Representation of Electron Configuration

The electron configuration of an atom can be represented by either electronic notation (s, p, d, f) or by orbital diagram. 

For instance, the electron configuration of the silicon, Si, atoms for which the atomic number is 14 (that is, the number of electrons is 14) is given below. 

In the orbital diagram notation, each subshell is divided into individual orbitals drawn as boxes. An arrow pointing upward corresponds to one type of spin (+1/2) and an arrow pointing down corresponds to the opposite spin (-1/2). Electrons in the same orbital with opposed spins are said to be paired, such as the electrons in the Is and 2s orbitals. These orbitals are completely filled orbitals. 

On the other hand, since electrons are placed one by one in a subshell with parallel spins, the corresponding arrows are drawn in the same direction, such as in the 3p electrons of the silicon atom. Such orbitals are half-filled orbitals. 

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Figure 28-7 Representation of electron configuration changes in dissociation of tetramethyldioxacyclobutane, 8, to T-, and S0 2-propanone. Spin-orbit coupling of the nonbonding and the cr-bonding orbital on oxygen (shaded) produces one molecule of ketone in the triplet (7,) state.

Knowledge Required (1) The symbolic representation of electron configuration. (2) The meaning of the term second period. (3) The allowed values for principal and angular momentum quantum numbers. (4) The order of filling of electron orbitals. (5) The ability to correlate symbolic representations with positions in the periodic table. 

Fig. I. I. Schematic representation of orbital configurations in the water molecule, (a) according to the simplified scheme of (i.i) in which 0(2s) and O(zpz) electrons do not participate in bond formation, (6) with approximately tetrahedral hybridization. The actual calculated electron density is shown in fig. 1.3.

A complete set of electronic configurations is built up upon these orbitals, following the Rumer procedure [3], along with a matrix representation of the Hamiltonian. The use of only one orbital per site allows us to draw simple diagrams to symbolize each configuration [3]. 

Figure 9.3. Schematic representation of electronic states associated with the Si vacancy. The shaded regions represent the conduction and valence states of the bulk. Left the vacancy configuration before any relaxation of the neighbors each broken bond contains one electron denoted by an up or a down arrow for the spin states, and all levels are degenerate, coincident with the Fermi level which is indicated by a dashed line. Right the reconstructed vacancy, with pairs of broken bonds forming bonding and antibonding states the former are fully occupied, the latter empty, and the two sets of states are separated by a small gap.

According to Bohr s account, the old quantum theory can be used to explain the periodic table in terms of the electronic structure of atoms. However, even just a casual examination of Bohr s account of chemical periodicity shows that the periodic table cannot be deduced from theory. The alleged explanation is more of an exercise in accounting for the known chemical facts in terms of an alternative representation based on the approximate model of electronic configurations. 

Note that, although there is a r esemblance, this ansatz is quite differ ent from the Born representation of Eq. (A.3) due to the time dependence of the electronic functions. By taking a single configuration. 

The electronic configuration for an element s ground state (Table 4.1) is a shorthand representation giving the number of electrons (superscript) found in each of the allowed sublevels (s, p, d, f) above a noble gas core (indicated by brackets). In addition, values for the thermal conductivity, the electrical resistance, and the coefficient of linear thermal expansion are included. 

A complete specification of how an atom s electrons are distributed in its orbitals is called an electron configuration. There are three common ways to represent electron configurations. One is a complete specification of quantum numbers. The second is a shorthand notation from which the quantum numbers can be inferred. The third is a diagrammatic representation of orbital energy levels and their occupancy. 

Construct an energy level diagram and the shorthand representation of the ground-state configuration of aluminum. Provide one set of valid quantum numbers for the highest-energy electron. 

As far as the molecular calculation is concerned, the use of an ab initio method is necessary for an adequate representation of the open-shell metastable N (ls2s) + He system with four outer electrons. The CIPSI configuration interaction method used in this calculations leads to the same rate of accuracy as the spin-coupled valence bond method (cf. the work on by Cooper et al. [19] or on NH" + by Zygelman et al. [37]). 

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