Computed Geometries, Frequencies and Reaction Barriers
A calculation is run to answer a question, and the answer has to be checked. Optimising a structure, computing its vibrations and locating the point at the top of a barrier are the three jobs that make a computed mechanism worth quoting.
What a learner can do afterwards
- Explains how a frequency calculation confirms that a structure is a minimum or a transition state
- Compares a computed geometry with an experimental one and comments on the size of the difference
- Extracts an activation barrier from computed energies and states which corrections were applied
- Says why a single-point energy on a poor geometry cannot support a claim about the intended optimized structure, while a deliberately specified geometry can serve a stated scan or diagnostic purpose
1 · Read
A frequency calculation checks what a structure is. At a converged stationary point, strictly positive frequencies for every nontrivial vibrational mode, apart from translations and rotations, mean a minimum. One imaginary frequency there means an unstable normal mode, with energy curving downward along that coordinate. That mode does not by itself show the intended bond motion or which minima connect. Confirm a transition state by following the path down both sides to its two minima.
Compare each computed geometry with experiment for the same bond type and the same kind of geometry, and judge the gap against the accuracy you need. As a rough guide, a bond off by a hundredth of an angstrom is often fine, while a bond off by a tenth usually warns that the method or the structure needs review. Experimental uncertainty also matters.
A barrier comes from corrected energies. Take the top-of-barrier energy plus its zero-point correction, and subtract the reactant energy plus its zero-point correction. The barrier depends on the difference between the two corrections, not on either one alone. For example, reactants at -50.0 with a correction of 0.3 give -49.7, and the top at -49.2 with a correction of 0.2 gives -49.0, so the barrier is 0.7. Quote the barrier with the zero-point corrections stated.
Do not quote a single-point energy on a poor geometry as the energy of the intended optimized structure. Optimise first. For a mechanism claim, confirm the transition state links the right two minima. Energies at deliberately specified geometries can still serve a stated scan or diagnostic purpose, with its limits stated.
Frequencies identify the structure, geometries face experiment, and barriers need their corrections stated.
2 · Watch
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Where it sits
Optional connections
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.