Global softness

Moreover, Berkowitz and Parr [39] have shown that the static density response may be expressed in terms of the softness kernel s(f,r/), the global softness S and the Fukui functions /(r) as follows ... 

Condensed-to-atom softness values for nucleophilic and electrophilic attacks can easily be estimated by multiplying the respective FF values by global softness value. 

It can be shown that grand potential of all the atoms in A and B becomes minimum, when A and B have an approximately equal global softness. Extending the idea to the atomic level, when two molecules A and B approach to each other to form a new ... 

The regiochemistry of methyl radical attack (CH3) to a series of substituted ethylenes (Scheme 12.6) [33]. Generally, the radical attack occurs at the less substituted end of of the olefins. It has been found that while there is no correlation between the global softness (5) for radicals and the barrier heights for radical addition, the barrier tends to decrease with the increase in electronegativity of the radicals. 

Notice that from local softness, global softness, and hardness when chemical potential is given. The corresponding condensed-to-atom variants may be defined as... 

Global Softness and Local Softness (Side Chains) of Amino Acids Computed at MP2/6-311G(d,p) in Ref. [18]... 

Equation 24.104 can be used to compute ab initio the similarity and differences between the members of a molecular family. In the case of amino acids, for instance, [18], Sf is chosen as a constant fragment (the amino-carboxyl part) and S2 corresponds to the local softness of the side chain. In Table 24.1, we report the average value of local softness (Si) computed for each group of amino acids local softness only permits to clearly distinguish between the different types of amino acids which have all nearly the same global softness. Calculations of S and S2 for each of the twenty amino acids permits to prove the linear relationship (Equation 24.104) and deduces the values of Sf and <2°(1) [18]. 

It should be recalled that 17 stands for the rigid geometry measure of the electronic global hardness, the inverse of the system global softness S = (dN/d Q. 

It should also be realized that the generalized softness matrix of Equations 30.12 and 30.16 represents the compliant description of the electronic coordinate N coupled to the system geometric relaxations (see Section 30.3). Indeed, the relaxed geometry global softness of the geometrical representation,... 

The HSAB principle classifies the interaction between acids and bases in terms of global softness. Pearson proposed the global HSAB principle [1,2]. The HSAB principles classify the interaction between acids and bases in terms of global softness... 

The global softness, S, is defined as the inverse of the global hardness, tj ... 

Prediction of interaction between metal clusters with oxide surface The HSAB principle classifies the interaction between acids and bases in terms of global softness. In the last few years, the reactivity index methodology was well established and had found its application in a wide variety of systems. This study deals with the viability of the reactivity index to monitor metal cluster interaction with oxide. Pure gold cluster of a size between 2 and 12 was chosen to interact with clean alumina (100) surface. A scale was derived in terms of intra- and intermolecular interactions of gold cluster with alumina surface to rationalize the role of reactivity index in material designing [43]. 

Global Softness, Fukui Function, and Local Softness of the Interacting Molecules... 

Renato, C., Alzate-Morales, J. H., William, T., Santos Juan C., and Ca rdenas, C. 2007. Theoretical study on CDK2 inhibitors using a global softness obtained from the density of states. J. Phys. Chem. B 111(12) 3293-3297. 

Vela, A. and Gazquez, J. L. 1990. A relationship between the static dipole polarizability, the global softness, and the Fukui function. J. Am. Chem. Soc. 112 1490-92. 

Claiming global pole position for soft drinks consumption in 2003, with a total of 112 billion litres of soft drinks consumed, the United States dominates (Figure 2.7). The United States is some way ahead of the second placed soft drinks market, Mexico, with consumption of 40 billion litres. As previously mentioned, China, in third place in 2003, has witnessed soft drinks grow rapidly in importance in recent years. China is now on track to overtake Mexico and become the second largest soft drinks market. Fourth place in 2003 was claimed by Brazil. The global soft drinks top five was completed by the more mature and established market of Germany, which was overtaken by Brazil in 2003. 

Global Soft Drinks Report (2003) Market Definitions and Market Commentary> 1997—2002, Zenith International Ltd, Bath, United Kingdom, pp. 1-7. 

Hie 1970 cyclamate ban ended the use of saccharin/cyclamate blends in many soft drinks markets. The effect of this was that the low-calorie soft drinks market remained small and static owing to the poor taste quality of products available. Hie intr oduction in 1982-83 of aspartame in particular, and acesulfame K to a lesser extent, into the global soft drinks market dramatically improved the... 

In a study of the reaction of alkynes with hydrogen isocyanide the condensed Fukui function was combined with the overall or global softness to try to rationalize the regioselectivity of attack on the triple bond [153] ... 

Since electron population is a pure number and global softness has the units of reciprocal energy, local softness logically has these units too, but the practice is to simply state that all these terms are in atomic units . 

It can be noted that the local softness is obtained by multiplication of the Fukui function with the global softness the local softness can thus be considered as a weighted distribution of the global softness over the molecule. Due to this fact, the local softness should be used as a intermolecular reactivity index, whereas the Fukui function is an intramolecular reactivity index. The definition of local hardness is less trivial and remains a matter of current debate. 

This softness matrix can be used to generate the local (regional) and global softness quantities ... 

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