Benchmark different models

[bsonghao]

Displaced models

These are two by two vibronic models with coupling strength in a descending order

Thermal internal energy

Partition function

[bsonghao]

Jahn Teller models

These are two by two vibronic models with coupling strength in a descending order

Thermal internal energy

Partition function

[ngraymon]

Thoughts

The plots look nice and are clean and well labeled!

• ev should be eV
• you could add (absolute value) or (dimensionless) to the y axis
• You could add $\lambda$=0.04 and so forth to the plots to quantify the coupling of each model (this also helps highlight that model 1 has no coupling)
• You might consider adding +/- 1kCal/mol envelope on the eV plots to show when the FCI becomes unacceptable?
• It would be nice to have another version of the plots where they all have the same y axis so you could compare curvature change with respect to the different coupling strengths. Image 6 horizontally arranged plots whose y axes are:
  • 0.25 eV to 1.0 eV (for the Jahn Teller)
  • 0.3 eV to 0.6 eV (for the Displaced)
• You don't need the Plot of in the figure title (and I would remove the title completely when including in any paper) It is simpler to say Janh-Teller 1 (\lambda=0.00eV) or Jahn-Teller 2 (\lambda=0.04eV) or even just add $\lambda = 0.04eV$ into the Legend. You can also alternatively draw it in a small text box in the corner of the plot. Example image of small text box in corners of plot

Questions

1. Are you able to calculate lower temperatures; or are there numerical challenges below 250K?

2. For your temperature range, how many actual data points are you plotting? I would assume that instead you are plotting over a T range in intervals of 50 or 25K? Or are you able to evaluate the y axis for all integer values of T?

3. For the 1(one) models It looks like the lines do not completely overlap, is this due to the approximate nature of the TFCC? Since the 1(one) models have no off-diagonal coupling and are completely independent H.O. the answer can be analytically evaluated and should be exactly the same as the FCI; no?

[ngraymon]

In addition: CONGRATS! 🍾 🥳 🎆 It appears that your implementation is working, I imagine it was a lot of hard work to get to this point!! 🏆