with two free parameters Delta1 and b, which describe the energy scale and length scale for the interaction.

R1 is just a reference distance ~ 2.4 A, introduced so that the prefactor Delta1 corresponds to a physically relevant scale.

The two parameter values I chose give a quantitative description of a wide range of properties [bond lengths, vibrational frequencies, and the associated isotope effects, when the quantum nuclear motion is taken into account.

Last week I found this nice paper

Solvent-Induced Red-Shifts for the Proton Stretch Vibrational Frequency in a Hydrogen-Bonded Complex. 1. A Valence Bond-Based Theoretical Approach

Philip M. Kiefer, Ehud Pines, Dina Pines, and James T. Hynes

It uses a similar two-diabatic state model and references earlier work of Hynes going back to 1991. A parameterisation like that above is used.

Below is a plot of Delta (kcal/mol) vs. R (Angstroms), comparing my parametrisation to Hynes.

The curve with the smaller slope is the parameterisation of Hynes.

**I found this agreement very satisfying and encouraging.**I have mostly been concerned with symmetrical complexes [where the proton affinity of the donor and acceptor is equal] and bonds of strong to moderate strength [R ~ 2.3-2.6 Angstroms] and have compared the theory to experimental data for solid state materials. In contrast, Hynes has been mostly concerned with asymmetric complexes in polar solvents with weaker bonds [R ~ 2.7-2.8 Angstroms].

I also felt bad that I had not referenced Hynes work. Then I went back and checked my first paper. To my relief, I found I had explicitly stated that the parameterisation in his 1991 paper was comparable to mine. It is amazing how quickly I forget stuff!

But the main point of this post is to raise two general questions.

1.

**Should I really be so happy?**Aren't I missing the point of simple models: to give insight into the essential physics and chemistry and describe trends in diverse set of systems. All that matters is that the parameters are "reasonable", i.e. not crazy.

2.

**What is a reasonable expectation for consistent parametrisation of simple models?**At what point does one abandon a model because it requires some parameters that are "unreasonable"? For example, if Hynes parameters differed by a factor of ten or more I would say there is a serious problem with the model. But I would not be that concerned by a 50 per cent discrepancy.

Here is a concrete example for 2. At a recent Telluride meeting, Dominika Zgid lampooned the fact that for cerium oxides, people doing DFT+U calculations have used values of U ranging from 1 to 10 eV in order to describe different experimental properties. To me this clearly shows that there is physics beyond DFT+U in these materials.

I welcome answers. I realise that the answers may be subjective.

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