Atomic orbital model for

Note it is not a trivial task to generate the above reducible representation. First, the character of -1 under 8C3. The -1 is a sum of (- ) + (- ) the calculation is very similar to that detailed in Appendix 4. Secondly, the character of 0 under 6S4. To obtain this, it is helpful to remember, as discussed in Section 15.2.2, that there is considerable freedom of choice of x and y axes at any phosphorus atom. The value of 0 ( = +1 - 1) is most readily obtained if x and y are chosen one to be symmetric and one antisymmetric with respect to reflection in the local mirror plane. See Appendix 4 of Symmetry and Structure, S. F. A. Kettle, Wiley, Chichester, 1995 for a detailed derivation. 

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Draw atomic-orbital models for each of the following substances. Each drawing should be large and clear with all bonds labeled as either values expected for the bond angles and whether the molecule or ion should be planar or nonplanar. 

Draw an atomic-orbital model for each of the compounds listed in Exercise 6-15 that is consistent with the geometry deduced for each. 

Draw atomic-orbital models for thiophene and imidazole that are consistent with their being planar compounds with six 77-electron systems associated with five atomic nuclei. 

Propadiene adds hydrogen chloride to yield 2-chloropropene. However, the possibility exists that initial attack of a proton might lead to the 2-propenyl cation (Section 6-6), which then would react with chloride ion to form 3-chloropropene. Using the rules for application of the resonance method (Section 6-5B) and the atomic-orbital model for 1,2-propadiene (Figure 13-4), rationalize why a 2-propenyl cation might not be formed easily by addition of a proton to 1,2-propadiene and why 2-chloropropene is the observed product. 

How do these differ from the Kekule structures usually written for benzene Devise an atomic-orbital model for benzyne. 

Exercise 16-1 Draw valence-bond structures and an atomic-orbital model for carbon monoxide. Why can the bond energy of this molecule be expected to be higher than for other carbonyl compounds (see Table 16-1) Explain why the dipole moment of CO is very small (0.13 debye).,... 

Exercise 21-5 Set up an atomic-orbital model for the enolate anion, CH2=CH—0 and consider how it should be formulated by the VB and MO methods. Write a hybrid structure of the general type of 18e and 21c for the enolate anion and predict the most likely positions of the atoms for the anion in its most stable configuration. 

Devise an atomic-orbital model for cyclooctatetraene in accord with the geometry expressed by formula 25a (Section 21-9A) and explain why electron delocalization is not likely to be important for a structure with this geometry... 

Exercise 23-11 Draw atomic-orbital models for benzenamine and its conjugate acid and describe the features of these models that account for the low base strength of benzenamine relative to saturated amines. 

Knowledge of how to set up an atomic orbital model for an organic molecule is crucial to the LCAO calculations described in these notes. Any reader who is familiar with atomic orbital representations can omit study of Chapter 1— or else only work the problems at the end of the chapter. 

Exercise 1-1. Make drawings of atomic orbital models for each of the following compounds. Each drawing should be large and clear with indication of the expected bond angles. Be sure that orbitals occupied by unshared pairs as well as those used by each atom in bond formation are correctly labeled. [Roberts, 1962, 22]... 

Solution of the numerical HF equations to full accuracy is routine in the case of atoms. We say that such calculations are at the Hartree-Fock limit. These represent the best solution possible within the orbital model. For large molecules, solutions at the HF limit are not possible, which brings me to my next topic. 

In order to retain the orbital model for a many-electron atom, Hartree assumed that each electron came under the influence of the nuclear charge and an average potential due to the remaining electrons. He therefore retained the form of the radial equation for a one-electron atom, equation 12.2, but assumed that the mutual potential energy U was the sum of... 

Starting with Bohr s version of 1913, the evolution of this model was examined in an attempt to highlight the assumptions and approximations that were made at each stage. As in the case of many other papers in this volume, there is an educational motivation for raising these questions, especially in view of the central role of the atomic orbital model at all levels of chemical education. My suspicion is that many chemical educators do not appreciate the extent to which this model is an approximation and the conditions under which it ceases to be applicable. 

The more generally familiar forms that are usually presented to beginning students in their study of the orbital model for atoms ... 

The classic case distinguishes between an atomic core, which is essentially unperturbed by bonding, and a valence shell whose content may be accessible to bond formation. Since we suppose this simplifying assumption to be maintained in the MO treatment, an atomic orbital belonging to the valence shell will be termed a valence atomic orbital (VAO). For the construction of MOs, we utilize the following general results of the MO/LCAO model ... 

The hypervalent chalcogen chemistry has been developed to higher coordinated species with various ligands,7 10 where TBP changes to square pyramidal (SP) or octahedral (Oh), etc. Additional atomic orbitals of E, such as an 5-orbital, may operate to stabilize the structures.10b The concept is also extended over linear a-bonds constructed by m ( > 4) atoms with n electrons (extended hypervalent bonds mc-ne (in > 4)).11 14 The approximate molecular orbital model for mc-ne (m > 4) is also exhibited in Scheme la, exemplified by 4c-6e. 

Saturated compounds such as the alkanes and their derivatives, which have normal tetrahedral angles for the bonds to carbon, can be formulated readily in terms of atomic orbitals with sp3 o- bonds to carbon. An example is shown in Figure 6-11, which also shows how an atomic-orbital model can be drawn in abbreviated style. The lines in this drawing correspond to bonds and are labeled as sp3 with sp3 (the overlapping orbitals of the C-C bond) or as sp3 with s (the overlapping orbitals of the C-H bonds). 

Atomic-orbital models, like that shown for benzene, are useful descriptions of bonding from which to evaluate the potential for electron delocalization. But they are cumbersome to draw routinely. We need a simpler representation of electron delocalization. 

Figure 6-21 Atomic-orbital model, valence-bond structures, and resonance-hybrid formula for the 2-propenyl radical...

Exercise 6-10 Set up an atomic-orbital model of each of the following structures with normal values for the bond angles. Evaluate each model for potential resonance (electron delocalization). If resonance appears to you to be possible, draw a set of reasonable valence-bond structures for each hybrid. ... 

Make an atomic-orbital model of benzenol, showing in detail the orbitals and electrons at the oxygen atom. From your model, would you expect one, or both, pairs of unshared electrons on oxygen to be delocalized over the ring What would be the most favorable orientation of the hydrogen of the hydroxyl group for maximum delocalization of an unshared electron pair ... 

ESR parameters of the anion radical of [l,2,5]thiadiazolo[3,4-c][l,2,5]thiadiazole show good agreement with those calculated by McLachlan s perturbation method using two models for the sulfur atom (sp/spd). The HMO method does not differentiate between the p -orbital and d-orbital models for the thiadiazole anion radicals. Due to the presence of a plane of symmetry through the sulfur atom, the contribution of the 3d-orbital is absorbed... 

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