Hardness and electrophilicity

Describes various global reactivity descriptors, such as electronegativity, hardness, and electrophilicity... 

A similar situation happens with the local electrophilicity. Then, it is necessary to derive new expressions, and conditions that the correct local counterparts of the global softness, hardness, and electrophilicity must fulfill. This work can also be considered as a possible alternative to the traditional expressions of local softness and electrophilicity, see Torrent-Sucarrat et al. (2008, 2010) Gal et al. (2011). 

Conceptual density functional theory has been quite successful in providing quantitative definitions for popular qualitative chemical concepts like electronegativity , hardness and electrophilicity . It has also been found to be useful in providing firm theoretical bases for the associated electronic structure principles. Various global and local reactivity descriptors " have played an important role in analyzing bonding, reactivity, stability, interactions and aromaticity in a variety of many-electron systems as well as a host of their physico-chemical properties. 

Robert G. Parr and his students have developed the field of conceptual DFT which is a theory of chemical reactivity within a broad density based quantum mechanical framework. Strong theoretical foundations and quantitative definitions of various popular qualitative chemical concepts like electronegativity hardness and electrophilicity been provided within conceptual DFT in addition to plausible rationales for the associated electronic structure principles. 

The regioisomer that have the higher value of T] and the lower values of ZPE, a and to, should correspond to the major product. The calculated hardness and electrophilicity power correctly predict the regioisomers I.a-I.c as the main adducts of the DA reactions. However, the calculated total energies and polarizabilities show a random behaviour. Therefore, neither of these two parameters can predict the predominant regioisomer of the DA reactions in a correct way. 

Reactivity and orientation in electrophilic aromatic substitution can also be related to the concept of hardness (see Section 1.2.3). Ionization potential is a major factor in determining hardness and is also intimately related to the process of (x-complex formation when an electrophile interacts with the n HOMO to form a new a bond. In MO terms, hardness is related to the gap between the LUMO and HOMO, t] = (sujmo %omo)/2- Thus, the harder a reactant ring system is, the more difficult it is for an electrophile to complete rr-bond formation. 

In a, P-unsaturated carbonyl compounds and related electron-deficient alkenes and alkynes, there exist two electrophilic sites and both are prone to be attacked by nucleophiles. However, the conjugated site is considerably softer compared with the unconjugated site, based on the Frontier Molecular Orbital analysis.27 Consequently, softer nucleophiles predominantly react with a, (i-unsaturated carbonyl compounds through conjugate addition (or Michael addition). Water is a hard solvent. This property of water has two significant implications for conjugate addition reactions (1) Such reactions can tolerate water since the nucleophiles and the electrophiles are softer whereas water is hard and (2) water will not compete with nucleophiles significantly in such... 

Bowman has surveyed the reactions of cx-substituted aliphatic nitro compounds with nucleophiles, which undergo either S l substitution or polar reaction (Scheme 5.16).118 The reactions between a wide variety of nucleophiles and BrCH2N02 are shown in Scheme 5.17.119a b All the thiolates, PhS02 and I attack Br to liberate the anion of nitromethane. The hard nucleophiles, MeO , OH, and BH4 attack the hard H+ electrophilic center. Phosphorous nucleophiles attackthe oxygen electrophilic center, and only Me2S attacks the carbon electrophilic center. 

An unusual observation was noted when ethanolic solutions of 2-alkyl-4(5)-aminoimidazoles (25 R = alkyl) were allowed to react with diethyl ethoxymethylenemalonate (62 R = H) [92JCS(P1)2789]. In addition to anticipated products (70), which were obtained in low yield ( 10%), the diimidazole derivatives (33 R = alkyl) were formed in ca.30% yield. The mechanism of formation of the diimidazole products (33) has been interpreted in terms of a reaction between the aminoimidazole (25) and its nitroimidazole precursor (27) during the reduction process. In particular, a soft-soft interaction between the highest occupied molecular orbital (HOMO) of the aminoimidazole (25) and the lowest unoccupied molecular orbital (LUMO) of the nitroimidazole (27) is favorable and probably leads to an intermediate, which on tautomerism, elimination of water, and further reduction, gives the observed products (33). The reactions of amino-imidazoles with hard and soft electrophiles is further discussed in Section VI,C. 

The most common method for the preparation of 1,2,3-benzothiadiazoles is the diazotization of 2-aminobenzenethiol. This method was discussed and exemplified in CHEC-II(1996). The method has been extended in recent years to include heterocyclic derivatives. The 2-aminothiophene 79 can be converted into the thienothiadiazole 82 on treatment with sodium nitrite in HC1 but in poor yield (16%). The bis(BOC)-protected derivative 80 or the mono(BOC)-protected derivative 81 when reacted under similar conditions afford product 82 in much higher yields (BOC = /-butoxycarbonyl Scheme 9). The increase in yield is explained in terms of hard and soft electrophilic character. The intermediate in the BOC-protected examples has a soft character allowing attack by sulfur to proceed more easily <1999JHC761>. 

Priebe and coworkers [107,178] have attempted to rationalize the product distribution in terms of Pearson s theory of hard and soft acids and bases (HSAB) [179], concluding as a broad generalization that soft bases (S-, N- and C-nucleophiles) form bonds at the softer C-3 electrophilic center, whereas hard bases (O-based nucleophiles) react preferentially at the harder C-l center to give glycosides. They acknowledge that other factors may overrule this interpretation, such as when C-nucleophiles give kinetic C-l-alkylated products whose formation is not reversible. 

The use of a dual descriptor defined in terms of the variation of hardness with respect to the external potential, and it is written as the difference between nucleophilic and electrophilic Fukui functions, Equation 12.21, can also be used as an alternative to rationalize the site reactivity [32] ... 

To the extent that the N+ correlation is successful it means that the pattern of nucleophilic reactivity is not influenced by the nature of the electrophilic center at which substitution takes place. On the other hand, according to the concepts of the theory of hard and soft acids and bases (HSAB) as applied to nucleophilic substitution reactions (Pearson and Songstad, 1967) one would expect that a significant change in the HSAB character of the electrophilic center as an acid should lead to changes in the pattern of nucleophilic reactivity observed. Specifically, in substitutions occurring at soft electrophilic centers, soft-base nucleophiles should be more reactive relative to other nucleophiles than they are in substitutions at harder electrophilic centers, and in substitutions at hard electrophilic centers hard-base nucleophiles should appear relatively more reactive compared to other nucleophiles than they do in substitutions at softer electrophilic centers. 

There would seem to be two positions one can take with respect to the interpretation of the behavior revealed by Figs 1 and 2. The first, which would undoubtedly be favored by proponents of HSAB, is that the large deviations of the points for soft-base nucleophiles in Fig. 2 show that HSAB considerations do play an important role in determining the relative order of reactivity of a series of nucleophiles in nucleophilic substitutions at different electrophilic centers when those centers differ significantly in their degree of hardness , and that the failure to observe sizeable deviations from the correlation line in Fig. 1... 

Fig. 8.4 Schematic showing relative softness and hardness of nucleophiles and electrophiles as an indicator of sites of reaction of electrophilic metabolites.

The classic hard nucleophile used in trapping hard metabolite electrophiles is cyanide. Indeed, with modern detection sensitivities it is now often possible to detect cyanide adducts from microsomal incubations that were quenched with acetonitrile, with the residual cyanide in the acetonitrile reacting with the electrophilic species. In an experiment designed specifically to generate and detect cyanide adducts, millimolar concentrations of cyanide may be included in a microsomal incubation with no detrimental effect on the metabolic turnover. 

Further examination of the results indicated that by invocation of Pearson s Hard-Soft Acid-Base (HSAB) theory (57), the results are consistent with experimental observation. According to Pearson s theory, which has been generalized to include nucleophiles (bases) and electrophiles (acids), interactions between hard reactants are proposed to be dependent on coulombic attraction. The combination of soft reactants, however, is thought to be due to overlap of the lowest unoccupied molecular orbital (LUMO) of the electrophile and the highest occupied molecular orbital (HOMO) of the nucleophile, the so-called frontier molecular orbitals. It was found that, compared to all other positions in the quinone methide, the alpha carbon had the greatest LUMO electron density. It appears, therefore, that the frontier molecular orbital interactions are overriding the unfavorable coulombic conditions. This interpretation also supports the preferential reaction of the sulfhydryl ion over the hydroxide ion in kraft pulping. In comparison to the hydroxide ion, the sulfhydryl is relatively soft, and in Pearson s theory, soft reactants will bond preferentially to soft reactants, while hard acids will favorably combine with hard bases. Since the alpha position is the softest in the entire molecule, as evidenced by the LUMO density, the softer sulfhydryl ion would be more likely to attack this position than the hydroxide. 

Swain and Scott found satisfactory correlations with Equation (27) which provided 5 values for a number of reactants. However, as indicated in Scheme 33, for the limited number of substrates conveniently studied,158,186 variations in 5 did not show a clearly discernible pattern (and no obvious correlation with reactivity). Moreover, Pearson and Songstad demonstrated that the correlations break down if extended to extremes of soft and hard electrophilic centers such as platinum, in the substitution of trara,s-[Pt(pyridine)2Cl2], or hydrogen in proton transfer reactions.255 Despite this, Swain and Scott s equation has stood the test of time and it is noteworthy that a serious breakdown in the correlations occurs only when the reacting atoms of both nucleophile and electrophile are varied. In this chapter we will restrict ourselves to carbon as an electrophilic center, and particularly, although not exclusively, to carbocations. 

Richard, the Marcus analysis, allied to the concept imbalance of bond making and charge development at the transition state, has provided an effective framework for tackling one of the outstanding problems for a general interpretation of reactivity. A reasonable conclusion might be that further measurements of equilibrium constants will be required to support and test the level of understanding achieved so far, and to probe more deeply the interpretation of hard and soft nucleophilicity in its application to reactions of electrophilic carbon atoms. 

A particular difficulty arises for the comparison of hard and soft nucleophiles. This difficulty indeed is amplified if one goes beyond carbocation reactions to consider softer or harder electrophilic centers, such as transition metals or protons. Interpreting differences between reacting atoms presents an ultimate challenge for attempts to understand reactivity. Richard has gone a considerable way toward offering a rational analysis of the principal factors to be considered in such an endeavor. However, this is one issue likely to attract attention in the next one hundred years of carbocation chemistry and in the wider field of electrophile nucleophile combination reactions. 

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