In our recent paper, “On the temperature dependence of liquid structure” published here, we present a method for calculating temperature derivatives of the radial distribution function from a simulation at a single temperature.
Wait, what do you mean liquid structure?
When we think of liquids – structure might be the last thing on your mind. After all, when you pour water into a cup, it immediately conforms to the shape of the cup. When we say liquid structure, we mean that when you look on the molecular level at any given molecule, it has interactions with the molecules around it. On average, this make it so there are certain distances at which other molecules are more likely to be found and similarly other distances at which other molecules are less likely to be found around our chosen molecule when compared to molecules that are too far away to feel these interactions (they instead feel a much stronger influence from molecules that are close to them). The radial distribution function (RDF), is a mathematical tool used by scientists to describe this ordering by counting the molecules found at a given distance away from the chosen molecule and then comparing whether at that distance the count is larger than what would be expected if the chosen molecule was not present (more ordered) or smaller (less ordered).
As we walk outwards from our chosen molecule, the RDF first has a region where no molecules are present (the above plot is zero). This occurs because our chosen molecule takes up space so no other molecules can be found there! Then we find a very large peak to the right of this region that indicating a region where molecules are more likely to be found surrounding our molecule, this is typically referred to as the first solvation shell. This is quickly followed by a region of depletion as the molecules in that first solvation shell all also take up space. These molecules all also cause ordering around themselves as well, causing a new region of greater order after that depletion, called the second solvation shell. The further out we move this alternating pattern of peaks and depletions gets weaker as less of the ordering is caused by our particular chosen molecule. Eventually, at very long distances there is no ordering from our chosen molecule and the RDF goes to a value of 1 (random ordering).
Okay, but why do we care?
For computational chemists, like myself, one of the first analysis most of us write are codes to calculate the RDF. A number of properties and molecular processes are directly related to the structure of the liquid. For instance, the process by which molecules move in a liquid, called diffusion, can be thought of as moving between the first and second solvation shells. The depth of the depletion between these solvation shells is related to (by a mathematical expression that I won’t delve into here) the ease at which molecules are able to diffuse within a particular liquid. A very crude way of thinking about this is in terms of two liquids, one viscous e.g. molasses, and one not e.g. water. The viscous one might have a deeper depletion in the RDF than the non-viscous one, making it more difficult for molecules to diffuse in molasses than in water. This is an imprecise way of describing this; however, this is just one of many ways that scientists can use the RDF to their advantage.
What I have yet to mention; however, is the importance of temperature as it relates to the RDF. As the temperature of a liquid changes, so does its structure. For instance, if you cool liquid water the peaks and depletions become significantly larger. In terms of the discussion of the previous paragraph, this means that things like diffusion also become more difficult as temperature is lowered. One key part of our work is that we have developed a way of predicting how temperature changes the RDF using only the information available from a single room temperature. In the video below, you can see how the predictions (red line) from room temperature (298 K) work over a large range of temperatures from predicting down to 235 K (blue line) up to 360 K (purple line).
In our work, we show that this method works very well for liquid water and can give us new scientific tools for understanding how its structure changes with temperature.