Is the tail correction method suitable for all crystal structures?

[aihaike]

Hi all,

I'm doing classical (Monte Carlo) simulations on crystal structures using so far the following tail correction where $$\rho(r)$$ is the pair correlation function and $$U(r)$$ the pair potential.

$$2N\pi\rho\int_{r_{c}}^{\infty}\mathrm{d}r\, r^{2}U(r)$$

It is usual to assume that $$\rho(r)=1$$ for $$r>=r_{c}$$.

I'm wondering if this approximation is suitable for crystals.
For fcc and hcp Lennard Jones systems, lattice sum has been implemented (J. Chem. Phys., Vol. 115, No. 11 ; J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York, 1954, pp. 1036–1039) and I'd like to know if there is a general approach to apply it to any crystal structure.
Martin Dove talks about that as well in his book "Introduction to Lattice Dynamics" but he uses a kind of Ewald summation and I'd prefer to use the same approach as for the Lennard Jonesium.

Thanks in advance,

Eric.

 

[eljose79]

Hi Eric,

Thank you for sharing your work on classical simulations of crystal structures. The tail correction you have used so far seems appropriate for pair potentials, but it may not be suitable for crystals. It is important to consider the long-range interactions and periodicity of crystals in your simulations.

As you mentioned, the lattice sum method has been used for fcc and hcp Lennard Jones systems. This method accounts for the long-range interactions by summing over all periodic images of the unit cell. This is a more accurate approach for crystals and can be extended to other crystal structures as well.

Another option is to use the Ewald summation method, which is a widely used technique for treating long-range interactions in crystals. This method involves splitting the potential into short-range and long-range components and using different approaches to calculate each part. This method has been used by Martin Dove in his book "Introduction to Lattice Dynamics" and can be applied to various crystal structures.

In general, there is no one-size-fits-all approach for simulating crystals, and the method you choose will depend on your specific system and goals. I recommend consulting with experts in the field and researching different methods to determine the most suitable approach for your simulations.

Best of luck with your research!

 

[charng]

The tail correction method is a useful tool for correcting for errors in classical simulations of crystal structures. However, it may not be suitable for all crystal structures.

The effectiveness of the tail correction method depends on the accuracy of the pair potential and the pair correlation function used. In the case of fcc and hcp Lennard Jones systems, the lattice sum method has been implemented and shown to be more accurate than the tail correction method. This has been demonstrated in the literature (J. Chem. Phys., Vol. 115, No. 11 ; J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York, 1954, pp. 1036–1039).

For other crystal structures, it may be necessary to use a different approach, such as Ewald summation, as mentioned by Martin Dove in his book "Introduction to Lattice Dynamics". This approach may be more suitable for some crystal structures and may produce more accurate results.

In general, it is important to carefully consider the specific crystal structure and the accuracy of the potential and correlation function when deciding on the most suitable method for correcting for errors in classical simulations. It may be necessary to use a combination of methods or to develop a new approach for certain crystal structures.