Multiplicity, Hund’s rule of maximum

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]

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 ... 

Hund s rule of maximum multiplicity predicts that the two electrons entering the -n level will occupy two different orbitals, so the electronic configuration can be written more explicitly as... 

The same phenomenon that leads to Hund s rule of maximum multiplicity in atoms (i.e., quantum-mechanical exchange stabilization) produces polarization of the electron spins in the C-H a bond. In a valence-bond treatment, the bond is comprised of one electron from a carbon sp2 orbital and another from a hydrogen Is orbital. Exchange forces act to polarize the sp2 electron so that its spin is parallel to the unpaired spin in the carbon 2p orbital this leaves the... 

Hund s rule of maximum multiplicity when electrons partially fill a subshell, they remain as unpaired as possible. 

This is sometimes called Hund s rule of maximum multiplicity, introduced in Section 2-2-3. 

Hund s Rule of Maximum Multiplicity. This rule has a spectroscopic basis and is mainly concerned with the situation when two orbitals of a sub-group are incompletely filled. This rule can be stated as ... 

The superscripts denote the number of electrons in each atomic orbital. Electrons must be paired (i.e., of equal and opposite spin) in atomic orbitals containing two electrons. Paired electrons do not contribute to the atomic or molecular spin angular momentum. Hund s rule of maximum multiplicity states that in the lowest energy configuration, the electrons must be spread over as many available orbitals of equal energy as possible, in order to maximize the spin multiplicity. Since three 2p orbitals are available in which 4 electrons must be distributed, the lowest electronic state therefore has two unpaired electrons in each of two 2p orbitals. Each unpaired electron contributes to the spin angular momentum. Thus 2S + 1 = 3 for the oxygen atom, and the term symbol is 3P. 

Hund s rule of maximum multiplicity applies i.e. degenerate orbitals are occupied singly before spin pairing occurs. 

This section gives the qualitative interpretation of the rules for degenerate excitations. We adopt the FZOA treatment, which has succeeded in giving a qualitative but clear description in many cases, e.g., Koopmans theorem for estimating the ionization potential (IP) and the electron affinity (EA), and Hund s rule of maximum multiplicity concerning the singlet-triplet separation. 

Determine the term symbols for the N atom. Show all work, (a) Determine the number of possible microstates, (b) Write out all the possible combinations of the electrons in a microstates table, (c) Extract the term symbols and determine the degeneracy of each term, (d) Determine the ground-state term symbol using Hund s rule of maximum multiplicity. 

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