Orbital similarities between molecules

The traditional view of molecular bonds is that they are due to an increased probability of finding electrons between two nuclei, as compared to a sum of the contributions of the pure atomic orbitals. The canonical MOs are delocalized over the whole molecule and do not readily reflect this. There is, furthermore, little similarity between MOs for systems which by chemical measures should be similar, such as a series of alkanes. The canonical MOs therefore do not reflect the concept of functional groups. 

As Fig. 6.9 illustrates, the orbitals are very close in a metal and form an almost continuous band of levels. In fact, it is impossible to detect the separation between levels. The bands behavior is in many respects similarly to the orbitals of the molecule as shown in Fig. 6.8 If there is little overlap between the electrons, the interaction is weak and the band is narrow. Such is the case for d orbitals (Fig. 6.10), which have pronounced shapes and orientations that are largely retained in the metal. Hence the over-... 

The close similarity between the photophysics of Ni(PP) and Ni(OEP) in coordinating solvents observed in this study argues strongly that the photodissociation (or photoassociation) of ligands is predicated upon metal-based excited states and that the decay pathways from porphyrin to metal d-orbital states are similar for the two molecules. Thus, our results corroborate the proposed photocycle of Molten and co-workers (3.4) and suggest that the initial excitation of the porphyrin ir-system rapidly (<10 s of psecs) decays to a d-d bottleneck excited state where ligation changes may occur. 

We show again the traditional five covalent Rumer diagrams for six electrons and six orbitals in a singlet coupling and emphasize that the similarity between the ring of orbitals and the shape of the molecule considerably simplifies the understanding of the S5mimetry for benzene. 

Superexchange is another mechanism of electron transfer over relatively large distances in which the solvent or matrix acts as a bridge between the donor molecule D and the acceptor molecule A. It differs from electron hopping in that the electron is at no time actually localized on a molecule of the medium there is an interaction between the orbitals of the molecules A, B and D which form a sort of very loose supermolecule over which the electron is delocalized (Figure 4.10). This mechanism seems plausible when the relevant orbitals of A, B and D are rather close in energy. This is similar to the requirement for the interaction of atomic orbitals to form a molecule. 

The Principle of Hard and Soft Acids and Bases states that hard acids form more stable complexes with hard bases and soft bases form more stable complexes with soft acids. In orbital terms hard molecules have a large gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), and soft molecules have a small HOMO-LUMO gap. In recent years it has been possible to correlate the hardness with the electronic properties of the atoms involved. Thus, if the enthalpy of ionisation (I) and the electron affinity (A) are known the so-called absolute hardness (t ) and absolute electronegativity (%) can be found from r = (I - A) / 2 and % = (I + A) / 2. For example, the first and second ionisation enthalpies of sodium are 5.14 and 47.29 eV. Thus for Na+, I = + 47.29 and A = + 5.14, so r = (47.29 - 5.14) / 2 = 21.1. Similarly for silver the first and second ionisation enthalpies are 7.58 and 21.49eV, so for Ag+ we have, n = (21.49 - 7.58) 12 = 6.9. 

Most chemists still tend to think about the structure and reactivity of atomic and molecular species in qualitative terms that are related to electron pairs and to unpaired electrons. Concepts utilizing these terms such as, for example, the Lewis theory of valence, have had and still have a considerable impact on many areas of chemistry. They are particularly useful when it is necessary to highlight the qualitative similarities between the structure and reactivity of molecules containing identical functional groups, or within a homologous series. Many organic chemistry textbooks continue to use full and half-arrows to indicate the supposed movement of electron pairs or single electrons in the description of reaction mechanisms. Such concepts are closely related to classical valence-bond (VB) theory which, however, is unable to compete with advanced molecular orbital (MO) approaches in the accurate calculation of the quantitative features of the potential surface associated with a chemical reaction. 

Recent mechanistic discussions of unimolecular decompositions of organic ions have invoked ion—molecule complexes as reaction intermediates [102, 105, 361, 634]. The complexes are proposed to be bound by long-range ion—dipole forces and to be sufficiently long-lived to allow hydrogen rearrangements to occur. The question of lifetime aside, there is more than a close similarity between the proposed ion—dipole intermediate and the assumed loose or orbiting transition state of phase space theory. 

The primary difference between covalent and ionic bonding is that with covalent bonding, we must invoke quantum mechanics. In molecular orbital (MO) theory, molecules are most stable when the bonding MOs or, at most, bonding plus nonbonding MOs, are each filled with two electrons (of opposite spin) and all the antibonding MOs are empty. This forms the quantum mechanical basis of the octet rule for compounds of the p-block elements and the 18-electron rule for d-block elements. Similarly, in the Heider-London (valence bond) treatment... 

In the latter way of looking at the build-up of molecules, the successive addition of electrons to a positively charged system is reminiscent of the manner in which the atoms of the Periodic Table were considered in Chapter 1. Here again there are certain configurations permitted the electron clouds, and these cloud shapes (or probability density functions) can be described using quantum numbers. Such probability density descriptions are called molecular orbitals in analogy to the much simpler atomic orbitals. Although the initial setup and subsequent mathematical treatment for molecules are much more complicated than for atoms, there arise certain similarities between the two types of orbitals. 

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