So, I have a system of n number of molecules inside a box which is supposed to be solid. I performed the md simulation of the system using stochastic integrator in a box. I know the lattice of the crystal, and thus the theoretical, and experimental lattice constant. Is there anyway to compute the lattice parameter of such system after you run an unbiased simulation for a while, and compute the lattice parameter from the information related to the box? Thanks.
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1$\begingroup$ I think that is possible, using radial distribution function or performing a Fourier transform of the atomic positions to identify the atomic/molecular positions that correspond to lattice sites, then measure the distances between neighboring lattice sites along the lattice vectors and average them over multiple lattice vectors to obtain an estimate of the lattice parameter. I am supposing that you can can extract the position coordinates of the atoms from the trajectory and you have applied periodic boundary conditions $\endgroup$– Jaafar MehrezCommented Dec 14, 2023 at 9:05
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$\begingroup$ What's wrong with running a NPT ensemble and averaging the lattice parameters over time? $\endgroup$– Ian BushCommented Dec 14, 2023 at 23:16
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1$\begingroup$ Hi Ian, but how do you get the lattice constant, the one I am looking for- from the size of the box??? $\endgroup$– Roshan ShresthaCommented Dec 15, 2023 at 5:40
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1$\begingroup$ You have the lattice vectors, i.e. the size of the box. You know how many unit cells this is supposed to be. You should be able to work out the shape of an individual unit cell from that. $\endgroup$– Ian BushCommented Dec 15, 2023 at 8:26
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1$\begingroup$ I think Ian's answer is correct, as long as there is indeed a single grain in the cell. Depending on how large n is and how the structure was initialized, the simulation could in principle also contain grain boundaries. In the radial distribution function that may give rise to side peaks that could be ignored, while looking at density of molecules in the simulation box includes the boundary in the average. $\endgroup$– leopold.talirzCommented Dec 17, 2023 at 23:00
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You probably need a barostat which can change the size of the periodic box. Ideally you want an anisotropic barostat so each box vector (and the angles between them) can be adjusted independently.
If you know the crystal structure (from xray) as well as the unit cell parameters you can start from that and run a simulation with a barostat to see how the simulated crystal differs from the real one - both in terms of atom positions and the unit cell. Make the starting periodic box be an exact multiple of the crystal unit cell (ie a supercell).
If you don't know the crystal structure, you're basically trying to do crystal structure prediction. This is usually done by genetic or particle swarm algorithms, not by simulation per se. It may be helpful to read some of the literature on that, there are many good recent algorithms in that space. For example:
- Oganov AR, editor. Modern methods of crystal structure prediction. John Wiley & Sons; 2011 Aug 4. https://onlinelibrary.wiley.com/doi/book/10.1002/9783527632831
- Oganov AR. Crystal structure prediction: reflections on present status and challenges. Faraday discussions. 2018;211:643-60. https://pubs.rsc.org/en/content/articlelanding/2018/fd/c8fd90033g/unauth
- CALYPSO or USPEX algorithms
If you want to see a phase transition in a simulation (eg liquid->solid), this is in general pretty hard because those happen more easily by heterogeneous nucleation. You can try to set up a simulation like that with a crystal seed in a liquid (which requires knowing the crystal structure to seed with) and then you should be able to see the seed grow during the simulation. Homogeneous nucleation is very much slower - both in reality and in simulations, supercooled water for example can exist as a liquid at low temperatures well below freezing for a very long time, and if sufficiently supercooled can transition to a glass instead of a crystal. Homogeneous nucleation can sometimes happen on a timescale of 10-100ns at very high pressures and temperatures, but cooling at normal pressure in simulations generally just gives you a supercooled liquid.
