## Recent Publications

Fabian, M. D. ; Shpiro, B. ; Baer, R. Linear scalability of density functional theory calculations without imposing electron localization. arXiv:2108.13478 [physics] Submitted. Publisher's VersionAbstract

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 localizationa 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.

Nguyen, M. ; Li, W. ; Li, Y. ; Baer, R. ; Rabani, E. ; Neuhauser, D. Tempering stochastic density functional theory. arXiv:2107.06218 [physics] Submitted. Publisher's VersionAbstract

We introduce a tempering approach with stochastic density functional theory (sDFT), labeled t-sDFT, which reduces the statistical errors in the estimates of observable expectation values. This is achieved by rewriting the electronic density as a sum of a "warm" component complemented by "colder" correction(s). Since the "warm" component is larger in magnitude but faster to evaluate, we use many more stochastic orbitals for its evaluation than for the smaller-sized colder correction(s). This results in a significant reduction of the statistical fluctuations and the bias compared to sDFT for the same computational effort. We the method's performance on large hydrogen-passivated silicon nanocrystals (NCs), finding a reduction in the systematic error in the energy by more than an order of magnitude, while the systematic errors in the forces are also quenched. Similarly, the statistical fluctuations are reduced by factors of around 4-5 for the total energy and around 1.5-2 for the forces on the atoms. Since the embedding in t-sDFT is fully stochastic, it is possible to combine t-sDFT with other variants of sDFT such as energy-window sDFT and embedded-fragmented sDFT.

Nazarov, V. U. ; Baer, R. The high frequency limit of spectroscopy. arXiv:2101.09467 [cond-mat] Submitted. Publisher's VersionAbstract

We consider a quantum-mechanical system, finite or extended, initially in its ground-state, exposed to a time-dependent potential pulse, with a slowly varying envelope and a carrier frequency \$\textbackslashomega\_0\$. By working out a rigorous solution of the time-dependent Schr\textbackslash"odinger equation in the high-\$\textbackslashomega\_0\$ limit, we show that the linear response is completely suppressed after the switch-off of the pulse. We show, at the same time, that to the lowest order in \$\textbackslashomega\_0ˆ\-1\\$, observables are given in terms of the linear density response function \$\textbackslashchi(\textbackslashrv,\textbackslashrv',\textbackslashomega)\$, despite the problem's nonlinearity. We propose a new spectroscopic technique based on these findings, which we name the Nonlinear High-Frequency Pulsed Spectroscopy (NLHFPS). An analysis of the jellium slab and sphere models reveals very high surface sensitivity of NLHFPS, which produces a richer excitation spectrum than accessible within the linear-response regime. Combining the advantages of the extraordinary surface sensitivity, the absence of constraints by the conventional dipole selection rules, and the ease of theoretical interpretation by means of the linear response time-dependent density functional theory, NLHFPS has the potential to evolve into a powerful characterization method in nanoscience and nanotechnology.

Shpiro, B. ; Fabian, M. D. ; Rabani, E. ; Baer, R. Forces from stochastic density functional theory under nonorthogonal atom-centered basis sets. arXiv:2108.06770 [physics] Submitted. Publisher's VersionAbstract

We develop a formalism for calculating forces on the nuclei within the linear-scaling stochastic density functional theory (sDFT) in a nonorthogonal atom-centered basis-set representation (Fabian et al. WIREs Comput Mol Sci. 2019;e1412. https://doi.org/10.1002/wcms.1412) and apply it to Tryptophan Zipper 2 (Trp-zip2) 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\textbackslash,eV/\textbackslashr\A\\$ (\$\textbackslashsim1.2\textbackslashtimes10ˆ\-3\E\_\h\/a\_\0\\$) when 120 stochastic orbitals are used, independently of systems 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.

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