My Research in Five Levels

By: Annabelle Carney, DuBay Group

UVA ChemSciComm

Primary School:

Everything around you is constantly interacting with its surroundings, just like how you and your friends play together! Imagine you and your best friend are laughing and running around, maybe even giving one another piggyback rides – an interaction between you two which might even make you smile and laugh. Scientists think about how the invisible-to-the-eye particles in the world around us move and interact with one another. These tiny interactions occur constantly in the whole world around us and shape our experience. Take water for example. The water you see in that glass is made up of millions of tiny water molecules. Each molecule is so small we cannot see it, but when we put many water molecules together, we can see them, because they interact with one another. The water molecules interact by constantly moving and bumping into each other, which results in them briefly being held together by very weak forces until they move apart. This is as if the water molecules are giving each other little piggyback rides too! The ways the water moves and interacts determines how the water is behaving. Although we don’t see these small movements, they are always happening. By studying these little movements, we can better understand the world around us to make new things. Scientists can study these kinds of movements with a computer, to better imagine how the particles are moving. To make sure their computer predictions matchwhat happens in nature, they are always looking for and correcting issues. By doing this, they can better understand the motion and behavior of tiny molecules that make up everything we see and touch every day. 

High School:

When looking at a glass of water, you might have thought about what happens on a molecular level when you mix some flavoring into it and it dissolves, or how the colored dyes go from a single drop to an entirely blue drink. Well, the flavoring moves through the water from an area of higher concentration, the drops you put in, to an area of lower concentration, the rest of your water, by interacting with the water molecules inside the cup. This process is known as diffusion; determining the extent a particle can diffuse in a particular chemical environment is an important measurement. Mixing lemonade from lemon juice, water, and sugar may seem very different from what scientists use to make the medicines that you take when you’re sick, but diffusion is a fundamental chemical concept that branches across many fields of knowledge and is commonly studied to develop the products you use in your day-to-day life. For instance, when making medicines, scientists can now use computers to predict what combinations of materials will protect you from the flu or help you get over a cold. Like all science, there is plenty of room for error. Using appropriate values within a computer simulation can reveal lots of information about how water molecules interact. However, errors can occur if the instructions provided don’t fit quite right. Scientists are researching the best methods to prevent and correct potential issues, such as underestimations of diffusion coefficients, which describe how quickly a molecule might move through a given chemical environment. By understanding the corrections to make, we can confidently describe diffusion and quantify how different molecules are moving and interacting throughout our cup of water.

College:

During your intro to college chemistry course, one of the first topics discussed pertains to atomistic and molecular interactions and how these interactions can be measured. Using computer code, molecular dynamics (MD) simulations can be used to visualize and quantify atomistic interactions by using fundamental chemistry and physics to track changes to a system over time. From these simulations, properties such as particle velocity can be described to elucidate how particular interactions influence a system. One important transport property calculated from these simulations is the diffusion coefficient, which is the measurement of the rate of natural, random, movements of particles through a specific chemical environment. The diffusion coefficient can inform on the extent of interactions and physical forces in the system that drive particle motion. When using MD, it is important to ensure that the size of the simulation box is compatible with the length of the interactions that influence particle behaviors. For example, when the simulation box is too small, artifacts known as finite-size effects (FSE) arise which unrealistically lower the diffusion coefficient because particles are interacting with their periodic images – a result of applying periodic boundary conditions to replicate a unit cell in all directions to approximate bulk behavior with a smaller model. If the interaction length is too long, or the simulation box too small, a particle can unphysically correlate with its periodic image, effectively disrupting proper transport mechanisms and behaviors. Since MD simulations are commonly used in the development of pharmaceuticals, it is important to understand and correct for these FSEs in both plain liquids, and increasingly complicated systems. As scientists, understanding and correcting for FSEs matters to provide a clear, accurate picture for developing important products from appropriate physical parameters and principles.

Graduate Student:

Molecular dynamics (MD) simulations, which integrate Newton’s equation of motion over time, allow scientists to study a system of interest with atomistic or molecular detail to gain insights that would often not be possible with traditional laboratory experiments. MD simulations can become prohibitively slow as the system size increases. Thus, to reduce computational cost, it is common to reduce the system down to a unit cell and replicate that unit cell in every dimension. This technique is referred to as periodic boundary conditions (PBC) and it vastly improves computational efficiency.  PBCs avoid edge-effects and allow for the approximation of a bulk system from which diffusion coefficients can be more accurately determined. Accurately determining the diffusion coefficient of the system being studied is particularly important in areas such as drug-discovery when looking at small scale, short- and long-range interactions of a system. Specifically, the theoretical MD model can help influence how wet-lab chemists approach their future experiments or compare those experiments to a simulation. However, when using PBCs, unphysical consequences like finite-size effects (FSE) can arise when the simulation size and the hydrodynamic interaction cut-offs within those simulations aren’t tuned appropriately. When this occurs, diffusion coefficients derived from the time correlation of particle velocities or displacements are not accurate which results in data that does not correctly describe the physical nature of the simulation. In fact, the diffusion coefficient has a 1/L FSE correction influenced by box length, L, due to insufficient interaction decay. Thus, the FSEs are most noticeable as the simulation box size decreases. This has previously been studied in broad systems, including rectangular and slab geometries, as well as in binary and ternary fluid mixtures, but the extent of the FSEs to the diffusion coefficient in more complex liquid simulations remains unclear. By examining FSEs in systems with liquid argon, and water, the effects of box sizes and their interactions can be evaluated to establish a foundation for future studies from which increasingly complex simulations (i.e. an adsorbate on a curved surface) will be conducted to better understand the influence of FSEs and inform simulation design.

Expert: 

The use of periodic boundary conditions (PBCs) in molecular dynamics (MD) simulations allows one to study larger, and potentially more complex, systems of interest in a computationally efficient manner. PBCs are regularly employed in simulations within the fields of theoretical chemistry, drug-discovery, material sciences, and a myriad of others that benefit from the understanding of atomistic or molecular behavior.  However, when using PBCs it is important to ensure sufficient hydrodynamic decay across periodic images to avoid introducing nontrivial, systemic artifacts commonly known as finite-size effects (FSEs), when investigating transport properties such as diffusion. In the absence of sufficient decay, particles in simulations will behave in an unphysical manner due to their interactions with their own periodic image. This arises when the simulation box is too small, or when the interaction cut-off values extend beyond half of the simulation box length, effectively violating the minimum image convention. As the simulation box increases in length, L, the FSEs are reduced, bulk behavior is more accurately modeled, and the accuracy of the diffusion coefficient, D, which is typically computed via the Stokes-Einstein or Green-Kubo relations, increases as . When the simulation box is too small, the diffusive behavior of the system is impacted, and the diffusion coefficient deviates from experimentally derived coefficients. This is typically mitigated by linear extrapolation of the coefficient from simulations on multiple box sizes to the infinite-size limit. Additionally, theoretical derivations have highlighted the 1/L FSE correction factor, stemming from long range hydrodynamic interaction decay of 1/r, that further justifies the corrections for small simulation boxes. Due to the broad range of applications for MD, accounting for PBCs and their potential FSEs is critical to provide accurate theoretical representations. Understanding FSEs first in simple simulations of liquid argon and liquid TIP3P [MCW(1] water, a geometrically rigid, three-site model with fixed bond angles and lengths commonly used for simulating water, and then eventually extending to more complex liquid simulations is foundational to improving the accuracy and confidence of transport-property modeling. Without accounting for FSEs, there is the possibility of under-reporting the magnitudes of the diffusion coefficients, an error that has the potential to cost theorists, wet-lab chemists, and drug-discovery researchers time, resources, and money.