Electron Configurations How Electrons Occupy Orbitals

An electron configuration shows the occupation of orbitals by electrons for a particular atom. For example, the electron configuration for a groimd-state (or lowest energy) hydrogen atom is  

The electron configuration tells us that hydrogen s single electron is in the Is orbital. 

Another way to represent this information is with an orbital diagram, which gives similar information but shows the electrons as arrows in a box representing the orbital. The orbital diagram for a ground-state hydrogen atom is  

The box represents the Is orbital, and tire arrow within the box represents the electron in the Is orbital. In orbital diagrams, the direction of the arrow (pointing up or pointing down) represents electron spin, a fxmdamental property of electrons. All electrons have spin. The Pauli exclusion principle states that orbitals may hold no more than two electrons with opposing spins. We s5mibolize this as two arrows pointing in opposite directions 

A helium atom, for example, has two electrons. The electron configuration and orbital diagram for helium are  

A FIGURE 8.1 Eka-aluminum and Eka-silicon Mendeleev s arrangement of elements in the periodic table allowed him to predict the existence of these elements, now known as gaUimn and germanium, and anticipate their properties. 

Notice the scientific approach in practice in the history of the periodic table. A number of related observations led to a scientific law—the periodic law. Mendeleev s table, an expression of the periodic law, had predictive power, as laws usually do. However, it did not explain why the properties of elements recurred, or why certain elements had similar properties. Recall from Chapter 1 that laws summarize behavior while theories explain behavior. The theory that explains the reasons behind the periodic law is qnantnm-mechanical theory. In this chapter, we turn to exploring the connection between the periodic table and quantum-mechanical theory. 

Quantum-mechanical theory describes the behavior of electrons in atoms. Since chemical bonding involves the transfer or sharing of electrons, quantum-mechanical theory helps us understand and describe chemical behavior. As we saw in Chapter 7, electrons in atoms exist within orbitals. An electron configuration for an atom shows the particular orbitals that electrons occupy for that atom. For example, consider the ground state—or lowest energy state—electron configuration for a hydrogen atom  

The Schrodinger equation for multielectron atoms has terms to account for the interactions of the electrons with one another that make it too complicated to solve exactly. However, approximate solutions indicate that the orbitals in multielectron atoms are hydrogen-like— they are similar to the s, p, d, and/orbitals that we examined in Chapter 7. In order to see how the electrons in multielection atoms occupy these hydrogen-Uke orbitals, we must examine two additional concepts the effects of electron spin, a fundamental property of all electrons that affects the number of electrons allowed in any one orbital and sublevel energy splitting, which determines the order of orbital filling within a level. 

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Figure 2.14. The molecular orbitals of gas phase carbon monoxide, (a) Energy diagram indicating how the molecular orbitals arise from the combination of atomic orbitals of carbon (C) and oxygen (O). Conventional arrows are used to indicate the spin orientations of electrons in the occupied orbitals. Asterisks denote antibonding molecular orbitals, (b) Spatial distributions of key orbitals involved in the chemisorption of carbon monoxide. Barring indicates empty orbitals.5 (c) Electronic configurations of CO and NO in vacuum as compared to the density of states of a Pt(lll) cluster.11 Reprinted from ref. 11 with permission from Elsevier Science.

Since NiO has the same crystal structure as MgO, with nearly the same lattice constant (4.21 Ain MgO and 4.17 Ain NiO [86]) and is a good insulator as well (the band gap of NiO is about 3.5 eV [87]) it can be expected that the adsorption of small molecules on its (100) surface plane is very similar to that on MgO( 100). However, there are two differences between the electronic structures of MgO and NiO. While the Mg + cations in MgO have a closed shell structure with a fully occupied 2p shell, the NP+ cations have a d configuration with two unpaired electrons and a A2g ground state in the octahedral environment in NiO. Further, the spins at the NP cations are antiferromagnetically coupled. This raises two immediate questions first, is there the possibility of a covalent chemical bond between the partially occupied orbitals at the Ni adsorption site and the adsorbed molecule, and second, are the d-orbitals at the NP+ cations completely localized or do they form delocalized, metal-Hke bands and how does this affect the adsorption properties ... 

How are electrons distributed to these atomic orbitals The atomic electron configurations are summarized in Tables 2.1-2.3. Electrons occupy the energetically lowest atomic orbitals two by two in closed-shell atoms such as the rare gases. However, it is not so simple in open-shell atoms. As a practical explanation. Hand s rule (Hund 1925a,b) is available. This rule consists of the following two rules ... 

As shown in the previous section, electron correlation can be essentially incorporated by a method that linearly combines excited CSFs with the ground CSF. This method is called the configuration interaction (Cl) method (McWeeny 1992). Slater indicated the lack of Cl in the Hartree-Fock method, before the Hartree-Fock SCF method was developed. In his paper published in 1929, in which he described how the formulation of the Hartree-Fock method is derived with the Slater determinant, he pointed out the problem of exchanging only occupied orbital electrons in the Slater determinants of wavefunctions and suggested a Cl method... 

The notation just introduced is rather more than a convenient shorthand for specifying which orbitals are occupied and by how many electrons. It expresses the fact that the MO approximation to the molecular wave function is a product of one-electron wave functions, i.e. orbitals, each taken to a power equal to the number of electrons occupying it. We recall that the irreducible representation of a product of coordinates is the direct product of their irreps extending the same idea to the product of orbitals, we see that the irrep of an electron configuration is simply the direct product of the irreps of its occupied... 

In the first-period elements, hydrogen and helium, electrons occupy the orbital of the first main energy level. Figure 3.4 provides a pattern to help you remember the order in which orbitals are filled according to the Aufbau principle. The groimd-state configurations in Figure 3.5 illustrate how the Aufbau principle, the Pauli exclusion principle, and Hund s rule are applied to atoms of elements in the second period. 

Scientists have a shorthand notation to indicate how many electrons occupy each orbital of an atom. This notation is called the electronic configuration of an element. Unless stated otherwise, it is assumed that the configuration represents the ground state of the atom, i.e., that all of the elements are in the lowest-energy subshells available. Superscripts indicate the number of electrons in a subshell. Table 17.2 gives the electronic configurations for the first eleven elements. 

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