Hunds rule

Hund s rules determine how the electrons go into the various shells in the ground state. 

Rule 1. Maximize S by placing as many electrons in the spin-up position as allowed by the Pauli exclusion principle. 

Rule 2. Maximize L consistent with the Pauli principle and Rule 1. 

Rule 3. If shell is less than half full, choose / = L S. If more than half full, / = L + S.  

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Strategy First (1) find out how many 3d electrons there are in Fe3+. Now (2) consider how those electrons will be distributed if Hunds rule is followed that corresponds to the high-spin complex. Finally (3) sprinkle as many electrons as possible into the lower three orbitals this is the low-spin complex. 

FIGURE 26 (a) MP2/6-31G(d) geometry of the cyclopropyl radical 40 according to Reference 246. (b) Spin-coupling scheme of the cyclopropyl radical according to the intra-atomic Hund rule and spin coupling within bonds. Hyperfine splitting aN at nucleus N will be > 0 ( < 0) if valence electrons at N possess oc (/ ) spin... 

According to the Hund rule, only the states with maximal spin multiplicity have the lowest energy among all possible states of a given electron configuration. As for multiplicity, it is defined with parallelism in spin orientations. Therefore, the interaction depicted in scheme EE3 is the most probable, because it, in contrast to that of schemes EE2 and EE4, leads to the state with the maximal spin multiplicity. That is the picture of microscopic ferromagnetism of an ion radical salt. 

In most cases the ground state (lowest energy) of the electron configuration of an atom is given by the Hund rules, according to which electrons occupy states fulfilling the following conditions. 

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]. 

Hund rules (1) Of the different multiplets resulting from different configurations of electrons in degenerate orbitals of an atom those with greatest multiplicity have the lowest energy (multiphcity rule). 

In the limiting case, if 2 — 1 =0. the system prefers to put electrons in separate orbitals and wifli the same spins (the empirical Hund rule see Fig. 8.22). 

In the case of d d, and configurations, the first three electrons successively occupy the orbitals from the t2g group, according to the Hund rule. The values of CSFE are -4Dq, -8Dq, and -12Dq, respectively. The d", d, d, (T configurations of the associated electrons involve two possible position modes either in the eg orbitals, with uncoupled spin, or in the t2g orbitals with coupled electronic spins. 

Now we can write electronic configurations for the rest of the atoms in the second row of the periodic table (Table 1.7). Notice that for nitrogen we face the same kind of choice just described for carbon. Does the seventh electron go into an already occupied 2p orbital or into the empty 2p orbital The configuration in which the 2py, 2py, and 2p orbitals are all singly occupied by electrons that have the same spin is lower in energy than any configuration in which a 2p orbital is doubly occupied. Again, Hund rules ... 

After determination of the relative energies of the d orbitals in a transition-metal complex, the distribution of the electrons has to be considered. Degenerate orbitals are filled according to Hunds rules one electron is added to each of the degenerate... 

A1.8 (i) According to Hunds rule, the ground term should have the S value as large as... 

Hund-rule total energy correction for the 4f configuration... 

Finally, the total RHF band energy per cell, band> calculated. Eband defined by the standard atomic expressions but is computed with the renormalized wave functions, including the self-consistent average 5d and 6s conduction band wave functions and occupation numbers. Eband differs from E ai of eq. (3) only by the exclusion of the Hund-rule correction for the 4f electrons discussed in section 2.2. 

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