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Here I assume that conventional superconductors refer to materials that undergo a superconducting transition at low temperature as described by the Bardeen-Cooper-Schrieffer theory (BCS). For those materials the effective attractive electron-electron interaction is mediated by phonons. How accurately can the superconducting transition temperature be computed from ab initio methods and what are the factors that limit the accuracy of those methods?

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  • $\begingroup$ One thing that limits the accuracy of these attempts at predicting $T_c$, is that whether dealing with conventional or high-temperature superconductors, the shear number of atoms/electrons involved is quite large, and often we are dealing with fairly heavy metal elements which require big basis sets, treatment of multi-reference character, relativistic and spin-orbit effects, among other things. Superconductivity is one of the hardest things for ab initio programs to treat accurately! $\endgroup$
    – Nike Dattani
    May 30, 2020 at 0:08

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I am not an expert in superconductivity but I believe that the crucial interaction that dictate the conventional superconductivity is the phonon-electron interaction which in the language of quantum chemistry can be regarded as a non-adiabatic nuclear dynamics which is beyond Bohr-Oppenheimer approximation. And I do not think conventional electronic calculations incorporate this effect.

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  • $\begingroup$ There seems to be a lot of subjective opinion statements in this answer. Could you modify it to contain more objective statements, please. $\endgroup$
    – Peter Morgan
    May 3, 2020 at 14:41
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    $\begingroup$ I am subjective because I am not certain if the statement is correct. However, I think part of the function of this platform is for discussion of open questions / ideas. If the statements are not correct, I welcome all criticism and corrections. $\endgroup$
    – Paulie Bao
    May 3, 2020 at 16:10
  • $\begingroup$ It's true that the Born-Oppenheimer decouples the electron and atomic wavefunctions, but the coupling can be computed afterwards by perturbation theory. $\endgroup$
    – Phil Hasnip
    Jan 5, 2022 at 21:30

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