Questions: Potential Energy Surfaces and Reaction Coordinates

Question 1

A chemist proposes to isolate a transition state and study its spectroscopic properties in the same way they would study a reaction intermediate. Why is this impossible?

• A. Transition states are too small to detect spectroscopically
• B. Transition states have no imaginary vibrational frequencies and therefore cannot absorb light
• C. Transition states are saddle points with no kinetic stability — any displacement leads downhill, so they have no lifetime
• D. Transition states can only exist in the gas phase, not in solution

Answer: (C)

A transition state is a first-order saddle point on the PES: it is a maximum along the reaction coordinate, so any motion along that coordinate causes the system to roll downhill toward reactants or products. Unlike an intermediate (which sits in a local minimum and can persist for some duration), the transition state has no barrier confining it — it exists at an energy maximum with zero lifetime. Spectroscopy requires a molecule to spend time in a given state, which intermediates can do but transition states cannot.

Question 2

Reaction A is highly exothermic (ΔE = −80 kJ/mol). Reaction B is highly endothermic (ΔE = +80 kJ/mol). According to Hammond's postulate, which statement best describes the transition states?

• A. Reaction A has an early TS resembling reactants; Reaction B has a late TS resembling products
• B. Reaction A has a late TS resembling products; Reaction B has an early TS resembling reactants
• C. Both have TS structures midway between reactants and products regardless of thermodynamics
• D. Hammond's postulate applies only to reactions in which bonds are broken homolytically

Answer: (A)

Hammond's postulate states the TS resembles whichever species it is closer to in energy. For an exothermic reaction, the TS is close in energy to the high-energy reactants (early TS: bonds barely stretched, structure resembles reactants). For an endothermic reaction, the TS is close in energy to the high-energy products (late TS: bonds nearly fully broken or formed, structure resembles products). This asymmetry lets chemists predict TS geometry — and therefore selectivity and rate sensitivity — from the sign of the reaction energy alone.

Question 3

The transition state of a reaction is simply a very short-lived intermediate.

• T. True
• F. False

Answer: False

This is a critical distinction. An intermediate occupies a local minimum on the PES — it is surrounded by energy barriers in all directions and therefore has some finite lifetime, however brief. A transition state is a first-order saddle point — a maximum along the reaction coordinate, meaning there is no barrier preventing it from converting to reactants or products. It has zero lifetime and cannot be isolated. The words 'intermediate' and 'transition state' describe topologically distinct features of the PES, not merely different lifetimes.

Question 4

The intrinsic reaction coordinate (IRC) can be described as the path a classical ball would follow rolling from the saddle point toward reactants or products with infinitesimal initial kinetic energy.

• T. True
• F. False

Answer: True

This physical picture captures the definition accurately. The IRC traces the minimum-energy path (steepest-descent path) from the transition state downhill in both directions — toward reactants and toward products. Starting from the saddle point and moving infinitesimally in the direction of the imaginary frequency (the downhill direction), the system follows the path of steepest descent, exactly as a ball with negligible kinetic energy would roll. The energy profile along the IRC is the familiar reaction energy diagram with its activation barrier.

Question 5

Explain what makes the transition state a 'saddle point' and why this distinguishes it from both reactant/product minima and from random points on the PES.

Model answer: A saddle point is simultaneously a maximum in one direction and a minimum in all perpendicular directions — like the highest point on a mountain pass, which is the lowest point along the ridge but the highest point on the trail between two valleys. For a transition state, the 'downhill' direction is the reaction coordinate (movement along it converts TS to reactants or products), while all directions perpendicular to the reaction coordinate are uphill (the TS is confined laterally). This makes the TS a maximum along the reaction pathway but stable against displacements in any other direction, which is why it has exactly one imaginary vibrational frequency.

Minima on the PES (reactants, products, intermediates) are downhill in all directions — any displacement raises the energy, providing stability. Arbitrary points are typically saddle-point-like in some directions but not in the structured first-order way. The transition state's defining property — one imaginary frequency, corresponding to the reaction-coordinate motion — is what identifies it computationally and explains why it cannot be isolated: the system 'wants' to move in that one downhill direction.