skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Direct Extraction of Excitation Energies from Ensemble Density-Functional Theory

; ; ;
Publication Date:
Sponsoring Org.:
OSTI Identifier:
Grant/Contract Number:
AC52-07NA27344; FG02-08ER46496; TZ2016003
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 119; Journal Issue: 3; Related Information: CHORUS Timestamp: 2017-07-21 22:12:22; Journal ID: ISSN 0031-9007
American Physical Society
Country of Publication:
United States

Citation Formats

Yang, Zeng-hui, Pribram-Jones, Aurora, Burke, Kieron, and Ullrich, Carsten A. Direct Extraction of Excitation Energies from Ensemble Density-Functional Theory. United States: N. p., 2017. Web. doi:10.1103/PhysRevLett.119.033003.
Yang, Zeng-hui, Pribram-Jones, Aurora, Burke, Kieron, & Ullrich, Carsten A. Direct Extraction of Excitation Energies from Ensemble Density-Functional Theory. United States. doi:10.1103/PhysRevLett.119.033003.
Yang, Zeng-hui, Pribram-Jones, Aurora, Burke, Kieron, and Ullrich, Carsten A. 2017. "Direct Extraction of Excitation Energies from Ensemble Density-Functional Theory". United States. doi:10.1103/PhysRevLett.119.033003.
title = {Direct Extraction of Excitation Energies from Ensemble Density-Functional Theory},
author = {Yang, Zeng-hui and Pribram-Jones, Aurora and Burke, Kieron and Ullrich, Carsten A.},
abstractNote = {},
doi = {10.1103/PhysRevLett.119.033003},
journal = {Physical Review Letters},
number = 3,
volume = 119,
place = {United States},
year = 2017,
month = 7

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on July 21, 2018
Publisher's Accepted Manuscript

Save / Share:
  • A new density-functional approach to calculate the excitation spectrum of many-electron systems is proposed. It is shown that the full linear density response of the interacting system, which has poles at the exact excitation energies, can rigorously be expressed in terms of the response function of the noninteracting (Kohn-Sham) system and a frequency-dependent exchange-correlation kernel. Using this expression, the poles of the full response function are obtained by systematic improvement upon the poles of the Kohn-Sham response function. Numerical results are presented for atoms. {copyright} {ital 1996 The American Physical Society.}
  • Representative atomic and molecular systems, including various inorganic and organic molecules with covalent and ionic bonds, have been studied by using density functional theory. The calculations were done with the commonly used exchange-correlation functional B3LYP followed by a comprehensive analysis of the calculated highest-occupied and lowest-unoccupied Kohn-Sham orbital (HOMO and LUMO) energies. The basis set dependence of the DFT results shows that the economical 6-31+G* basis set is generally sufficient for calculating the HOMO and LUMO energies (if the calculated LUMO energies are negative) for use in correlating with molecular properties. The directly calculated ionization potential (IP), electron affinity (EA),more » electronegativity (c), hardness (h), and first electron excitation energy (t) are all in good agreement with the available experimental data. A generally applicable linear correlation relationship exists between the calculated HOMO energies and the experimental/calculated IP's. We have also found satisfactory linear correlation relationships between the calculated LUMO energies and experimental/calculated EA's (for the bound anionic states), between the calculated average HOMO/LUMO energies and c values, between the calculated HOMO-LUMO energy gaps and h values, and between the calculated HOMO-LUMO energy gaps and experimental/calculated first excitation energies. By using these linear correlation relationships, the calculated HOMO and LUMO energies can be employed to semi-quantitatively estimate ionization potential, electron affinity, electronegativity, hardness, and first excitation energy.« less
  • The state-averaged (SA) spin restricted ensemble referenced Kohn-Sham (REKS) method and its state interaction (SI) extension, SI-SA-REKS, enable one to describe correctly the shape of the ground and excited potential energy surfaces of molecules undergoing bond breaking/bond formation reactions including features such as conical intersections crucial for theoretical modeling of non-adiabatic reactions. Until recently, application of the SA-REKS and SI-SA-REKS methods to modeling the dynamics of such reactions was obstructed due to the lack of the analytical energy derivatives. Here, the analytical derivatives of the individual SA-REKS and SI-SA-REKS energies are derived. The final analytic gradient expressions are formulated entirelymore » in terms of traces of matrix products and are presented in the form convenient for implementation in the traditional quantum chemical codes employing basis set expansions of the molecular orbitals. Finally, we will describe the implementation and benchmarking of the derived formalism in a subsequent article of this series.« less
  • Kohn-Sham (KS) time-dependent density functional theory (TDDFT) with most exchange-correlation functionals is well known to systematically underestimate the excitation energies of Rydberg and charge-transfer excited states of atomic and molecular systems. To improve the description of Rydberg states within the KS TDDFT framework, Gaiduk et al. [Phys. Rev. Lett. 108, 253005 (2012)] proposed a scheme that may be called HOMO depopulation. In this study, we tested this scheme on an extensive dataset of valence and Rydberg excitation energies of various atoms, ions, and molecules. It is also tested on a charge-transfer excitation of NH{sub 3}-F{sub 2} and on the potentialmore » energy curves of NH{sub 3} near a conical intersection. We found that the method can indeed significantly improve the accuracy of predicted Rydberg excitation energies while preserving reasonable accuracy for valence excitation energies. However, it does not appear to improve the description of charge-transfer excitations that are severely underestimated by standard KS TDDFT with conventional exchange-correlation functionals, nor does it perform appreciably better than standard TDDFT for the calculation of potential energy surfaces.« less