Molecular orbital theory, definition

As molecular orbital theory evolved over the years, several variations of Langmuir s definition of isosterism were expressed by others these are discussed in more recent publications [68, 69]. Burger s definition [68] of isosterism encompasses the aspects of the previous definitions and states that isosteres are chemical substances, atoms, or substituents that possess near equal or similar molecular shape and volume, approximately the same distribution of electrons, and which exhibit similar physicochemical properties. A few examples of isosteric atoms and substituents are provided in Figure 4.6. Many more examples are available in the literature [69-72], including metal isosteres [73]. 

Earlier in this chapter, you learned the definition of bond order in the valence bond theory. In molecular orbital theory, the bond order is defined as one-half the difference between the number of electrons in bonding orbitals and the number of electrons in antibonding orbitals. Mathematically, this can be expressed as... 

To go into this idea quantitatively, we need definitions of hardness and softness, and a rank order for acids and bases on a scale of hardness. This has been done in two ways one based on molecular orbital theory, and the other on density functional theory. 

Molecular orbital theory has played the central role in the definition and understanding of problems of electronic structure. The charge density plays the corresponding role in the definition and understanding of the concepts associated with molecular structure. The previous chapters have shown that atoms, bonds, and structure are indeed consequences of the dominant topological property exhibited by a molecular charge distribution. What remains to be done is to demonstrate that the topological atom and its properties have a basis in quantum mechanics. 

The first point to be made concerning acids and bases is that so-called acid-base theories are in reality definitions of what an acid or base is they are not theories in the sense of valence bond theory or molecular orbital theory. In a very real sense, we can make an acid be anything we wish the differences between the various acid-base concepts are not concerned with which is right but which is most convenient to use in a particular situation. All of the current definitions of acid-base behavior are compatible with each other. In fact, one of the objects in the following presentation of many different definitions is to emphasize their basic parallelism and hence to direct the students toward a cosmopolitan attitude toward acids and bases which will stand them in good stead in dealing with various chemical situations, whether they be in aqueous solutions of ions, organic reactions, nonaqueotis titrations, or other situations. 

Orbitals can also be defined for many-electron systems, and the molecular orbital theory mentioned in the previous section is indeed based on this possibility. In order to assess the significance and limitations of the molecular orbital scheme and the meaning of a and n orbitals, we have to discuss the definition and the determination of orbitals in a many-electron system at some length. 

Hard and soft acid and base theory gives access to an early part of the slope in a reaction profile like that in Fig. 3.3, just as perturbation molecular orbital theory does. Using the definitions of absolute electronegativity and absolute hardness derived in Equations 3.5 and 3.6, the (fractional) number of electrons AN transferred is given by Equation 3.14. 

By definition, the Fukui function represents the change in electron density due to addition or removal of electrons from the system. Recalling results from the frontier molecular orbital theory, where the magnitude of the highest-occupied and lowest-unoccupied molecular orbitals are used to discern the propensity of a molecular site to attack by electron acceptors and electron donors, respectively, we deduce that the... 

Molecular orbital theory starts with the definition of a set of molecular spin orbitals (SOs) ... 

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