Molecular orbitals conjugation and resonance

In Chapters 4 and 6 we have distinguished between a molecular orbitals and 7T molecular orbitals in diatomic molecules on the basis of the symmetry of the m.o.s with respect to rotation around the intemuclear axis whereas a a orbital has cylindrical symmetry, a tt orbital changes sign upon a rotation of 180°. In Chapters 7 and 8 we have extended the notion of a orbitals to polyatomic molecules by referring to the local symmetry with respect to each X-Y intemuclear axis. We will now study systems of tt m.o.s in polyatomic species. 

As before, the electronic wavefunction is constructed as a Slater determinant whose elements are the occupied spin-orbitals, both of a and tt symmetry. In the case of open-shell species or if configuration interaction is considered, then more than one determinant must be used. 

Nevertheless, a separate discussion of a and tt molecular orbitals is possible and useful in many qualitative discussions and even whenever more rigorous quantitative energy considerations are needed provided that the interplay of a and tt electrons is taken into account, as is in fact necessary within either set of a and tt electrons. 

The study of these species will follow closely the cases of BeHi and BH3 in Chapter 7, by taking advantage of the identical geometries linear for CO2 and BeH2 and trigonal planar for COg and BH3. 

The essential difference between the nature of the m.o.s in BeH2 and in CO2 is that the peripheral atoms in carbon dioxide (O atoms) contribute with four valence atomic orbitals and not just one as in BeH2. However, the 2s a.o. of the oxygen atom is of sufficiently low energy relative to the 2p a.o.s (as well as relative to the carbon valence a.o.s) in order to be considered - to an acceptable approximation for many purposes - as a core orbital (besides the Is orbitals of C and O). We thus have three (from O) -I- four (from C) +three (from 0)= 10 a.o.s to define 10 valence m.o.s. Orthogonality relations associated with the symmetry of the various orbitals enable those 10 a.o.s to be divided into three sets as shown in Fig. 9.1. 

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This section deals with analytical properties of the Hiickel molecular orbital theory and the associated isolated molecule method of predicting the active positions in a conjugated molecule. We shall deal with polarizability coefficients defined as certain partial derivatives with respect to the coulomb and resonance integrals described in Section III. The important derivatives are those relating to the total tt electron energy and to the charges q, fi ee valences and bond orders... 

Gutman, L, Milun, M.andTrinajStic, N. (1977) Graph theory and molecular orbitals. 19. Nonparametric resonance energies of arbitrary conjugated systems. /. Am. Chem. Soc., 99, 1692—1704. 

A familiar feature of the electronic theory is the classification of substituents, in terms of the inductive and conjugative or resonance effects, which it provides. Examples from substituents discussed in this book are given in table 7.2. The effects upon orientation and reactivity indicated are only the dominant ones, and one of our tasks is to examine in closer detail how descriptions of substituent effects of this kind meet the facts of nitration. In general, such descriptions find wide acceptance, the more so since they are now known to correspond to parallel descriptions in terms of molecular orbital theory ( 7.2.2, 7.2.3). Only in respect of the interpretation to be placed upon the inductive effect is there still serious disagreement. It will be seen that recent results of nitration studies have produced evidence on this point ( 9.1.1). 

A very good example is the conductance of a dianthra[a,c]naphtacene starphenelike molecule presented in Fig. 20, interacting with three metallic nano-pads. The EHMO-NESQC T(E) transmission spectrum per tunnel junction looks like a standard conjugated molecule T(E) with well-identified molecular orbitals and their resonances. For the Fig. 20 case all the T(E) are the same. One can note a small deviation after the LUMO resonance, due to a little asymmetry in the adsorption site between the three branches on the nano-pads [127]. A lot of asymmetric star-like three-molecular-branches system can be constructed, in particular in reference to chemical composition of the central node. This had been analyzed in detail [60]. But in this case, each molecule becomes a peculiar case. The next section presents one application of this central-node case to construct molecule OR and molecule XOR logic gates. 

Delocalization of charge in the conjugate base anion through resonance is a stabilizing factor and will be reflected by an increase in acidity. Drawing resonance structures allows us to rationalize that the negative charge is not permanently localized on a particular atom, but may be dispersed to other areas of the structure. We should appreciate that a better interpretation is that the electrons are contained in a molecular orbital that spans several atoms. 

Resonance-stabilized systems include car-boxylate groups, as in formate aliphatic hydrocarbons with conjugated double bonds, such as 1,3-butadiene and the systems known as aromatic ring systems. The best-known aromatic compound is benzene, which has six delocalized k electrons in its ring. Extended resonance systems with 10 or more 71 electrons absorb light within the visible spectrum and are therefore colored. This group includes the aliphatic carotenoids (see p.l32), for example, as well as the heme group, in which 18 k electrons occupy an extended molecular orbital (see p. 106). 

These simple molecular orbital pictures provide useful descriptions of the structures and spectroscopic properties of planar conjugated molecules such as benzene and naphthalene, and heterocychc species such as pyridine. Heats of combustion or hydrogenation reflect the resonance stabilization of the ground states of these systems. Spectroscopic properties in the visible and near-ultraviolet depend on the nature and distribution of low-lying excited electronic states. The success of the simple molecular orbital description in rationalizing these experimental data speaks for the importance of symmetry in determining the basic characteristics of the molecular energy levels. 

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