Polyatomic molecules valence bond approach

So far we have discussed chemical bonding only in terms of electron pairs. However, the properties of a molecule cannot always be explained accurately by a single structure. A case in point is the O3 molecule, discussed in Section 9.8. There we overcame the dilemma by introducing the concept of resonance. In this section we will tackle the problem in another way—by applying the molecular orbital approach. As in Section 9.8, we will use the benzene molecule and the carbonate ion as examples. Note that in discussing the bonding of polyatomic molecules or ions, it is convenient to determine fust the hybridization state of the atoms present (a valence bond approach), followed by the formation of appropriate molecular orbitals. 

The embedded diatomics in molecules (EDIM) method is an extension of the embedded atom method (EAM) [146] to molecules using the diatomics in molecules (DIM) approach. The DIM method is based on a valence bond approach to electronically structure calculations. It constructs the polyatomic potential surfaces from the atom and diatom fragment ground and electronic excited states. Since these states are often well known either from experiment or calculations, the input to the scheme is often readily available. By construction, the potential obtained by the theory approaches the correct limit when the molecule is split into its various fragments [141]. 

Hiickel s application of this approach to the aromatic compounds gave new confidence to those physicists and chemists following up on the Hund-Mulliken analysis. It was regarded by many people as the simplest of the quantum mechanical valence-bond methods based on the Schrodinger equation. 66 Hiickel s was part of a series of applications of the method of linear combination of atom wave functions (atomic orbitals), a method that Felix Bloch had extended from H2+ to metals in 1928 and that Fowler s student, Lennard-Jones, had further developed for diatomic molecules in 1929. Now Hiickel extended the method to polyatomic molecules.67... 

Two basic methods, the valence-bond (VB) and the molecular orbital (MO) method, have been developed for the determination of approximate state functions. In practice, the MO method constitutes the simplest and most efficient approach for the treatment of polyatomic molecules. And, in fact, all the calculations for the systems under consideration have been carried out within the framework of the MO theory. 

F 2p character than F 2s character and is also bonding with respect to the FI orbital. This set of orbitals (2cr, 3a) illustrates a central feature of the MO approach. Whereas a simple Lewis structure or valence picture would draw a localized electron pair interaction between two orbitals, the MO picture attributes some bonding character to two separate molecular orbitals. This simple MO diagram illustrates the difficulty of determining a meaningful definition for bond order in a polyatomic molecule. No single MO completely represents the bonding between two atoms. 

This function gives as much weight to the ionic forms as to the covalent forms. So the molecular orbital approach greatly overvalues the ionic contributions. At these crude levels of proximation, the valence bond method gives dissociation energies closer to the experimental values. However, more sophisticated versions of the molecular orbital approach are the methods of choice for obtaining quantitative results on both diatomic and polyatomic molecules. See Sections 11.6-11.8. 

The generalized valence bond (GVB) approach was one of the first methods where semilocalized orbitals, as developed by Coulson and Fischer, have been employed to polyatomic molecules [66-72]. GVB is typically applied within a restricted formulation introducing two simplifications for the construction of the VB structures (for a simple diatomic molecule AB, there are two VB structures the so-called ionic structures, and A B+, and a covalent structure, A-—B). In... 

The approach to the question of binding from the theoretical side is made more difficult by the fact that, excepting for rectilinear molecules, there no longer exists an axis of rotational symmetry, so that the introduction of quantum numbers with a simple physical significance for the molecule as a whole or for the individual electrons cannot be accomplished in so satisfactory a manner as for diatomic molecules. The field of chemical evidence to be explained, on the other hand, is much wider since for polyatomic molecules we not only have to accoimt for the existence of compounds of a certain chemical composition and the non-existence of others, but also for the occurrence of isomers the directed nature of the valences and the phenomena of free or partially free rotation of radicals around a chemical bond. It is therefore not surprising that the present stage of theory and experiment for polyatomic molecules is in many ways more summary and qualitative than for diatomic molecules. 

The accurate representation of multidimensional potential energy surfaces is a formidable problem. A common approach is to employ an expression that incorporates as much physical insight as possible in the functional form and which has a number of parameters that are adjusted to empirical data. Examples of this approach are found in applications of the London-Eyring-Polyani-Sato (LEPS), valence-bond (VB), diatomics-in-molecules (DIM), and many-body expansion methods to polyatomic systems. 

An advantage of VSEPR is its foundation upon Lewis electron-pair bond theory. No mention need be made of orbitals and overlap. If you can write down a Lewis structure for the molecule or polyatomic ion in question, with all valence electrons accounted for in bonding or nonbonding pairs, there should be no difficulty in arriving at the VSEPR prediction of its likely shape. Even when there may be some ambiguity as to the most appropriate Lewis structure, the VSEPR approach leads to the same result. For example, the molecule HIO, could be rendered, in terms of Lewis theory as ... 

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