Pauli exclusion rule

Having looked at some of the similarities between the two popular EDA schemes, let us now divert our attention to some of their differences. One of the major flaws of the KM analysis is its definition of POL and CT terms that are not evaluated by employing proper antisynunetrized intermediate wavefunctions. For example, when two subsystems are separated by short intermolecular distances such as in cation-jt complexes, the POL and CT terms in KM analysis are unusually blown up (Table 15.3). This problem, however, gets rectified in the RVS scheme as all wavefunctions satisfy the Pauli exclusion rule by using proper antisymmetrized wavefunctions. 

The triplet repulsion arises due to the Pauli exclusion rule and is often referred to as a Pauli repulsion. 

The four quantum numbers that characterize an electron in an atom have now been considered. There is an important rule, called the Pauli exclusion principle, that relates to these numbers. It requires that no two electrons in an atom can have the same set of four quan-... 

Hund s rule, like the Pauli exclusion principle, is based on experiment It is possible to determine the number of unpaired electrons in an atom. With solids, this is done by studying their behavior in a magnetic field. If there are unpaired electrons present the solid will be attracted into the field. Such a substance is said to be paramagnetic. If the atoms in the solid contain only paired electrons, it is slightly repelled by the field. Substances of this type are called diamagnetic. With gaseous atoms, the atomic spectrum can also be used to establish the presence and number of unpaired electrons. 

Electrons occupy orbitals in such a way as to minimize the total energy of an atom by maximizing attractions and minimizing repulsions in accord with the Pauli exclusion principle and Hund s rule. 

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. 

C08-0030. Write brief explanations of (a) screening (b) the Pauli exclusion principle (c) the aufbau principle (d) Hund s rule and (e) valence electrons. 

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 next element is lithium, with three electrons. But the third electron does not go in the Is orbit. The reason it does not arises from one the most important rules in quantum mechanics. It was devised by Wolfgang Pauli (and would result in a Nobel Prize for the Austrian physicist). The rule Pauli came up with is called the Pauli exclusion principle it is what makes quantum numbers so crucial to our understanding of atoms. 

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. 

Despite his numerous achievements, Mendeleyev is remembered mainly for the periodic table. Central to his concept was the conviction that the properties of the elements are a periodic function of their atomic masses. Today, chemists believe that the periodicity of the elements is more apparent when the elements are ordered by atomic number, not atomic mass. However, this change affected Mendeleyevs periodic table only slightly because atomic mass and atomic number are closely correlated. The periodic table does not produce a rigid rule like Paulis exclusion principle. The information one can extract from a periodic table is less precise. This is because its groupings contain elements with similar, but not identical, physical and chemical properties. 

Pattinson s lead white, 14 785 Pauli exclusion principle, silicon-based semiconductors and, 22 235 Pauling, Linus, 25 747-748 Pauling s rules, 22 453... 

In order to assign the four quantum numbers for a particular electron, first begin with the electron in the lowest energy level, n = 1. Assign the value of n, then the corresponding values of /, mh and finally ms. Once you have finished all the possible electrons at n = 1, repeat the procedure with n = 2. Don t forget about Hund s rule and the Pauli exclusion principle. The quantum numbers for the six electrons in carbon would be ... 

Fig. 6 The Huckel MOs of the three isomeric benzoquinodimethanes [8]. The bonding MOs of the ortho- and para-isomers are filled according to the Pauli exclusion principle. The electron configuration of the non-bonding MOs of the metaisomer is dictated by Hund s rule.

The video clip at www. brightredbooks.net will help you understand the Pauli exclusion principle, the aufbau principle and Hund s rule. 

Consider the electronic configuration of carbon again Is 2s 2pl Remember, there are three different p orbitals in the 2p subshell the p orbital lies on the x-axis the p orbital lies on the y-axis and the p orbital lies on the z-axis. The different p orbitals are degenerate. To obey Hund s rule, these degenerate orbitals must be filled singly before spin pairing occurs. To obey the Pauli exclusion principle, when an orbital is full with two electrons, these electrons must have opposite spins. This is not shown using spectroscopic notation, but is seen when orbital box notation is used. 

The filling of atomic orbitals follows an n + , n) orbital scheme known as the Madelung [75-77] or Klechkovskii [78] rule. In this orbital scheme, the electron occupies free states with the smallest value of the sum A = + of the principal quantum number n and the azimuthal quantum number ( according to the Pauli exclusion principle. In the presence of several states with identical N, the state with... 

Using the above definitions for the four quantum numbers, we can list what combinations of quantum numbers are possible. A basic rule when working with quantum numbers is that no two electrons in the same atom can have an identical set of quantum numbers. This rule is known as the Pauli Exclusion Principle named after Wolfgang Pauli (1900-1958). For example, when n = 1,1 and mj can be only 0 and m can be + / or -1/ This means the K shell can hold a maximum of two electrons. The two electrons would have quantum numbers of 1,0,0, + / and 1,0,0,- /, respectively. We see that the opposite spin of the two electrons in the K orbital means the electrons do not violate the Pauli Exclusion Principle. Possible values for quantum numbers and the maximum number of electrons each orbital can hold are given in Table 4.3 and shown in Figure 4.7. 

The treatment of atoms with more than one electron (polyelectronic atoms) requires consideration of the effects of interelectronic repulsion, orbital penetration towards the nucleus, nuclear shielding, and an extra quantum number (the spin quantum number) which specifies the intrinsic energy of the electron in any orbital. The restriction on numbers of atomic orbitals and the number of electrons that they can contain leads to a discussion of the Pauli exclusion principle, Hund s rules and the aufbau principle. All these considerations are necessary to allow the construction of the modern form of the periodic classification of the elements. 

Notice the similarities between the two parts of Table 1.1 and the form of the Periodic Table given in Figure 1.3. The quantum rules, the Pauli exclusion principle and the aufbau principle combine to explain the general structure of the Periodic Table. 

Each orbital can therefore contain no more than two electrons, with opposite spin quantum numbers. This rule, which affects the order in which electrons may fill orbitals, is known as the Pauli exclusion principle. Table 2.3 summarizes the configuration of electron orbitals for the first three shells. The orbitals are labeled with the numerical value of n and a letter corresponding to the value of l (s, p, d, f..). As you can see from Table 2.3, the n = 1 shell can hold up to two electrons, both in the s orbital, the n - 2 shell can hold up to eight electrons (2 in the s and 6 in the p orbital), the n - 3 can hold up to 18 electrons (2 s, 6 p, and 10 d), and the n 4 shell can hold up to 32 electrons (2 s, 6 p, 10 d, and 14 f). The lowest energy orbitals are occupied first. So for hydrogen, which has one electron, the electron resides in the Is orbital. For lithium, which has three electrons, two are in the Is orbital and the third is in the 2s orbital. For silicon (Z = 14), there are two electrons in Is, two electrons in 2s, six electrons in 2p, two electrons in 3s, and two electrons in 3p. 

The rotational energy levels for a homonuclear diatomic molecule follow Eq. 8.16, but the allowed possibilities for j are different. (The rules for a symmetric linear molecule with more than two atoms are even more complicated, and beyond the scope of this discussion.) If both nuclei of the atoms in a homonuclear diatomic have an odd number of nuclear particles (protons plus neutrons), the nuclei are termed fermions if the nuclei have an even number of nuclear particles, they are called bosons. For a homonuclear diatomic molecule composed of fermions (e.g., H— H or 35C1—35C1), only even-j rotational states are allowed. (This is due to the Pauli exclusion principle.) A homonuclear diatomic molecule composed of bosons (e.g., 2D—2D or 14N—14N) can only have odd- j rotational levels. 

If each of the six n electrons in benzene occupied a single atomic n orbital and there were no interaction, each would have an energy of a. The total energy would then be 6a, which is zero if we assume, as above, that a is the zero of our energy scale. However, when the atomic orbitals interact to produce the MOs, the six electrons will now occupy these MOs according to Hund s rule and the Pauli exclusion principle. The first two will enter the A orbital, and the remaining four occupy the E orbitals. The total energy of the system is then... 

This implies that the bra expression <0 av - aa is the adjoint of the corresponding ket expression a --- aj 0>. The equivalence of the operator and determi-nantal formalism ensures that all operators act in accordance with the Pauli exclusion principle for fermions. The following anticommutation rules thus follow at once ... 

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