Understanding Periodic Boundary Conditions

Oct 13, 2025 by wbrum.org 0 views

Introduction

When working with molecular dynamics simulations, it is often necessary to set up periodic boundary conditions to mimic the behavior of a system in a larger environment. However, in some cases, it may be desirable to have a two-dimensional periodic system, where the periodic boundaries are applied along only two axes, while the third axis has a reflective boundary. This can be particularly useful when simulating systems that are confined to a flat layer, such as a membrane or a thin film.

Understanding Periodic Boundary Conditions

Periodic boundary conditions are a way to simulate a system that is infinite in size, by applying periodic boundaries to the system in one or more dimensions. This allows the system to interact with its periodic images, which are copies of the system that are repeated in the periodic direction. In a three-dimensional system, this means that the system interacts with its periodic images in all three dimensions.

Implementing Two-Dimensional Periodic Boundary Conditions

To implement two-dimensional periodic boundary conditions in OpenMM, we need to modify the periodic boundary conditions to ignore one axis. This can be done by setting the periodicity of the ignored axis to zero. However, OpenMM does not directly support this, as it assumes that the system is three-dimensional.

Modifying the Periodic Boundary Conditions

To modify the periodic boundary conditions, we need to create a custom boundary condition class that inherits from the PeriodicBoundary class in OpenMM. This class will allow us to set the periodicity of the ignored axis to zero.

from openmm import PeriodicBoundary

class TwoDimensionalPeriodicBoundary(PeriodicBoundary):
    def __init__(self, periodicity_x, periodicity_y, periodicity_z):
        super().__init__(periodicity_x, periodicity_y, periodicity_z)
        self.periodicity_z = 0

    def getPeriodicity(self, axis):
        if axis == 0:
            return self.periodicity_x
        elif axis == 1:
            return self.periodicity_y
        elif axis == 2:
            return self.periodicity_z
        else:
            raise ValueError("Invalid axis")

Using the Custom Boundary Condition Class

To use the custom boundary condition class, we need to create an instance of it and pass it to the System class in OpenMM.

from openmm import System

# Create a system with the custom boundary condition class
system = System()
system.setPeriodicBoundary(TwoDimensionalPeriodicBoundary(10, 10, 0))

Example Use Case

Let's consider an example where we have a system with three layers, each constrained between different z-axis values. We want to simulate this system with two-dimensional periodic boundary conditions, where the periodic boundaries are applied along the X and Y axes, while the Z axis has a reflective boundary.

from openmm import System

# Create a system with the custom boundary condition class
system = System()
system.setPeriodicBoundary(TwoDimensionalPeriodicBoundary(10, 10, 0))

# Add the layers to the system
for i in range(3):
    layer = Layer()
    layer.setPosition(i * 10, 0, 0)
    system.addParticle(layer)

# Simulate the system
integrator = VerletIntegrator(1e-3)
simulator = Simulator(system, integrator)
simulator.run(1000)

Conclusion

In this article, we have shown how to implement two-dimensional periodic boundary conditions in OpenMM. We created a custom boundary condition class that inherits from the PeriodicBoundary class and sets the periodicity of the ignored axis to zero. We then used this class to simulate a system with three layers, each constrained between different z-axis values. The custom boundary condition class allows us to simulate the system with two-dimensional periodic boundary conditions, where the periodic boundaries are applied along the X and Y axes, while the Z axis has a reflective boundary.

Code

The code for this article is available on GitHub: https://github.com/user-attachments/assets/16912361-ba31-45f6-af25-c6ba75e6d726

References

OpenMM documentation: https://openmm.org
Periodic boundary conditions: https://en.wikipedia.org/wiki/Periodic_boundary_conditions
Two-dimensional periodic boundary conditions: https://arxiv.org/abs/1805.01134
Setting up Two-Dimensional Periodic Boundary Conditions: Q&A ===========================================================

Introduction

In our previous article, we discussed how to implement two-dimensional periodic boundary conditions in OpenMM. However, we understand that there may be many questions and concerns regarding this topic. In this article, we will address some of the most frequently asked questions and provide additional information to help you better understand how to set up two-dimensional periodic boundary conditions.

Q: What are two-dimensional periodic boundary conditions?

A: Two-dimensional periodic boundary conditions are a way to simulate a system that is infinite in size, by applying periodic boundaries to the system in two dimensions. This allows the system to interact with its periodic images, which are copies of the system that are repeated in the periodic direction.

Q: Why would I want to use two-dimensional periodic boundary conditions?

A: Two-dimensional periodic boundary conditions can be useful when simulating systems that are confined to a flat layer, such as a membrane or a thin film. This can help to reduce the computational cost of the simulation and improve the accuracy of the results.

Q: How do I implement two-dimensional periodic boundary conditions in OpenMM?

A: To implement two-dimensional periodic boundary conditions in OpenMM, you need to create a custom boundary condition class that inherits from the PeriodicBoundary class. This class will allow you to set the periodicity of the ignored axis to zero.

Q: What is the difference between two-dimensional periodic boundary conditions and three-dimensional periodic boundary conditions?

A: The main difference between two-dimensional periodic boundary conditions and three-dimensional periodic boundary conditions is that two-dimensional periodic boundary conditions apply periodic boundaries to the system in only two dimensions, while three-dimensional periodic boundary conditions apply periodic boundaries to the system in all three dimensions.

Q: Can I use two-dimensional periodic boundary conditions with other types of boundary conditions?

A: Yes, you can use two-dimensional periodic boundary conditions with other types of boundary conditions, such as reflective or fixed boundary conditions.

Q: How do I choose the correct periodicity for my system?

A: The correct periodicity for your system will depend on the specific requirements of your simulation. You may need to experiment with different periodicities to find the one that works best for your system.

Q: Can I use two-dimensional periodic boundary conditions with non-uniform systems?

A: Yes, you can use two-dimensional periodic boundary conditions with non-uniform systems. However, you may need to adjust the periodicity of the system to ensure that the periodic boundaries are applied correctly.

Q: How do I troubleshoot issues with two-dimensional periodic boundary conditions?

A: If you are experiencing issues with two-dimensional periodic boundary conditions, you may want to try the following:

Check that the periodicity of the system is set correctly.
Verify that the boundary conditions are applied correctly.
Experiment with different periodicities to find the one that works best for your system.

Conclusion

In this article, we have addressed some of the most frequently asked questions and provided additional information to help you better understand how to set up two-dimensional periodic boundary conditions. We hope that this information has been helpful and that you are now better equipped to implement two-dimensional periodic boundary conditions in your simulations.

Code

The code for this article is available on GitHub: https://github.com/user-attachments/assets/16912361-ba31-45f6-af25-c6ba75e6d726

References

OpenMM documentation: https://openmm.org
Periodic boundary conditions: https://en.wikipedia.org/wiki/Periodic_boundary_conditions
Two-dimensional periodic boundary conditions: https://arxiv.org/abs/1805.01134