Fukui theorem

The conclusion we have arrived at is what may be called a generalized Fukui theorem, which states that the reaction path near the minimum goes along the lowest eigenfrequency direction (see Tachibana and Fukui [1979]). Further consideration of the Fukui theorem is addressed in Section 8.3. Here we note only that this theorem is not valid when the instanton path is constrained by the symmetry of potential to lie totally along the direction of one of initial state modes. 

Note that in the present case, neither the Fukui theorem [Fukui, 1970] mentioned in Section 8.4 nor the similar statement concerning the initial direction of the instanton path (see Section 4.1) are valid. Both state that the reaction coordinate (IRC in the case of Fukui theorem or instanton) near the minimum of the surface is directed along the coordinate of the vibration with the lowest frequency. That would mean for our case that... 

These concepts play an important role in the Hard and Soft Acid and Base (HSAB) principle, which states that hard acids prefer to react with hard bases, and vice versa. By means of Koopmann s theorem (Section 3.4) the hardness is related to the HOMO-LUMO energy difference, i.e. a small gap indicates a soft molecule. From second-order perturbation theory it also follows that a small gap between occupied and unoccupied orbitals will give a large contribution to the polarizability (Section 10.6), i.e. softness is a measure of how easily the electron density can be distorted by external fields, for example those generated by another molecule. In terms of the perturbation equation (15.1), a hard-hard interaction is primarily charge controlled, while a soft-soft interaction is orbital controlled. Both FMO and HSAB theories may be considered as being limiting cases of chemical reactivity described by the Fukui ftinction. 

In a second approach of the reactivity, one fragment A is represented by its electronic density and the other, B, by some reactivity probe of A. In the usual approach, which permits to define chemical hardness, softness, Fukui functions, etc., the probe is simply a change in the total number of electrons of A. [5,6,8] More realistic probes are an electrostatic potential cf>, a pseudopotential (as in Equation 24.102), or an electric field E. For instance, let us consider a homogeneous electric field E applied to a fragment A. How does this field modify the intermolecular forces in A Again, the Hellman-Feynman theorem [22,23] tells us that for an instantaneous nuclear configuration, the force on each atom changes by... 

This issue was addressed in [2] for electron-transfer reactivities. The nuclear Fukui functions and softnesses defined there are valid for gapless systems. The analysis begins with nuclear forces specified through the Feynman-Hellmann theorem [48],... 

A local version of the electrophilicity can be obtained by multiplying to with the relevant Fukui function. These concepts play an important role in the Hard and Soft Acid and Base (HSAB) principle, which states that hard acids prefer to react with hard bases, and vice versa." By means of Koopmans theorem (Section 3.4) the hardness is... 

The experimental electrofugality in the 5 1 reactions of substituted benzhydryl phenyl sulflnates is directly related to the theoretical electrofugality calculated using Koopman s theorem and nucleophilic Fukui functions.It is suggested that the... 

This implies that the nuclear Fukui function can also be interpreted in terms of the contributions to binding (//r) < 0) and antibinding (/ (r) < 0) regions in the moleeule within the framework of Berlin s theorem. Illustrative examples and applications of this function have been performed. Also... 

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