Frontier function

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... 

The Fukui function (the frontier function) was defined by Parr and Yang [144] as... 

The above equations provide a correspondence between this local parameter and the frontier orbital theory of chemical reactions [79] and thus justifies the nomenclature of Fukui (frontier) function. A large value off, f+, or f° at a particular site denotes the high probability of electrophilic, nucleophilic, or radical attack to take place at that site. 

As above, one can express the electronic density and the frontier function by the orbital partitioning, for example, for an electrophilic attack ... 

An immediate application with major implications for the frontier functions can be rendered in connection with the electrical charge transfer occurring in the molecular formation of chemical reactions. 

Further on, the charge transfer in the approximation of the frozen electronic core for both systems is considered, so that the difference of the frontier functions can be accordingly considered (Bartolotti, 1980 Robles Bartolotti, 1984 Parr, Zhou, 1993 Harbola, 1992) ... 

The analysis of these relations shows how much the charge transfer depends on the frontier functions. In this case, an integral of the Fukui functions with a large orbital overlapping, has the role to reduce the inhibitory effects induced by the chemical strengths of the two chemical systems and to promote the charges transfer. 

In terms of chemical reactivity analysis, as the initial value of the electronic potential dp is big the system s reactivity will be established with high values of the frontier functions, extending (3.99) to become... 

Another spin contribution can be identified in the frozen-core approximation, in order to express the frontier functions from the Principle CRSabove, as in next exposed. 

For these local functions a conservation of the HOMO or LUMO orbital type involved in the calculation of a given ionization case is noted, with the specification that in the situation (b) the difference rather than the summation of probabilities for the orbital frontier functions is involved. 

However, for the other set of frontier functions, one continues with specializations ... 

These expressions can be numerically implemented for a set of coefficients for the initial atomic orbitals in the system, as well as for other basis functions (e.g., of hydrogenic, Gaussian, or Slater type). An alternative method for computational implementation is to self-consistently solve the equations from the Hohenbeig-Kohn-Sham density functional theory, properly modified in order to include the extension of the spin characterization, wherefrom the molecular orbitals corresponding to the electronic distribution and of spin may directly result, hence, retaining only the HOMO and LUMO orbitals in the electronic frozen-core approximation with the help of which one can calculate and represent the contours of the frontier functions in any of the above (a) to (d) variants. 

You can use HyperChem to investigate the reactivity of molecules and their functional groups. One method is to use Frontier Molec-... 

It is important to realize that whenever qualitative or frontier molecular orbital theory is invoked, the description is within the orbital (Hartree-Fock or Density Functional) model for the electronic wave function. In other words, rationalizing a trend in computational results by qualitative MO theory is only valid if the effect is present at the HF or DFT level. If the majority of the variation is due to electron correlation, an explanation in terms of interacting orbitals is not appropriate. 

F3 see Siloxanes Flame resistance 38, 73 Flexible spacers 47, 68 Fluctuations in composition 164 Free-radical polymerization 54-57, 60 Frontier orbitals 196 Functional polymers 148, 155, 164 Functionalizations 155-157... 

It is probably true that many of the descriptions of physical and solid state reaction mechanisms now existing in the literature are only partially correct. It would appear that part of the frontier of knowledge for Chemistry of The Solid State wiU lie in measurement of physical and chemical properties of inorgcuiic compounds as a function of purity. 

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 ,... 

Chloro(2,4,6-tri-/-butylphenylimino)phosphine, Cl—P NAr (Ar = 2,4,6-But3C6H2), has been reacted with a variety of Ni° complexes, yielding cr-complexes of P-functionalized iminophos-phines.2508 The structure of [Ni(PEt3)2(Cl P =NAr)2] (Ar = 2,4,6-Bu 3C6H2 (1043)) has been obtained the complex is almost perfectly tetrahedral with the chloroiminophosphine //-bonded as a consequence of its carbene-like frontier orbitals.2509... 

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