# Criteria of periodic boundary condition

• mmssm
In summary, a periodic boundary condition is a mathematical condition used to simulate an infinite system by imposing a repeating boundary. It requires a repeating boundary, consistent particle distances, and consistent system properties. The advantages include the ability to simulate larger systems with fewer particles and study periodic structures. However, it assumes an infinite system and can introduce artificial interactions near the boundary. The appropriate size for the boundary depends on the system and desired accuracy.
mmssm
We used to apply periodic boundary condition to simulate an infinite system. What will happen if the interactions between atoms do not drop to zero even when they are infinitely far away? Is the periodic boundary still valid? How can I prove the periodic boundary condition is valid or not? thanks.

This is indeed a problem, encountered e.g. when you consider a system with dipoles.
There exist methods to split off the long range part of the fields, namely Ewald summation.

## 1. What is a periodic boundary condition?

A periodic boundary condition is a mathematical condition used in simulations or calculations to mimic an infinite system by imposing a repeating boundary, where the system is repeated in all directions. This allows for the simulation of a larger system with fewer particles or a smaller computational cost.

## 2. What are the criteria for a periodic boundary condition?

The criteria for a periodic boundary condition include having a repeating boundary, maintaining the same distance between particles in each repetition, and ensuring that the properties of the system are consistent across the boundary.

## 3. What are the advantages of using a periodic boundary condition?

The advantages of using a periodic boundary condition include the ability to simulate larger systems with fewer particles, reducing computational costs, and allowing for the study of systems with periodic structures, such as crystals or polymers.

## 4. What are the limitations of using a periodic boundary condition?

One limitation of using a periodic boundary condition is that it assumes an infinite system, which may not accurately reflect the real-world system being studied. Additionally, periodic boundary conditions can introduce artificial interactions between particles near the boundary, affecting the accuracy of the simulation.

## 5. How do you choose the appropriate size for the periodic boundary in a simulation?

The appropriate size for the periodic boundary in a simulation depends on the specific system being studied and the desired level of accuracy. Generally, the boundary should be large enough to minimize interactions between particles near the boundary, but not too large to significantly increase computational costs.

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