is a negative constant (ρ < 0). An EWG (σ > 0) will destabilize the transition state carrying a positive charge, making the kA/kH < 1 [lg(kA/kH) < 0]. An EDG (σ < 0) will stabilize the transition state carrying a positive charge, making the kA/kH > 1 [lg(kA/kH) > 0]. Both EWG and EDG require a negative ρ constant to maintain the Hammett equation. For the reactions which develop a negative charge (or destroy a positive charge) in the transition state of the rate‐determining step, ρ in the Hammett equation is a positive constant (ρ > 0). An EWG (σ > 0) will stabilize the transition state carrying a negative charge, making the kA/kH > 1 [lg(kA/kH) > 0]. An EDG (σ < 0) will destabilize the transition state carrying a negative charge, making the kA/kH < 1 [lg(kA/kH) < 0]. Both EWG and EDG require a positive ρ constant to maintain the Hammett equation.
When a reaction occurs on the aromatic ring to develop a positive or a negative charge in the transition state, the influence of a substituent (EWG or EDG) on the reaction rate is usually stronger than that on a reaction taking place in the side group. Therefore, the absolute value of the ρ constant for a reaction occurring on the aromatic ring is often greater than the absolute value of the ρ constant for a reaction occurring on the side group (exceptions exist). All this is illustrated by the reactions in Figure 1.6, with all the ρ constants taken from Ref. [1].
Figure 1.6a is an electrophilic aromatic substitution reaction (occurring on the aromatic ring) via an arenium cation (a positive charge is developed in the transition state). The substituent can strongly interact with the positive charge in the transition state formed in the ring, giving rise to a big negative ρ constant (ρ = –12.1) for the reaction. Figure 1.6b is a nucleophilic aromatic substitution reaction (occurring on the aromatic ring) via an intermediate Meisenheimer anion (a negative charge is developed in the transition state). The substituent can strongly interact with the negative charge in the transition state, giving rise to a positive ρ constant (ρ = 3.9) for the reaction. On the other hand, Figure 1.6c reaction takes place at the first atom of a side chain attaching to the aromatic ring and the ring is intact in the reaction. A carbocation is formed in the course of the reaction, thus a positive charge is developed in the transition state. The ρ constant for this reaction is negative (ρ = –4.54). Its absolute value is much smaller than that of the ρ constant for Reaction (a) occurring in the ring. As the substituent is distanced from the reactive center, its electronic effect on the reaction is getting smaller. Figure 1.6d reaction occurs in the side group, with a negative charge in the phenoxide oxygen destroyed (equivalent to development of a positive charge). Therefore, the reaction has a small negative ρ constant (ρ = –1.12). Its absolute value is substantially smaller than those of the ρ constants for Reactions (a) and (b), indicating weaker electronic effects of substituents on the side groups relative to the effects on the ring. Figure 1.6e reaction also occurs on the side group, with a positive charge in the nitrogen atom destroyed (equivalent to development of a negative charge) in the course of the reaction. For this reaction, the Hammett equation can be established using the acid dissociation constants of XC6H4NH3+, formulated as lg(KA/KH) = ρσ, where KA and KH are dissociation constants of XC6H4NH3+ and C6H5NH3+, respectively. Since the reaction occurs on the side group and destroys a positive charge, it has a small positive ρ constant (ρ = 2.77).
FIGURE 1.6 The ρ constants for various reactions of substituted benzenes. (a) Electrophilic aromatic substitution, (b) Nucleophilic aromatic substitution, (c) Hydrolysis, (d) SN2 reaction, and (e) Dissociation.
1.8 THE MOLECULAR ORBITAL THEORY
1.8.1 Formation of Molecular Orbitals from Atomic Orbitals
The microscopic particles such as electrons possess dual properties, which are particle‐like behavior and wave‐like behavior. The latter can be quantitatively characterized by the wavefunction (ψ), which is a function of the space coordinates (x, y, z in three dimensions) of an electron. The one‐electron wavefunction in an atom is called atomic orbital (AO). The square of a wavefunction (ψ2) is the probability of finding an electron (also called electron density). The atomic orbitals in the valence shells of the atoms of main group elements include s and p orbitals. Their shapes in the three‐dimensional space are illustrated in Figure 1.7.
FIGURE 1.7 The shapes of the s and p orbitals in the three‐dimensional space.
Studying the behavior of fundamental particles in chemistry must eventually go beyond the classical laws. It requires that chemical bonding in molecules be explained as a superposition phenomenon of electron wavefunctions. When two atoms (such as hydrogen atoms) approach each other, their valence electrons will start interacting. This makes the wavefunctions (atomic orbitals) of the interacting atoms superimpose (overlap). Mathematically, such a superposition phenomenon (also called orbital overlap) can be expressed in terms of the linear combinations of atomic orbitals (LCAOs) leading to a set of new wavefunctions in a molecule, called molecular orbitals (MOs) which are shown in Equations 1.58 and 1.59 [2].
ψ1 and ψ2 represent atomic orbitals of the two approaching atoms 1 and 2, respectively. c11, c12, c21, and c22 are constants (positive, zero, or negative). Φ1 and Φ2 are the resulting molecular orbitals from linear combinations of ψ1 and ψ2. By the nature, the molecular orbitals are one‐electron wavefunctions. However, they can approximately characterize the behavior of electrons in a many‐electron molecule. In principle, the number of molecular orbitals formed is equal to the number of participating atomic orbitals which overlap in a molecule. In other words, the participating atomic orbitals can combine linearly in
