Atoms Hund’s rules

Angular Parts. Many Electron atoms - Hund s Rules - Build-up Process - Maximum Multiplicity - Periodic Table - s-, p- and /-block Elements - Long Form of the Periodic Table. 

The Pauli Exclusion Principle Diamagnetism and Paramagnetism The Shielding Effect in Many-Electron Atoms Hund s Rule General Rules for Assigning Electrons to Atomic Orbitals... 

Procedure. To go from an STO-3G ealeulation to a CBS-4 ealeulation, simply replaee STO-3G with CBS-4 in the route seetion of the program used in Computer Projeet 8-1. Complete Table 8-2 by filling in the CBS-4 Energies of the atoms and ions listed in eolumns 1 and 3 of Table 8-2 and put them into eolumns 2 and 4 of the table. You will notiee that some of the simpler atoms (H through Be) do not have a listed CBS-4 Energies, but they do have an SCF energy, whieh should be used in its plaee. Caleulate the IP and eomplete eolumn 5. Pay speeial attention to spin niultiplieity and Hund s rule. The spin niultiplieity is rr + 1 where n is the number... 

Hund s rule (Section 1 1) When two orbitals are of equal en ergy they are populated by electrons so that each is half filled before either one is doubly occupied Hybrid orbital (Section 2 6) An atomic orbital represented as a mixture of vanous contributions of that atom ss p d etc orbitals... 

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. 

The atomic number of iron is 26 its election configuration is ls22s22p63s23p64s23d6. All the orbitals are filled except those in the 3d sublevel, which is populated according to Hund s rule to give four 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. 

In Fig. 1 there is indicated the division of the nine outer orbitals into these two classes. It is assumed that electrons occupying orbitals of the first class (weak interatomic interactions) in an atom tend to remain unpaired (Hund s rule of maximum multiplicity), and that electrons occupying orbitals of the second class pair with similar electrons of adjacent atoms. Let us call these orbitals atomic orbitals and bond orbitals, respectively. In copper all of the atomic orbitals are occupied by pairs. In nickel, with ou = 0.61, there are 0.61 unpaired electrons in atomic orbitals, and in cobalt 1.71. (The deviation from unity of the difference between the values for cobalt and nickel may be the result of experimental error in the cobalt value, which is uncertain because of the magnetic hardness of this element.) This indicates that the energy diagram of Fig. 1 does not change very much from metal to metal. Substantiation of this is provided by the values of cra for copper-nickel alloys,12 which decrease linearly with mole fraction of copper from mole fraction 0.6 of copper, and by the related values for zinc-nickel and other alloys.13 The value a a = 2.61 would accordingly be expected for iron, if there were 2.61 or more d orbitals in the atomic orbital class. We conclude from the observed value [Pg.347]

It is well known that Hund s rule is applicable to atoms, but hardly so to the exchange coupling between two singly occupied molecular orbitals (SOMOs) of a diradical with small overlap integrals. Several MO-based approaches were then developed. Diradicals were featured by a pair of non-bonding molecular orbitals (NBMOs), which are occupied by two electrons [65-67]. Within the framework of Hiickel MO approximation, the relationship between the number of NBMOs,... 

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. 

Two electrons in an atom exert an influence on each other, i.e. their spins and their orbital angular momenta are coupled. Two electrons are termed paired if they coincide in all of their quantum numbers except the magnetic spin quantum number. In such an electron pair the magnetic moments of the electrons compensate each other. Unpaired electrons in different orbitals tend to orient their spins parallel and thus produce an accordingly larger magnetic field (Hund s rule) they have the same magnetic spin quantum number and differ in some other quantum number. 

The coupling of the spins of the electrons in an atom is accounted for by adding their magnetic spin quantum numbers. Since they add up to zero for paired electrons, it is sufficient to consider only the unpaired electrons. The spins of n unpaired electrons add up according to Hund s rule to a total spin quantum number S = n. The magnetic moment of these n electrons, however, is not the scalar sum of the single magnetic moments. The... 

In atoms with partially filled p, d, or / subshells, the electrons stay unpaired as much as possible. This effect is called Hund s rule of maximum multiplicity. Thus the configuration of the nitrogen and oxygen atoms are as follows ... 

When following the Aufbau principle, the orbitals begin filling at the lowest energy and continue to fill until we account for all the electrons in an atom. Filling begins with the n = 1 level followed by the n = 2 level, and then the n = 3 level. However, there are exceptions in this sequence. In addition, Hund s rule states that the sublevels within a particular orbital will half fill before the electrons pair up in a sublevel. 

Be able to write both the energy-level diagram and the electronic configuration of an atom or ion by applying both the Aufbau build-up principle and Hund s rule. 

E—The four electrons in the oxygen 2p orbitals are arranged with one pair and two unpaired electrons with parallel spins. This makes the oxygen atom paramagnetic. This arrangement is due to Hund s rule. 

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