Electronic structure Hunds rules

In general, linear 7r-electron systems with Z1r = 2N electrons at the lowest energy levels have closed-shell singlet states while cyclic systems reach closed shell structures only when ZT = 4N + 2. Cyclic 7r-electron systems with Zn 4N + 2 will therefore exhibit multiplet ground states according to Hund s rules, and should be chemically reactive because of the unpaired electrons. Hiickel s rule that predicts pronounced stability for so-called aromatic ring systems with 4jV + 2 7r-electrons is based on this shell structure. The comparison with cyclic systems further predicts that ring closure of linear 7r-electron systems should be exothermic by an amount... 

Our next exan le, the TMM diradical, is a more challenging case because its frontier orbitals are exactly degenerate. The 7C-system of TMM is shown in Figure 6 four ic-electrons are distributed over four molecular ji-type orbitals. Due to the exact degeneracy between the two e orbitals at the Ds structure, Hund s rule predicts the ground state of the molecule to be a triplet 2 state (similar to the T-state in ethylene). This is confirmed by both the experimental and theoretical findings (38-43). 

The remaining two are the unchanged 2py and orbitals. There are six electrons to be placed in these orbitals, and for the linear structure, the lowest two, A and B, will be filled, and the Ipy, and 2p will have a single electron each. Hund s rule suggests that the triplet state with parallel spins will be lower in energy than the singlet state (Fig. 7.1). For an related, alternative valence-shell electron-pair repulsion (VESPR) theory treatment see Chapter 11 by Platz in this volume. 

At infinite separation between the FenO and Fe O moieties, 3xP. and 3xF+do not interact with 3vF3- Hund s rule requires that 3vF gives the dissociation products of lowest energy. Eq.(18) indicates that each of them involves an S = 1 state. A variation on the derivation of this result is provided in Ref. [47(a)], where three 5=1 and Ms = 0 wavefunctions are used to describe the electronic structure of the FeII02FeII(5 =1) complex. 

The electronic structure of the carbon atom in its ground state is s22s22p2, with the two 2p electrons unpaired, following Hund s rule. In order to account for the normal four-covalence of carbon, we must consider that it is promoted to a valence state based on the configuration 2s2px2py2pz. The ion C4+ does not arise in any normal chemical process the C4 ion may possibly exist in some carbides. In general, however, carbon forms covalent bonds. 

The energy-ordering scheme (5-58) coupled with the Pauli or exclusion principle and Hund s rule leads us to a simple prescription for building up the electronic configurations of atoms. This aufbau principle is familiar to chemists and leads naturally to a correlation between electronic structure and the periodic table. The procedure is to place all the electrons of the atom into atomic orbitals, two to an orbital, starting at the... 

In addition to the conditions for the electronic structures of multielectron atoms established by the monoelectronic wave functions and their relative energies mentioned above, other restrictions should also be considered. One of them is the Pauli principle stating that no two electrons can have the same quantum numbers. Thus one orbital can contain a maximum of two electrons provided they have different spin quantum numbers. Other practical rules or restrictions refer to the influence of interelectronic interactions on the electronic structures established by Hund s rules. The electrons with the same n and / values will occupy first orbitals with different nti and the same rris (paired spins). 

D. A. Hrovat and W. T. Borden, in Modern Electronic Structure Theory and Applications in Organic Ghemistry, E. R. Davidson, Ed., World Scientific Publishing, New York, 1997, pp. 171-195. Violations of Hund s Rule in Organic Diradicals—Where to Look for Violations... 

With this scheme at hand, one has to count the number of valence electrons of the molecule and place them into the corresponding molecnlar orbitals, observing both, the Aufbau principle and the Hund s rule. This will yield an approximate, albeit appealing, picture of the electronic structure of the -member ring molecule of interest. 

In particular, we have reviewed here how aromaticity can account for the electronic structure of ring-like molecules made of both main group metals and metalloids and transition metals. Of the many ways and indexes to characterize aromaticity, a loosely defined concept in itself, we have demonstrated that the very first of them, namely the analysis of the valence molecular orbitals complanented with the Aufbau principle and the Hund s rule for their occupation, and the Hiickel electron counting rules, yields a very appealing, albeit approximate, picture to assess the aromaticity of any particular ring-like molecule. 

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