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For example, GPAW supports both plane-wave and atomic-orbital methods. I know that atomic-orbital methods can have difficulty with electrons occupying vacancies for example, but what types of systems are good or bad for atomic-orbital based methods.

To be clear I would like to know what types of systems have which pros and cons for both methods. I am particularly curious about metal vs semiconductor and surface vs bulk vs nanoparticle etc.

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    $\begingroup$ Does this answer your question? What are the positives and negatives of periodic DFT codes that don't use plane-wave basis sets? $\endgroup$ – Susi Lehtola Aug 12 at 19:44
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    $\begingroup$ I wouldn't really say so, I am less curious about the fundamental pros/cons and more interested in what systems work for what types of DFT better. The obvious example is gas phase molecules are better with orbital methods and bulk structures are better with orbitals (always true?). $\endgroup$ – Tristan Maxson Aug 12 at 21:52
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    $\begingroup$ I have added some better details about what I am asking specifically, my questions somewhat arose from reading that question originally. $\endgroup$ – Tristan Maxson Aug 12 at 21:56
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The clearest example in my mind is if you want to understand the orbital-based contributions to some phenomena (e.g. bonding, a reaction energy), particularly if the periodic material being modeled is more like a molecular solid where the chemical picture of orbitals is more intuitive than bands. There are several schemes out there that try to go from PAW to localized basis set-like results though, including the periodic extension to natural bonding orbitals (NBOs), Solid State Adaptive Natural Density Partitioning (SSAdNDP), and the LOBSTER code.

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