What is an Intrinsic Barrier or Intrinsic Rate Constant?

The main goal of our research is to advance the chemist’s understanding of chemical reactivity. For example, why do certain reactions have high activation barriers while other reactions that may look quite similar and have a comparable thermodynamic driving force, have low activation barriers? Since most of chemistry deals with chemical reactions, this is one of the most important and fundamental questions that a chemist can ask.

Before one can address the problem, some definitions are in order. When discussing chemical reactivity it is important to distinguish between the thermodynamic driving force of the reaction ( ΔG^o) and a purely kinetic factor known as the intrinsic barrier (). For a reaction with forward and reverse rate constants k₁ and k_-1, respectively (eq 1), the intrinsic barrier, , is defined as = = when ΔG^o = 0.

If one prefers to deal with rate and equilibrium constants instead of free energies, one can define an intrinsic rate constant k_o as k_o = k₁ = k_-1 when K₁ = 1 (K₁ = k₁/k_-1 is the equilibrium constant). Both treatments are equivalent.

The theoretical as well as practical significance of or k _o is that they are representative of a whole reaction series and independent of the thermodynamic driving force of a particular member of that series. An example of such a series would be the deprotonation of a carbon acid, e.g. phenylnitromethane, by a series of primary amines. Hence, understanding the factors that affect intrinsic barriers is to understand a great deal about chemical reactivity.

Transition State Imbalance

A key feature that helped unravel some of the factors that determine intrinsic barriers is the realization that the majority of elementary chemical reactions involve more than one concurrent molecular process such as bond formation/bond cleavage, solvation/desolvation, delocalization/localization of charge, etc., and that often these processes have made unequal progress at the transition state. When this is the case, the reaction is said to have an "imbalanced transition state." Reaction progress at the transition state then becomes an ambiguous concept that depends on which process is chosen as the reaction coordinate.

Reaction coordinate diagrams based on two progress variables deal qualitatively with this problem. Such a diagram is shown in Fig. 2 for the deprotonation of arylnitromethane. The lower left corner represents the reactants, the upper right corner represents the products, while the lower right corner is a hypothetical intermediate whose negative charge is localized on the sp³-hybridized carbon.

Figure 2. Energy surface diagram for the deprotonation of arylnitromethane. The energy axis is perpindicular to the square surface.

Connection between Imbalance and Intrinsic Barrier

It appears that reactions with strongly imbalanced transition states have large intrinsic barriers. Why? Let us illustrate the problem with the arylnitromethane deprotonation, eq 2.

We look at the situation where the pKa of BH is the same as the pKa of the nitroalkane so that k₁ = k_-1 = k_o. The imbalance, shown in exaggerated form by placing all the negative charge (δ-) onto the carbon of the transition state, implies that the resonance delocalization of the charge into the nitro group of the product anion is only minimally developed at the transition state. This means that the transition state cannot derive any significant stabilization from the resonance effect. That this leads to a high intrinsic barrier is most easily appreciated by considering the reaction in the k_-1 direction: In order to reach the transition state, the charge has to be localized onto the carbon which entails loss of the resonance stabilization of the nitronate anion, a process that requires energy. This energy represents a large fraction of the intrinsic barrier. The stronger the resonance stabilization of the anion, the larger the intrinsic barrier. On the other hand, in the deprotonation of a carbon acid that leads to a carbanion with little resonance stabilization, there is only a small imbalance, and hence the intrinsic barrier is low because not much energy is required to localize the charge on carbon at the transition state. A case in point is the deprotonation of dicyanoalkanes, eq 3.

How do we know that charge delocalization lags behind proton transfer (Fig. 2, eq 2)? Usually transition state imbalances are recognized on the basis of structure-reactivity coefficients when substituents at different positions within the transition state give conflicting reports about charge development at the reaction site. For example, in the deprotonation of arylnitroalkanes by amines the so-called Brønsted aCH value is larger than the Brønsted βB value. αCH measures the sensitivity of the k₁ to changes in the acidity constant of the arylnitromethane () via changes of the aryl group, i.e., αCH is the slope of a plot of log k₁ vs. log . βB measures the sensitivity of k₁ to changes in the basicity of the base (amine), i.e., βB is the slope of a plot of log k₁ vs. . As long as the base is not involved in resonance effects of its own, βB can be regarded as an approximate measure of the degree of charge transfer at the transition state. On the other hand, aCH is not such a measure for the following reason. The localization of the negative charge on the carbon of the transition state brings this charge close to the aryl group while in the nitronate ion it is far from the aryl group. This renders the transition state and with it k₁ disproportionately sensitive to the substituent in the aryl group and leads to an enhanced αCH value, hence αCH > βB.

The preceding discussion seems to imply that if the transition state were balanced, i.e. if charge delocalization and resonance stabilization would have progressed synchronously with proton transfer, the intrinsic barrier would be lower. Why , then, is there a lag that leads to a higher barrier? Since a basic law of nature requires physical and chemical processes to follow paths of minimum free energy, a constraint must exist that makes it impossible for delocalization to be synchronous with proton transfer. A qualitative understanding of this constraint may be gained by considering the generalized representation of a proton transfer shown in eq 4. For simplicity, eq 4 refers to a situation with complete charge delocalization and complete C—Y pi-bond formation in the carbanion, as is probably true for Y = NO2. One can, however, easily generalize to a situation where delocalization is incomplete.

We now ask how large δY, the fraction of charge that ends up on Y, could possibly be. It seems reasonable to expect that δY will depend not only on δB, the amount of charge transferred from the base, but also on the degree of C—Y pi-bond formation. In other words, if the C—Y pi-bond is not fully developed, and it cannot be in the transition state, only a fraction of δB will end up as δY. The simplest assumption is that this fraction is proportional to the C—Y pi-bond order, and that in turn the C—Y pi-bond order is proportional to δB. This means that δY is proportional to (δB) ² and given by eq 5, with c being a proportionality constant. For the case shown in eq 4, c = 1.

δY = c(δB)²

(5)

This can be seen when solving eq 5 for the products where δB = δY = 1. Hence for a transition state where δB is, say, 0.5, we have δY = 0.25, implying δC = 0.25 for the charge on the carbon.

Resonance and Aromaticity

There exists strong evidence that, whenever a reaction leads to a resonance stabilized product, the intrinsic barrier is high and increasingly so the greater the resonance stabilization. This is not only true for proton transfer from carbon acids but for all chemical reactions, i.e., the formation of any resonance stabilized carbanions, carbocations, radicals, etc. The reason for this state of affairs is always the same, i.e., the development  of the resonance effect lags behind bond changes at the transition state because of the constraints discussed above (see eqs 4 and 5).

Recently we asked the question whether the same would be true for reactions that lead to aromatic products, i.e., does the development of the aromatic stabilization also lag behind bond changes at the transition state? In view of the centrality of the concept of aromaticity, this is an important question. Preliminary results summarized in a recent paper reproduced on my web page titled “The Principle of Nonperfect Synchronization: How Does It Apply to Aromatic Systems?” suggest the opposite, i.e., aromaticity appears to develop ahead of bond changes. These are very interesting and surprising findings and much of our current research is devoted to examine whether or not this is a general phenomenon and to try to understand the reasons for it.

Other Research Interests

Because of its generality, the PNS provides a framework for understanding structure-reactivity relationships in numerous types of reactions. Even though the study of Proton Transfers in solution as well as the gas phase has been a major focus of my research group, we have also applied the PNS to the Physical Organic Chemistry of Transition Metal Carbene Complexes and to Nucleophilic Vinylic Substitution Reactions; these topics are described in some detail under their respective headings.

 [The Bernasconi Group Home Page]

Some Key References

1. C. F. Bernasconi, “Intrinsic Barriers of Reactions and the Principle of Nonperfect Synchronization,” Acc. Chem. Res.20, 301-308 (1987).


2. C. F. Bernasconi, “The Principle of Non-perfect Synchronization,” Adv. Phys. Org. Chem.27, 119-238 (1992).


3. C. F. Bernasconi, “The Principle of Non-perfect Synchronization: More Than a Qualitative Concept?” Acc. Chem. Res. 25, 9-16 (1992).


4. C. F. Bernasconi and W. Sun, “Physical Organic Chemistry of Transition Metal Carbene Complexes. 24. Thermodynamic and Kinetic Acidities of Phenyl Substituted (Benzylmethoxycarbene)pentacarbonylchromium(0) Complexes. Is There a Transition State Imbalance?” J. Am. Chem. Soc. 124, 2299-2304 (2002).


5. C. F. Bernasconi and V. Ruddat, “Physical Organic Chemistry of Transition Metal Carbene Complexes. 25. Kinetic and Thermodynamic Acidities of Substituted (Methyl­thio­phenylcarbene)pentacarbonyl tungsten(0) and (Benzoxymethylcarbene)pentacrabonyl tungsten(0) in Aqueous Acetonitrile. Evidence for Transition State Imbalances,” J. Am. Chem. Soc. 124, 14968-14976 (2002).


6. C. F. Bernasconi, M. Ali and J. C. Gunter, “Kinetic and Thermodynamic Acidities of Substituted 1-Benzyl-1-methoxy-2-nitroethylenes. Strong Reduction of the Transition State Imbalance Compared to Other Nitroalkanes,” J. Am. Chem. Soc. 125, 151-157 (2003).


7. C. F. Bernasconi, M. L. Ragains, and S. Bhattacharya, “Reactions that Generate Aromatic Molecules: Is Aromatic Stabilization Less or More Advanced than Bond Changes at the Transition State? Kinetic and Thermodynamic Acidities of Rhenium Carbene Complexes,” J. Am. Chem. Soc.125, 12328-12336 (2003).


8. C. F. Bernasconi, V. Ruddat, P. J. Wenzel, and H. Fischer, “Kinetic and Thermodynamic Acidities of Pentacarbonyl(cyclobutenylidene)chromium Complexes. Effect of Anti­aromaticity in the Conjugate Anion. An Experimental and Computational Study,” J. Org. Chem. 69, 5232-5239 (2004).


9. C. F. Bernasconi, “The Principle of Nonperfect Synchronization: How Does It Apply to Aromatic Systems?” J. Phys. Org. Chem.17, 951-956 (2004).