Configurational forces in electronic structure calculations using Kohn-Sham density functional theory

Journal Article · Fri Apr 20 00:00:00 EDT 2018 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.97.165132· OSTI ID:1540845

Motamarri, Phani ^[1]; Gavini, Vikram ^[1]

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1. University of Michigan, Ann Arbor, MI (United States)

Here we derive the expressions for configurational forces in Kohn-Sham density functional theory, which correspond to the generalized variational force computed as the derivative of the Kohn-Sham energy functional with respect to the position of a material point x. These configurational forces that result from the inner variations of the Kohn-Sham energy functional provide a unified framework to compute atomic forces as well as stress tensor for geometry optimization. Importantly, owing to the variational nature of the formulation, these configurational forces inherently account for the Pulay corrections. The formulation presented in this work treats both pseudopotential and all-electron calculations in a single framework, and employs a local variational real-space formulation of Kohn-Sham density functional theory (DFT) expressed in terms of the nonorthogonal wave functions that is amenable to reduced-order scaling techniques. We demonstrate the accuracy and performance of the proposed configurational force approach on benchmark all-electron and pseudopotential calculations conducted using higher-order finite-element discretization. To this end, we examine the rates of convergence of the finite-element discretization in the computed forces and stresses for various materials systems, and, further, verify the accuracy from finite differencing the energy. Wherever applicable, we also compare the forces and stresses with those obtained from Kohn-Sham DFT calculations employing plane-wave basis (pseudopotential calculations) and Gaussian basis (all-electron calculations). Finally, we verify the accuracy of the forces on large materials systems involving a metallic aluminum nanocluster containing 666 atoms and an alkane chain containing 902 atoms, where the Kohn-Sham electronic ground state is computed using a reduced-order scaling subspace projection technique

• Research Organization: Univ. of Michigan, Ann Arbor, MI (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES); Toyota Research Institute; National Science Foundation (NSF)
• Grant/Contract Number: SC0008637; SC0017380; AC02-05CH11231; 1053145; ACI-1053575
• OSTI ID: 1540845
• Alternate ID(s): OSTI ID: 1434184
• Journal Information: Physical Review. B, Vol. 97, Issue 16; ISSN 2469-9950
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
density functional theory
density functional theory development
electronic structure
finite-element method