Covalent states

FIGURE 2.3. The energetics of a heterolytic bond cleavage reaction in a polar solvent. The specific example shown corresponds to the CH3OCH3— CH3 + CH30 reaction in water. The energy of the covalent state does not include the effect of the solvent on this state, but a more consistent treatment (e.g., eq. (2.21) should account for the polarization of the solvent toward the charges of the ionic state. This would result in destabilization of H31. 

Covalent bonds, 15,18-19,109 Covalent states, 47, 53, 145 Cysteine, structure of, 110... 

Both the ionic and the covalent structure of sphalerite, for instance, are singlet structures, with no unpaired electrons, so that either extreme or any intermediate is possible, and in such a case evidence from various properties of the particular substance must be considered to decide which extreme is more closely approached. On the other hand, in a crystal such as (NH FeFg or (7V774)3Z e(GW)s the lowest ionic state of the [FeXft] complex does not combine with the lowest covalent state, so that the transition from one extreme to the other is discontinuous. The actual state of the complex in the crystal can be determined from the multiplicity. With an ionic state, Fe+++ and -For ( C Nthe F or... 

Turning to macromolecular inorganic compounds, say ZnS, the two hypothetical ionic extremes are Zn2+S2- and Zn6-S6+ (an inverted, unusual formulation). We can imagine a continuous array of possible electron distributions between these extreme limits, one of which is the electron-pair covalent bonding state. The association of covalency with = Ay in Eqn. III.3 warrants non-polar formal MOs. However, a different situation arises when electrons are permitted to enter the empty MO skeleton. The electron-pair "covalent state corresponds to... 

With these insights on the meaning of s3, we now outline a possible outcome of the ESP analysis for the two VB state picture of the BuCl Svl dissociation. Let us imagine following the reaction from the solute equilibrium geometry, where the BuCl system is largely electronically localized in the covalent state 2>. It is reasonable to expect that the product of the... 

Figure 3 displays the molecular partition of the fragments for the three states previously discussed in the quantum mechanical section, at d= 6 k. Figure 3 A and 3 B respectively display the and 2 covalent states, and Figure 3 C shows the ionic 82 Charge Transfer state. It is worth examining the striking features of the molecular partitions in each case. In the A1 molecular partition, the disynaptic basin V(Cli, CI2), indicated by an arrow, corresponds to the Cl—Cl bond [22]. Two basins are found around Li, one corresponding to its core C(Li), and the second one, V(Li), to its valence odd electron (L shell). The 82 covalent state is characterized by two monosynaptic basins, Vi(Li) and V2(Li), located on both sides of the C(Li) basin in the molecular plane. They correspond to the half-filled 2p AO of Li. As when dealing with the previous state, the Cl atoms are bonded through a disynaptic basin, still noted V(Cli, CI2). In the ionic state, the Cl atoms are linked by a (3, -I) saddle point, or.

There can be resonance between covalent and ionic states. In the molecule H H a complete shift of the electron pair to the left would have the effect to make the left-hand H atom a negative ion, leaving the right-hand one as a positive ion. Next to the state H H there will be two others, H H+ and H+H , which closely resemble the electrostatic model for the H2 molecule. Since the three states are resonating, the states H H+ and H+H will make a contribution to the bonding energy, too in this case, however, their contribution will be relatively small, because the energy of the covalent state H H certainly is much lower than that of the ionic states. H H+ and H+H-. 

All these reaction channels can be described in terms of the motion of the system along two potential energy surfaces, one of which corresponds to the covalent state, M + X2, and the other to the ion state M+ + X2. These surfaces cross at comparatively large distances R0 (Table 3) which are determined from the equation... 

An intriguing example which highlights the idea of femtosecond chemistry is the photodissociation of Nal (Rose, Rosker, and Zewail 1988 Rosker, Rose, and Zewail 1988). Figure 16.6 illustrates the potential energy curves involved in the fragmentation. The pump pulse excites Nal to a covalent state which, in the diabatic picture, correlates with Na +... 

In conjugated molecules, there are a few covalent structures (see Scheme 7.1) and in most cases, the lowest lying excited state, or one of the lowest lying ones, is covalent. Among the most well-known covalent states are the so-called... 

Before continuing with the discussion, it is instructive to relate these VB states to those that arise from the MO picture of benzene. Benzene possesses degenerate pairs of HOMOs and LUMOs, and hence the excitations from the two HOMOs to the two LUMOs give rise to four singlet excited states of the following symmetries B2u, E2g, and Blu. As can be seen from Fig. 7.4a—c, the B2u is the covalent state made from the Kekule structures, while E2g is the covalent state made from the Dewar structures. The Blu state is predominantly ionic, made from the monoionic VB structures (see those in Chapter 5) (5). The excited Alg state made from the Dewar VB structures (Fig. 7.4c) corresponds to higher rank MO excitation. 

Thus, as we did for the allyl radical case, here too the bonding characteristics of the two covalent states of benzene can be deduced from the respective wave functions. As discussed in Chapter 5, each Kekule structure can be generated by a product of the corresponding bond wave functions, each having a spin factor a(l)(3(2)- 3(l)a(2). Each Kekule structure possesses the two spin alternant QC determinants, which are related to each other by a cyclic permutation of the spins over the ring, and are shown in Fig. 7.4d. To illustrate clearly the building blocks of the two Kekule structures, we express them as a sum of all the permutations of the QC determinants, as follows ... 

To deduce the bonding features of the covalent states, Aig and 1 B g, we express as we did before for benzene, the Kekule structures as follows ... 

The dimensionality of the space spanned by covalent states is much less than the full number of basis states of the Hubbard model. This is one of the reasons of the success in the application of the above VB Hamiltonians to the study of low-lying energy levels of the transition metal compounds and organic molecules with conjugated bonds. The covalent VB approach is very useful especially for predictions as to ground state spin multiplicity and spin ordering [14,17-20],... 

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