Significant role of quantum nuclear motion in hydrogen bonding

I recently finished a preprint that I am particularly proud of
Effect of quantum nuclear motion on hydrogen bonding
Ross H. McKenzie, Christiaan Bekker, Bijyalaxmi Athokpam, Sai G. Ramesh

I welcome any comments. I hope to submit to J. Chem. Phys. at the end of the week.

Many of the issues involved I have blogged about before. Here I will just mention two issues that I found particularly interesting. Both relate to the significance of very small changes in bond lengths due to quantum nuclear effects [tunneling and zero-point motion].

In hydrogen bonded complexes [A-H...B] one observes a subtle secondary isotope effect: when the hydrogen atom is replaced by a deuterium atom the distance R between the A and B atoms changes slightly, on the scale of one-hundredth of an Angstrom [and denoted Delta R]. Furthermore, as shown below, the variation of Delta R with R is a non-trivial non-monotonic function.

In the paper we show that for R less than 2.7 A these trends are captured semi-quantitatively by a very simple calculation which assumes that the effect is dominated by the variation with R of the zero-point energy of the A-H stretch.

This leads to the second result that I found both surprising and impressive. When R ~ 2.5 A, the D for H isotope substitution increases R to about 2.54 A. This apparently small change has another secondary effect: it produces a significant change in the energy barrier in the potential energy curve for the A-D stretch, compared to the A-H stretch. This in turn significantly changes the A-D stretch vibrational frequency. Indeed the A-H and A-D stretch can have similar frequencies, whereas for isolated molecules the frequency ratio would be close to 1.4=sqrt(2). This explains rather complicated and large isotope effects I blogged about more than two years ago.