Reactivity of α,β-unsaturated carbonyl compounds towards nucleophilic addition reaction: a local hard–soft acid–base approach

The Fukui function fk+ and local softness sk+ are assigned as reactivity parameters for nucleophilic addition reaction in acrolein, methylacrylate, methylmethacrylate, acryloylchloride, cinnamaldehyde and cinnamoylchloride.

All calculations were performed at the HF level of theory using 6-31G, 6-31G** and TZV basis sets.

The condensed local softness calculated using a Löwdin population is compared with the local softness calculated from a Mulliken population.

The most probable sites for nucleophilic attack on the α,β-unsaturated carbonyl compounds are determined from local reactivity descriptors: they are quite reliable to predict the reactivity relative to atomic charges.


The chemical reactivity of a molecule is often interpreted in terms of charge distribution of its atoms.

Atomic charges are used to indicate the preferred direction for a reagent to approach a substrate.

Although the chemists have an intuitive feeling for the reactivity based on charge distribution, assigning precise reactivity from atomic charge failed in several cases.1,2

In recent years, reactivity descriptors3–7 such as hardness, softness, Fukui function etc. have emerged as powerful tools in predicting the reactive sites of molecules.

These reactivity descriptors are derived from density functional theory.

Global hardness and global softness8–12 represent the reactivity of a molecule as a whole.

On the other hand, the Fukui function13 defines the reactivity of an atom in a molecule and it is a local property.

Fukui function and local softness, which is closely related, are suited to describe the relative reactivity of different substrates.

Pearson's hard–soft acid–base (HSAB) 12,14–16 principle suggested that hard–hard and soft–soft interactions are favorable over hard–soft interactions.17–19

Again it has been found that soft–soft interactions are preferred in the site of the maximum Fukui function, i.e. frontier control,20–22 but on the other hand, hard–hard interactions are preferred in the site of the minimum Fukui function,23,24i.e. charge control.

In this paper we have presented the reactivity parameters, the local softness sk+ and sk and Fukui functions fk+ and fk of α,β-unsaturated carbonyl compounds, namely acrolein (H2CCHCHO), methylacrylate (H2CCHCOOCH3), methylmethacrylate (H2CC(CH3)COOCH3), cinnamaldehyde (C6H5CHCHCHO), cinnamoylchloride (C6H5CHCHCOCl) and acryloylchloride (H2CCHCOCl), and the most reactive sites of nucleophilic attack were derived.

In these compounds the carbonyl carbon is slightly positive, due to mesomeric and resonance effects.

The β-carbon, which is conjugated with the carbonyl carbon develops partial positive charge.

Experimentally it has been found that a nucleophile attacks at the β-carbon atom of α,β-unsaturated carbonyl compounds.25

Here we have investigated the reactive sites of these carbonyl compounds towards a nucleophile using a local hard–soft acid–base approach.

Theoretical aspects

Within the framework of density functional theory (DFT) 3 the global hardness (η) 9–12 of an N electron system is defined as: where E, N, μ and v(r⃑) are the energy, number of electrons, chemical potential and external potential, respectively.

Again, the inverse of global hardness with a factor of ½ is defined as global softness (S),The local property, Fukui function4f(r) is defined as the derivative of electron density, ρ(r⃑), with respect to the number of electrons at a constant external potential, v(r⃑).

Similarly local softness, s(r⃑), is defined as the derivative of electron density, ρ(r⃑), with respect to the chemical potential, μ, at constant external potential,Applying the finite difference approximation, three types of condensed Fukui functions23 are found from electronic population analyses26.where, qk(N), qk(N + 1) and qk(N − 1) are atomic charges for atom k in the N, (N + 1) and (N − 1)-electron systems.

The Fukui functions fk+ and fk and local softness sk+ and sk are calculated from SCF calculation using 6-31G, 6-31G** and TZV basis sets27,28 and all these calculations are performed with the program GAMESS29.

Results and discussion

The α,β-unsaturated carbonyl compounds contain two reactive sites, the carbonyl group site and the carbon–carbon double bond site.

Hence, two types of nucleophilic addition reaction can be assigned as the direct addition reaction and conjugated addition reaction.

However, to what extent a given nucleophile undergoes the direct addition and conjugated addition is dependent on the steric and electronic factors.

If the carbonyl carbon is more sterically congested and weakly electrophilic, the conjugated addition will occur more readily than the direct addition, on the other hand if the β-carbon is more sterically congested the direct addition will take place predominantly.

Thus the nucleophilic reagents add to the conjugated system in such a way so as to form the most stable intermediate anion.30

The tendency of the α,β-unsaturated carbonyl compounds to undergo nucleophilic addition is not simply due to the electron withdrawing ability of the carbonyl group, but to the existence of a conjugated system that permits the formation of the resonance stabilized anion.

Theoretically atomic charges, Fukui functions and local softness values can be calculated for each atom in the molecule and they provide an insight in directing the incoming nucleophiles for the attack on the carbon atoms of the α,β-unsaturated carbonyl compounds.

Atomic charges

The atomic charges derived from Mulliken population analysis (MPA) and Löwdin population analysis (LPA) for Cα, Cβ and Ccarbonyl atoms of α,β-unsaturated carbonyl compounds are given in Table 1.

It is seen from Table 1 that both MPA and LPA derived charges have negative values for Cα and Cβ atoms.

Since the charges of the Ccarbonyl atoms are positive, a nucleophile should attack at the carbonyl atoms.

However, experimentally it has been found that in most of the cases the nucleophilic addition takes place at the β-carbon atom.

Hence it is difficult to predict the reactive sites of these compounds from atomic charge values.

In our recent studies,31,33 Fukui function and local softness appear to be better reactivity descriptors for studying the acidity and basicity of zeolites.

Roy et al32. used the reactivity descriptors to study the most preferable protonation sites in aniline and substituted anilines in the gas phase.

Thus, the Fukui function and the local softness are found to be superior to atomic charges in determining the reactive sites in molecules.

Fukui function

The Fukui function values for the Cα, Cβ and Ccarbonyl atoms are presented in Table 2.

Both MPA and LPA derived Fukui functions for the Cβ and Ccarbonyl atoms are positive.

The negative Fukui function is observed for the Cα atom in acrolein and acryloyl chloride.

The negative values of Fukui functions indicate a very low probability for nucleophilic attack to take place at those sites.

Recently, Hirao and co-workers,31,32 suggested that the Fukui function of an atom should be always positive.

They found that the Fukui function calculated using Hirshfeld population analysis become positive although MPA derived Fukui function for some atoms become negative in the same calculation.

In our present study, the LPA derived Fukui functions are found to be positive for all the atoms.

While comparing the Fukui function values calculated using 6-31G, 6-31G** and TZV basis sets, it appears that the β-carbon of each of the molecule has maximum values.

This indicates that the incoming nucleophile will preferably attack the β-carbon atom which is in agreement with the experimental results.25

Moreover, the Fukui function values for β-carbon with less bulky groups at α and β positions are more than those of the molecules where more bulky groups are present at α and β positions.

For all the molecules the reactivity of the atoms for nucleophilic attack decreases in the order: Cβ > Ccarbonyl > Cα while considering the MPA derived Fukui functions.

The LPA derived Fukui functions also predict the same trend bearing a disorder in case of methylacrylate.

Local softness

The local softness values of all the molecules calculated with different basis sets such as 6-31G, 6-31G** and TZV are given in Table 3.

Like Fukui functions, local softness values predict the similar trend of reactivity.

The reactivity of the atoms for nucleophilic attack decreases in the order: Cβ > Ccarbonyl > Cα bearing slight disorder for LPA derived softness values.

From the softness values a reactivity order for molecules could be derived.

From Table 2 and Table 3 it is seen that Fukui function and local softness values are more at the β-carbon atoms in the molecules with less bulky groups.

Hence, β-carbon atoms of α,β-unsaturated carbonyl compounds are more reactive and prone for nucleophilic attacks when less bulky groups are present.


Local reactivity descriptors are shown to be very powerful in predicting the reactivity of α,β-unsaturated compounds.

From the Fukui functions and local softness values it is concluded that the β-carbon atoms of the α,β-unsaturated carbonyl compounds are more reactive towards a nucleophile.

The reactivities of the three types of carbon atoms are found to decrease in the order: Cβ > Ccarbonyl > Cα in all of the molecules.

The local softness values are dependent on the substituents present at the β-carbon atoms.

The local softness values of β-carbon atoms with less bulky groups are greater than those with more bulky groups.

These results provide an insight in comparing the intermolecular reactivities of various α,β-unsaturated carbonyl compounds.