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Title: Excitation spectra of aromatic molecules within a real-space G W -BSE formalism: Role of self-consistency and vertex corrections

Journal Article · · Physical Review B
ORCiD logo [1];  [2];  [3];  [3];  [2];  [4]
  1. Univ. of Illinois at Chicago, Chicago, IL (United States); National Institute of Standards and Technology, Gaithersburg, MD (United States)
  2. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  3. Univ. of Texas at Austin, Austin, TX (United States)
  4. Univ. of Illinois at Chicago, Chicago, IL (United States)
+ Show Author Affiliations

We present first-principles calculations on the vertical ionization potentials (IPs), electron affinities (EAs), and singlet excitation energies on an aromatic-molecule test set (benzene, thiophene, 1,2,5-thiadiazole, naphthalene, benzothiazole, and tetrathiafulvalene) within the GW and Bethe-Salpeter equation (BSE) formalisms. Our computational framework, which employs a real-space basis for ground-state and a transition-space basis for excited-state calculations, is well suited for high-accuracy calculations on molecules, as we show by comparing against G0W0 calculations within a plane-wave-basis formalism. We then generalize our framework to test variants of the GW approximation that include a local density approximation (LDA)-derived vertex function (ΓLDA) and quasiparticle-self-consistent (QS) iterations. We find that ΓLDA and quasiparticle self-consistency shift IPs and EAs by roughly the same magnitude, but with opposite sign for IPs and the same sign for EAs. G0W0 and QSGWΓLDA are more accurate for IPs, while G0W0ΓLDA and QSGW are best for EAs. For optical excitations, we find that perturbative GW-BSE underestimates the singlet excitation energy, while self-consistent GW-BSE results in good agreement with previous best-estimate values for both valence and Rydberg excitations. Finally, our work suggests that a hybrid approach, in which G0W0 energies are used for occupied orbitals and G0W0ΓLDA for unoccupied orbitals, also yields optical excitation energies in good agreement with experiment but at a smaller computational cost.

Research Organization:
Univ. of Illinois at Chicago, Chicago, IL (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC0001853; FG02-09ER16072; AC02-05CH11231; SC0008877
OSTI ID:
1351305
Alternate ID(s):
OSTI ID: 1294714; OSTI ID: 1454482
Journal Information:
Physical Review B, Vol. 94, Issue 8; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 41 works
Citation information provided by
Web of Science

References (102)

Band-Gap Problem in Semiconductors Revisited: Effects of Core States and Many-Body Self-Consistency journal August 2002
A systematic benchmark of the ab initio Bethe-Salpeter equation approach for low-lying optical excitations of small organic molecules journal June 2015
Hybrid density functional theory meets quasiparticle calculations: A consistent electronic structure approach journal October 2013
Optical properties of solids within the independent-quasiparticle approximation: Dynamical effects journal November 1996
Self-consistent calculation of total energies of the electron gas using many-body perturbation theory journal January 2001
Coulomb-hole summations and energies for G W calculations with limited number of empty orbitals: A modified static remainder approach journal April 2013
Electron transmission study of the temporary negative ion states of selected benzenoid and conjugated aromatic hydrocarbons journal January 1987
Self-consistent solution of the Dyson equation for atoms and molecules within a conserving approximation journal April 2005
Coupled-cluster calculations of the lowest 0–0 bands of the electronic excitation spectrum of naphthalene journal January 2014
Fully self-consistent GW calculations for atoms and molecules journal October 2006
GW Γ approximation for electron self-energies in semiconductors and insulators journal March 1994
Quasiparticle and optical properties of rutile and anatase TiO 2 journal August 2010
Compensation of Dynamical Quasiparticle and Vertex Corrections in Optical Spectra journal February 1997
Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules III: A Benchmark of GW Methods journal January 2016
BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures journal June 2012
Inclusion of Vertex Corrections in the Self-Consistent Calculation of Quasiparticles in Metals journal November 2001
QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials journal September 2009
Benchmark Many-Body GW and Bethe–Salpeter Calculations for Small Transition Metal Molecules journal August 2014
Ground-state properties of simple elements from GW calculations journal July 2009
Lowest-order corrections to the RPA polarizability and GW self-energy of a semiconducting wire journal July 1996
All-electron G W methods implemented in molecular orbital space: Ionization energy and electron affinity of conjugated molecules journal November 2011
Influence of the Core-Valence Interaction and of the Pseudopotential Approximation on the Electron Self-Energy in Semiconductors journal September 2008
Many-Body Perturbation Theory Using the Density-Functional Concept: Beyond the G W Approximation journal May 2005
Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies journal October 1986
Implementation of an all-electron GW approximation based on the projector augmented wave method without plasmon pole approximation: Application to Si, SiC, AlAs, InAs, NaH, and KH journal April 2003
Ionization Potentials of Solids: The Importance of Vertex Corrections journal March 2014
Electronic excitations: density-functional versus many-body Green’s-function approaches journal June 2002
Ground and ionic states of 1,2,5-thiadiazoles: An UV-photoelectron spectroscopic and theoretical study journal March 2010
Vertex correction calculations for an electron gas journal September 1974
Electron linewidths of wide-gap insulators: Excitonic effects in LiF journal August 2004
Theoretical study of the radiationless deactivation mechanisms of photo-excited thiophene journal March 2012
Fast and Accurate Electronic Excitations in Cyanines with the Many-Body Bethe–Salpeter Approach journal February 2014
TD-DFT benchmarks: A review journal April 2013
First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications journal March 2011
All-Electron Self-Consistent G W Approximation: Application to Si, MnO, and NiO journal September 2004
Generating relativistic pseudo-potentials with explicit incorporation of semi-core states using APE, the Atomic Pseudo-potentials Engine journal April 2008
Benchmarking the Bethe–Salpeter Formalism on a Standard Organic Molecular Set journal June 2015
Charge-transfer excitations in molecular donor-acceptor complexes within the many-body Bethe-Salpeter approach journal October 2011
A benchmark theoretical study of the electron affinities of benzene and linear acenes journal August 2008
An experimental and theoretical study of the valence shell photoelectron spectrum of the benzene molecule journal November 1997
Benchmark of G W methods for azabenzenes journal December 2012
Coupled-cluster reference values for the GW27 and GW100 test sets for the assessment of GW methods journal March 2015
Penning Ionization of Thiophene, Furan, and Pyrrole by Collision with He*(2 3 S) Metastable Atoms journal January 1996
Improved local-field corrections to the G 0 W approximation in jellium: Importance of consistency relations journal November 1997
The self-energy beyond GW: Local and nonlocal vertex corrections journal October 2009
Effect of self-consistency on quasiparticles in solids journal July 2006
Impact of widely used approximations to the G 0 W 0 method: an all-electron perspective journal February 2012
Systematic Vertex Corrections through Iterative Solution of Hedin's Equations Beyond the GW Approximation journal February 1998
Time-dependent density-functional theory for molecules and molecular solids journal November 2009
Modeling the Excited States of Biological Chromophores within Many-Body Green’s Function Theory journal November 2009
Fully self-consistent GW calculations for molecules journal February 2010
Lowest-order vertex-correction contribution to the direct gap of silicon journal April 1994
Benchmarking the performance of time-dependent density functional methods journal March 2012
GW 100: Benchmarking G 0 W 0 for Molecular Systems journal November 2015
New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem journal August 1965
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
Optical excitations in organic molecules, clusters, and defects studied by first-principles Green’s function methods journal May 2006
Effects of self-consistency and plasmon-pole models on G W calculations for closed-shell molecules journal September 2014
Quasiparticle Self-Consistent G W Theory journal June 2006
Resolution-of-identity approach to Hartree–Fock, hybrid density functionals, RPA, MP2 and GW with numeric atom-centered orbital basis functions journal May 2012
Improving virtual Kohn–Sham orbitals and eigenvalues: Application to excitation energies and static polarizabilities journal December 1998
Levels of self-consistency in the GW approximation journal March 2009
Fully self-consistent G W and quasiparticle self-consistent G W for molecules journal April 2014
First-order corrections to random-phase approximation GW calculations in silicon and diamond journal May 1998
PARSEC – the pseudopotential algorithm for real-space electronic structure calculations: recent advances and novel applications to nano-structures journal April 2006
Benchmarking the Starting Points of the GW Approximation for Molecules journal December 2012
Vertex corrections in localized and extended systems journal October 2007
Threshold photoelectron study of naphthalene, anthracene, pyrene, 1,2-dihydronaphthalene, and 9,10-dihydroanthracene journal June 2011
Photoelectron spectra and electronic structures of some naphtho[1,2-d]thiazoles journal July 1993
Electron-electron interactions and the bandwidth of metals journal June 1989
Excited States of Dicyanovinyl-Substituted Oligothiophenes from Many-Body Green’s Functions Theory journal February 2012
Benchmarking Second Order Methods for the Calculation of Vertical Electronic Excitation Energies: Valence and Rydberg States in Polycyclic Aromatic Hydrocarbons † journal October 2009
The electronic states of 1,2,5-thiadiazole studied by VUV absorption spectroscopy and ab initio configuration interaction methods journal June 2008
Self-consistent G W : All-electron implementation with localized basis functions journal August 2013
Self-Consistent Approximations in Many-Body Systems journal August 1962
Fully self-consistent GW self-energy of the electron gas journal January 1998
G W calculations using the spectral decomposition of the dielectric matrix: Verification, validation, and comparison of methods journal April 2013
Quantitative molecular orbital energies within a G0W0 approximation journal September 2012
First-principles GW calculations for DNA and RNA nucleobases journal March 2011
Enhanced static approximation to the electron self-energy operator for efficient calculation of quasiparticle energies journal November 2010
Photoelectron Spectrum and Electronic Structure of Tetrathiofulvalene (TTF) journal October 1974
Electron-hole excitations and optical spectra from first principles journal August 2000
Photoelectron properties of DNA and RNA bases from many-body perturbation theory journal August 2011
Self-consistent GW and higher-order calculations of electron states in metals journal September 1996
Fundamental and excitation gaps in molecules of relevance for organic photovoltaics from an optimally tuned range-separated hybrid functional journal August 2011
Inclusion of Vertex Corrections in the Self-Consistent Calculation of Quasiparticles in Metals text January 2001
GW 100: Benchmarking G0W0 for molecular systems text January 2015
Ground State Properties of Simple Elements from GW Calculations text January 2009
Fully selfconsistent GW calculations for molecules text January 2010
Quasiparticle and Optical Properties of Rutile and Anatase TiO$_{2}$ text January 2010
Enhanced Static Approximation to the Electron Self-Energy Operator for Efficient Calculation of Quasiparticle Energies text January 2010
First-principles GW calculations for DNA and RNA nucleobases text January 2011
Photoelectron properties of DNA and RNA bases from many-body perturbation theory text January 2011
Charge-transfer excitations in molecular donor-acceptor complexes within the many-body Bethe-Salpeter approach text January 2011
Quantitative Molecular Orbital Energies within a $G_0W_0$ Approximation text January 2012
Coulomb-hole summations and energies for GW calculations with limited number of empty orbitals: a modified static remainder approach text January 2012
Predictive GW calculations using plane waves and pseudopotentials text January 2014
All-electron self-consistent GW approximation: Application to Si, MnO, and NiO text January 2003
Quasiparticle Self-Consistent GW Theory text January 2005
Optical excitations in organic molecules, clusters and defects studied by first-principles Green's function methods text January 2006
Vertex corrections in localized and extended systems text January 2007
Systematic vertex corrections through iterative solution of Hedin's equations beyond the GW approximation text January 1997

Cited By (9)

Modeling Excited States of Confined Systems book January 2018
Ab initio modelling of local interfaces in doped organic semiconductors journal January 2020
Exploring connections between statistical mechanics and Green’s functions for realistic systems: Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green’s function journal November 2016
On the possibility of singlet fission in crystalline quaterrylene journal May 2018
Bethe–Salpeter equation for absorption and scattering spectroscopy: implementation in the exciting code journal August 2019
Modeling Excited States of Confined Systems book January 2020
Exploring connections between statistical mechanics and Green's functions for realistic systems. Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green's function text January 2016
On the Possibility of Singlet Fission in Crystalline Quaterrylene text January 2017
Dynamical configuration interaction: Quantum embedding that combines wave functions and Green's functions text January 2018

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