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Title: Approximating Quasiparticle and Excitation Energies from Ground State Generalized Kohn–Sham Calculations

Journal Article · · Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory

Quasiparticle energies and fundamental band gaps specifically are critical properties of molecules and materials. It was rigorously established that the generalized Kohn–Sham HOMO and LUMO orbital energies are the chemical potentials of electron removal and addition and thus good approximations to band edges and fundamental gaps from a density functional approximation (DFA) with minimal delocalization error. For other quasiparticle energies, their connection to the generalized Kohn–Sham orbital energies has not been established but remains highly interesting. We provide the comparison of experimental quasiparticle energies for many finite systems with calculations from the GW Green function and localized orbitals scaling correction (LOSC), a recently developed correction to semilocal DFAs, which has minimal delocalization error. Extensive results with over 40 systems clearly show that LOSC orbital energies achieve slightly better accuracy than the GW calculations with little dependence on the semilocal DFA, supporting the use of LOSC DFA orbital energies to predict quasiparticle energies. This also leads to the calculations of excitation energies of the N-electron systems from the ground state DFA calculations of the (N – 1)-electron systems. Findings show good performance with accuracy similar to TDDFT and the delta SCF approach for valence excitations with commonly used DFAs with or without LOSC. For Rydberg states, good accuracy was obtained only with the use of LOSC DFA. Our report highlights the pathway to quasiparticle and excitation energies from ground density functional calculations.

Research Organization:
Temple Univ., Philadelphia, PA (United States). Energy Frontier Research Center (EFRC) Center for Complex Materials from First Principles (CCM)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)
Grant/Contract Number:
SC0012575
OSTI ID:
1566514
Journal Information:
Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory, Vol. 123, Issue 3; ISSN 1089-5639
Publisher:
American Chemical SocietyCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 26 works
Citation information provided by
Web of Science

References (87)

Many-Body Theory Exposed!: Propagator Description of Quantum Mechanics in Many-Body Systems book May 2008
Interacting Electrons: Theory and Computational Approaches book June 2016
New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem journal August 1965
The GW method journal March 1998
Electronic excitations: density-functional versus many-body Green’s-function approaches journal June 2002
Fully self-consistent GW self-energy of the electron gas journal January 1998
Inhomogeneous Electron Gas journal November 1964
Self-Consistent Equations Including Exchange and Correlation Effects journal November 1965
Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy journal December 1982
Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities journal November 1983
Exact differential equation for the density and ionization energy of a many-particle system journal November 1984
Comment on “Significance of the highest occupied Kohn-Sham eigenvalue” journal December 1997
Correlated optimized effective-potential treatment of the derivative discontinuity and of the highest occupied Kohn-Sham eigenvalue: A Janak-type theorem for the optimized effective-potential model journal February 1999
Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory journal May 2012
Perspective on “Density-functional theory for fractional particle number: derivative discontinuities of the energy” book January 2000
Degenerate Ground States and a Fractional Number of Electrons in Density and Reduced Density Matrix Functional Theory journal May 2000
Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction journal April 2008
Interpretation of the Kohn–Sham orbital energies as approximate vertical ionization potentials journal February 2002
Physical interpretation and evaluation of the Kohn–Sham and Dyson components of the ε–I relations between the Kohn–Sham orbital energies and the ionization potentials journal July 2003
The power of exact conditions in electronic structure theory journal February 2017
Does the ionization potential condition employed in QTP functionals mitigate the self-interaction error? journal January 2017
Towards an exact correlated orbital theory for electrons journal December 2009
Challenging adiabatic time-dependent density functional theory with a Hubbard dimer: the case of time-resolved long-range charge transfer journal January 2014
Challenges for Density Functional Theory journal December 2011
Insights into Current Limitations of Density Functional Theory journal August 2008
Development of exchange-correlation functionals with minimal many-electron self-interaction error journal May 2007
Coulomb-attenuated exchange energy density functionals journal July 1996
Combining long-range configuration interaction with short-range density functionals journal August 1997
A long-range correction scheme for generalized-gradient-approximation exchange functionals journal August 2001
On Koopmans’ theorem in density functional theory journal November 2010
Semiempirical hybrid density functional with perturbative second-order correlation journal January 2006
Doubly hybrid density functional for accurate descriptions of nonbond interactions, thermochemistry, and thermochemical kinetics journal March 2009
Fractional Charge Behavior and Band Gap Predictions with the XYG3 Type of Doubly Hybrid Density Functionals journal June 2014
Tuned Range-Separated Hybrids in Density Functional Theory journal March 2010
Accurate Electron Affinities and Orbital Energies of Anions from a Nonempirically Tuned Range-Separated Density Functional Theory Approach journal March 2017
Fundamental Gaps in Finite Systems from Eigenvalues of a Generalized Kohn-Sham Method journal December 2010
Localized orbital scaling correction for systematic elimination of delocalization error in density functional approximations journal September 2017
An extension of the coupled cluster formalism to excited states (I) journal January 1981
A linear response, coupled-cluster theory for excitation energy journal March 1984
The equation-of-motion coupled-cluster method: Excitation energies of Be and CO journal December 1989
Calculation of properties with the coupled-cluster method journal January 1977
Some aspects of the time-dependent coupled-cluster approach to dynamic response functions journal September 1983
Excitation energies of BH, CH2 and Ne in full configuration interaction and the hierarchy CCS, CC2, CCSD and CC3 of coupled cluster models journal September 1995
Spin-orbit coupling constants from coupled-cluster response theory journal January 2000
CI method for the study of general molecular potentials journal January 1968
The improved virtual orbital-complete active space configuration interaction method, a “packageable” efficient ab initio many-body method for describing electronically excited states journal February 2001
Natural orbitals as substitutes for optimized orbitals in complete active space wavefunctions journal September 2004
Ab initio floating occupation molecular orbital-complete active space configuration interaction: An efficient approximation to CASSCF journal June 2010
Second-order perturbation theory with a CASSCF reference function journal July 1990
Second‐order perturbation theory with a complete active space self‐consistent field reference function journal January 1992
Self‐Consistent Molecular Orbital Methods. X. Molecular Orbital Studies of Excited States with Minimal and Extended Basis Sets journal September 1971
Single-Reference ab Initio Methods for the Calculation of Excited States of Large Molecules journal November 2005
On the calculation of multiplet energies by the hartree-fock-slater method journal January 1977
TD-DFT benchmarks: A review journal April 2013
On the determination of excitation energies using density functional theory journal January 2000
Density Functional Vertical Self-Consistent Reaction Field Theory for Solvatochromism Studies of Solvent-Sensitive Dyes journal April 2004
Trapping of excitons at chemical defects in polyethylene journal October 2004
Rydberg energies using excited state density functional theory journal September 2008
Δ self-consistent field method to obtain potential energy surfaces of excited molecules on surfaces journal August 2008
Self-consistent-field calculations of core excited states journal March 2009
Assessment of the ΔSCF density functional theory approach for electronic excitations in organic dyes journal February 2011
Vertical excitation energies from the adiabatic connection journal November 2016
Double excitations within time-dependent density functional theory linear response journal April 2004
Conical intersections and double excitations in time-dependent density functional theory journal March 2006
Improving virtual Kohn–Sham orbitals and eigenvalues: Application to excitation energies and static polarizabilities journal December 1998
Molecular excitation energies to high-lying bound states from time-dependent density-functional response theory: Characterization and correction of the time-dependent local density approximation ionization threshold journal March 1998
Asymptotic correction approach to improving approximate exchange–correlation potentials: Time-dependent density-functional theory calculations of molecular excitation spectra journal November 2000
The importance of the asymptotic exchange-correlation potential in density functional theory journal September 2003
Does density functional theory contribute to the understanding of excited states of unsaturated organic compounds? journal October 1999
Long-range charge-transfer excited states in time-dependent density functional theory require non-local exchange journal August 2003
Failure of Time-Dependent Density Functional Theory for Long-Range Charge-Transfer Excited States:  The Zincbacteriochlorin−Bacteriochlorin and Bacteriochlorophyll−Spheroidene Complexes journal March 2004
First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications journal March 2011
Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules III: A Benchmark of GW Methods journal January 2016
Excitation energies from particle-particle random phase approximation: Davidson algorithm and benchmark studies journal September 2014
Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis journal August 1980
Generalized Gradient Approximation Made Simple journal October 1996
Density‐functional thermochemistry. III. The role of exact exchange journal April 1993
Photoelectron spectroscopy of azulenes journal January 1980
Breaking the Theoretical Scaling Limit for Predicting Quasiparticle Energies: The Stochastic G W Approach journal August 2014
Stochastic GW Calculations for Molecules journal September 2017
Atomic and Molecular Electron Affinities:  Photoelectron Experiments and Theoretical Computations journal January 2002
Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3 journal April 2008
Communication: Can excitation energies be obtained from orbital energies in a correlated orbital theory? journal October 2018
An extension of the coupled cluster formalism to excited states journal January 1981
Density-functional exchange-correlation potentials and orbital eigenvalues for light atoms journal May 1984
Exact results for the charge and spin densities, exchange-correlation potentials, and density-functional eigenvalues journal March 1985
Exchange and Correlation in Open Systems of Fluctuating Electron Number text January 2007

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Charge transfer excitation energies from ground state density functional theory calculations journal April 2019
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