Polyatomic molecules delocalized bonding

According to molecular orbital theory, the delocalization of electrons in a polyatomic molecule spreads the bonding effects of electrons over the entire Energy molecule. 

The molecular orbital theory of polyatomic molecules follows the same principles as those outlined for diatomic molecules, but the molecular orbitals spread over all the atoms in the molecule. We say that the electrons that occupy these orbitals are delocalized over the atoms in the molecule. An electron pair in a bonding orbital helps to bind together the whole molecule, not just an individual pair of atoms. The energies of molecular orbitals in polyatomic molecules can be studied experimentally by using ultraviolet and visible spectroscopy (see Major Technique 2). 

The generalized valence bond (GVB) method was the earliest important generalization of the Coulson—Fischer idea to polyatomic molecules (13,14). The method uses OEOs that are free to delocalize over the whole molecule during orbital optimization. Despite its general formulation, the GVB method is usually used in its restricted form, referred to as GVB SOPP, which introduces two simplifications. The first one is the perfect-pairing (PP) approximation, in which only one VB structure is generated in the calculation. The wave function may then be expressed in the simple form of Equation 9.1, as a product of so-called geminal two-electron functions ... 

A severe inconvenience of describing each bond of a polyatomic molecule by one covalent and two ionic components is that the number of VB structures grows exponentially with the size of the molecule. Coulson and Fischer [17] proposed a very elegant way to incorporate left-right correlation into a single and formally covalent VB structure of the HL type. To this end they used deformed or rather slightly delocalized orbitals as exemplified in eq 6 for H2. 

The delocalized picture of m.o.s for polyatomic molecules requires some adaptation of the distinction between a and tt m.o.s, particularly for nonlinear molecules. If tt m.o.s continue to be defined as linear combinations of p orbitals having parallel axes, a m.o.s are to be regarded as the remaining m.o.s, even though, in general, they no longer have internuclear lines as axes of cylindrical symmetry. In Chapter 8, we will see how to reconcile delocalized m.o.s with the classical structural formulae involving bonds between adjacent atoms. 

We have seen so far that MOs resulting from the LCAO approximation are delocalized among the various nuclei in the polyatomic molecule even for the so-called saturated a bonds. The effect of delocalization is even more important when looking to the n electron systems of conjugated and aromatic hydrocarbons, the systems for which the theory was originally developed by Hiickel (1930, 1931, 1932). In the following, we shall consider four typical systems with N n electrons, two linear hydrocarbon chains, the allyl radical (N = 3) and the butadiene molecule (N = 4), and two closed hydrocarbon chains (rings), cyclobutadiene (N = 4) and the benzene molecule (N = 6). The case of the ethylene molecule, considered as a two n electron system, will however be considered first since it is the reference basis for the n bond in the theory. 

The contents of Part 1 is based on such premises. Using mostly 2x2 Hiickel secular equations, Chapter 2 introduces a model of bonding in homonuclear and heteronuclear diatomics, multiple and delocalized bonds in hydrocarbons, and the stereochemistry of chemical bonds in polyatomic molecules in a word, a model of the strong first-order interactions originating in the chemical bond. Hybridization effects and their importance in determining shape and charge distribution in first-row hydrides (CH4, HF, H20 and NH3) are examined in some detail in Section 2.7. 

To our knowledge, apart from a brief and elementary outline of a new approach developed by the present authors (5), no simple systematic didactic method for accomplishing the aforementioned goals has been reported (particularly for polyatomic molecules). While excellent introductory descriptions of bonding concepts exist (6,7), no attempts seem to have been made to find a pictorial substitute for a substantial portion of group theory as applied to molecular orbitals or to elaborate in detail the equivalence of the localized and delocalized bonding views on an elementary level. Our approach has been developed and tested in a freshman chemistry course for majors at Iowa State University for a number of years. In the present paper we give and justify a more elaborate discussion of this pictorial method which leads to delocalized and localized MO s for a wide variety of polyatomic molecules. The key concept is that delocalized and localized MO s can be deduced from an appropriate extension of the characteristics of AO s. More specifically, the symmetry and directional characteristics of MO s are obtained from the symmetry and directional characteristics of AO s. 

The success of the preceding scheme for diatomic molecules I7,i8,i , 20,21) ied Hund 22> and Mulliken 23> to apply the same theory to polyatomic molecules. In the beginning, there seemed to be no direct relation between molecular orbitals (MO s) and the bonds in a chemical formula, because MO s normally extend over the whole molecule and are not restricted to the region between two atoms. The difficulty was overcome by using equivalent localized MO s instead of the delocalized ones 24>25>. The mathematical definition of equivalent MO s was given only in 1949 by Lennard-Jones and his coworkers 26.27), but the concept of localization... 

In triangular H3 each hydrogen atom furnishes one AO and 2/3 of an electron, the number of neighbors being two for any hydrogen so, the simplest delocalized bond is a a bond. Actually, a bonds in polyatomic molecules are only localized if they involve e.g. spn hybrids ( = 1,2,3), i.e. if the AO basis functions can be transformed 35,36,37) jn such a way that any of the resulting hybrid AO s can overlap in only one direction. 

Localized and Alternative bonding descriptions are often possible in polyatomic molecules, involving delocalized either localized (two center) or delocalized (three or more center) molecular orbitals. The orbitals overall electron distributions predicted may be the same in both models. 

Bonding in many polyatomic molecules, such as ozone or benzene, can often be best described in toms of delocalized molecular orbitals. 

With the aid of computers, molecular orbital theory can be applied to polyatomic molecules and ions, yielding results that correlate very well with experimental measurements. These applications are beyond the scope of this text. However, the delocalization of electrons over an entire molecule is an important contribution of molecular orbital theory to our basic understanding of chemical bonding. For example, consider the Lewis structure and valence bond diagram of ozone ... 

For diamagnetic polyatomic molecules, it is easy to write down standard Lewis stractmes that have electron-pair bonds and lone-pairs of electrons. It is then also easy to generate increased-valence structures from them. To do this, we must delocalize one or more lone-pair electrons into either two-centre bonding oibitals or two-centre antibonding orbitals, both types of orbitals being vacant in the standard Lewis structures. In this chapter, we shall describe these delocalizations into bonding orbitals. 

Generalized valence bond perfect pairing (GVB/PP) and spin-coupled valence bond (SCVB) calculations for tri- and polyatomic molecules use multicentre, delocalized orbitals (i.e. 3-centre or many-centre orbitals) to accommodate the active space electrons. To quote Ref 27 The GVB/PP wavefimctions are antisymmetrized products of paired orbitals and represent a single valence bond structure.. .. The SC method is based on a single configuration in which each electron is described by a distinct orbital. The complete spin state is utilized. For example, a 4-electron 3-centre SC wavefunction involves four non-orthogonal 3-centre or-... 

It is generally best to use the bonding theory that most easily describes the bonding in a particular molecule or polyatomic ion. In species that can be represented by two or more resonance structures, the pi bonds are delocalized, meaning that they are spread out over the molecule and not constrained to just two atoms. Localized bonds are those constrained to two atoms. Many species are best described using a combination of valence bond theory and molecular orbital theory. 

None of these Lewis structures represents the SO3 molecule accurately. The bonds in SO3 are actually equivalent—equal in length and strength, which we would not expect if two were single bonds and one were a double bond. Each individual resonance structure implies that electron pairs are localized in specific bonds or on specific atoms. The concept of resonance allows us to envision certain electron pairs as delocalized over several atoms [ Ml Section 9.7]. Delocalization of electron pairs imparts additional stability to a molecule (or polyatomic ion), and a species that can be represented by two or more resonance structures is said to be resonance stabilized. 

The use of multicenter bond indices as a measure of aromaticity was initially proposed by Giambiagi et al. [95]. These indices measure the extension of the electron delocalization to all centers of the ring which is expected to be large for aromatic systems. Bultinck et al. [96] employed the multicenter bond indices computed from Mulliken-type calculation as a measure of local aromaticity in polyatomic hydrocarbon. Thus, the n-center delocalization index, (A ) can be compnted in the framework of quantum theory of atoms in molecules (QTAIM). 

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