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At some temperature a crystal lattice of a solid can be rearranged or to say it more precise - got new positions of its cores. This phenomenon is well-known to be called a second-order phase transition (SOPT). More precise specification of crystal lattice rearranging for different solids can be learned and studied from books and experiments, for example, with X-ray diffractometer or other tools (if any).

Can a SOPT temperature and new positions of cores of a crystal lattice of a solid be obtained with Hartee-Fock (or DFT) calculation? Maybe it is possible to do based on data obtained from a solution of the Hartree-Fock (Kohn-Sham) equation. Can the Broyden algorithm be applied to implement this calculation?

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    $\begingroup$ In general, HF or DFT calculations are done only at 0K. There are a few packages that implemented a mix DFT/Classical Dynamics where you can use other temperatures than 0K. $\endgroup$
    – Camps ♦
    Commented Mar 11, 2023 at 14:33
  • $\begingroup$ @Camps Thanks! What the software is it? $\endgroup$
    – SFriendly
    Commented Mar 12, 2023 at 9:24
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    $\begingroup$ Do you just want to know whether a phase transition exists, or do you also want to know the transition pathway? $\endgroup$
    – Phil Hasnip
    Commented Mar 12, 2023 at 23:13
  • $\begingroup$ @PhilHasnip Thanks! The transition pathway: mainly the temperature at which a crystal lattice begins to rearrange as well as positions of cristal lattice nodes after rearranging. But it is an interesting thing is it possible to calculate all the way of a crystall lattice nodes from the beginning of a phase transition to the end of its? $\endgroup$
    – SFriendly
    Commented Mar 13, 2023 at 11:32
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    $\begingroup$ MALA project (Github repository). $\endgroup$
    – Camps ♦
    Commented Mar 13, 2023 at 11:58

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In classic DFT approach you run geometry optimization for both phases which gives you electronic energies, then compute frequencies which gives you thermodynamic parameters, including tempurature-dependent free energy. Finally, you use the obtained G(T) to find a SOPT temperature G1(T) = G2(T).

This functionality is available in any solid-state DFT software (VASP, CP2K, QEspresso, etc.), just search smth like "how to compute phase diagram in %YOUR_PACKAGE_NAME%".

However, the plain DFT is not the best way to get the transition pathway. You can do it by localising a transition state (keywords are TS (transition state) and NEB (nudged elastic band)), but it will consider SOPT as a simultaneous process, and to the best of my knowledge it's not how it works.

For the purpose you need run ab initio molecular dynamics, starting from the low-temperature structure and slowly increasing the simulation temperature. Though it's really time-demanding computations. The other way is to parameterized the MM force field specifically for your system, but this step can be challenging enough to drop the problem completely.

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  • $\begingroup$ Thanks for the answer! $\endgroup$
    – SFriendly
    Commented Mar 16, 2023 at 9:20
  • $\begingroup$ Is it correct that calculations will be simplified if a goal is to obtain only end positions of crystal lattice nodes of a solid after SOPT? $\endgroup$
    – SFriendly
    Commented Mar 16, 2023 at 23:32
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    $\begingroup$ @SFriendly absolutely, that's a standard problem. I higly recommend to read "Density Functional Theory. A Practical Introduction" by Sholl and Steckel, it's a compact DFT textbook (c.a. 200 pages) written for novices in a nice and clear language. I just looked at its table of contents, and it answers your question perfectly, chapter by chapter $\endgroup$
    – Ivan Chernyshov
    Commented Mar 17, 2023 at 6:27
  • $\begingroup$ Thanks for the comment! $\endgroup$
    – SFriendly
    Commented Mar 17, 2023 at 9:32

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