Linear-scaling techniques for Kohn–Sham density functional theory are essential to describe the ground state properties of extended systems. Still, these techniques often rely on the localization of the density matrix or accurate embedding approaches, limiting their applicability. In contrast, stochastic density functional theory (sDFT) achieves linear- and sub-linear scaling by statistically sampling the ground state density without relying on embedding or imposing localization. In return, ground state observables, such as the forces on the nuclei, fluctuate in sDFT, making optimizing the nuclear structure a highly non-trivial problem. In this work, we combine the most recent noise-reduction schemes for sDFT with stochastic optimization algorithms to perform structure optimization within sDFT. We compare the performance of the stochastic gradient descent approach and its variations (stochastic gradient descent with momentum) with stochastic optimization techniques that rely on the Hessian, such as the stochastic Broyden–Fletcher–Goldfarb–Shanno algorithm. We further provide a detailed assessment of the computational efficiency and its dependence on the optimization parameters of each method for determining the ground state structure of bulk silicon with varying supercell dimensions.
Skip Nav Destination
CHORUS
Article navigation
14 January 2023
Research Article|
January 11 2023
Structure optimization with stochastic density functional theory
Ming Chen
;
Ming Chen
a)
(Conceptualization, Data curation, Formal analysis, Methodology, Software, Writing – original draft, Writing – review & editing)
1
Department of Chemistry, Purdue University
, West Lafayette, Indiana 47907, USA
a)Author to whom correspondence should be addressed: [email protected]
Search for other works by this author on:
Roi Baer
;
Roi Baer
(Writing – review & editing)
2
Fritz Haber Center of Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem
, Jerusalem 91904, Israel
Search for other works by this author on:
Eran Rabani
Eran Rabani
(Conceptualization, Funding acquisition, Supervision, Writing – review & editing)
3
Department of Chemistry, University of California
, Berkeley, California 94720, USA
4
Materials Sciences Division, Lawrence Berkeley National Laboratory
, Berkeley, California 94720, USA
5
The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University
, Tel Aviv 69978, Israel
Search for other works by this author on:
a)Author to whom correspondence should be addressed: [email protected]
J. Chem. Phys. 158, 024111 (2023)
Article history
Received:
September 15 2022
Accepted:
December 19 2022
Citation
Ming Chen, Roi Baer, Eran Rabani; Structure optimization with stochastic density functional theory. J. Chem. Phys. 14 January 2023; 158 (2): 024111. https://doi.org/10.1063/5.0126169
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
DeePMD-kit v2: A software package for deep potential models
Jinzhe Zeng, Duo Zhang, et al.
CREST—A program for the exploration of low-energy molecular chemical space
Philipp Pracht, Stefan Grimme, et al.
Freezing point depression of salt aqueous solutions using the Madrid-2019 model
Cintia P. Lamas, Carlos Vega, et al.
Related Content
Stochastic density functional theory: Real- and energy-space fragmentation for noise reduction
J. Chem. Phys. (May 2021)
Overlapped embedded fragment stochastic density functional theory for covalently-bonded materials
J. Chem. Phys. (January 2019)
Equilibrium configurations of large nanostructures using the embedded saturated-fragments stochastic density functional theory
J. Chem. Phys. (June 2017)
Tempering stochastic density functional theory
J. Chem. Phys. (November 2021)
Energy window stochastic density functional theory
J. Chem. Phys. (September 2019)