This Thursday, 18.11 at 11:00 am we will have a FH seminar where two members from the group of Prof. Roi Baer, Dr. Marcel Fabian and Ben Shpiro will give lectures titled:
 "Linear scalability of density functional theory calculations without imposing electron localization" (Dr. Marcel Fabian) and  
"Forces from stochastic DFT: a formalism in a nonorthogonal basis-set representation" (Ben Shpiro)


Dr. Marcel  Fabian:
Linear scaling density functional theory approaches to electronic structure are often based on the tendency of electrons to localize even in large atomic and molecular systems. However, in many cases of actual interest, for example in semiconductor nanocrystals, system sizes can reach very large extension before significant electron localization sets in and the scaling of the numerical methods may deviate strongly from linear. Here, we address this class of systems, by developing a massively parallel density functional theory (DFT) approach which doesn't rely on electron localization and is formally quadratic scaling, yet enables highly efficient linear wall-time complexity in the weak scalability regime. The approach extends from the stochastic DFT method described in Fabian et. al. WIRES: Comp. Mol. Science, e1412 (2019), but is fully deterministic. It uses standard quantum chemical atom-centered Gaussian basis sets for representing the electronic wave functions combined with Cartesian real space grids for some of the operators and for enabling a fast solver for the Poisson equation. Our main conclusion is, that when a processor-abundant high performance computing (HPC) infrastructure is available, this type of approach has the potential to allow the study of large systems in regimes where quantum confinement or electron delocalization prevents linear-scaling.

Ben Shpiro:
Stochastic density functional theory (sDFT) is a highly parallelizable linear-scaling approach in which the reduced scaling is achieved without imposing (or relying on) a sparse structure to the Kohn-Sham density matrix, and as such may be applicable to a wide variety of systems in biology and material science. Observables in sDFT are calculated in a trace-based formalism using the stochastic trace formula and can therefore be regarded as random variables, with an expected value and fluctuation. Due to the non-linear nature of the SCF iterations, sDFT observables are also characterized by a bias error, whose magnitude can be controlled by increasing sampling as well as by employing a fragment-based, variance-reducing technique. Noisy forces calculated from sDFT have been shown to be useful for geometry optimization when implemented in a Langevin dynamics framework yet it is key to make sure that the errors are governed by the fluctuations rather than the bias. In this talk, I will introduce our new formalism for the calculation of forces using sDFT in a nonorthogonal, atom-centered, basis-set, which also includes the treatment of Pulay force terms acting on the nuclei. I will present a statistical analysis of the sDFT errors in the forces acting on a Tryptophan Zipper 2 peptide solvated in water. Results indicate that the sDFT bias in the forces is small and independent of system size, paving the way for future Langevin dynamics structural studies of peptides in solution. 


Shpiro B, Fabian MD, Rabani E, Baer R. Forces from stochastic density functional theory under nonorthogonal atom-centered basis sets, https://arxiv.org/pdf/2108.06770v1.pdf

Fabian MD*, Shpiro B*, Rabani E, Neuhauser D, Baer R. Stochastic density functional theory. WIREs Comput Mol Sci. 2019;e1412.