Reaction Kinetics and Potential Energy Surfaces
Dynamics on a Potential Energy Surface
Rate Theory
Chemical kinetics relates time-dependent concentration changes to microscopic barriers. For an elementary reaction, the Arrhenius form is often a useful approximation, while transition state theory refines this using activated complex partition functions and free-energy barriers .
The role of the saddle point
A transition state is a first-order saddle point on the potential energy surface: it is a maximum along the reaction coordinate and a minimum along all orthogonal coordinates.
In transition state theory, the rate constant is most directly related to which barrier?
TST expresses the rate in terms of the free energy of activation, .
Correct answer:
Microscopic vs Macroscopic Kinetics
Observed kinetics can reflect elementary steps, pre-equilibria, diffusion limits, catalyst resting states, or hidden intermediates. Rate laws therefore need mechanistic interpretation rather than mere curve fitting.
How to Diagnose a Mechanism from Rate Data
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Step 1: Determine the empirical rate law.
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Step 2: Test temperature dependence for activation parameters.
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Step 3: Compare isotope effects and solvent effects.
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Step 4: Build a plausible sequence of elementary steps.
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Step 5: Validate the mechanism with spectroscopy or computation.
Why is a first-order saddle point associated with a reaction transition state?
One imaginary vibrational frequency corresponds to the reaction coordinate.
Correct answer: Because it is unstable along one coordinate but stable along all others, matching the barrier crossing geometry.
Arrhenius vs Eyring
Arrhenius equation
- Empirical form with
- Useful for quick fitting
- Less direct structural interpretation
Eyring equation
- Derived from statistical mechanics
- Uses and
- Connects mechanism to thermodynamics
What does a negative entropy of activation often suggest?
A negative typically indicates a more ordered activated complex.
Correct answer: A highly ordered transition state
What is meant by a reaction coordinate?
The reaction coordinate tracks the minimum-energy path conceptually.
Correct answer: It is a collective coordinate that parameterizes progress from reactants through the transition state to products.