Questions: Bimolecular Collision Dynamics and Trajectory Analysis

Question 1

Trajectory studies on two reactions reveal: Reaction A requires high translational energy to react regardless of vibrational state; Reaction B reacts readily when reactants have high vibrational excitation even at modest translational energies. What does this demonstrate?

• A. Reaction B has a lower activation energy, so any energy source can provide the threshold needed
• B. Energy partitioning matters: vibrational excitation can drive reaction in Reaction B, meaning not all collision energy is equally effective — the mode of energy determines outcome
• C. Reaction A has a larger collision cross-section because higher translational energy creates wider impact parameter windows
• D. Both reactions demonstrate that total collision energy is the only relevant variable, regardless of how it is distributed between modes

Answer: (B)

This is a key finding of trajectory analysis that simple collision theory misses. In collision theory, activation energy is treated as a single threshold regardless of energy mode. Trajectory calculations show that specific energy modes (translational vs. vibrational) can be more or less effective depending on the shape of the potential energy surface. For some reactions, vibrationally excited reactants reach the transition state geometry more easily. Option D states the simple-collision-theory assumption that trajectory analysis disproves.

Question 2

What does the maximum impact parameter b_max physically represent in bimolecular trajectory analysis?

• A. The minimum separation distance between two molecules at which long-range forces begin to act
• B. The average perpendicular offset distance between molecules in a thermal gas sample
• C. The largest perpendicular offset between molecule centers at which a collision still has a nonzero probability of leading to reaction at a given energy
• D. The equilibrium bond length of the transition state complex

Answer: (C)

b_max is the critical cutoff: collisions with impact parameter b > b_max are too glancing to deliver energy to the reactive bond, so they scatter without reaction. Collisions with b ≤ b_max have a geometry that can reach the transition state. The reaction cross-section σ_r = πb²_max represents the effective target area — the disk of approach geometries that can lead to reaction. This is why the steric factor in collision theory is less than one: b_max is smaller than the total collision cross-section.

Question 3

The steric factor in simple collision theory accounts for the fact that not all collision orientations can lead to a successful reaction, even when energy is sufficient.

• T. True
• F. False

Answer: True

The steric factor p (always ≤ 1) is the fraction of collisions that have the correct geometry to reach the transition state. Simple collision theory introduces p as a correction factor without explaining its microscopic origin. Trajectory analysis provides that explanation: only collisions with b ≤ b_max AND the right molecular orientation deliver energy to the reactive bond. This is why p can be very small for reactions requiring a specific approach geometry.

Question 4

According to trajectory analysis, translational energy and vibrational energy in the reactant molecules are equally effective at promoting any bimolecular reaction.

• T. True
• F. False

Answer: False

Trajectory calculations show that the effectiveness of different energy modes depends on the shape of the potential energy surface. For reactions where bond breaking requires stretching along a specific coordinate, vibrational excitation in that mode can be more effective than translational energy. Conversely, some reactions are promoted more by relative translational energy. The equivalence of energy modes is an assumption of simple collision theory that trajectory analysis explicitly tests and often refutes.

Question 5

Why is the steric factor in simple collision theory often much less than one, and what does trajectory analysis reveal about the physical origin of this factor?

Model answer: The steric factor is less than one because only a fraction of all collision geometries can actually deliver energy to the reactive bond and reach the transition state. Simple collision theory counts all collisions above the energy threshold, but most of those collisions approach from the wrong angle or hit the wrong part of the molecule. Trajectory analysis makes this explicit: there is a maximum impact parameter b_max, beyond which collisions are too glancing to react, and within that range, only specific orientation angles are reactive. The steric factor is essentially the ratio of the reactive solid angle to all possible approach angles.

Trajectory analysis transforms the steric factor from an empirical fudge into a measurable geometric property of the potential energy surface. By running thousands of trajectories with varying b and orientation, one can map exactly which approach geometries lead to products. This directly explains why some reactions have very small steric factors (only head-on collisions at a specific atom react) while others are geometrically forgiving.