Over the past few years I have advocated a simple diabatic state model to describe hydrogen bonding in a diverse range of molecular complexes. In my first paper I suggested the following parameterisation of the matrix element coupling the two diabatic states
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.
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.