Electrons in Conjugated Molecules

Butadiene, CH2=CH-CH=CH2, will be used to illustrate the way in which the particle-in-a-box wavefunctions can be applied to conjugated molecules, a term applied to hydrocarbon molecules with alternate single and double carbon-carbon bonds. To understand the nature of the bonding in such molecules it is necessary to anticipate the shapes of the atomic orbitals, a subject that will be discussed more fully in Chapter 6. 

An electron attached to an atom can have a variety of wavefunctions, and these are known as atomic orbitals. Spherically symmetric waveHinctiorrs are called s orbitals. There are also dunb-bel shaped orbitals aligned along the three Cartesian axes, and these are known as p . p and p orbitals. 

O bonded carbon framework (non-linearity of carbon chain ignored) 

A more sophisticated method of treating the ji electrons in conjugated molecules, known as the HOckel approximation, will be fully discussed in Chapter 8. 

Two electrons can occupy each state, with their spins paired. Since 

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Theoretical estimations and experimental investigations tirmly established (J ) that large electron delocalization is a perequisite for large values of the nonlinear optical coefficients and this can be met with the ir-electrons in conjugated molecules and polymers where also charge asymmetry can be adequately introduced in order to obtain non-centrosymmetric structures. Since the electronic density distribution of these systems seems to be easily modified by their interaction with the molecular vibrations we anticipate that these materials may possess large piezoelectric, pyroelectric and photoacoustic coefficients. 

Apply the particle-in-a-box model to electrons in onedimensional semiconductor quantum wells and to n electrons in conjugated molecules... 

In this section we consider a particle trapped in a one-dimensional potential well with infinitely high sides, as shown in Figure 2.1. Later in the chapter this model will be applied to electrons trapped in so called quantum wells and also to the delocalized n electrons in conjugated molecules such as butadiene. 

The meaning of the word aromaticity has evolved as understanding of the special properties of benzene and other aromatic molecules has deepened. Originally, aromaticity was associated with a special chemical reactivity. The aromatic hydrocarbons were considered to be those unsaturated systems that underwent substitution reactions in preference to addition. Later, the idea of special stability became more important. Benzene can be shown to be much lower in enthalpy than predicted by summation of the normal bond energies for the C=C, C—C, and C—H bonds in the Kekule representation of benzene. Aromaticity is now generally associated with this property of special stability of certain completely conjugated cyclic molecules. A major contribution to the stability of aromatic systems results from the delocalization of electrons in these molecules. 

Scheme 13 tt conjugations and numer of it electrons in inorganic molecules... 

Having been introduced to the concepts of operators, wavefunctions, the Hamiltonian and its Schrodinger equation, it is important to now consider several examples of the applications of these concepts. The examples treated below were chosen to provide the learner with valuable experience in solving the Schrodinger equation they were also chosen because the models they embody form the most elementary chemical models of electronic motions in conjugated molecules and in atoms, rotations of linear molecules, and vibrations of chemical bonds. 

In order to perform calculations on larger molecules in a reasonable amount of time, approximations are made, which may involve the neglect of certain terms, or the inclusion of experimentally determined parameters. The best known and simplest example of this level of approximation are Hiickel Molecular Orbital (HMO) calculations, which treat only pi-electrons, in conjugated hydrocarbons, with neglect of overlap (1). While obviously limited in use, HMO methods are still used in certain research applications. 

The mechanism of the hydrogen atom contribution to the >v electronic interaction of a molecule seems not to be uniform, but to depend upon the structure of the molecular system. One may suppose that the nature of such a hydrogen bond is due to the electron ability of the hydrogen atom (under certain conditions) to participate in the interaction with -electrons of neighbouring atoms and transmit this interaction throughout the conjugated bond system, which in its turn favours sharing the electrons in a molecule. 

In Eqs. (9-11), l means the total number of -electrons in the molecule, m is the total number of orbitals in conjugation, n is the number of... 

It may be said that the condition necessary for a molecule to be aromatic is a relatively high specific delocalization energy (DE divided by either the number of bonds over which the conjugated system extends or the number of electrons in conjugation) and that the sufficient condition is a relatively low reactivity (judged by the values of theoretical indices) under the conditions under which aromaticity is to be exhibited. Such a theoretical aromaticity (Ar) can be expressed formally as ... 

Both terms, however, are dependent on the total charge density of the atom. It is not surprising, therefore, that 13C shifts of atoms in conjugated molecules vary approximately linearly with the jr-electron density at the atoms (<513C= 160 Aq71). Of the available all-valence electron methods, chemical shifts have been calculated only by the CNDO approximation. 

Reactions of hydrated electrons with organic compounds, 7, 115 Reactivity indices in conjugated molecules, 4, 73 Refractivity, molecular, and polarizability, 3, 1... 

Molecules must be ionized easily in order to be electron donors. There exist two such cases Ji-electrons in conjugate electron systems (alkenes, alkynes and aromatic... 

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