Maximum multiplicity, rule

The number of electrons in an atom is equal to the atomic number, which for carbon is 6 and the electronic ground state for carbon has the configuration l5, 2s, 2p. Of the six electrons in the neutral atom, four are available for the formation of chemical bonds in the outer L shell. When electrons enter a level of fixed n and / values, according to Hund s maximum multiplicity rule, the available orbitals are occupied singly until each orbit is so occupied before electron pairing occurs. 

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 ... 

In accord with the first rule, the electrons remain unpaired as long as possible when filling a set of orbitals because that is how the maximum multiplicity is achieved. With regard to the third rule, if a state is exactly half filled, the sum of the m values that gives the L vector is 0 and L + S and L — S are identical so only one / value is possible. 

Hund s rules tell us that the ground state of the ion has (a) the maximum multiplicity and (b) the maximum values of L consistent with maximum multiplicity. The ground states for the various dn configurations 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. 

The ground state of an atom may be chosen by application of Hund s rules. Hund s first rule is that of maximum multiplicity. It states that the ground state will be that having the largest value of 5, in the case of carbon the 3F. Such a system having a maximum number of parallel spins will be stabilized by the exchanf e energy resulting from their more favorable spatial distribution compared with that of paired electrons (see Pauli principle. Chapter 2). 

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. 

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 ... 

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