Volume 19, Issue 1
Towards Translational Invariance of Total Energy with Finite Element Methods for Kohn-Sham Equation

Gang Bao, Guanghui Hu & Di Liu

Commun. Comput. Phys., 19 (2016), pp. 1-23.

Published online: 2018-04

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  • Abstract

Numerical oscillation of the total energy can be observed when the Kohn-Sham equation is solved by real-space methods to simulate the translational move of an electronic system. Effectively remove or reduce the unphysical oscillation is crucial not only for the optimization of the geometry of the electronic structure, but also for the study of molecular dynamics. In this paper, we study such unphysical oscillation based on the numerical framework in [G. Bao, G. H. Hu, and D. Liu, An h-adaptive finite element solver for the calculations of the electronic structures, Journal of Computational Physics, Volume 231, Issue 14, Pages 4967-4979, 2012], and deliver some numerical methods to constrain such unphysical effect for both pseudopotential and all-electron calculations, including a stabilized cubature strategy for Hamiltonian operator, and an a posteriori error estimator of the finite element methods for Kohn-Sham equation. The numerical results demonstrate the effectiveness of our method on restraining unphysical oscillation of the total energies.

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@Article{CiCP-19-1, author = {}, title = {Towards Translational Invariance of Total Energy with Finite Element Methods for Kohn-Sham Equation}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {1}, pages = {1--23}, abstract = {

Numerical oscillation of the total energy can be observed when the Kohn-Sham equation is solved by real-space methods to simulate the translational move of an electronic system. Effectively remove or reduce the unphysical oscillation is crucial not only for the optimization of the geometry of the electronic structure, but also for the study of molecular dynamics. In this paper, we study such unphysical oscillation based on the numerical framework in [G. Bao, G. H. Hu, and D. Liu, An h-adaptive finite element solver for the calculations of the electronic structures, Journal of Computational Physics, Volume 231, Issue 14, Pages 4967-4979, 2012], and deliver some numerical methods to constrain such unphysical effect for both pseudopotential and all-electron calculations, including a stabilized cubature strategy for Hamiltonian operator, and an a posteriori error estimator of the finite element methods for Kohn-Sham equation. The numerical results demonstrate the effectiveness of our method on restraining unphysical oscillation of the total energies.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.190115.200715a}, url = {http://global-sci.org/intro/article_detail/cicp/11078.html} }
TY - JOUR T1 - Towards Translational Invariance of Total Energy with Finite Element Methods for Kohn-Sham Equation JO - Communications in Computational Physics VL - 1 SP - 1 EP - 23 PY - 2018 DA - 2018/04 SN - 19 DO - http://doi.org/10.4208/cicp.190115.200715a UR - https://global-sci.org/intro/article_detail/cicp/11078.html KW - AB -

Numerical oscillation of the total energy can be observed when the Kohn-Sham equation is solved by real-space methods to simulate the translational move of an electronic system. Effectively remove or reduce the unphysical oscillation is crucial not only for the optimization of the geometry of the electronic structure, but also for the study of molecular dynamics. In this paper, we study such unphysical oscillation based on the numerical framework in [G. Bao, G. H. Hu, and D. Liu, An h-adaptive finite element solver for the calculations of the electronic structures, Journal of Computational Physics, Volume 231, Issue 14, Pages 4967-4979, 2012], and deliver some numerical methods to constrain such unphysical effect for both pseudopotential and all-electron calculations, including a stabilized cubature strategy for Hamiltonian operator, and an a posteriori error estimator of the finite element methods for Kohn-Sham equation. The numerical results demonstrate the effectiveness of our method on restraining unphysical oscillation of the total energies.

Gang Bao, Guanghui Hu & Di Liu. (2020). Towards Translational Invariance of Total Energy with Finite Element Methods for Kohn-Sham Equation. Communications in Computational Physics. 19 (1). 1-23. doi:10.4208/cicp.190115.200715a
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