Electronic band gaps from quantum Monte Carlo methods

Abstract

We develop a method for calculating the fundamental electronic gap of semiconductors and insulators using grand canonical Quantum Monte Carlo simulations. We discuss the origin of the bias introduced by supercell calculations of finite size and show how to correct the leading and subleading finite size errors either based on observables accessible in the finite-sized simulations or from DFT calculations. Our procedure is applied to solid molecular hydrogen and compared to experiment for carbon and silicon crystals.

Variational and diffusion quantum Monte Carlo calculations with the CASINO code

“…Alternatively the permittivity tensor can be evaluated using the small-k limit of the static structure factor, which can be evaluated using ground-state QMC calculations. 147 Beyond-leading-order finite-size effects in the quasiparticle bands and therefore quasiparticle gap arise due to the fact that the charge-density distributions in the quasiparticles have quadrupole moments in general; the resulting chargequadrupole interactions give an O(N −1) finite-size error in 3D materials. The addition of charges to a finite simulation cell also causes long-range oscillatory behavior in the electronic pair density.…”

Monte Carlo Assisted FTIR Spectroscopy: A Python Tool for the Determination of the Constituents in Blended Biopolymer Samples

“…When estimating the probability of an event occurring, one can simulate an independent number of samples from the event and compute the event's proportion of times. [ 145–147 ]…”

“…When estimating the probability of an event occur-ring, one can simulate an independent number of samples from the event and compute the event's proportion of times. [145][146][147] Therefore, this work is focused on building a Python tool. This tool is capable of solving, via Monte Carlo, followed by the rootmean-square error (RMSE) minimization, the chemical composition of a polymeric sample expressed by a microorganism that accumulates energy the form of Levan, Curdlan, and Paenan.…”

Electronic energy gap closure and metal-insulator transition in dense liquid hydrogen

“…However, to address the IM transition it is necessary to have calculations for temperatures below and above the critical point of the LLPT. In this paper, we perform a fully consistent characterisation of the IM transition in liquid hydrogen extending to liquids our recently developed method for accurately computing energy gaps within QMC for ideal [41] and thermal crystals [42].…”