of Electrons in Atoms [letter dated September 8], Philosophical Magazine, 50(6), 878-879,1925, quoted from p. 878. 

The distributions of electrons in atoms of the noble gases have been determined by physicists by experimental and theoretical methods that are too complex to be discussed here. The results obtained are shown in Figure 5-3. It is seen that for the atoms neon, argon, krypton, and xenon the electrons are arranged about the atomic nuclei in two or more concentric shells. 

The properties of elements and the formation of chemical bonds are consequences of the shapes and energies of the wavefunctions that describe the distribution of electrons in atoms. We need information about the shapes of these wavefunctions... 

The distribution of electrons in atoms and molecules dictates numerous molecular properties. First, we should note that molecular properties are generally values that quantify certain characteristics or features of a molecule, in particular a response by the molecule to some influence. For instance, the force constant, k, of the bond of a diatomic molecule is the second-order energy response to stretching or compressing the bond. That is, the energy s quadratic dependence on the bond length varies with the value k, where... 

---