Simulating the electronic properties of solids with methods like coupled cluster theory is a new frontier in the development of wavefunction quantum chemistry methods. While these methods increase the accuracy of the treatment of correlation, they also use the supercell approximation, which can neglect the treatment of long-range correlation. These long-range interactions are particularly important when it comes to small gap systems such as semiconductors or metals. The error made in these energies is termed “finite size errors”, as they result from treating an infinite system with a finite supercell. The impact of these errors can be prominently seen in the energy differences between different phases where the electronic structure changes during the transition. In such phase transitions, the finite size errors in the energies are different between the two phases, so they do not cancel when taking energy differences. In the example of the phase transition between the β-Sn and diamond phases of silicon, finite size errors are still reported to be the leading order source of error (at 30-60 meV/atom in the energy or 1-2 GPa in the transition pressure). I will give a presentation on three themes related to my research group’s study of finite size errors: (1) Twist angle selection, which are approaches using connectivity or the transition structure factor to identify a special twist angle at which to perform calculations. (2) Testing power-law extrapolations, where improved basis sets and twist averaging allows us to provide high fidelity data on the scaling of the coupled cluster correlation energy on approach to the thermodynamic limit. (3) Machine learning interpolations, where we fit a function to the part of the wavefunction that is missing due to simulating finite systems, and integrate over this fit to find the energy.

Finite size effects in periodic coupled cluster theory calculations for solids

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ACS Fall 2022

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