Effects of Molecular Asymmetry

Secondary isotope effects through two or three bonds are sometimes helpful in structural elucidation, particularly when an exchangeable hydrogen can easily be replaced by deuterium and its effect on the chemical shift of a nearby carbon nucleus observed. 

As we have seen, the chemical shift of a nucleus depends on its immediate environment. When two nuclei are in environments that are not equivalent by symmetry, we can anticipate that their chemical shifts will be different, with the magnitude of the difference depending on details of the environment. In many 

The asymmetry responsible for the nonequivalence of the chemical shifts of Ha and HB need not be due to an immediately adjacent asymmetric carbon atom. For example, the CH2 protons in 

FIGURE 4.13 H NMR spectrum (60 MHz) of the isopropyl group of piperitone in CDC13. Each of the nonequivalent methyl groups, M, and M2, is spin coupled to the isopropyl proton and thus gives two lines as indicated and discussed in Chapter 5. 

It should be emphasized that the presence of some sort of asymmetry is a necessary condition for chemical nonequivalence of two protons (or two methyl groups, etc.).This does not mean, however, that the molecule must be completely devoid of a plane of symmetry. For example, in the situation we have been considering, suppose that R is the group CH2X, giving the molecule IV  

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In Eq. (2.30), F is the Fock operator and Hcore is the Hamiltonian describing the motion of an electron in the field of the spatially fixed atomic nuclei. The operators and K. are operators that introduce the effects of electrons in the other occupied MOs. Hence, when i = j, J( (= K.) is the potential from the other electron that occupies the same MO, i ff IC is termed the exchange potential and does not have a simple functional form as it describes the effect of wavefunction asymmetry on the correlation of electrons with identical spin. Although simple in form, Eq. (2.29) (which is obtained after relatively complex mathematical analysis) represents a system of differential equations that are impractical to solve for systems of any interest to biochemists. Furthermore, the orbital solutions do not allow a simple association of molecular properties with individual atoms, which is the model most useful to experimental chemists and biochemists. A series of soluble linear equations, however, can be derived by assuming that the MOs can be expressed as a linear combination of atomic orbitals (LCAO)44 ... 

Indeed, the existence of purely conformational optical activity is not a unique macromolecular requisite, being well known in low molecular weight atro-pisomerism. However, in polymers it assumes a very specific characteristic connected with the occurrence of cooperative effects which allow transmittance of molecular asymmetry along the chain to very long distances [3]. 

Abstract Several facets of pyridinocalixarene chemistry have been investigated including reaction pathways for their formation from the base-catalyzed alkylation of the parent calixarenes with PicCl-HCl, effect of the nature and identity of the base on regio- and stereoselective O-alkylations, creation of molecular asymmetry in calix[4]arenes and enantiomeric resolution, conformation and conformational mobility, and complexation. 

Finally, we should mention that the asymmetry of molecular shape, polyphilic effects and conformational constraints are the dominant factors in the stabilization of polar ordering in achiral mesogens. The examples presented above are, therefore, highly significant. They show that many liquid crystalline structures are intrinsically polar and may be effectively stabilized by suitable design of the mesogenic molecules. 

The computed results in Fig. 36 capture the observed phase behaviour of mikto arm-star copolymer melts. The effect of the molecular asymmetry seems to saturate for n > 3, and phase boundaries do not change significantly as a function of 0 or higher asymmetry. 

Theoretical calculations have also permitted one to understand the simultaneous increase of reactivity and selectivity in Lewis acid catalyzed Diels-Alder reactions101-130. This has been traditionally interpreted by frontier orbital considerations through the destabilization of the dienophile s LUMO and the increase in the asymmetry of molecular orbital coefficients produced by the catalyst. Birney and Houk101 have correctly reproduced, at the RHF/3-21G level, the lowering of the energy barrier and the increase in the endo selectivity for the reaction between acrolein and butadiene catalyzed by BH3. They have shown that the catalytic effect leads to a more asynchronous mechanism, in which the transition state structure presents a large zwitterionic character. Similar results have been recently obtained, at several ab initio levels, for the reaction between sulfur dioxide and isoprene1. ... 

Local structural features have been postulated for amorphous polymer systems, based on the asymmetry of chain-like molecules. Flory (56) has shown that molecular asymmetry in itself is no barrier to a dense random packing of the chains are sufficiently flexible. Robertson (57) suggests, however, that some degree of local alignment is required simply to accomodate linearly connected sequences in the rather limited space available. Unfortunately, Calculations of local cooperative effects are extremely difficult and sensitive to specific assumptions about available packing arrangements. 

These results make it clear that the forms of t]0 — rjs and Je° are completely independent of model details. Only the numerical coefficient of Je° contains information on the properties of the model, and even then the result depends on both molecular asymmetry and flexibility. Furthermore, polydispersity effects are the same in all such free-draining models. The forms from the Rouse theory cany over directly, so that t]0 - t]s, translated to macroscopic terms, is proportional to Mw and Je° is proportional to the factor A/2M2+, /A/w. Unfortunately, no such general analysis has been made for models with intramolecular hydrodynamic interaction, and of course these results apply in principle only to cases where intermolecular interactions are negligible. 

Table XI (73) shows the Stokes radii and frictional ratio obtained by the study of purified acid phosphatase. The preparations show molecular homogeneity during filtration on Sephadex G-100, in the analytical ultracentrifuge, and during immunolectrophoresis. These data obtained by chromatography on Sephadex G-200 indicate that human prostatic acid phosphatase has an effective Stokes radius of 47.1 A and a frictional ratio of 1.56, suggesting considerable molecular asymmetry.

There have been some impressive, relatively recent examples of molecular rectification. Compound 11.52 has proved to be an extremely efficient molecular rectifier, able to actually function as a rectification device by intramolecular tunnelling either as a monolayers or multilayer macroscopic film or on a nanoscopic level.51 Switchable rectification has been demonstrated for a related dye shown in Figure 11.36. The electrical asymmetry can be chemically switched, off and then back on, by treatment with acid and base, respectively. Protonation disrupts the intramolecular charge-transfer axis, destroying the rectification effect.52 Recent calculations, however, suggest that there may be relatively unpromising theoretical limits on the rectification possible by a single molecule.53... 

The discovery of confinement resonances in the photoelectron angular distribution parameters from encaged atoms may shed light [36] on the origin of anomalously high values of the nondipole asymmetry parameters observed in diatomic molecules [62]. Following [36], consider photoionization of an inner subshell of the atom A in a diatomic molecule AB in the gas phase, i.e., with random orientation of the molecular axis relative to the polarization vector of the radiation. The atom B remains neutral in this process and is arbitrarily located on the sphere with its center at the nucleus of the atom A with radius equal to the interatomic distance in this molecule. To the lowest order, the effect of the atom B on the photoionization parameters can be approximated by the introduction of a spherically symmetric potential that represents the atom B smeared over... 

The determination of the asymmetry parameters and the direction cosines, together with x-ray investigations of the crystal structure, will shed some light on the crystal field effect in solids. NQR powder spectra can only permit very rough and qualitative conclusions on the intermolecular forces. The results on the Mentschukin complexes with AsCl3 show that the metal-chlorine bond is virtually unaffected by the formation of molecular compounds. From singlecrystal NQR spectroscopy, particularly on the As nucleus, some geometrical information about the molecular compounds can be expected. 

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