Polyatomic molecules molecular orbital approach

D.K.Hoffinann, R.Ruedenberg, J. G. Verkade Molecular Orbital Bonding Concepts in Polyatomic Molecules ANovel Pictorial 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. 

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. 

Notice the power of the molecular orbital approach. Every electron that enters a bonding molecular orbital stabilizes the molecule or polyatomic ion, and every electron that enters an antibonding molecular orbital destabilizes it. The emphasis on electron pairs has been removed. One electron in a bonding molecular orbital stabilizes half as much as two, so a bond order of one-half is nothing mysterious. 

The molecular orbital (MO) approach to the electronic structure of diatomic, and also polyatomic, molecules is not the only one which is used but it lends itself to a fairly qualitative description, which we require here. 

Molecular orbital bonding concepts in polyatomic molecules a novel pictorial approach. D. K. Hoffman, K. Ruedenberg and J. G. Verkade, Struct. Bonding (Berlin), 1977, 33, 57-96 (14). 

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. 

A key question about the use of any molecular theory or computer simulation is whether the intermolecular potential model is sufficiently accurate for the particular application of interest. For such simple fluids as argon or methane, we have accurate pair potentials with which we can calculate a wide variety of physical properties with good accuracy. For more complex polyatomic molecules, two approaches exist. The first is a full ab initio molecular orbital calculation based on a solution to the Schrddinger equation, and the second is the semiempirical method, in which a combination of approximate quantum mechanical results and experimental data (second virial coefficients, scattering, transport coefficients, solid properties, etc.) is used to arrive at an approximate and simple expression. 

There are three different schemes for building up the electronic states of diatomic molecules (a) from separated atoms, (b) from the united atom, and (c) from the molecular orbitals of the diatomic molecule itself. It is the correlation between the electronic states of the diatomic molecule as built up from the separated atoms and as determined from the molecular orbitals of the diatomic which is most valuable for any general consideration of reactions and excited states. The correlation of molecular states obtained by these two methods is not limited solely to diatomic molecules but also forms a valid approach for polyatomic molecular systems. The correlation of separated atoms with the hypothetical united atom has value for diatomics and has been applied to simple polyatomic molecules, especially those with a heavy atom or two and a number of hydrogen atoms. However, it is conceptually less appealing even for simple polyatomic molecules and completely inapplicable for complex polyatomic molecules. 

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. 

The existence of more than two nuclei in polyatomic molecules means that molecular orbitals are polycentric, extending, in principle, over the whole molecule. It is in this sense that molecular orbitals in polyatomic systems are said to be delocalized. Within the linear combination of atomic orbitals (l.c.a.o.) approach, valence m.o.s are approximated by linear combinations of the valence a.o.s of all the intervening atoms. Just as for diatomic molecules, this is an approximation because only a finite set of basis fimctions are being used. The eventual inclusion of virtual a.o.s of energy close to the valence orbital energies can help to improve the results. 

Molecular Orbital Bonding Concepts in Polyatomic Molecules a Novel Pictorial Approach... 

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. 

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