Electron configuration principles

Aufbau principle In building up the electronic configuration of an atom or a molecule in its ground state, the electrons are placed in the orbitals in order of increasing energy. 

To arrive at the electronic configuration of an atom the appropriate number of electrons are placed in the orbitals in order of energy, the orbitals of lower energy being filled first (Aufbau principle ), subject to the proviso that for a set of equivalent orbitals - say the three p orbitals in a set - the electrons are placed one... 

The progression of sections leads the reader from the principles of quantum mechanics and several model problems which illustrate these principles and relate to chemical phenomena, through atomic and molecular orbitals, N-electron configurations, states, and term symbols, vibrational and rotational energy levels, photon-induced transitions among various levels, and eventually to computational techniques for treating chemical bonding and reactivity. 

The electron configuration is the orbital description of the locations of the electrons in an unexcited atom. Using principles of physics, chemists can predict how atoms will react based upon the electron configuration. They can predict properties such as stability, boiling point, and conductivity. Typically, only the outermost electron shells matter in chemistry, so we truncate the inner electron shell notation by replacing the long-hand orbital description with the symbol for a noble gas in brackets. This method of notation vastly simplifies the description for large molecules. 

Solvatochromic shifts are rationalized with the aid of the Franck-Condon principle, which states that during the electronic transition the nuclei are essentially immobile because of their relatively great masses. The solvation shell about the solute molecule minimizes the total energy of the ground state by means of dipole-dipole, dipole-induced dipole, and dispersion forces. Upon transition to the excited state, the solute has a different electronic configuration, yet it is still surrounded by a solvation shell optimized for the ground state. There are two possibilities to consider ... 

This reactivity pattern can be rationalized in terms of a diabatic model which is based upon the principle of spin re-coupling in valence (VB) bond theory [86]. In this analysis the total wavefunction is represented as a combination of two electronic configurations arising from the reactant (reaction coordinate. At the outset of the reaction, is lower in energy than [Pg.141]

Aufbau principle (Section 1.3) The rules for determining the electron configuration of an atom. 

This is the property we now call spin angular momentum. Pauli found that he could obtain Stoner s classification of electronic configurations from the following simple assumption which constitutes the famous exclusion principle in its original form. 

Figure 3. Alfred Mayer s experiments with magnets floating in water (illustrated in one of his publications with this sketch) were the template J. J. Thomson used to develop hi9 first electron configurations (see Figure 4. Mayer found that the magnets adopted different patterns depending on the number introduced, leading Thomson to suspect that similar principles would pertain to electron configurations.

Of course, most of what I have said so far is well known. Nevertheless, I hope to have given these issues a new perspective by adopting an almost perversely rigorous approach in demanding that every aspect of electronic configurations should be strictly deducible from quantum mechanics. Although I am not in a position to propose a better explanation, I do not think that we should be complacent about what the present explanation achieves. As I have tried to argue, in terms of deduction from theoretical principles, the present semi-empirical explanation is not fully adequate. 

The origin of electronic configuration Is frequently and inaccurately attributed to Niels Bohr, who introduced quantum theory to tire study of the atom. But Bohr essentially tidied up Thomson s pre-quantum configurations and took advantage of a more accurate knowledge erf the number of electrons each of the elements actually possessed. Furtlrer developments in quantum theory, including Pauli s occlusion principle and Schrodjtiger s equation. 

We account for the ground-state electron configuration of an atom by using the building-up principle in conjunction with Fig. 1.41, the Pauli exclusion principle, and Hund s rule. 

The ground-state electron configurations tor Cr and Cu are not those predicted by the building-up principle. Give their actual electron configurations and explain what causes them to deviate from the expected configuration. 

When N valence atomic orbitals overlap, they form N molecular orbitals. The ground-state electron configuration of a molecule is deduced by using the building-up principle to accommodate all the valence electrons in the available molecular orbitals. The bond order is the net number of bonds that hold the molecule together. 

The ground-state electron configurations of diatomic molecules are deduced by forming molecular orbitals from all the valence-sbell atomic orbitals of the two atoms and adding the valence electrons to the molecular orbitals in order of increasing energy, in accord ivith the building-up principle. 

What Do We Need to Know Already This chapter draws on many of the principles introduced in the preceding chapters. In particular, it makes use of the electron configurations of atoms and ions (Sections 1.13 and 2.1) and the classification of species as Lewis acids and bases (Section 10.2). Molecular orbital theory (Sections 3.8 through 3.12) plays an important role in Section 16.12. 

For practical implementations it is necessary to represent the molecular electronic wave functions as a linear combination of some convenient set of basis functions. In principle any choice of basis set is permissible although the basis set must span any electronic configuration of the molecule. This implies that the basis must form a complete set. 

Conventional presentaticsis of DFT start with pure states but sooner w later encounter mixed states and d sities (ensemble densities is the usual formulation in the DFT literature) as well. These arise, for example in formation or breaking of chemical bonds and in treatments of so-called static correlation (situations in which several different one-electron configurations are nearly degenerate). Much of the DFT literature treats these problems by extension and generalization from pure state, closed shell system results. A more inclusively systematic treatment is preferable. Therefore, the first task is to obtain the Time-Dependent Variational Principle (TDVP) in a form which includes mixed states. 

A neutral helium atom has two electrons. To write the ground-state electron configuration of He, we apply the aufbau principle. One unique set of quantum numbers is assigned to each electron, moving from the most stable orbital upward until all electrons have been assigned. The most stable orbital is always ly( = l,/ = 0, JW/ = 0 ). 

The physical and chemical properties of the elements show regular periodic trends that can be explained using electron configurations and nuclear charges. We focus on the physical properties of the elements in this section. A preliminary discussion of the chemical properties of some of the elements appears in Section Other chemical properties are discussed after we introduce the principles of chemical bonding in Chapters 9 and 10. 

Electron configurations of transition metal complexes are governed by the principles described in Chapters. The Pauli exclusion principle states that no two electrons can have identical descriptions, and Hund s rule requires that all unpaired electrons have the same spin orientation. These concepts are used in Chapter 8 for atomic configurations and in Chapters 9 and 10 to describe the electron configurations of molecules. They also determine the electron configurations of transition metal complexes. 

The last rule needed to generate electron configurations for all the atoms in the periodic table came from a German scientist named Friedrich Hund. Hund s rule can be expressed in several ways. The most precise definition is that atoms in a higher total spin state are more stable than those in a lower spin state. Thus, the sixth electron in carbon-12 must have the same spin as the fifth one. The Pauli exclusion principle then requires that it fill an empty p orbital. 

In contrast, it is accepted practice that referring to, for example, an iron(III) complex implies that this compound contains an iron ion with a high-, intermediate-, or low-spin electron configuration. Since n for a d" configuration is, at least in principle, a measurable quantity, it has been suggested [3] that an oxidation number n, which is derived from a known d configuration, should be specified as physical or spectroscopic oxidation number (state) [4—6]. 

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