Hund exception

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. 

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 first attempts to rationalize the magnetic properties of rare earth compounds date back to Hund [10], who analysed the magnetic moment observed at room temperature in the framework of the old quantum theory, finding a remarkable agreement with predictions, except for Eu3+ and Sm3+ compounds. The inclusion by Laporte [11] of the contribution of excited multiplets for these ions did not provide the correct estimate of the magnetic properties at room temperature, and it was not until Van Vleck [12] introduced second-order effects that agreement could be obtained also for these two ions. 

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. 

The filling of the 3d subshell generally proceeds according to Hund s rule (Section 5.12) with one electron adding to each of the five 3d orbitals before a second electron adds to any one of them. There are just two exceptions to the expected regular filling pattern, chromium and copper ... 

It must be stressed that the above examples serve only to illustrate the way in which the Hund rules are applied. When ions are in crystal lattices the basic coupling between spin momenta and orbital momenta differs from what has been assumed above, and under certain conditions the rules are not obeyed. For instance six-coordinated Fe2+ and Co3+ ions contain six d electrons which most commonly have one pair with opposed spins and four with parallel spins but, in exceptional circumstances, have three pairs with opposed spins and two unfilled states. These differences have a marked effect on their magnetic properties (cf. Section 9.1) and also alter their ionic radii (Table 2.2). The possibility of similar behaviour exists for six-coordinated Cr2+, Mn3+, Mn2+ and Co2+ ions but occurs only rarely [1]. 

The solution to this problem and the last rule needed to generate the electron configurations for all the atoms came from a German scientist named Friedrich Hund (1896-1997). Hund s rule states that an atom with a higher total spin state is more stable than one with a lower spin state. Because electrons with opposite spin states cancel each other, electrons in p orbitals (and other orbitals except for s) will remained unpaired if possible. Thus, two electrons (or three, for that matter) in a p subshell would remained unpaired. So, 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. 

Hund s rules are inviolate in predicting the correct ground state of an atom. There are occasional exceptions when the rules are used to predict the ordering of excited stales. 

The building-up principle in combination with the Pauli exclusion principle and Hund s rule accounts for the ground-state electron configurations of atoms. The principle is generally valid, but there are exceptions. 

No Rydberg state ever exactly corresponds to a pure Hund s case, except at n = 00 or 3, but rather to a situation in an intermediate Hund s case, and it is necessary to choose, to describe it, a basis set corresponding to any one of the pure Hund s cases. The energy terms to be added in each Hund s case are different depending on this choice of basis set. To clarify these choices, consider first the simple case of atoms. 

These two transition paths must terminate on substates with different values of S7/j, except when X — 0. However, X = 0 is possible only for integer-S (even number of electrons) molecules. For integer-S1 molecules, the interference effect demands a X = 0 virtual state (0+ or e-symmetry for 1X+, 3X, 5X+ 0 or /-symmetry for 1X, 3X+, 5X"). In the case (b) limit, there is no X = 0 character in the F2 spin-components of 3X states and in the F2 and P4 components of 5X states. For half-integer-S molecules, the interference effect is most visible when the initial and final 2S+1n states are near opposite extremes of Hund s case (a) vs. (b) coupling. 

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