At the workshop a couple of talks have brought home to me two important organising principles for understanding and describing quantum effects involving hydrogen bonding in condensed phases. These are relevant to a wide range of problems from properties of bulk water to proton transfer in enzymes.
1. Competing quantum effects.
In hydrogen bonding as the donor acceptor distance decreases the hydrogen bonding gets stronger. This decreases the frequency of the O-H stretch on the donor and increases the frequency of the O-H bend.
[This can be seen in Figures 5 and 6 in my CPL]. Consequently, their are two competing contributions to the zero-point energy. These reduce the total quantum effect and also make it more challenging to calculate accurately.
This idea was highlighted in a 2007 JCP by Scott Habershon, Tom Markland, and David Manolopoulos and a 2012 PNAS by Tom Markland and Bruce Berne.
On tuesday, Tom Markland highlighted how these competing quantum effects were important for understanding isotope effects in the enzyme Ketosteroid isomerase.
2. Rate processes dominated by rare quantum events
If one looks at the average bond lengths in aqueous systems one might think that the hydrogen bonds are weak. However, due to quantum and thermal fluctuations there are rare events where oxygen atoms are sufficiently close together that there are transient strong hydrogen bonds where protons can be delocalised between two oxygen atoms.
This was highlighted in a talk by Michele Ceriotti.
These ideas were first developed by Dominik Marx and Mark Tuckerman and are nicely summarised in Section 2 in this review. The key figure is below. The left and right plots correspond to a quantum and a classical simulation, respectively.