Perspective on a challenge: predicting the photochemistry of cyclobutanone

This Perspective reviews a 2023 community challenge where over 70 researchers used diverse computational methods to predict the photochemistry of cyclobutanone and its time-resolved MeV-UED signal, ultimately demonstrating the qualitative predictive power of nonadiabatic molecular dynamics while highlighting the critical impact of electronic-structure theory choices on simulation outcomes.

The Gist

Imagine you are a chef trying to predict exactly how a specific cake will behave if you drop it from a great height. You know it will crack, maybe crumble, and turn into a pile of crumbs. But you want to know: How fast does it fall? Which pieces break off first? Does it bounce? And most importantly, can you build a computer simulation that predicts this so perfectly that you don't even need to drop the real cake?

This paper is the story of a massive, global "cooking competition" where 70+ scientists (the chefs) tried to solve this exact problem, but with a molecule called cyclobutanone instead of a cake.

Here is the breakdown of their adventure, told in simple terms.

The Challenge: The "Molecular Movie" Prediction

In 2023, a group of scientists issued a challenge: "We are going to zap a molecule with a laser (like a camera flash) and film it breaking apart using a super-fast electron camera. But before we do the experiment, you must predict exactly what the movie will look like."

The molecule, cyclobutanone, is a tiny ring of atoms. When hit by a 200-nanometer laser, it gets excited, wobbles, and eventually snaps open to form new chemicals. The goal was to use computer simulations to predict the "movie" (the experimental data) before the real film was shot.

The Cast of Characters: 15 Different Teams

Fifteen different research teams from around the world (from the US, UK, Europe, China, etc.) signed up. They all had the same goal, but they used different "kitchen tools" (mathematical methods) to cook up their predictions.

Think of it like 15 different people trying to predict the weather.

• Team A uses a super-complex supercomputer model.
• Team B uses a simpler, faster model.
• Team C uses a model that guesses based on past patterns.

The Three Big Ingredients

To make their prediction, every team had to get three things right. The paper analyzes how well they did with each:

1. The Starting Line (Photoexcitation)

Before the molecule breaks, it has to be "woken up" by the laser.

• The Analogy: Imagine a crowd of people (the molecules) standing in a room. The laser is a shout that wakes them up. But the people aren't standing perfectly still; they are jiggling and breathing.
• The Problem: Some teams assumed everyone was standing perfectly still. Others tried to account for the jiggling. Some even tried to guess exactly which people the laser would hit based on the "loudness" of the shout.
• The Verdict: It turns out, how you describe the "jiggling" at the start matters a lot. If you get the starting position wrong, the whole movie goes off the rails.

2. The Rules of the Game (Electronic Structure)

This is the most critical part. The scientists had to calculate the "energy map" of the molecule.

• The Analogy: Imagine the molecule is a ball rolling down a hill. The "Electronic Structure" is the map of that hill. Is it a smooth slide? Is there a tiny bump (a barrier) the ball has to jump over? Is the hill made of mud or ice?
• The Problem: Some teams used "Simple Maps" (Single-reference methods). These maps were great for the top of the hill but failed when the ball got to the bottom where the terrain got rocky and complex. Other teams used "Detailed Maps" (Multireference methods) that could handle the rocky terrain but were harder to draw.
• The Verdict: The "Simple Maps" often got stuck or predicted the ball would roll forever. The "Detailed Maps" were much better at predicting that the ball would actually jump over a small bump and roll down the other side. This was the biggest lesson: You need a very detailed map to predict how a molecule breaks.

3. The Movie Camera (Nonadiabatic Dynamics)

Once the molecule starts moving, how do you track it?

• The Analogy: Imagine you are filming a race. Do you follow one runner? Do you follow 100 runners? Do you use a drone?
• The Problem: Some teams simulated just a few "runners" (trajectories), while others simulated hundreds. Some used "drone shots" (quantum mechanics), while others used "ground-level cameras" (classical physics).
• The Verdict: Surprisingly, it didn't matter too much which camera you used, as long as your "Map" (Ingredient #2) was good. If your map was wrong, even the best camera would film a wrong movie.

The Results: Did They Win?

When the real experiment happened at SLAC (a giant lab in California) and Shanghai, the scientists compared their predicted movies with the real one.

• The Good News: The field of computational chemistry is getting really good! Most teams predicted the general story correctly: The molecule gets excited, wobbles for a split second, snaps open, and turns into specific new chemicals (like carbon monoxide and propene). They also correctly guessed that the molecule doesn't change its "spin" (a quantum property) during this process.
• The Bad News: The timing was off. Some teams said the molecule broke apart in 100 femtoseconds (a quadrillionth of a second), while others said it took 2,000. Because the "Map" (Electronic Structure) wasn't perfect for everyone, the speed of the movie varied wildly.
• The Missing Piece: None of the teams predicted a specific "glitch" in the camera signal caused by the excited state of the molecule. It was like predicting the car crash but forgetting to mention the smoke.

The Big Takeaway

This paper is essentially a "Calibration Exercise." It's like a flight simulator test for scientists.

1. We are almost there: We can predict what happens in these chemical reactions qualitatively (the story is right).
2. We need better maps: To get the timing and speed right, we need much more accurate ways to calculate the energy of molecules, especially when they are breaking apart.
3. Teamwork wins: No single team could have solved this alone. By comparing 15 different approaches, the community learned exactly where their tools fail and how to fix them.

In short: The scientists successfully predicted the "plot" of the molecular movie, but they are still working on getting the "special effects" and "frame rate" perfect. This challenge proved that while we aren't quite at the point of perfect prediction, we are definitely ready to start making the movies!

Technical Summary

1. Problem Statement

The central question addressed by this work is whether the field of nonadiabatic molecular dynamics (NAMD) has matured enough to be predictive rather than merely interpretative. To test this, a community-wide prediction challenge was organized in 2023.

• Target System: Gas-phase cyclobutanone photoexcited at 200 nm.
• Target Observable: The time-resolved mega-electronvolt ultrafast electron diffraction (MeV-UED) signal.
• Context: The challenge required 15 theoretical groups (involving >70 researchers) to simulate the photochemistry and predict the UED signal before the experimental data was available from the SLAC National Accelerator Laboratory (and independently from Shanghai Jiao Tong University).
• Scientific Gap: While the photochemistry of cyclobutanone is known to involve ring-opening (Norrish Type-I) and intersystem crossing, the specific timescales, branching ratios between C2 (ketene/ethylene) and C3 (cyclopropane/propene + CO) channels, and the role of Rydberg vs. valence states were not fully resolved.

2. Methodology

The paper analyzes the diverse strategies employed by the 15 participating groups, categorized into four main computational components:

A. Photoexcitation (Initial Conditions)

• Sampling: Most groups used a Harmonic Wigner distribution based on the ground-state geometry. However, significant variations existed regarding the treatment of the low-frequency ring-puckering mode (harmonic vs. 1D quantum vs. anharmonic Born-Oppenheimer MD).
• Laser Pulse Treatment: Most groups treated the 200 nm pulse implicitly by applying an energy window to select initial conditions matching the laser bandwidth. Some groups ignored this, while others used explicit weighting based on oscillator strength.
• Electronic Structure for Sampling: A critical debate arose regarding whether to use the same electronic structure method for sampling initial geometries as for the subsequent dynamics. Some groups used high-level methods (e.g., MP2, CCSD) for sampling and switched to multireference methods for dynamics, raising concerns about artifacts from geometry relaxation.

B. Electronic Structure

A wide "zoo" of methods was tested, ranging from single-reference to multireference approaches:

• Single-Reference: EOM-CCSD, LR-TDDFT (with various functionals like PBE0, B3LYP, CAM-B3LYP), and ADC(2).
• Multiconfigurational: SA-CASSCF (various active spaces, e.g., (12/12), (8/10)), MCSCF, and FOMO-CASCI.
• Multireference: XMS-CASPT2 (extended multi-state complete active space second-order perturbation theory) and MRCI.
• Key Finding: Single-reference methods generally described the initial $S_2(3s)$ Rydberg state well but failed to capture the barrier for the adiabatic transition to valence character. XMS-CASPT2 was identified as crucial for correctly describing the barrier height controlling the ring-opening timescale.

C. Nonadiabatic Dynamics

• Mixed Quantum/Classical (MQC): The most common approach, primarily Fewest-Switches Surface Hopping (FSSH) with decoherence corrections (DC-FSSH). Other variants included MASH (Mapping-Approach to Surface Hopping) and Ehrenfest dynamics.
• Trajectory Basis Functions (TBF): Methods like AIMS (Ab Initio Multiple Spawning), AIMC (Ab Initio Multiple Cloning), and DD-vMCG (Direct-Dynamics Variational Multiconfigurational Gaussian).
• Quantum Dynamics: MCTDH (Multi-Configuration Time-Dependent Hartree) using model Hamiltonians (Linear/Quadratic Vibronic Coupling).
• Simulation Times: Varied significantly from 0.2 ps to 10 ps, complicating direct comparisons of product yields.

D. Calculation of Observables

• MeV-UED Signal: Calculated using the Independent Atom Model (IAM) for the elastic scattering contribution.
• Inelastic Scattering: Most groups missed the inelastic scattering contribution from the $S_2(3s)$ Rydberg state, which is responsible for the intense low-momentum transfer feature observed experimentally. Only a few groups attempted to estimate this.
• Analysis: Signals were analyzed via difference pair-distribution functions ($\Delta rPDF$) and lineouts at specific bond distances (e.g., 2.35 Å for ring opening, 3.70 Å for fragmentation).

3. Key Contributions and Results

A. Consensus on Photophysics

• Initial State: All groups agreed the molecule is excited to the $S_2(3s)$ Rydberg state.
• Intersystem Crossing (ISC): A major consensus was that ISC is negligible on the sub-picosecond to picosecond timescale for gas-phase cyclobutanone at 200 nm.
• Mechanism: The primary pathway involves an adiabatic evolution from the Rydberg state to a valence state, crossing a barrier, followed by ring-opening and nonadiabatic transitions to $S_1$ and $S_0$.

B. The Critical Role of Electronic Structure

The most significant finding was the dramatic impact of the electronic structure method on the predicted timescales:

• SA-CASSCF: Predicted extremely fast ring-opening (tens of femtoseconds) because it failed to capture the barrier height between the Rydberg minimum and the transition state (predicting a barrierless path).
• XMS-CASPT2: Correctly predicted a small but non-negligible barrier, resulting in a lifetime for the $S_2$ state of a few hundred femtoseconds, which aligned much better with experimental data.
• Single-Reference (TDDFT/EOM-CCSD): Often predicted the molecule remained trapped in the $S_2$ minimum for picoseconds, failing to initiate ring-opening within the experimental window.

C. Comparison with Experiment

• Qualitative Success: The challenge demonstrated that NAMD is qualitatively predictive. Most multireference approaches correctly identified the formation of C2 (ketene/ethylene) and C3 (cyclopropane/propene + CO) products.
• Quantitative Discrepancies:
  • Timescales: Methods using SA-CASSCF were too fast; TDDFT was too slow. XMS-CASPT2 provided the best match to the experimental decay constant (~0.23–0.29 ps).
  • Signal Features: Most theoretical signals missed the intense low-$s$ feature in the UED signal caused by inelastic scattering from the Rydberg electron.
  • Product Ratios: The C3:C2 branching ratios varied significantly between groups, largely due to differences in simulation duration and the specific electronic structure method used.

4. Significance and Outlook

A. Calibration Exercise

The authors frame this challenge as a "calibration exercise" for computational photochemistry. It highlighted that while the field can predict what happens (product identity), predicting when it happens (kinetics) remains highly sensitive to methodological choices, particularly the electronic structure.

B. "Photochemical Accuracy"

The paper introduces the concept that chemical accuracy (often ~1 kcal/mol or 4 kJ/mol) may not be sufficient for photochemistry. A barrier height error of ~4 kJ/mol can change reaction rates by a factor of 3, leading to order-of-magnitude errors in excited-state lifetimes.

C. Recommendations for the Field

The perspective provides a "To-Do List" for future research:

1. Benchmarking: Electronic structure methods must be benchmarked beyond the Franck-Condon region (optimizing transition states and conical intersections) before running dynamics.
2. Reporting Standards: Researchers must report active spaces, basis sets, and specific code parameters in detail to ensure reproducibility.
3. Inelastic Scattering: Future observables calculations must rigorously include inelastic scattering contributions to match MeV-UED data.
4. Community Collaboration: There is a need for closer interaction between dynamics practitioners and electronic structure developers to address pathological cases (like the Rydberg-valence crossing in cyclobutanone).

Conclusion

The challenge concludes that nonadiabatic molecular dynamics is "nearly" predictive. It successfully reproduced the qualitative photochemical outcome and, when using high-level multireference methods (XMS-CASPT2), achieved near-quantitative agreement with experimental timescales. However, the sensitivity to the electronic structure method and the difficulty in calculating complex observables (like inelastic scattering) indicate that the field is not yet robust enough for "black-box" prediction without careful, system-specific validation.