1
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Diaz-Andres A, Tonnelé C, Casanova D. Electronic Couplings for Triplet-Triplet Annihilation Upconversion in Crystal Rubrene. J Chem Theory Comput 2024; 20:4288-4297. [PMID: 38743825 PMCID: PMC11137828 DOI: 10.1021/acs.jctc.4c00185] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2024] [Revised: 05/06/2024] [Accepted: 05/06/2024] [Indexed: 05/16/2024]
Abstract
Triplet-triplet annihilation photon upconversion (TTA-UC) is a process able to repackage two low-frequency photons into light of higher energy. This transformation is typically orchestrated by the electronic degrees of freedom within organic compounds possessing suitable singlet and triplet energies and electronic couplings. In this work, we propose a computational protocol for the assessment of electronic couplings crucial to TTA-UC in molecular materials and apply it to the study of crystal rubrene. Our methodology integrates sophisticated yet computationally affordable approaches to quantify couplings in singlet and triplet energy transfer, the binding of triplet pairs, and the fusion to the singlet exciton. Of particular significance is the role played by charge-transfer states along the b-axis of rubrene crystal, acting as both partial quenchers of singlet energy transfer and mediators of triplet fusion. Our calculations identify the π-stacking direction as holding notable triplet energy transfer couplings, consistent with the experimentally observed anisotropic exciton diffusion. Finally, we have characterized the impact of thermally induced structural distortions, revealing their key role in the viability of triplet fusion and singlet fission. We posit that our approaches are transferable to a broad spectrum of organic molecular materials, offering a feasible means to quantify electronic couplings.
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Affiliation(s)
- Aitor Diaz-Andres
- Donostia
International Physics Center (DIPC), Donostia 20018, Euskadi, Spain
| | - Claire Tonnelé
- Donostia
International Physics Center (DIPC), Donostia 20018, Euskadi, Spain
- IKERBASQUE,
Basque Foundation for Science, Bilbao 48009, Euskadi, Spain
| | - David Casanova
- Donostia
International Physics Center (DIPC), Donostia 20018, Euskadi, Spain
- IKERBASQUE,
Basque Foundation for Science, Bilbao 48009, Euskadi, Spain
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2
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Taylor JT, Tozer DJ, Curchod BFE. On the description of conical intersections between excited electronic states with LR-TDDFT and ADC(2). J Chem Phys 2023; 159:214115. [PMID: 38059547 DOI: 10.1063/5.0176140] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2023] [Accepted: 11/14/2023] [Indexed: 12/08/2023] Open
Abstract
Conical intersections constitute the conceptual bedrock of our working understanding of ultrafast, nonadiabatic processes within photochemistry (and photophysics). Accurate calculation of potential energy surfaces within the vicinity of conical intersections, however, still poses a serious challenge to many popular electronic structure methods. Multiple works have reported on the deficiency of methods like linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) or algebraic diagrammatic construction to second-order [ADC(2)]-approaches often used in excited-state molecular dynamics simulations-to describe conical intersections between the ground and excited electronic states. In the present study, we focus our attention on conical intersections between excited electronic states and probe the ability of AA LR-TDDFT and ADC(2) to describe their topology and topography, using protonated formaldimine and pyrazine as two exemplar molecules. We also take the opportunity to revisit the performance of these methods in describing conical intersections involving the ground electronic state in protonated formaldimine-highlighting in particular how the intersection ring exhibited by AA LR-TDDFT can be perceived either as a (near-to-linear) seam of intersection or two interpenetrating cones, depending on the magnitude of molecular distortions within the branching space.
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Affiliation(s)
- Jack T Taylor
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
| | - David J Tozer
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
| | - Basile F E Curchod
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom
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3
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Dar DB, Maitra NT. Oscillator strengths and excited-state couplings for double excitations in time-dependent density functional theory. J Chem Phys 2023; 159:211104. [PMID: 38038212 DOI: 10.1063/5.0176705] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Accepted: 11/08/2023] [Indexed: 12/02/2023] Open
Abstract
Although useful to extract excitation energies of states of double-excitation character in time-dependent density functional theory that are missing in the adiabatic approximation, the frequency-dependent kernel derived earlier [Maitra et al., J. Chem. Phys. 120, 5932 (2004)] was not designed to yield oscillator strengths. These are required to fully determine linear absorption spectra, and they also impact excited-to-excited-state couplings that appear in dynamics simulations and other quadratic response properties. Here, we derive a modified non-adiabatic kernel that yields both accurate excitation energies and oscillator strengths for these states. We demonstrate its performance on a model two-electron system, the Be atom, and on excited-state transition dipoles in the LiH molecule at stretched bond-lengths, in all cases producing significant improvements over the traditional approximations.
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Affiliation(s)
- Davood B Dar
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
| | - Neepa T Maitra
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
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4
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Mejia-Rodriguez D, Aprà E, Autschbach J, Bauman NP, Bylaska EJ, Govind N, Hammond JR, Kowalski K, Kunitsa A, Panyala A, Peng B, Rehr JJ, Song H, Tretiak S, Valiev M, Vila FD. NWChem: Recent and Ongoing Developments. J Chem Theory Comput 2023; 19:7077-7096. [PMID: 37458314 DOI: 10.1021/acs.jctc.3c00421] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2023]
Abstract
This paper summarizes developments in the NWChem computational chemistry suite since the last major release (NWChem 7.0.0). Specifically, we focus on functionality, along with input blocks, that is accessible in the current stable release (NWChem 7.2.0) and in the "master" development branch, interfaces to quantum computing simulators, interfaces to external libraries, the NWChem github repository, and containerization of NWChem executable images. Some ongoing developments that will be available in the near future are also discussed.
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Affiliation(s)
- Daniel Mejia-Rodriguez
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Edoardo Aprà
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Jochen Autschbach
- Department of Chemistry, University at Buffalo, State University of New York, Buffalo, New York 14260-3000, United States
| | - Nicholas P Bauman
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Eric J Bylaska
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Niranjan Govind
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Jeff R Hammond
- Accelerated Computing, NVIDIA Helsinki Oy, Porkkalankatu 1, 00180 Helsinki, Finland
| | - Karol Kowalski
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Alexander Kunitsa
- Zapata Computing, Inc., 100 Federal Street, Boston, Massachusetts 02110, United States
| | - Ajay Panyala
- Advanced Computing, Mathematics, and Data Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Bo Peng
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - John J Rehr
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - Huajing Song
- Physics and Chemistry of Materials, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Sergei Tretiak
- Physics and Chemistry of Materials, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Marat Valiev
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Fernando D Vila
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
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5
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Bradbury NC, Allen T, Nguyen M, Ibrahim KZ, Neuhauser D. Optimized attenuated interaction: Enabling stochastic Bethe-Salpeter spectra for large systems. J Chem Phys 2023; 158:2882253. [PMID: 37094001 DOI: 10.1063/5.0146555] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2023] [Accepted: 04/03/2023] [Indexed: 04/26/2023] Open
Abstract
We develop an improved stochastic formalism for the Bethe-Salpeter equation (BSE), based on an exact separation of the effective-interaction W into two parts, W = (W - vW) + vW, where the latter is formally any translationally invariant interaction, vW(r - r'). When optimizing the fit of the exchange kernel vW to W, using a stochastic sampling W, the difference W - vW becomes quite small. Then, in the main BSE routine, this small difference is stochastically sampled. The number of stochastic samples needed for an accurate spectrum is then largely independent of system size. While the method is formally cubic in scaling, the scaling prefactor is small due to the constant number of stochastic orbitals needed for sampling W.
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Affiliation(s)
- Nadine C Bradbury
- Department of Chemistry and Biochemistry, UCLA, Los Angeles, California 90095-1569, USA
| | - Tucker Allen
- Department of Chemistry and Biochemistry, UCLA, Los Angeles, California 90095-1569, USA
| | - Minh Nguyen
- Department of Chemistry and Biochemistry, UCLA, Los Angeles, California 90095-1569, USA
| | - Khaled Z Ibrahim
- Computer Science Department, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, California 94720, USA
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, and California Nanoscience Institute, UCLA, Los Angeles, California 90095-1569, USA
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6
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Orlando R, Romaniello P, Loos PF. Exploring new exchange-correlation kernels in the Bethe–Salpeter equation: A study of the asymmetric Hubbard dimer. ADVANCES IN QUANTUM CHEMISTRY 2023. [DOI: 10.1016/bs.aiq.2023.02.007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/30/2023]
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7
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Quintero-Monsebaiz R, Monino E, Marie A, Loos PF. Connections between many-body perturbation and coupled-cluster theories. J Chem Phys 2022; 157:231102. [PMID: 36550046 DOI: 10.1063/5.0130837] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
Here, we build on the works of Scuseria et al. [J. Chem. Phys. 129, 231101 (2008)] and Berkelbach [J. Chem. Phys. 149, 041103 (2018)] to show connections between the Bethe-Salpeter equation (BSE) formalism combined with the GW approximation from many-body perturbation theory and coupled-cluster (CC) theory at the ground- and excited-state levels. In particular, we show how to recast the GW and Bethe-Salpeter equations as non-linear CC-like equations. Similitudes between BSE@GW and the similarity-transformed equation-of-motion CC method are also put forward. The present work allows us to easily transfer key developments and the general knowledge gathered in CC theory to many-body perturbation theory. In particular, it may provide a path for the computation of ground- and excited-state properties (such as nuclear gradients) within the GW and BSE frameworks.
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Affiliation(s)
- Raúl Quintero-Monsebaiz
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Enzo Monino
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Antoine Marie
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
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8
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Förster A, Visscher L. Quasiparticle Self-Consistent GW-Bethe-Salpeter Equation Calculations for Large Chromophoric Systems. J Chem Theory Comput 2022; 18:6779-6793. [PMID: 36201788 PMCID: PMC9648197 DOI: 10.1021/acs.jctc.2c00531] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
The GW-Bethe–Salpeter equation
(BSE) method
is promising for calculating the low-lying excitonic states of molecular
systems. However, so far it has only been applied to rather small
molecules and in the commonly implemented diagonal approximations
to the electronic self-energy, it depends on a mean-field starting
point. We describe here an implementation of the self-consistent and
starting-point-independent quasiparticle self-consistent (qsGW)-BSE approach, which is suitable for calculations on
large molecules. We herein show that eigenvalue-only self-consistency
can lead to an unfaithful description of some excitonic states for
chlorophyll dimers while the qsGW-BSE vertical excitation
energies (VEEs) are in excellent agreement with spectroscopic experiments
for chlorophyll monomers and dimers measured in the gas phase. Furthermore,
VEEs from time-dependent density functional theory calculations tend
to disagree with experimental values and using different range-separated
hybrid (RSH) kernels does change the VEEs by up to 0.5 eV. We use
the new qsGW-BSE implementation to calculate the
lowest excitation energies of the six chromophores of the photosystem
II (PSII) reaction center (RC) with nearly 2000 correlated electrons.
Using more than 11,000 (6000) basis functions, the calculation could
be completed in less than 5 (2) days on a single modern compute node.
In agreement with previous TD-DFT calculations using RSH kernels on
models that also do not include environmental effects, our qsGW-BSE calculations only yield states with local characters
in the low-energy spectrum of the hexameric complex. Earlier works
with RSH kernels have demonstrated that the protein environment facilitates
the experimentally observed interchromophoric charge transfer. Therefore,
future research will need to combine correlation effects beyond TD-DFT
with an explicit treatment of environmental electrostatics.
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Affiliation(s)
- Arno Förster
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HVAmsterdam, The Netherlands
| | - Lucas Visscher
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HVAmsterdam, The Netherlands
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9
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Loos PF, Romaniello P. Static and dynamic Bethe-Salpeter equations in the T-matrix approximation. J Chem Phys 2022; 156:164101. [PMID: 35490009 DOI: 10.1063/5.0088364] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
While the well-established GW approximation corresponds to a resummation of the direct ring diagrams and is particularly well suited for weakly correlated systems, the T-matrix approximation does sum ladder diagrams up to infinity and is supposedly more appropriate in the presence of strong correlation. Here, we derive and implement, for the first time, the static and dynamic Bethe-Salpeter equations when one considers T-matrix quasiparticle energies and a T-matrix-based kernel. The performance of the static scheme and its perturbative dynamical correction are assessed by computing the neutral excited states of molecular systems. A comparison with more conventional schemes as well as other wave function methods is also reported. Our results suggest that the T-matrix-based formalism performs best in few-electron systems where the electron density remains low.
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Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Pina Romaniello
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, Toulouse, France
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10
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Li J, Jin Y, Su NQ, Yang W. Combining localized orbital scaling correction and Bethe-Salpeter equation for accurate excitation energies. J Chem Phys 2022; 156:154101. [PMID: 35459294 PMCID: PMC9033305 DOI: 10.1063/5.0087498] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2022] [Accepted: 03/29/2022] [Indexed: 11/14/2022] Open
Abstract
We applied localized orbital scaling correction (LOSC) in Bethe-Salpeter equation (BSE) to predict accurate excitation energies for molecules. LOSC systematically eliminates the delocalization error in the density functional approximation and is capable of approximating quasiparticle (QP) energies with accuracy similar to or better than GW Green's function approach and with much less computational cost. The QP energies from LOSC, instead of commonly used G0W0 and evGW, are directly used in BSE. We show that the BSE/LOSC approach greatly outperforms the commonly used BSE/G0W0 approach for predicting excitations with different characters. For the calculations of Truhlar-Gagliardi test set containing valence, charge transfer, and Rydberg excitations, BSE/LOSC with the Tamm-Dancoff approximation provides a comparable accuracy to time-dependent density functional theory (TDDFT) and BSE/evGW. For the calculations of Stein CT test set and Rydberg excitations of atoms, BSE/LOSC considerably outperforms both BSE/G0W0 and TDDFT approaches with a reduced starting point dependence. BSE/LOSC is, thus, a promising and efficient approach to calculate excitation energies for molecular systems.
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Affiliation(s)
- Jiachen Li
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Ye Jin
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Neil Qiang Su
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
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11
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Bintrim SJ, Berkelbach TC. Full-frequency dynamical Bethe-Salpeter equation without frequency and a study of double excitations. J Chem Phys 2022; 156:044114. [PMID: 35105075 PMCID: PMC8807000 DOI: 10.1063/5.0074434] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2021] [Accepted: 12/31/2021] [Indexed: 01/30/2023] Open
Abstract
The Bethe-Salpeter equation (BSE) that results from the GW approximation to the self-energy is a frequency-dependent (nonlinear) eigenvalue problem due to the dynamically screened Coulomb interaction between electrons and holes. The computational time required for a numerically exact treatment of this frequency dependence is O(N6), where N is the system size. To avoid the common static screening approximation, we show that the full-frequency dynamical BSE can be exactly reformulated as a frequency-independent eigenvalue problem in an expanded space of single and double excitations. When combined with an iterative eigensolver and the density fitting approximation to the electron repulsion integrals, this reformulation yields a dynamical BSE algorithm whose computational time is O(N5), which we verify numerically. Furthermore, the reformulation provides direct access to excited states with dominant double excitation character, which are completely absent in the spectrum of the statically screened BSE. We study the 21Ag state of butadiene, hexatriene, and octatetraene and find that GW/BSE overestimates the excitation energy by about 1.5-2 eV and significantly underestimates the double excitation character.
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Affiliation(s)
- Sylvia J. Bintrim
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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12
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Maitra NT. Double and Charge-Transfer Excitations in Time-Dependent Density Functional Theory. Annu Rev Phys Chem 2021; 73:117-140. [PMID: 34910562 DOI: 10.1146/annurev-physchem-082720-124933] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Time-dependent density functional theory has emerged as a method of choice for calculations of spectra and response properties in physics, chemistry, and biology, with its system-size scaling enabling computations on systems much larger than otherwise possible. While increasingly complex and interesting systems have been successfully tackled with relatively simple functional approximations, there has also been increasing awareness that these functionals tend to fail for certain classes of approximations. Here I review the fundamental challenges the approximate functionals have in describing double excitations and charge-transfer excitations, which are two of the most common impediments for the theory to be applied in a black-box way. At the same time, I describe the progress made in recent decades in developing functional approximations that give useful predictions for these excitations. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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Affiliation(s)
- Neepa T Maitra
- Department of Physics, Rutgers University at Newark, Newark, New Jersey, USA;
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13
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Di Sabatino S, Loos PF, Romaniello P. Scrutinizing GW-Based Methods Using the Hubbard Dimer. Front Chem 2021; 9:751054. [PMID: 34778206 PMCID: PMC8586429 DOI: 10.3389/fchem.2021.751054] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2021] [Accepted: 09/28/2021] [Indexed: 12/03/2022] Open
Abstract
Using the simple (symmetric) Hubbard dimer, we analyze some important features of the GW approximation. We show that the problem of the existence of multiple quasiparticle solutions in the (perturbative) one-shot GW method and its partially self-consistent version is solved by full self-consistency. We also analyze the neutral excitation spectrum using the Bethe-Salpeter equation (BSE) formalism within the standard GW approximation and find, in particular, that 1) some neutral excitation energies become complex when the electron-electron interaction U increases, which can be traced back to the approximate nature of the GW quasiparticle energies; 2) the BSE formalism yields accurate correlation energies over a wide range of U when the trace (or plasmon) formula is employed; 3) the trace formula is sensitive to the occurrence of complex excitation energies (especially singlet), while the expression obtained from the adiabatic-connection fluctuation-dissipation theorem (ACFDT) is more stable (yet less accurate); 4) the trace formula has the correct behavior for weak (i.e., small U) interaction, unlike the ACFDT expression.
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Affiliation(s)
- S. Di Sabatino
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS and ETSF, Toulouse, France
| | - P.-F. Loos
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
| | - P. Romaniello
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS and ETSF, Toulouse, France
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14
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Monino E, Loos PF. Spin-Conserved and Spin-Flip Optical Excitations from the Bethe-Salpeter Equation Formalism. J Chem Theory Comput 2021; 17:2852-2867. [PMID: 33724811 PMCID: PMC8154368 DOI: 10.1021/acs.jctc.1c00074] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
![]()
Like adiabatic time-dependent
density-functional theory (TD-DFT),
the Bethe–Salpeter equation (BSE) formalism of many-body perturbation
theory, in its static approximation, is “blind” to double
(and higher) excitations, which are ubiquitous, for example, in conjugated
molecules like polyenes. Here, we apply the spin-flip ansatz (which considers the lowest triplet state as the reference configuration
instead of the singlet ground state) to the BSE formalism in order
to access, in particular, double excitations. The present scheme is
based on a spin-unrestricted version of the GW approximation
employed to compute the charged excitations and screened Coulomb potential
required for the BSE calculations. Dynamical corrections to the static
BSE optical excitations are taken into account via an unrestricted
generalization of our recently developed (renormalized) perturbative
treatment. The performance of the present spin-flip BSE formalism
is illustrated by computing excited-state energies of the beryllium
atom, the hydrogen molecule at various bond lengths, and cyclobutadiene
in its rectangular and square-planar geometries.
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Affiliation(s)
- Enzo Monino
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Route de Narbonne, 31062 Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Route de Narbonne, 31062 Toulouse, France
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15
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Bintrim SJ, Berkelbach TC. Full-frequency GW without frequency. J Chem Phys 2021; 154:041101. [PMID: 33514108 PMCID: PMC7843153 DOI: 10.1063/5.0035141] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2020] [Accepted: 12/13/2020] [Indexed: 01/30/2023] Open
Abstract
Efficient computer implementations of the GW approximation must approximate a numerically challenging frequency integral; the integral can be performed analytically, but doing so leads to an expensive implementation whose computational cost scales as O(N6), where N is the size of the system. Here, we introduce a new formulation of the full-frequency GW approximation by exactly recasting it as an eigenvalue problem in an expanded space. This new formulation (1) avoids the use of time or frequency grids, (2) naturally obviates the need for the common "diagonal" approximation, (3) enables common iterative eigensolvers that reduce the canonical scaling to O(N5), and (4) enables a density-fitted implementation that reduces the scaling to O(N4). We numerically verify these scaling behaviors and test a variety of approximations that are motivated by this new formulation. The new formulation is found to be competitive with conventional O(N4) methods based on analytic continuation or contour deformation. In this new formulation, the relation of the GW approximation to configuration interaction, coupled-cluster theory, and the algebraic diagrammatic construction is made especially apparent, providing a new direction for improvements to the GW approximation.
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Affiliation(s)
- Sylvia J. Bintrim
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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16
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Sanz-Rodrigo J, Ricci G, Olivier Y, Sancho-García JC. Negative Singlet–Triplet Excitation Energy Gap in Triangle-Shaped Molecular Emitters for Efficient Triplet Harvesting. J Phys Chem A 2021; 125:513-522. [DOI: 10.1021/acs.jpca.0c08029] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Affiliation(s)
- J. Sanz-Rodrigo
- Department of Physical Chemistry, University of Alicante, E-03080 Alicante, Spain
| | - G. Ricci
- Unité de Chimie Physique Théorique et Structurale & Laboratoire de Physique du Solid, Namur Institute of Structured Matter, Université de Namur, B-5000 Namur, Belgium
| | - Y. Olivier
- Unité de Chimie Physique Théorique et Structurale & Laboratoire de Physique du Solid, Namur Institute of Structured Matter, Université de Namur, B-5000 Namur, Belgium
| | - J. C. Sancho-García
- Department of Physical Chemistry, University of Alicante, E-03080 Alicante, Spain
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17
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Abstract
We discuss the physical properties and accuracy of three distinct dynamical (i.e., frequency-dependent) kernels for the computation of optical excitations within linear response theory: (i) an a priori built kernel inspired by the dressed time-dependent density-functional theory kernel proposed by Maitra et al. [J. Chem. Phys. 120, 5932 (2004)], (ii) the dynamical kernel stemming from the Bethe-Salpeter equation (BSE) formalism derived originally by Strinati [Riv. Nuovo Cimento 11, 1-86 (1988)], and (iii) the second-order BSE kernel derived by Zhang et al. [J. Chem. Phys. 139, 154109 (2013)]. The principal take-home message of the present paper is that dynamical kernels can provide, thanks to their frequency-dependent nature, additional excitations that can be associated with higher-order excitations (such as the infamous double excitations), an unappreciated feature of dynamical quantities. We also analyze, for each kernel, the appearance of spurious excitations originating from the approximate nature of the kernels, as first evidenced by Romaniello et al. [J. Chem. Phys. 130, 044108 (2009)]. Using a simple two-level model, prototypical examples of valence, charge-transfer, and Rydberg excited states are considered.
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Affiliation(s)
- Juliette Authier
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
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18
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Loos PF, Blase X. Dynamical correction to the Bethe-Salpeter equation beyond the plasmon-pole approximation. J Chem Phys 2020; 153:114120. [PMID: 32962392 DOI: 10.1063/5.0023168] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Bethe-Salpeter equation (BSE) formalism is a computationally affordable method for the calculation of accurate optical excitation energies in molecular systems. Similar to the ubiquitous adiabatic approximation of time-dependent density-functional theory, the static approximation, which substitutes a dynamical (i.e., frequency-dependent) kernel by its static limit, is usually enforced in most implementations of the BSE formalism. Here, going beyond the static approximation, we compute the dynamical correction of the electron-hole screening for molecular excitation energies, thanks to a renormalized first-order perturbative correction to the static BSE excitation energies. The present dynamical correction goes beyond the plasmon-pole approximation as the dynamical screening of the Coulomb interaction is computed exactly within the random-phase approximation. Our calculations are benchmarked against high-level (coupled-cluster) calculations, allowing one to assess the clear improvement brought by the dynamical correction for both singlet and triplet optical transitions.
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Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Xavier Blase
- Université Grenoble Alpes, CNRS, Institut NEEL, F-38042 Grenoble, France
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19
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Blase X, Duchemin I, Jacquemin D, Loos PF. The Bethe-Salpeter Equation Formalism: From Physics to Chemistry. J Phys Chem Lett 2020; 11:7371-7382. [PMID: 32787315 DOI: 10.1021/acs.jpclett.0c01875] [Citation(s) in RCA: 70] [Impact Index Per Article: 17.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The Bethe-Salpeter equation (BSE) formalism is steadily asserting itself as a new efficient and accurate tool in the ensemble of computational methods available to chemists in order to predict optical excitations in molecular systems. In particular, the combination of the so-called GW approximation, giving access to reliable ionization energies and electron affinities, and the BSE formalism, able to model UV/vis spectra, has shown to provide accurate singlet excitation energies with a typical error of 0.1-0.3 eV. With a similar computational cost as time-dependent density-functional theory (TD-DFT), BSE is able to provide an accuracy on par with the most accurate global and range-separated hybrid functionals without the unsettling choice of the exchange-correlation functional, resolving further known issues (e.g., charge-transfer excitations). In this Perspective, we provide a historical overview of BSE, with a particular focus on its condensed-matter roots. We also propose a critical review of its strengths and weaknesses in different chemical situations.
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Affiliation(s)
- Xavier Blase
- Université Grenoble Alpes, CNRS, Institut NEEL, F-38042 Grenoble, France
| | - Ivan Duchemin
- Université Grenoble Alpes, CEA, IRIG-MEM-L Sim, 38054 Grenoble, France
| | - Denis Jacquemin
- Université de Nantes, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
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20
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Loos PF, Fromager E. A weight-dependent local correlation density-functional approximation for ensembles. J Chem Phys 2020; 152:214101. [DOI: 10.1063/5.0007388] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS, Université de Strasbourg, Strasbourg, France
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21
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Loos PF, Scemama A, Duchemin I, Jacquemin D, Blase X. Pros and Cons of the Bethe-Salpeter Formalism for Ground-State Energies. J Phys Chem Lett 2020; 11:3536-3545. [PMID: 32298578 DOI: 10.1021/acs.jpclett.0c00460] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The combination of the many-body Green's function GW approximation and the Bethe-Salpeter equation (BSE) formalism has shown to be a promising alternative to time-dependent density functional theory (TD-DFT) for computing vertical transition energies and oscillator strengths in molecular systems. The BSE formalism can also be employed to compute ground-state correlation energies thanks to the adiabatic-connection fluctuation-dissipation theorem (ACFDT). Here, we study the topology of the ground-state potential energy surfaces (PESs) of several diatomic molecules near their equilibrium bond length. Using comparisons with state-of-art computational approaches (CC3), we show that ACFDT@BSE is surprisingly accurate and can even compete with lower-order coupled cluster methods (CC2 and CCSD) in terms of total energies and equilibrium bond distances for the considered systems. However, we sometimes observe unphysical irregularities on the ground-state PES in relation with difficulties in the identification of a few GW quasiparticle energies.
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Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31077 Toulouse, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31077 Toulouse, France
| | - Ivan Duchemin
- Université Grenoble Alpes, CEA, IRIG-MEM-L Sim, 38054 Grenoble, France
| | - Denis Jacquemin
- Laboratoire CEISAM - UMR CNRS 6230, Université de Nantes, 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France
| | - Xavier Blase
- Université Grenoble Alpes, CNRS, Institut NEEL, F-38042 Grenoble, France
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22
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Lewis AM, Berkelbach TC. Ab Initio Linear and Pump-Probe Spectroscopy of Excitons in Molecular Crystals. J Phys Chem Lett 2020; 11:2241-2246. [PMID: 32109074 DOI: 10.1021/acs.jpclett.0c00031] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Linear and nonlinear spectroscopies are powerful tools used to investigate the energetics and dynamics of electronic excited states of both molecules and crystals. While highly accurate ab initio calculations of molecular spectra can be performed relatively routinely, extending these calculations to periodic systems is challenging. Here, we present calculations of the linear absorption spectrum and pump-probe two-photon photoemission spectra of the naphthalene crystal using equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD). Molecular acene crystals are of interest due to the low-energy multiexciton singlet states they exhibit, which have been studied extensively as intermediates involved in singlet fission. Our linear absorption spectrum is in good agreement with experiment, predicting a first exciton absorption peak at 4.4 eV, and our two-photon photoemission spectra capture the qualitative behavior of multiexciton states, whose double-excitation character cannot be captured by current methods. The simulated pump-probe spectra provide support for existing interpretations of two-photon photoemission experiments in closely related acene crystals such as tetracene and pentacene.
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Affiliation(s)
- Alan M Lewis
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, United States
| | - Timothy C Berkelbach
- Department of Chemistry, Columbia University, New York, New York 10027, United States
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
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23
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Marut C, Senjean B, Fromager E, Loos PF. Weight dependence of local exchange–correlation functionals in ensemble density-functional theory: double excitations in two-electron systems. Faraday Discuss 2020; 224:402-423. [DOI: 10.1039/d0fd00059k] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We discuss the construction of first-rung weight-dependent exchange–correlation density-functional approximations for He and H2 specifically designed for the computation of double excitations within Gross–Oliveira–Kohn-DFT.
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Affiliation(s)
- Clotilde Marut
- Laboratoire de Chimie et Physique Quantiques
- Université de Toulouse
- CNRS
- UPS
- France
| | - Bruno Senjean
- Instituut-Lorentz
- Universiteit Leiden
- 2300 RA Leiden
- The Netherlands
- Division of Theoretical Chemistry
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique
- Institut de Chimie
- CNRS
- Université de Strasbourg
- Strasbourg
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24
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Mester D, Kállay M. Combined Density Functional and Algebraic-Diagrammatic Construction Approach for Accurate Excitation Energies and Transition Moments. J Chem Theory Comput 2019; 15:4440-4453. [PMID: 31265275 DOI: 10.1021/acs.jctc.9b00391] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
A composite of time-dependent density functional theory (TDDFT) and the second-order algebraic-diagrammatic construction [ADC(2)] approach is presented for efficient calculation of spectral properties of molecules. Our method can be regarded as a new excited-state double-hybrid (DH) approach or a dressed TDDFT scheme, but it can also be interpreted as an empirically tuned ADC(2) model. Several combinations of exchange-correlation functionals and spin-scaling schemes are explored. Our best-performing method includes the Perdew, Burke, and Ernzerhof exchange and Perdew's 1986 correlation functional and employs the scaled-opposite-spin approximation for the higher-order terms. The computation time of the new method scales as the fourth power of the system size, and an efficient cost-reduction approach is also presented, which further speeds up the calculations. Our benchmark calculations show that the proposed model outperforms not only the existing DH approaches and ADC(2) variants but also the considerably more expensive coupled-cluster methods.
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Affiliation(s)
- Dávid Mester
- Department of Physical Chemistry and Materials Science , Budapest University of Technology and Economics , P.O. Box 91, H-1521 Budapest , Hungary
| | - Mihály Kállay
- Department of Physical Chemistry and Materials Science , Budapest University of Technology and Economics , P.O. Box 91, H-1521 Budapest , Hungary
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25
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Olevano V, Toulouse J, Schuck P. A formally exact one-frequency-only Bethe-Salpeter-like equation. Similarities and differences between GW+BSE and self-consistent RPA. J Chem Phys 2019; 150:084112. [DOI: 10.1063/1.5080330] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Affiliation(s)
- Valerio Olevano
- Université Grenoble Alpes, 38000 Grenoble, France
- CNRS, Institut Néel, 38042 Grenoble, France
- European Theoretical Spectroscopy Facility (ETSF)
| | - Julien Toulouse
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
| | - Peter Schuck
- Université Grenoble Alpes, 38000 Grenoble, France
- Institut de Physique Nucléaire, IN2P3-CNRS, Université Paris-Sud, 91406 Orsay, France
- CNRS, Laboratoire de Physique et de Modélisation des Milieux Condensés, 38042 Grenoble, France
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26
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Loos PF, Boggio-Pasqua M, Scemama A, Caffarel M, Jacquemin D. Reference Energies for Double Excitations. J Chem Theory Comput 2019; 15:1939-1956. [DOI: 10.1021/acs.jctc.8b01205] [Citation(s) in RCA: 79] [Impact Index Per Article: 15.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Martial Boggio-Pasqua
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Michel Caffarel
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Denis Jacquemin
- Laboratoire CEISAM (UMR 6230), CNRS, Université de Nantes, 44399 Cedex 3 Nantes, France
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27
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Véril M, Romaniello P, Berger JA, Loos PF. Unphysical Discontinuities in GW Methods. J Chem Theory Comput 2018; 14:5220-5228. [DOI: 10.1021/acs.jctc.8b00745] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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28
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Blase X, Duchemin I, Jacquemin D. The Bethe–Salpeter equation in chemistry: relations with TD-DFT, applications and challenges. Chem Soc Rev 2018; 47:1022-1043. [DOI: 10.1039/c7cs00049a] [Citation(s) in RCA: 120] [Impact Index Per Article: 20.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
We review the Bethe–Salpeter formalism and analyze its performances for the calculation of the excited state properties of molecular systems.
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Affiliation(s)
- Xavier Blase
- Univ. Grenoble Alpes
- CNRS
- Inst NEEL
- F-38042 Grenoble
- France
| | - Ivan Duchemin
- Univ. Grenoble Alpes
- CEA
- INAC-MEM
- L-Sim
- F-38000 Grenoble
| | - Denis Jacquemin
- CEISAM UMR CNRS 6230
- Université de Nantes
- 44322 Nantes Cedex 3
- France
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29
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Maggio E, Kresse G. GW Vertex Corrected Calculations for Molecular Systems. J Chem Theory Comput 2017; 13:4765-4778. [DOI: 10.1021/acs.jctc.7b00586] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Emanuele Maggio
- Faculty of Physics
and Center
for Computational Materials Science, University of Vienna, Sensengasse
8/12, A-1090 Vienna, Austria
| | - Georg Kresse
- Faculty of Physics
and Center
for Computational Materials Science, University of Vienna, Sensengasse
8/12, A-1090 Vienna, Austria
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30
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Li J, Holzmann M, Duchemin I, Blase X, Olevano V. Helium Atom Excitations by the GW and Bethe-Salpeter Many-Body Formalism. PHYSICAL REVIEW LETTERS 2017; 118:163001. [PMID: 28474954 DOI: 10.1103/physrevlett.118.163001] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2016] [Indexed: 06/07/2023]
Abstract
The helium atom is the simplest many-body electronic system provided by nature. The exact solution to the Schrödinger equation is known for helium ground and excited states, and it represents a benchmark for any many-body methodology. Here, we check the ab initio many-body GW approximation and the Bethe-Salpeter equation (BSE) against the exact solution for helium. Starting from the Hartree-Fock method, we show that the GW and the BSE yield impressively accurate results on excitation energies and oscillator strength, systematically improving the time-dependent Hartree-Fock method. These findings suggest that the accuracy of the BSE and GW approximations is not significantly limited by self-interaction and self-screening problems even in this few electron limit. We further discuss our results in comparison to those obtained by time-dependent density-functional theory.
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Affiliation(s)
- Jing Li
- Université Grenoble Alpes, 38000 Grenoble, France
- CNRS, Institut Néel, 38042 Grenoble, France
| | - Markus Holzmann
- Université Grenoble Alpes, 38000 Grenoble, France
- CNRS, LPMMC, 38042 Grenoble, France
- European Theoretical Spectroscopy Facility (ETSF), 38000 Grenoble, France
| | - Ivan Duchemin
- Université Grenoble Alpes, 38000 Grenoble, France
- CEA, INAC-MEM L_Sim, 38054 Grenoble, France
| | - Xavier Blase
- Université Grenoble Alpes, 38000 Grenoble, France
- CNRS, Institut Néel, 38042 Grenoble, France
| | - Valerio Olevano
- Université Grenoble Alpes, 38000 Grenoble, France
- CNRS, Institut Néel, 38042 Grenoble, France
- European Theoretical Spectroscopy Facility (ETSF), 38000 Grenoble, France
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31
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Park YC, Senn F, Krykunov M, Ziegler T. Self-Consistent Constricted Variational Theory RSCF-CV(∞)-DFT and Its Restrictions To Obtain a Numerically Stable ΔSCF-DFT-like Method: Theory and Calculations for Triplet States. J Chem Theory Comput 2016; 12:5438-5452. [DOI: 10.1021/acs.jctc.6b00333] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Young Choon Park
- Department
of Chemistry, University of Calgary, 2500 University Drive Northwest, Calgary, Alberta T2N-1N4, Canada
| | - Florian Senn
- Department
of Chemistry, University of Calgary, 2500 University Drive Northwest, Calgary, Alberta T2N-1N4, Canada
| | - Mykhaylo Krykunov
- Department
of Chemistry and Biomolecular Sciences, University of Ottawa, 75 Laurier Avenue East, Ottawa, Ontario K1N-6N5, Canada
| | - Tom Ziegler
- Department
of Chemistry, University of Calgary, 2500 University Drive Northwest, Calgary, Alberta T2N-1N4, Canada
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32
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Maitra NT. Perspective: Fundamental aspects of time-dependent density functional theory. J Chem Phys 2016; 144:220901. [DOI: 10.1063/1.4953039] [Citation(s) in RCA: 228] [Impact Index Per Article: 28.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Neepa T. Maitra
- Department of Physics and Astronomy, Hunter College and the Physics Program at the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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33
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Trevisanutto PE, Vignale G. Ab initio electronic structure of quasi-two-dimensional materials: A "native" Gaussian-plane wave approach. J Chem Phys 2016; 144:204122. [PMID: 27250294 DOI: 10.1063/1.4951686] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Ab initio electronic structure calculations of two-dimensional layered structures are typically performed using codes that were developed for three-dimensional structures, which are periodic in all three directions. The introduction of a periodicity in the third direction (perpendicular to the layer) is completely artificial and may lead in some cases to spurious results and to difficulties in treating the action of external fields. In this paper we develop a new approach, which is "native" to quasi-2D materials, making use of basis function that are periodic in the plane, but atomic-like in the perpendicular direction. We show how some of the basic tools of ab initio electronic structure theory - density functional theory, GW approximation and Bethe-Salpeter equation - are implemented in the new basis. We argue that the new approach will be preferable to the conventional one in treating the peculiarities of layered materials, including the long range of the unscreened Coulomb interaction in insulators, and the effects of strain, corrugations, and external fields.
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Affiliation(s)
- Paolo E Trevisanutto
- Graphene Research Centre and CA2DM, National University of Singapore, Singapore 117542, Singapore and Singapore Synchrotron Light Source, National University of Singapore, Singapore 117603, Singapore
| | - Giovanni Vignale
- Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA
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34
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Rebolini E, Toulouse J. Range-separated time-dependent density-functional theory with a frequency-dependent second-order Bethe-Salpeter correlation kernel. J Chem Phys 2016; 144:094107. [DOI: 10.1063/1.4943003] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
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35
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Li Z, Liu W. Critical Assessment of TD-DFT for Excited States of Open-Shell Systems: I. Doublet–Doublet Transitions. J Chem Theory Comput 2015; 12:238-60. [DOI: 10.1021/acs.jctc.5b01158] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Zhendong Li
- Beijing National Laboratory
for Molecular Sciences, Institute of Theoretical and Computational
Chemistry, State Key Laboratory of Rare Earth Materials Chemistry
and Applications, College of Chemistry and Molecular Engineering,
and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
| | - Wenjian Liu
- Beijing National Laboratory
for Molecular Sciences, Institute of Theoretical and Computational
Chemistry, State Key Laboratory of Rare Earth Materials Chemistry
and Applications, College of Chemistry and Molecular Engineering,
and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
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36
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Ziegler T, Krykunov M, Autschbach J. Derivation of the RPA (Random Phase Approximation) Equation of ATDDFT (Adiabatic Time Dependent Density Functional Ground State Response Theory) from an Excited State Variational Approach Based on the Ground State Functional. J Chem Theory Comput 2015; 10:3980-6. [PMID: 26588541 DOI: 10.1021/ct500385a] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The random phase approximation (RPA) equation of adiabatic time dependent density functional ground state response theory (ATDDFT) has been used extensively in studies of excited states. It extracts information about excited states from frequency dependent ground state response properties and avoids, thus, in an elegant way, direct Kohn-Sham calculations on excited states in accordance with the status of DFT as a ground state theory. Thus, excitation energies can be found as resonance poles of frequency dependent ground state polarizability from the eigenvalues of the RPA equation. ATDDFT is approximate in that it makes use of a frequency independent energy kernel derived from the ground state functional. It is shown in this study that one can derive the RPA equation of ATDDFT from a purely variational approach in which stationary states above the ground state are located using our constricted variational DFT (CV-DFT) method and the ground state functional. Thus, locating stationary states above the ground state due to one-electron excitations with a ground state functional is completely equivalent to solving the RPA equation of TDDFT employing the same functional. The present study is an extension of a previous work in which we demonstrated the equivalence between ATDDFT and CV-DFT within the Tamm-Dancoff approximation.
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Affiliation(s)
- Tom Ziegler
- Department of Chemistry, University of Calgary , University Drive 2500, Calgary Alberta T2N1N4, Canada
| | - Mykhaylo Krykunov
- Department of Chemistry, University of Calgary , University Drive 2500, Calgary Alberta T2N1N4, Canada
| | - Jochen Autschbach
- Department of Chemistry, State University of New York . 312 Natural Sciences Complex. Buffalo, New York 14260-3000, United States
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37
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Säkkinen N, Peng Y, Appel H, van Leeuwen R. Many-body Green’s function theory for electron-phonon interactions: The Kadanoff-Baym approach to spectral properties of the Holstein dimer. J Chem Phys 2015; 143:234102. [DOI: 10.1063/1.4936143] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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38
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Zhou JS, Kas JJ, Sponza L, Reshetnyak I, Guzzo M, Giorgetti C, Gatti M, Sottile F, Rehr JJ, Reining L. Dynamical effects in electron spectroscopy. J Chem Phys 2015; 143:184109. [DOI: 10.1063/1.4934965] [Citation(s) in RCA: 52] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jianqiang Sky Zhou
- Laboratoire des Solides Irradiés, École Polytechnique, CNRS, CEA-DSM-IRAMIS, Université Paris-Saclay, F-91128 Palaiseau, France
- European Theoretical Spectroscopy Facility (ETSF)
| | - J. J. Kas
- European Theoretical Spectroscopy Facility (ETSF)
- Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA
| | - Lorenzo Sponza
- Department of Physics, King’s College London, London WC2R 2LS, United Kingdom
| | - Igor Reshetnyak
- Laboratoire des Solides Irradiés, École Polytechnique, CNRS, CEA-DSM-IRAMIS, Université Paris-Saclay, F-91128 Palaiseau, France
- European Theoretical Spectroscopy Facility (ETSF)
| | - Matteo Guzzo
- Institut für Physik und IRIS Adlershof, Humboldt-Universität zu Berlin, D-12489 Berlin, Germany
| | - Christine Giorgetti
- Laboratoire des Solides Irradiés, École Polytechnique, CNRS, CEA-DSM-IRAMIS, Université Paris-Saclay, F-91128 Palaiseau, France
- European Theoretical Spectroscopy Facility (ETSF)
| | - Matteo Gatti
- Laboratoire des Solides Irradiés, École Polytechnique, CNRS, CEA-DSM-IRAMIS, Université Paris-Saclay, F-91128 Palaiseau, France
- European Theoretical Spectroscopy Facility (ETSF)
- Synchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin, BP 48, F-91192 Gif-sur-Yvette, France
| | - Francesco Sottile
- Laboratoire des Solides Irradiés, École Polytechnique, CNRS, CEA-DSM-IRAMIS, Université Paris-Saclay, F-91128 Palaiseau, France
- European Theoretical Spectroscopy Facility (ETSF)
| | - J. J. Rehr
- European Theoretical Spectroscopy Facility (ETSF)
- Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA
| | - Lucia Reining
- Laboratoire des Solides Irradiés, École Polytechnique, CNRS, CEA-DSM-IRAMIS, Université Paris-Saclay, F-91128 Palaiseau, France
- European Theoretical Spectroscopy Facility (ETSF)
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Seidu I, Krykunov M, Ziegler T. Applications of Time-Dependent and Time-Independent Density Functional Theory to Electronic Transitions in Tetrahedral d0 Metal Oxides. J Chem Theory Comput 2015; 11:4041-53. [DOI: 10.1021/acs.jctc.5b00298] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Issaka Seidu
- Department of Chemistry, University of Calgary, University
Drive 2500, Calgary, AB T2N-1N4, Canada
| | - Mykhaylo Krykunov
- Department of Chemistry, University of Calgary, University
Drive 2500, Calgary, AB T2N-1N4, Canada
| | - Tom Ziegler
- Department of Chemistry, University of Calgary, University
Drive 2500, Calgary, AB T2N-1N4, Canada
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Jacquemin D, Duchemin I, Blase X. Benchmarking the Bethe-Salpeter Formalism on a Standard Organic Molecular Set. J Chem Theory Comput 2015; 11:3290-304. [PMID: 26207104 PMCID: PMC4504186 DOI: 10.1021/acs.jctc.5b00304] [Citation(s) in RCA: 118] [Impact Index Per Article: 13.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2015] [Indexed: 12/17/2022]
Abstract
We perform benchmark calculations of the Bethe-Salpeter vertical excitation energies for the set of 28 molecules constituting the well-known Thiel’s set, complemented by a series of small molecules representative of the dye chemistry field. We show that Bethe-Salpeter calculations based on a molecular orbital energy spectrum obtained with non-self-consistent G0W0 calculations starting from semilocal DFT functionals dramatically underestimate the transition energies. Starting from the popular PBE0 hybrid functional significantly improves the results even though this leads to an average -0.59 eV redshift compared to reference calculations for Thiel’s set. It is shown, however, that a simple self-consistent scheme at the GW level, with an update of the quasiparticle energies, not only leads to a much better agreement with reference values, but also significantly reduces the impact of the starting DFT functional. On average, the Bethe-Salpeter scheme based on self-consistent GW calculations comes close to the best time-dependent DFT calculations with the PBE0 functional with a 0.98 correlation coefficient and a 0.18 (0.25) eV mean absolute deviation compared to TD-PBE0 (theoretical best estimates) with a tendency to be red-shifted. We also observe that TD-DFT and the standard adiabatic Bethe-Salpeter implementation may differ significantly for states implying a large multiple excitation character.
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Affiliation(s)
- Denis Jacquemin
- Laboratoire
CEISAM - UMR CNR 6230, Université
de Nantes, 2 Rue de la
Houssinière, BP 92208, 44322 Nantes Cedex 3, France
- Institut
Universitaire de France, 103 bd St. Michel, 75005 Paris Cedex 5, France
| | - Ivan Duchemin
- INAC,
SP2M/L_Sim, CEA/UJF Cedex 09, Université
Grenoble Alpes, 38054 Grenoble, France
| | - Xavier Blase
- CNRS,
Inst NEEL, F-38042 Grenoble, France
- Institut
NEEL, Université Grenoble Alpes, F-38042 Grenoble, France
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41
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Casida ME, Huix-Rotllant M. Many-Body Perturbation Theory (MBPT) and Time-Dependent Density-Functional Theory (TD-DFT): MBPT Insights About What Is Missing In, and Corrections To, the TD-DFT Adiabatic Approximation. DENSITY-FUNCTIONAL METHODS FOR EXCITED STATES 2015; 368:1-60. [DOI: 10.1007/128_2015_632] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
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Habenicht BF, Tani NP, Provorse MR, Isborn CM. Two-electron Rabi oscillations in real-time time-dependent density-functional theory. J Chem Phys 2014; 141:184112. [DOI: 10.1063/1.4900514] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Bradley F. Habenicht
- Chemistry and Chemical Biology, University of California Merced, Merced, California 95343, USA
| | - Noriyuki P. Tani
- Chemistry and Chemical Biology, University of California Merced, Merced, California 95343, USA
| | - Makenzie R. Provorse
- Chemistry and Chemical Biology, University of California Merced, Merced, California 95343, USA
| | - Christine M. Isborn
- Chemistry and Chemical Biology, University of California Merced, Merced, California 95343, USA
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Zhekova H, Krykunov M, Autschbach J, Ziegler T. Applications of Time Dependent and Time Independent Density Functional Theory to the First π to π* Transition in Cyanine Dyes. J Chem Theory Comput 2014; 10:3299-307. [DOI: 10.1021/ct500292c] [Citation(s) in RCA: 76] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Hristina Zhekova
- Department of Chemistry, University of Calgary, University Drive 2500, Calgary AB T2N-1N4, Canada
| | - Mykhaylo Krykunov
- Department of Chemistry, University of Calgary, University Drive 2500, Calgary AB T2N-1N4, Canada
| | - Jochen Autschbach
- Department of Chemistry, State University of New York, 312 Natural
Sciences Complex, Buffalo, New York 14260-3000, United States
| | - Tom Ziegler
- Department of Chemistry, University of Calgary, University Drive 2500, Calgary AB T2N-1N4, Canada
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Kaduk B, Tsuchimochi T, Van Voorhis T. Analytic energy gradients for constrained DFT-configuration interaction. J Chem Phys 2014; 140:18A503. [DOI: 10.1063/1.4862497] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Gieseking RL, Mukhopadhyay S, Risko C, Marder SR, Brédas JL. 25th anniversary article: Design of polymethine dyes for all-optical switching applications: guidance from theoretical and computational studies. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2014; 26:68-83. [PMID: 24302357 DOI: 10.1002/adma.201302676] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2013] [Revised: 07/29/2013] [Indexed: 06/02/2023]
Abstract
All-optical switching--controlling light with light--has the potential to meet the ever-increasing demand for data transmission bandwidth. The development of organic π-conjugated molecular materials with the requisite properties for all-optical switching applications has long proven to be a significant challenge. However, recent advances demonstrate that polymethine dyes have the potential to meet the necessary requirements. In this review, we explore the theoretical underpinnings that guide the design of π-conjugated materials for all-optical switching applications. We underline, from a computational chemistry standpoint, the relationships among chemical structure, electronic structure, and optical properties that make polymethines such promising materials.
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Affiliation(s)
- Rebecca L Gieseking
- School of Chemistry and Biochemistry Center for Organic Photonics and Electronics and Center for Organic Materials for All-Optical Switching, Georgia Institute of Technology, Atlanta, Georgia, 30332-0400, USA
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Constricted Variational Density Functional Theory Approach to the Description of Excited States. DENSITY-FUNCTIONAL METHODS FOR EXCITED STATES 2014; 368:61-95. [DOI: 10.1007/128_2014_611] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
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47
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Zhang Y, Hua W, Bennett K, Mukamel S. Nonlinear Spectroscopy of Core and Valence Excitations Using Short X-Ray Pulses: Simulation Challenges. DENSITY-FUNCTIONAL METHODS FOR EXCITED STATES 2014; 368:273-345. [DOI: 10.1007/128_2014_618] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
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48
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Seidu I, Krykunov M, Ziegler T. The formulation of a constricted variational density functional theory for double excitations. Mol Phys 2013. [DOI: 10.1080/00268976.2013.852261] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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49
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Zhang D, Steinmann SN, Yang W. Dynamical second-order Bethe-Salpeter equation kernel: A method for electronic excitation beyond the adiabatic approximation. J Chem Phys 2013; 139:154109. [DOI: 10.1063/1.4824907] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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50
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Farzad F, Farsi H, Raissi H. Quantum chemical studies on molecular conformations, energetic and intramolecular hydrogen bonding in ground and electronic excited state of (thioxosilyl) ethyleneselenol. J Sulphur Chem 2013. [DOI: 10.1080/17415993.2013.819873] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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