Cyclopropane point group

FIGURE 18. Symmetry-adapted linear combinations of the LMOs Acc and Ach of cyclopropane (point group Djh) belonging to the irreducible representations A, E, and E. Of these, the Acc combinations 3a and 3e, which form the FCM orbital set, mix with the Ach combinations 2a and 2e to form the CMOs of the same symmetry behaviour. The orbitals la and le are of carbon Is parentage, and have orbital energies around — 290eV. Note that only the relative phases and not the absolute contributions of the individual LMOs Acc and Ach are implied... 

The smaller related species cyclopropane (point group D h) represents a well-known case of the E e JT effect in the radical cation. It displays the characteristic double-peaked PE spectral profile and has been characterized ab initio in terms of its JT distorted structures and in terms of its spectral profile. Similarly well studied is the next larger analogue, the cyclopentadienyl radical, especially since the recent, combined experimental and theoretical analysis of T. Miller and coworkers. ... 

List all the symmetry elements of the following molecules, assign each to a point group, and state whether they form enantiomers (a) lactic acid, (b) trans-[Co(ethylenediamine)2Cl2], (c) c -[Co(ethylenediamine)2Cl2], (d) cyclopropane,... 

Seven of these were found after cyclopropanation of e- and trans-n-Cg2(COOEt)4 (n = 2-4) (4-7) with diethylmalonate (Figure 10.6) [20]. In a few cases, such as the Cj-symmetric adduct 8 (e,e,e-addition pattern), the structure can be assigned based on NMR spectroscopy alone. NMR spectroscopy allows for the determination of the point group of the adduct. The e,e,e-addition pattern is the only one that has Cj-symmetry and as a consequence the assignment is unambiguous. The same is true for the Dj-symmetrical adduct 9. Conversely, C2-, C - or Cj-symmetry of trisadducts can arise from different addition patterns. The structural assignment of such adducts requires the additional analysis of their possible formation pathways. 

The MOs and electronic states of carbene have been discussed in Chapter 7. The orbital and state correlation diagrams for addition of CH2 to ethylene is shown in Figure 14.9. The Walsh bonding picture for the MOs of cyclopropane requires that the and a MOs of the ethylene also be included in the diagram. The a2 and least-motion pathway preserves a vertical plane of symmetry (as well as the other elements of the C2v point group), and the... 

Cyclopropane bond angle, 16 bonding, 84-85 correlation diagrams, 207 electronic states, 207 hybridization, 16 point group of, 5 structure of, 16, 84 Walsh orbitals, 85 Cyclopropanes... 

Draw formulae for all the isomers of dichloro cyclopropane and predict the relative signal intensities in their H NMR spectra. Compare your answer with results obtained from a determination of the symmetry elements and point groups. 

Figure 4.1-10 Typical normal vibrations of cyclopropane. The length of the vector arrow and the diameter of its head are proportional to the amplitude. The name of the characteristic vibrations, the vibrational species of the point group D3/, and the calculated frequencies are given (Spiekermann et al, 1980).

The valence molecular orbitals of cyclopropane accessible to the helium lamp are 18 in number derived from H(ls) (13.6 eV), C(2s) (19.5 eV) and C(2p) (10.7 eV), they span the following irreducible representations of the point group. 

TABLE 1. Energies of the molecular orbitals of cyclopropane E (in eV) calculated by the SCF method, together with their irreducible representations in the Dajj point group and the vertical ionization energies / (in eV) derived from the He(I) photoelectron spectra of the vapour... 

Figure 1. Compact bond diagram of cyclopropane viewed as a composite of Ca - Cjj and H (CH2) fragments. Note deexcited ( doubly occupied) core. Orbital symmetry classification is with respect to the 62 point group.

Figure 1. The MO s of the various cyclic AO arrays of cyclopropane. Note that all except the P ring are HUckel arrays. The P ring is a Mbbius array. The symmetry classification of the MO s is with respect to the point group. Electron allotment produces six C-H and three C-C bonds.

For each of the following, determine the molecular and corresponding crystallographic point groups (a) a piece of 8.5" x 11" paper (no lines), (b) staggered ferrocene, (c) eclipsed ferrocene, (d) hydrogen peroxide, (e) cyclopropane. 

To illustrate further how operations can fall into the same class, we will look at the 31i point group, for which cyclopropane (Figure 5.5) serves as an example molecule. Figure 5.5 also shows some example symmetry elements from Dsh. The principal C3 axis is perpendicular to the plane of the three C atoms and passes through the centre of the triangle... 

Figure 5.5 Cyclopropane as an example molecule belonging to the Djh point group.

Another point for structural diversification is the sulfonamide group. Imai had already shown that a wide variety of groups could be introduced at this position to optimize the reaction. Since a wide variety of sulfonyl chlorides are commercially available, a number of different types of groups could be examined (Scheme 3.34). Testing of a variety of aryl and alkyl groups on the 1,2-cyclohexanediamine backbone demonstrates that the simple methanesulfonamide 122 is clearly superior or equal to many other analogs in the cyclopropanation of cinnamyl alcohol (Table 3.11). Another concern which was directly addressed by this survey was the question of catalyst solubility. 

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