This figure shows a molecular worm representing a butane molecule as it navigates through the chemical labyrinth of a typical alkane-cracking zeolite. The alogorithm was used to compute the shortest path for the butane molecule to traverse one unit of the periodic zeolite structure. (Image courtesy of Maciej Haranczyk)
With the passage of a molecule through the labyrinth of a chemical system being so critical to catalysis and other important chemical processes, computer simulations are frequently used to model potential molecule/labyrinth interactions. In the past, such simulations have been expensive and time-consuming to carry out, but now researchers with the Lawrence Berkeley National Laboratory (Berkeley Lab) have developed a new algorithm that should make future simulations easier and faster to compute, and yield much more accurate results.
“There are 190 zeolite structures known to exist today, but they constitute only a very small fraction of the 2.5 million structures that are feasible on theoretical grounds,” Haranczyk says. “The development of a database of hypothetical zeolite structures has long been regarded as an important step toward designer catalysts as it could, in principle, be screened for zeolites of any property. However, brute-force screening of all possible zeolite structures through molecular dynamics characterization is computationally infeasible, hence the need for rapid triaging based on an initial analysis of various properties.”
The successful testing of the molecular worm algorithm on a typical alkane-cracking zeolite opens an immediate door to its use in screening for new zeolites as well as a wide variety of other porous materials. The algorithm should also prove valuable in the search for materials that can capture carbon emissions before they enter the atmosphere. With further refinements, it could also one day be applied to proteins, especially enzymes.
A key to the success of this new algorithm was its departure from the traditional treatment of molecules as hard spheres with fixed radii. Instead, Haranczyk and Sethian constructed “molecular worms” from blocks connected by flexible links. These molecular worms provide a more realistic depiction of a molecule’s geometry, thereby providing a more accurate picture of how that molecule will navigate through a given chemical labyrinth, as Sethian explains.
“In practice, most molecules of interest, even the simplest solvents or gases, rarely have a spherical shape, and treating molecules as such may lead to errors,” he says. “Our molecular worms are able to change shape during the traversing of a chemical labyrinth, which allows them to reach areas not accessible to either a single large spherical probe or a rigid real-shape probe. This significantly extends the range of probes and structures that can be efficiently examined.”
As a molecule navigates through a chemical system, its access to a particular site or place within that system determines the extent to which catalysis and other chemical reactions may occur. Many of these critical sites are either buried in clefts, pockets or hidden cavities, or else represent channel systems. The accessible volume of a chemical system – the free volume available to a penetrating molecule – is also critical to the system’s physical properties, including diffusion, viscosity and electrical conductivity. Predicting whether a molecule will be able to traverse through a given chemical labyrinth is the first question that a simulation must answer, followed by identifying the shortest transverse route, finding the largest probe that can transverse though the system, and calculating accessible volume.
Haranczyk, looking to automate the process by which the void spaces of porous materials are analyzed, had an idea for a probe that would walk through the inside a material and map it. Sethian had been working on mathematic techniques that can be used in robotic navigations and path planning, as well as a host of algorithms for computing geometries in complex settings.
“What’s exciting here is to bring together two disparate worlds to build a new technology” says Sethian.
Predicting whether a molecule can traverse chemical labyrinths of channels, tunnels, and buried cavities usually requires performing computationally intensive molecular dynamics simulations. Often one wants to screen molecules to identify ones that can pass through a given chemical labyrinth or screen chemical labyrinths to identify those that allow a given molecule to pass. Because it is impractical to test each molecule/labyrinth pair using computationally expensive methods, faster, approximate methods are used to prune possibilities, “triaging” the ability of a proposed molecule to pass through the given chemical labyrinth. Most pruning methods estimate chemical accessibility solely on geometry, treating atoms or groups of atoms as hard spheres with appropriate radii. Here, we explore geometric configurations for a moving “molecular worm,” which replaces spherical probes and is assembled from solid blocks connected by flexible links. The key is to extend the fast marching method, which is an ordered upwind one-pass Dijkstra-like method to compute optimal paths by efficiently solving an associated Eikonal equation for the cost function. First, we build a suitable cost function associated with each possible configuration, and second, we construct an algorithm that works in ensuing high-dimensional configuration space: at least seven dimensions are required to account for translational, rotational, and internal degrees of freedom. We demonstrate the algorithm to study shortest paths, compute accessible volume, and derive information on topology of the accessible part of a chemical labyrinth. As a model example, we consider an alkane molecule in a porous material, which is relevant to designing catalysts for oil processing.