Geometry Optimization of Crystals

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Discussion Overview

The discussion revolves around the optimization of crystal geometry, specifically focusing on finding the minimum energy configuration of a monoclinic crystal structure with multiple internal parameters and atomic species. Participants explore various computational methods and challenges associated with energy minimization in this context.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant describes difficulties in achieving satisfactory energy minimization using the conjugate gradient method and mentions better results with the Nelder-Mead simplex method, though still not achieving a close-to-zero L2-norm of forces.
  • Another participant suggests using Gaussian software and emphasizes the importance of using the correct method and basis set, noting that Cartesian coordinates are preferable to internal coordinates derived from crystallographic data.
  • A third participant questions the applicability of the interatomic potentials being used, highlighting that these potentials can be system-specific and may not be suitable for the participant's specific crystal structure, suggesting that ab-initio methods might be more appropriate.
  • The original poster acknowledges the limitations of molecular dynamics (MD) and expresses interest in understanding simultaneous energy minimization of a unit cell with respect to both cell vectors and internal coordinates, referencing a specific article for further reading.

Areas of Agreement / Disagreement

Participants express differing views on the effectiveness of various computational methods and the applicability of interatomic potentials, indicating that multiple competing perspectives remain without a consensus on the best approach for energy minimization.

Contextual Notes

Participants note limitations related to the choice of interatomic potentials and the challenges of achieving stability in the L2 structure, as well as the unresolved nature of simultaneous minimization techniques.

handsomecat
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I'm stuck with a problem of finding the minimum energy of an inorganic crystal. Crystal is of monoclinic structure with 18 parameters to specify its internal coordinates and 2 atomic species. Am using a classical interatomic potential found in literature.

The minimization involves both the 18 parameters and the cell vectors.

Have tried conjugate gradient method but algorithm never gives me a satisfactory minimum - the L2-norm of the forces is far from zero.

The best results I got was with the Nelder-Mead simplex method. Even then, the L2-norm of the forces at the termination of the algorithm was not close to zero.

Any pointers? I was thinking of trying Damped MD next ...
 
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Try using Gaussian software...use proper method and basis set...all u need is the cartesian coordinates (not the internal coordinates which u get directly from x-ray crystallographic data)
 
Hello handsomecat,

Are you sure the potentials you are using are applicable to your specific system. Interatomic pair potentials tend to be system and model specific. For instance, the transferability of a Fe-C potential for diffusion modeling isn't transferable to modeling to structure of cementite (Fe3C). The main reason being that the potentials aren't just pair dependent, but also depend on the chemical environment of that pair. Maybe based on these potentials the L2 structure isn't stable. Use a ab-initio code to avoid the pitfalls of pair-potentials.

Modey3
 
Hi Modey3, thanks for your comments.

I have already performed ab-initio calculations and have given up on using MD for that purpose :) I am certainly aware of the shortcomings of using MD interatomic potentials (something that has given me much grief in the past 4-5 years!)

However, as a matter of interest, I never stopped wondering about how energy minimization of a unit cell wrt cell vectors and internal coordinates is done simultaneously. Nevertheless, I've found an article and all readers can refer to this article:

Bernard G. Prommer et al. Journal of Computational Physics 131, 233- 240.
 

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