Molecular orbital model molecules

Valence bond and molecular orbital theory both incorporate the wave description of an atom s electrons into this picture of H2 but m somewhat different ways Both assume that electron waves behave like more familiar waves such as sound and light waves One important property of waves is called interference m physics Constructive interference occurs when two waves combine so as to reinforce each other (m phase) destructive interference occurs when they oppose each other (out of phase) (Figure 2 2) Recall from Section 1 1 that electron waves m atoms are characterized by their wave function which is the same as an orbital For an electron m the most stable state of a hydrogen atom for example this state is defined by the Is wave function and is often called the Is orbital The valence bond model bases the connection between two atoms on the overlap between half filled orbifals of fhe fwo afoms The molecular orbital model assembles a sef of molecular orbifals by combining fhe afomic orbifals of all of fhe atoms m fhe molecule... 

Thus there are five bonding electrons giving a bond order of 2.5, consistent with the bond length of 115 pm, versus 121 pm for the four-electron bond in O2 and 110 pm for the six-electron bond in N2. For these and other related molecules, the double-quartet model is a convenient and useful alternative to the conventional molecular orbital model. Moreover, it shows that for a singly bonded terminal atom such as F or Cl there is a ring of six nonbonding electrons rather than three separate lone pairs. As we will see in Chapters 7 and 8, this conclusion is confirmed by the analysis of electron density distributions. 

A molecular orbital model (MO) treats all electrons belonging to a fixed number of solvent molecules plus an excess electron in the resultant field of the nuclei of the molecules as being in a fixed configuration. The nuclei belonging to a particular molecule normally keep the ground state structure of that molecule. The relative distances and orientations of these molecules are varied until energetic, and if possible configurational, stability is obtained. In some cases, molecular distortions have been considered. 

Chemical bonding can be described in terms of a molecular orbital model. The molecular orbital approach is based on the idea that, as electrons in atoms occupy atomic orbitals, electrons in molecules occupy molecular orbitals. Molecular orbitals have many of the same properties as atomic orbitals. They are populated by electrons, beginning with the orbital with the lowest energy and a molecular orbital is full when it contains two electrons of opposite spin. 

The valence bond model of covalent bonding is easy to visualize and leads to a satisfactory description for most molecules. It does, however, have some problems. Perhaps the most serious flaw in the valence bond model is that it sometimes leads to an incorrect electronic description. For this reason, another bonding description called molecular orbital (MO) theory is often used. The molecular orbital model is more complex than the valence bond model, particularly for larger molecules, but sometimes gives a more satisfactory accounting of chemical and physical properties. 

In many cases more refined molecular orbital models give a better agreement between theory and experiment. Self-consistent field- 80 81> or CNDO-82> calculations as well as other ab initio calculations 83>84) were performed and the results of several different approaches for phosphorous compounds were critically evaluated by M. Pelavin 77). For the nitrogen compounds two different linear relationships, one for cations and for neutral molecules, the other for anoins, were observed 82), a phenomenon which might be explained with a Madelung contribution. 

We start with some biographical notes on Erich Huckel, in the context of which we also mention the merits of Otto Schmidt, the inventor of the free-electron model. The basic assumptions behind the HMO (Huckel Molecular Orbital) model are discussed, and those aspects of this model are reviewed that make it still a powerful tool in Theoretical Chemistry. We ask whether HMO should be regarded as semiempirical or parameter-free. We present closed solutions for special classes of molecules, review the important concept of alternant hydrocarbons and point out how useful perturbation theory within the HMO model is. We then come to bond alternation and the question whether the pi or the sigma bonds are responsible for bond delocalization in benzene and related molecules. Mobius hydrocarbons and diamagnetic ring currents are other topics. We come to optimistic conclusions as to the further role of the HMO model, not as an approximation for the solution of the Schrodinger equation, but as a way towards the understanding of some aspects of the Chemical Bond. 

MOLECULAR ORBITAL MODEL FOR CYCLIC CONJUGATED MOLECULES... 

The solution of the H atom problem of Chapter 1 provides us with the concept of atomic orbitals. Its extension provides a model for the electronic structure of the heavier atoms which can be developed into an MO model for molecules. Molecular orbitals formed from linear combinations of the same AOs provide a serviceable conceptual model for the electronic structures of molecules. The same AOs provide an approach to the electronic structure of extended systems with periodic geometric structures. It is useful because it avoids the nightmare of 1023 MOs dreamed above. 

Another model often used to describe bonding is the molecular orbital model. To introduce the assumptions, methods, and results of this model, we will consider the simplest of all molecules, H2, which consists of two protons and two electrons. A very stable molecule, H2 is lower in energy than the separated hydrogen atoms by 432 kj/mol. 

Recent valence bond studies of multiple bonds in molecules with only s, /7-orbitals indicate that bent bonds are preferred to the usual <7 and tt bonds. This has potentially important implications for the description of multiple metal-metal bonds. However, the description of E, IT and A ion states in photoemission from a ground state of bent bonds is not so obvious as in the <7, tt, -molecular orbital model. We examine these issues in the present contribution. 

In the course of investigating multiple bonds in molecules and complexes by the valence bond approach, we have recently found that such multiple bonds are more accurately described as bent bonds rather than as a and tt bonds (7-5). In order to understand the potential implications of these results for multiple metal-metal bonds, it is important to brieffy review the basic assumptions of the valence bond model and compare them to those of the more familiar molecular orbital model of bonding. 

The molecular orbital model as a linear combination of atomic orbitals introduced in Chapter 4 was extended in Chapter 6 to diatomic molecules and in Chapter 7 to small polyatomic molecules where advantage was taken of symmetry considerations. At the end of Chapter 7, a brief outline was presented of how to proceed quantitatively to apply the theory to any molecule, based on the variational principle and the solution of a secular determinant. In Chapter 9, this basic procedure was applied to molecules whose geometries allow their classification as conjugated tt systems. We now proceed to three additional types of systems, briefly developing firm qualitative or semiquantitative conclusions, once more strongly related to geometric considerations. They are the recently discovered spheroidal carbon cluster molecule, Cgo (ref. 137), the octahedral complexes of transition metals, and the broad class of metals and semi-metals. 

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