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Computation 2017, 5(2), 28; doi:10.3390/computation5020028

Geometric Derivation of the Stress Tensor of the Homogeneous Electron Gas

1
Department of Physics, Temple University, Philadelphia 19122-1801, PA, USA
2
Department of Physics, University of Missouri, Columbia, MO 65211, USA
3
Theoretical Division & Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico, NM 87545, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Dennis Salahub
Received: 4 May 2017 / Revised: 23 May 2017 / Accepted: 2 June 2017 / Published: 8 June 2017
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Abstract

The foundation of many approximations in time-dependent density functional theory (TDDFT) lies in the theory of the homogeneous electron gas. However, unlike the ground-state DFT, in which the exchange-correlation potential of the homogeneous electron gas is known exactly via the quantum Monte Carlo calculation, the time-dependent or frequency-dependent dynamical potential of the homogeneous electron gas has not been known exactly, due to the absence of a similar variational principle for excited states. In this work, we present a simple geometric derivation of the time-dependent dynamical exchange-correlation potential for the homogeneous system. With this derivation, the dynamical potential can be expressed in terms of the stress tensor, offering an alternative to calculate the bulk and shear moduli, two key input quantities in TDDFT. View Full-Text
Keywords: time-dependent DFT; dynamical exchange-correlation potential; homogeneous electron gas; stress tensor; bulk modulus; shear modulus time-dependent DFT; dynamical exchange-correlation potential; homogeneous electron gas; stress tensor; bulk modulus; shear modulus
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Tao, J.; Vignale, G.; Zhu, J.-X. Geometric Derivation of the Stress Tensor of the Homogeneous Electron Gas. Computation 2017, 5, 28.

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