Computer scientists, cartographers, social scientists, and many others use the concepts of networks to understand patterns that lead to a phenomenon, and nowhere is the concept of networks more relevant than in chemistry. Atoms forming bonds to create a molecule is a type of network, and at a larger scale, so too are the interactions between the many molecules that make up the liquids and solids that surround us. Using an algorithm originally designed to improve searches for webpages over the immense network that is the internet, the scientists at the Interfacial Dynamics in Radioactive Environments and Materials (IDREAM) Energy Frontier Research Center use the patterns in these chemical networks to better understand the chemical reactions that occur within nuclear waste.
Complexity of a chemical reaction. An exciting advantage of modeling and simulation is the ability to predict the chemical reactions that molecules undergo over time. Technically, a chemical reaction is a rare event—thus, observing one in a computer simulation can be a challenge. Scientists also want to learn about the myriad potential reactions that molecules could undergo. After all, the molecules in nuclear waste experience extremes in temperature, radiation, or pressure that could lead to lots of different reactions being possible. To overcome the problem of observing rare chemical reactions, and exploring all the reactions that may be possible, computational chemists must first determine the collective change in all of the atomic positions during a reaction process, also known as the reaction coordinates. With the correct reaction coordinates in hand, simulations can force the reaction to occur faster than would normally be observed, and test what reactions may become important in the extreme environments of nuclear waste.
The biggest challenge for scientists is to determine these reaction coordinates, which can be complex and involve changes to distances and angles between atoms as well as the concerted movement of groups of molecules. All of these can be involved in the total change in energy during a reaction process. The combined representation for all of these changes is called the collective reaction coordinate. To explore and discover new collective reaction coordinates, researchers have turned to the networks of chemical interactions between atoms and molecules. Within a chemical network, atoms or molecules become a vertex that is connected to another vertex by some type of chemical interaction. This interaction could be a covalent bond, or a weaker force, like the hydrogen bonds that make up water. Analyzing the patterns of chemical networks inside molecules and between collections of molecules opens new possibilities of how to understand changes that may occur in a chemical reaction.
PageRank™ algorithm. Named after Larry Page, a founding member of Google, the algorithm is used to rank websites based on the network associated with their connectivity to other websites. The points or “vertices” in the network represent webpages, and the lines or “edges” are the hyperlinks between sites. Each vertex is then assigned some probability. This probability describes the chance that an internet surfer clicking randomly through the hyperlinks will end up at a website. More generally, it is the probability of ending up at a given vertex from randomly moving across connected websites in the network. This probability is the page rank value, and every website vertex in a network is assigned a value that determines how often you are likely to visit it by randomly walking through a graph. The higher the probability a website has, the higher the value will be, and Google will place it at the top of a list of search results. These probabilities mean that the PageRank™ algorithm can measure the connectivity pattern about a website.
In place of reaction coordinates. When considering a chemical network, one made of atomic or molecular vertices and edges based on interactions, scientists can use PageRank™ to uniquely describe both the nearby and faraway patterns about that vertex. This means that PageRank™ can describe the chemical environment about an atom or a molecule. As the environment about an atom or molecule changes during a chemical reaction, the surrounding connectivity, and therefore the connectivity value, will correspondingly change. Recent research has highlighted that PageRank™ can track complex changes that occur during a chemical reaction by measurement of this connectivity and can be used as a new collective reaction coordinate. The power of this method is that all of the complexity of a chemical reaction can be reduced to the systematic change in value over time.
Navigating the energy landscape. The importance behind the idea of PageRank™ lies in connecting the patterns in the chemical network to the energy landscape of a chemical system. Every geometry of all of the atoms has an associated energy. All the possible positions of all of the atoms create a highly dimensional energy landscape. For a chemical reaction, the reactant and the product will represent two points on the energy landscape. Finding the path between these two points is very often not an easy task.
To visualize this problem, picture the energy landscape as a series of mountains and valleys. Imagine now that you are in a mountain town (A) and are trying to find all the easiest routes to a nearby valley town (B). To do this, you might try all the nearest paths leading downhill and even some of the smaller uphill paths. You can make some guesses of what the right way may be, but you’re never really sure. Eventually you’ll find a path to town B, but it may not be the fastest or most efficient route. This is similar to what happens in traditional methods of trying to find reaction pathways by changing individual atom positions, or distances between molecules. You can follow the energy landscape by changing atomic positions or distances, but it is nearly intractable to learn about all aspects of the energy surface and find the “best” route between a reactant and a product.
However, if you take the position that each point on an energy landscape is really just a set of different chemical networks, characterized by their own page ranking, then the path between a reactant and a product amounts to understanding the change in the chemical network and thus the change in the page rank value. Going back to the mountain analogy, this means that your path is well defined between towns A and B. In this way, computational scientists can use PageRank™ to predict chemical reactions that molecules undergo over time and explore the range of possible reactions for an atom or molecule.
Learning about changing forms of aluminum and extreme electrolyte solutions. This research is immediately relevant to scientists in IDREAM, where an outstanding problem is the transformation of aluminum hydroxide in solution from a tetrahedral geometry to that of an octahedral one. This structural change is pivotal in better understanding how to dissolve the aluminum metal remnants in nuclear waste left over from the metal cladding that had been used to encase nuclear fuel rods. Additionally, these reactions are occurring in electrolytes that have a huge concentration of ions. Water is actually a solute and not a solvent due to the extremely high ionic strength. The presence of ions that may come together and form extended networks of interactions can strongly influence the transformations of aluminum. Thus, within the nuclear waste studied by IDREAM, the chemical reactions involve complex changes to large groups of molecules and atoms—a situation ideal for using the PageRank™ algorithm.
Using a technique called “biasing,” scientists at IDREAM slowly changed the page rank for tetrahedral aluminum hydroxide to force the aluminum to first adopt a penta-coordinated intermediate state. Then they slowly changed the ranking again to form the octahedral aluminum hydroxide. Along this path, they monitored the energy to understand and map out the energy landscape for this chemical reaction. As they observed the energy landscape going from the tetrahedral to octahedral forms, they determined it involves going uphill—meaning this process is unfavored in the conditions used within the simulation (pure water). Future simulations will examine how this energy landscape changes when increasing the concentration of ions and making the simulation more representative of the conditions in nuclear waste. This invaluable tool will allow researchers to better study and understand this transformation process that is vital in the aluminum dissolution problem in nuclear tank waste.
A new tool for computational scientists. This powerful new method is immediately applicable to many computational analyses of transitional pathways. It’s not just limited to tracking coordination changes, but any chemical interaction that can be represented by chemical networks that change over the course of that interaction. Now, an algorithm originally designed to bring you the most relevant webpage you were searching for can bring a molecular dynamics simulation to a result you would rarely find otherwise.
