14.4 Potential energy surfaces and reaction coordinates

Potential energy surfaces and reaction coordinates are crucial tools for understanding chemical reactions. They provide a visual representation of how energy changes as molecules interact, helping us grasp the energetics and mechanisms behind chemical transformations.

These concepts are essential in Chemical Kinetics and Reaction Dynamics, as they explain why some reactions happen quickly while others are slow. By mapping out energy landscapes, we can predict reaction rates, identify transition states, and understand how catalysts work their magic.

Potential energy surfaces and reactions

Graphical representation of potential energy

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• A potential energy surface is a graphical representation of the potential energy of a system as a function of its geometry or atomic coordinates
  • The potential energy is plotted on the vertical axis, while the atomic coordinates or geometry parameters are plotted on the horizontal axes
  • Example: For a diatomic molecule (H₂), the potential energy surface would be a 2D plot with the potential energy on the y-axis and the bond length on the x-axis
• The shape of the potential energy surface is determined by the interactions between the atoms or molecules in the system
  • These interactions include bond stretching, angle bending, and torsional motions
  • The potential energy surface accounts for the combined effect of all these interactions on the system's potential energy

Reaction progress and pathways

• The potential energy surface describes how the potential energy changes as the reaction progresses from reactants to products
  • Reactants and products are represented by minima on the potential energy surface, corresponding to stable molecular geometries
  • Example: In the H₂ + I₂ → 2HI reaction, the reactants (H₂ and I₂) and products (HI) are represented by minima on the potential energy surface
• The reaction pathway is the minimum energy path on the potential energy surface that connects the reactants and products
  • It represents the most energetically favorable route for the reaction to proceed
  • The reaction pathway passes through the transition state, which is the highest-energy point along the path

Reaction coordinates and transition states

Reaction coordinate components

• A reaction coordinate is a one-dimensional representation of the progress of a chemical reaction, typically plotted against the potential energy of the system
  • It is a simplified representation of the multidimensional potential energy surface, focusing on the most important geometric changes during the reaction
  • Example: In the SN2 reaction (CH₃Br + OH⁻ → CH₃OH + Br⁻), the reaction coordinate might be the C-Br bond length, as it is the most significant geometric change during the reaction
• Reactants are the starting materials of a chemical reaction and are represented by a minimum on the potential energy surface at the beginning of the reaction coordinate
• Products are the final compounds formed after a chemical reaction and are represented by a minimum on the potential energy surface at the end of the reaction coordinate

Transition state characteristics

• The transition state is the highest-energy point along the reaction coordinate, representing the activated complex formed during the reaction
  • It is a transient, unstable state that exists only briefly during the reaction
  • Example: In the SN2 reaction (CH₃Br + OH⁻ → CH₃OH + Br⁻), the transition state occurs when the C-Br bond is partially broken and the C-OH bond is partially formed
• The transition state is characterized by a saddle point on the potential energy surface
  • At the saddle point, the energy is at a maximum along the reaction coordinate but a minimum in all other directions
  • This means that the transition state is a maximum in the direction of the reaction progress but a minimum in all other geometric parameters

Catalyst effects on potential energy

Catalyst function

• A catalyst is a substance that increases the rate of a chemical reaction without being consumed in the process
  • Catalysts work by providing an alternative reaction pathway with a lower activation energy compared to the uncatalyzed reaction
  • Example: In the Haber-Bosch process for ammonia synthesis (N₂ + 3H₂ ⇌ 2NH₃), iron (Fe) is used as a catalyst to lower the activation energy and increase the reaction rate

Activation energy and catalysis

• The activation energy is the minimum energy required for reactants to overcome the energy barrier and form the transition state
  • It is the difference in energy between the reactants and the transition state
  • A lower activation energy results in a faster reaction rate, as more reactant molecules have sufficient energy to reach the transition state
• The presence of a catalyst lowers the activation energy by stabilizing the transition state or by providing a different reaction mechanism with a lower energy barrier
  • Catalysts can stabilize the transition state through various interactions, such as forming temporary bonds or providing a favorable orientation for the reactants
  • Some catalysts provide a different reaction mechanism with a lower activation energy, such as in enzymatic reactions where the enzyme's active site facilitates the formation of the transition state
• On the potential energy surface, the effect of a catalyst is represented by a new reaction pathway with a lower energy barrier, resulting in a faster reaction rate

Endothermic vs exothermic reactions

Endothermic reactions

• Endothermic reactions absorb heat from the surroundings during the reaction, resulting in an increase in the enthalpy of the system
  • The enthalpy change (ΔH) for an endothermic reaction is positive, indicating that the system gains heat
  • Example: The thermal decomposition of calcium carbonate (CaCO₃ → CaO + CO₂) is an endothermic reaction, as it requires heat input to break the bonds in CaCO₃
• On the potential energy surface, endothermic reactions have products with higher potential energy than the reactants
  • The transition state is higher in energy than both the reactants and products
  • The difference in potential energy between the reactants and products is equal to the enthalpy change (ΔH) of the reaction

Exothermic reactions

• Exothermic reactions release heat to the surroundings during the reaction, resulting in a decrease in the enthalpy of the system
  • The enthalpy change (ΔH) for an exothermic reaction is negative, indicating that the system loses heat
  • Example: The combustion of methane (CH₄ + 2O₂ → CO₂ + 2H₂O) is an exothermic reaction, as it releases heat when the bonds in CH₄ and O₂ are broken and new bonds in CO₂ and H₂O are formed
• On the potential energy surface, exothermic reactions have products with lower potential energy than the reactants
  • The transition state is higher in energy than the products but lower than the reactants
  • The difference in potential energy between the reactants and products is equal to the negative of the enthalpy change (-ΔH) of the reaction