### Citation:

### Abstract:

We develop a formalism for calculating forces on the nuclei within the linear-scaling stochastic density functional theory (sDFT) in a nonorthogonal atomcentered basis set representation (Fabian et al. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2019, 9, e1412, 10.1002/wcms.1412) and apply it to the Tryptophan Zipper 2 (Trpzip2) peptide solvated in water. We use an embedded-fragment approach to reduce the statistical errors (ﬂuctuation and systematic bias), where the entire peptide is the main fragment and the remaining 425 water molecules are grouped into small fragments. We analyze the magnitude of the statistical errors in the forces and ﬁnd that the systematic bias is of the order of 0.065 eV/Å (∼1.2 × 10−3Eh/a0) when 120 stochastic orbitals are used, independently of system size. This magnitude of bias is suﬃciently small to ensure that the bond lengths estimated by stochastic DFT (within a Langevin molecular dynamics simulation) will deviate by less than 1% from those predicted by a deterministic calculation.

*Last updated on 03/23/2022*