• Open Access

Koopmans-Compliant Spectral Functionals for Extended Systems

Ngoc Linh Nguyen, Nicola Colonna, Andrea Ferretti, and Nicola Marzari
Phys. Rev. X 8, 021051 – Published 23 May 2018
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Abstract

Koopmans-compliant functionals have been shown to provide accurate spectral properties for molecular systems; this accuracy is driven by the generalized linearization condition imposed on each charged excitation, i.e., on changing the occupation of any orbital in the system, while accounting for screening and relaxation from all other electrons. In this work, we discuss the theoretical formulation and the practical implementation of this formalism to the case of extended systems, where a third condition, the localization of Koopmans’s orbitals, proves crucial to reach seamlessly the thermodynamic limit. We illustrate the formalism by first studying one-dimensional molecular systems of increasing length. Then, we consider the band gaps of 30 paradigmatic solid-state test cases, for which accurate experimental and computational results are available. The results are found to be comparable with the state of the art in many-body perturbation theory, notably using just a functional formulation for spectral properties and the generalized-gradient approximation for the exchange and correlation functional.

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  • Received 22 August 2017
  • Revised 31 January 2018

DOI:https://doi.org/10.1103/PhysRevX.8.021051

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ngoc Linh Nguyen1,*, Nicola Colonna1, Andrea Ferretti2, and Nicola Marzari1

  • 1Theory and Simulations of Materials (THEOS), and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
  • 2Centro S3, CNR-Istituto Nanoscienze, 41125 Modena, Italy

  • *linh.nguyen@epfl.ch

Popular Summary

Density functional theory (DFT) is a mathematical tool for describing the electronic structure of systems of interacting particles, and it has proven to be an accurate and efficient approach to predicting fundamental properties of materials. However, this theory is not meant to correctly describe the energy bands of solids or to distinguish metals, semiconductors, and insulators. These properties are key to designing materials for electronics, energy harvesting or conversion, and photonics. The correct and established approach to calculating electronic levels from first principles, known as many-body perturbation theory, is also computationally expensive. We show how functional theories can provide a much simpler approach.

We start with frequency-dependent functionals that are derived from DFT, which imposes the correct theoretical response to the removal or addition of an electron (the so-called Koopmans’s condition). We show how these functionals provide a novel dynamical formalism where electronic properties, and not only total energies, can be correctly accounted for. Our work discusses the theoretical formulation and the practical implementation of Koopmans-compliant functionals for solids, finding that the spectral properties computed for semiconducting and insulating systems are in excellent agreement with experiments and with the state of the art in many-body perturbation theory.

These results allow for the study of electronic and optical properties of complex systems with unprecedented simplicity, and they also serve as a useful reference in developing novel simulation tools for excited-state calculations.

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Vol. 8, Iss. 2 — April - June 2018

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