I am looking to implement a Hartree-Fock program to study periodic, condensed matter system, however, I literally cannot find a single reference or example anywhere for how to do this. In the past, I wrote a basic Hartree-Fock program for molecules and quantum chemistry simulations involving a few atoms, however, I am unsure how to generalize this method and incorporate periodic boundary conditions. Does anyone know of any resources for periodic, momentum-space Hartree-Fock calculations? Specifically, I’m looking for something to guide me through the numerical implementation. I’ve come across plenty of condensed matter papers which employ this technique to study real materials, but none of them go into the details of what they did. They simply list the results of the Hartree-Fock calculation and act like it was some easy, trivial thing to do, and yet I cannot find a single example of this calculation anywhere—am I missing something?
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3$\begingroup$ Pisani et al. "Hartree-Fock ab initio treatment of Crystalline Systems" is one possibility $\endgroup$– Ian BushCommented Jul 8 at 13:21
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$\begingroup$ Related question: mattermodeling.stackexchange.com/questions/10693/… $\endgroup$– Tyberius ♦Commented Jul 8 at 14:09
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$\begingroup$ Just be be absolutely clear you are talking about using a local basis set such as Gaussians here, and not plane waves? $\endgroup$– Ian BushCommented Jul 9 at 12:16
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$\begingroup$ @IanBush Either will work, for the time being. I'm really just looking for any simple example/implementation at all of a periodic Hartree-Fock calculations, and, from there, I can modify and recycle the code as needed. I've been struggling with designing a program from scratch, so that's why I'm looking for another reference to aid in implementation. $\endgroup$– meer23Commented Jul 10 at 6:54
1 Answer
As Ian Bush already pointed out in a comment above, the work by Pisani et al on the Gaussian basis implementation the CRYSTAL program is the original reference for periodic Hartree-Fock. More recently, implementations of periodic Hartree-Fock have been added to TURBOMOLE, PySCF, and Q-Chem, for example. You should be able to find details on this implementations via Google Scholar, for example; the most recent publications on the codes themselves are good places to hunt for more detailed references.
For example, for the lattermost program, see J. Chem. Theory Comput. 18, 7336 (2022) and J. Chem. Theory Comput. 19, 5773 (2023) for recent work on fast Hartree-Fock algorithms.
A recent focus article on condensed phase quantum chemistry may also be useful, see https://arxiv.org/pdf/2403.13207
