Frontier orbitals defined

You can use the information obtained from semi-empirical calculations to investigate many thermodynamic and kinetic aspects of chemical processes. Energies and geometries of molecules have clear relation ships to chemical ph en om ena. 0ther quan tities, like atomic charges and Frontier Orbitals, are less defined but provide useful qualitative results. 

Goddart, J. D., Orlova, G., 1999, Density Functional Theory with Fractionally Occupied Frontier Orbitals and the Instabilities of the Kohn-Sham Solutions for Defining Diradical Transition States Ring-Opening Reactions ,... 

Chemical bonds are defined by their frontier orbitals. That is, by the highest molecular orbital that is occupied by electrons (HOMO), and the lowest unoccupied molecular orbital (LUMO). These are analogous with the top of the valence band and the bottom of the conduction band in electron band theory. However, since kinks are localized and non-periodic, band theory is not appropriate for this discussion. 

Based on the orbital approximations, it is clear that/(r) is the DFT analog of the frontier orbital regioselectivity for nucleophilic (f (r)) and electrophilic (/ (r)) attack. It is then reasonable to define a reactivity indicator for radical attack by analogy to the corresponding orbital indicator,... 

The Fukui functions generalize the concept of frontier orbitals by including the relaxation of the orbital upon the net addition or removal of one electron. Because the number of electrons of an isolated system can only change by discrete integer number, the derivative in Equation 24.37 is not properly defined. Only the finite difference approximation of Equation 24.37 allows to define these Fukui functions (noted here by capital letters) F1 (r)... 

The preferred orientation for electrophiles is out of the plane defined by the Y-S-Z bonds, and about 20° from the normal (n) to the plane [50], whereas nucleophiles tend to lie in the plane, and cluster close to the line defined by the extension of the Y-S (or Z-S) bond. Similar interactions have been observed for selenium (Ramasubbu and Parthasarathy, 1984). The conclusion, as before, is that these interactions are frontier-orbital controlled, with the HOMO being a sulphur lone pair, and the LUMO an antibonding o- C-y(Z) orbital. 

Mulliken s model is entirely compatible with the descriptions given previously in this Section, since charge shifts that result from polarization are already taken into account in forming the cr-complex by subsequent changes in hybridization. Fukui s model, upon which the definition of the superdelocalizability is based, resembles Mulliken s only in the use of a pseudo-TT orbital , and the formulation of the hyperconjugation problem is quite different, since )3 is taken by Fukui to be small, so that 8f can be defined by perturbation formulae. In particular, the bonding of the pseudo-TT orbital in Fukui s model primarily involves the least bound, or frontier orbitals, whereas in Mulliken s model the most bound MO is involved. 

These reactions are characterized by the phenomenon that the frontier orbitals of the reactants maintain a defined stereochemical orientation throughout the w hole reaction. Most noteworthy in this respect, is the principle of orbital symmetry conservation ( Woodward-Hoffmann rules la), but the phenomenon is much more general, as shown by the following examples of Self-Immolative Stereoconversion or Chirality Transfer . This term describes processes by which a stereocenter in the starting material is sacrificed to generate a stereocenter in the product in an unambiguous fashion. This is, of course, the case in classical SN2-displacements. 

The Fukui function or frontier function was introduced by Parr and Yang in 1984 [144], They generously gave it a name associated with the pioneer of frontier molecular orbital theory, who emphasized the roles of the HOMO and LUMO in chemical reactions. In a reaction a change in electron number clearly involves removing electrons from or adding electrons to the HOMO or LUMO, respectively, i.e. the frontier orbitals whose importance was emphasized by Fukui.4 The mathematical expression (below) of the function defines it as the sensitivity of the electron density at various points in a species to a change in the number of electrons in the species. If electrons are added or removed, how much is the electron density... 

To use frontier orbital theory efficiently, we have to understand its approximations, which define its limitations. This is not really complicated and requires more common sense than mathematical skills. So, don t worry about words like operator or about maths that we do not need to use.1 Just to prove how little maths is in fact required, let us re-examine the previous section point by point. 

Parr and collaborators [8-12] showed how Fukui s frontier-orbital concept could be grounded in a rigorous many-electron theory, density-functional theory (DFT) [8,16-18], They used the ensemble formulation of DFT to introduce the expectation value Jf of the total electron number as a continuous variable. They then defined the Fukui functions... 

Equations (63) and (64) resolve issue four. Nuclear reactivity indices have been defined and clearly display the drivers of the nuclear response to transfers of electrons into and out of the system. The rescaled frontier-orbital density /5F(r) drives that response through the screened force, Eq. (65), when Jf is changed directly, Eq. (63), and the local DOS g(r, fi) drives it when fi is changed, Eq. (64). 

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