1
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Loos PF, Jacquemin D. A mountaineering strategy to excited states: Accurate vertical transition energies and benchmarks for substituted benzenes. J Comput Chem 2024; 45:1791-1805. [PMID: 38661240 DOI: 10.1002/jcc.27358] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2024] [Revised: 02/09/2024] [Accepted: 02/15/2024] [Indexed: 04/26/2024]
Abstract
In an effort to expand the existing QUEST database of accurate vertical transition energies [Véril et al. WIREs Comput. Mol. Sci. 2021, 11, e1517], we have modeled more than 100 electronic excited states of different natures (local, charge-transfer, Rydberg, singlet, and triplet) in a dozen of mono- and di-substituted benzenes, including aniline, benzonitrile, chlorobenzene, fluorobenzene, nitrobenzene, among others. To establish theoretical best estimates for these vertical excitation energies, we have employed advanced coupled-cluster methods including iterative triples (CC3 and CCSDT) and, when technically possible, iterative quadruples (CC4). These high-level computational approaches provide a robust foundation for benchmarking a series of popular wave function methods. The evaluated methods all include contributions from double excitations (ADC(2), CC2, CCSD, CIS(D), EOM-MP2, STEOM-CCSD), along with schemes that also incorporate perturbative or iterative triples (ADC(3), CCSDR(3), CCSD(T)(a) ⋆ , and CCSDT-3). This systematic exploration not only broadens the scope of the QUEST database but also facilitates a rigorous assessment of different theoretical approaches in the framework of a homologous chemical series, offering valuable insights into the accuracy and reliability of these methods in such cases. We found that both ADC(2.5) and CCSDT-3 can provide very consistent estimates, whereas among less expensive methods SCS-CC2 is likely the most effective approach. Importantly, we show that some lower order methods may offer reasonable trends in the homologous series while providing quite large average errors, and vice versa. Consequently, benchmarking the accuracy of a model based solely on absolute transition energies may not be meaningful for applications involving a series of similar compounds.
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Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, France
| | - Denis Jacquemin
- Nantes Université, CNRS, CEISAM UMR 6230, Nantes, France
- Institut Universitaire de France (IUF), Paris, France
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2
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Holzer C, Franzke YJ. Beyond Electrons: Correlation and Self-Energy in Multicomponent Density Functional Theory. Chemphyschem 2024; 25:e202400120. [PMID: 38456204 DOI: 10.1002/cphc.202400120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2024] [Revised: 03/07/2024] [Accepted: 03/08/2024] [Indexed: 03/09/2024]
Abstract
Post-Kohn-Sham methods are used to evaluate the ground-state correlation energy and the orbital self-energy of systems consisting of multiple flavors of different fermions. Starting from multicomponent density functional theory, suitable ways to arrive at the corresponding multicomponent random-phase approximation and the multicomponent Green's functionG W ${GW}$ approximation, including relativistic effects, are outlined. Given the importance of both of this methods in the development of modern Kohn-Sham density functional approximations, this work will provide a foundation to design advanced multicomponent density functional approximations. Additionally, theG W ${GW}$ quasiparticle energies are needed to study light-matter interactions with the Bethe-Salpeter equation.
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Affiliation(s)
- Christof Holzer
- Karlsruhe Institute of Technology (KIT), Institute of Theoretical Solid State Physics, Kaiserstraße 12, 76131, Karlsruhe, Germany
| | - Yannick J Franzke
- Friedrich Schiller University Jena, Otto Schott Institute of Materials Research, Löbdergraben 32, 07743, Jena, Germany
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3
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Becker S. Understanding Cooperativity in Homo- and Heterometallic Complexes: From Basic Concepts to Design. Chempluschem 2024; 89:e202300619. [PMID: 38317458 DOI: 10.1002/cplu.202300619] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2023] [Revised: 12/12/2023] [Accepted: 02/05/2024] [Indexed: 02/07/2024]
Abstract
Cooperative effects have attracted considerable attention in recent years. These effects are ubiquitous in chemistry and biology and can govern interactions of proteins with other biomolecules, mechanisms of supramolecular recognition and polymerization, catalysis, assembly of compounds on surfaces, and physical properties such as magnetic, electronic or optical properties, e. g. Consequently, the understanding of cooperative effects can lead to a structure-property relation that can pave the way to future applications in various research areas; however, with regard to cooperative effects in homo- and heterometallic complexes, we still are at the beginning of understanding. Nevertheless, concepts to describe cooperativity of metal centers as well as methodologies to investigate and model these effects have emerged over the last years. This concept article gives an overview of these existing concepts, approaches, and strategies to understand cooperative effects in homo- and heterometallic complexes. Special emphasis is put on concepts to define cooperative effects, their quantification, as well as methods to investigate cooperative effects.
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Affiliation(s)
- Sabine Becker
- Fachbereich Chemie, RPTU Kaiserslautern-Landau, Erwin-Schroedinger-Str. 54, 67663, Kaiserslautern, Germany
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4
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Amblard D, Blase X, Duchemin I. Static versus dynamically polarizable environments within the many-body GW formalism. J Chem Phys 2024; 160:154104. [PMID: 38624115 DOI: 10.1063/5.0203637] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2024] [Accepted: 03/28/2024] [Indexed: 04/17/2024] Open
Abstract
Continuum- or discrete-polarizable models for the study of optoelectronic processes in embedded subsystems rely mostly on the restriction of the surrounding electronic dielectric response to its low frequency limit. Such a description hinges on the assumption that the electrons in the surrounding medium react instantaneously to any excitation in the central subsystem, thus treating the environment in the adiabatic limit. Exploiting a recently developed embedded GW formalism with an environment described at the fully ab initio level, we assess the merits of the adiabatic limit with respect to an environment where the full dynamics of the dielectric response are considered. Furthermore, we show how to properly take the static limit of the environment's susceptibility by introducing the so-called Coulomb-hole and screened-exchange contributions to the reaction field. As a first application, we consider a C60 molecule at the surface of a C60 crystal, namely, a case where the dynamics of the embedded and embedding subsystems are similar. The common adiabatic assumption, when properly treated, generates errors below 10% on the polarization energy associated with frontier energy levels and associated energy gaps. Finally, we consider a water molecule inside a metallic nanotube, the worst case for the environment's adiabatic limit. The error on the gap polarization energy remains below 10%, even though the error on the frontier orbital polarization energies can reach a few tenths of an electronvolt.
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Affiliation(s)
- David Amblard
- University Grenoble Alpes, CNRS, Inst NEEL, F-38042 Grenoble, France
| | - Xavier Blase
- University Grenoble Alpes, CNRS, Inst NEEL, F-38042 Grenoble, France
| | - Ivan Duchemin
- University Grenoble Alpes, CEA, IRIG-MEM-L_Sim, 38054 Grenoble, France
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5
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Madden E, Zwijnenburg MA. The effect of particle size on the optical and electronic properties of hydrogenated silicon nanoparticles. Phys Chem Chem Phys 2024; 26:11695-11707. [PMID: 38563473 DOI: 10.1039/d4cp00119b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/04/2024]
Abstract
We use a combination of many-body perturbation theory and time-dependent density functional theory to study the optical and electronic properties of hydrogen terminated silicon nanoparticles. We predict that the lowest excited states of these silicon nanoparticles are excitonic in character and that the corresponding excitons are completely delocalised over the volume of the particle. The size of the excitons is predicted to increase proportionally with the particle size. Conversely, we predict that the fundamental gap, the optical gap, and the exciton binding energy increase with decreasing particle size. The exciton binding energy is predicted to counter-act the variation in the fundamental gap and hence to reduce the variation of the optical gap with particle size. The variation in the exciton binding energy itself is probably caused by a reduction in the dielectric screening with decreasing particle size. The intensity of the excited state corresponding to the optical gap and other low energy excitations are predicted to increase with decreasing particle size. We explain this increase in terms of the 'band structure' becoming smeared out in reciprocal space with decreasing particle size, increasing the 'overlap' between the occupied and unoccupied quasiparticle states and thus, the oscillator strength. Fourier transforms of the lowest excitons show that they inherit the periodicity of the frontier quasiparticle states. This, combined with the delocalisation of the exciton and the large exciton binding energy, means that the excitons in silicon nanoparticles combine aspects of Wannier-Mott, delocalisation and effect of periodicity of the underlying structure, and Frenkel, large exciton binding energy, excitons.
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Affiliation(s)
- Eimear Madden
- Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, UK.
| | - Martijn A Zwijnenburg
- Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, UK.
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6
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Knysh I, Raimbault D, Duchemin I, Blase X, Jacquemin D. Assessing the accuracy of TD-DFT excited-state geometries through optimal tuning with GW energy levels. J Chem Phys 2024; 160:144115. [PMID: 38602292 DOI: 10.1063/5.0203818] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2024] [Accepted: 03/25/2024] [Indexed: 04/12/2024] Open
Abstract
We study the accuracy of excited state (ES) geometries using optimally tuned LC-PBE functionals with tuning based on GW quasiparticle energies. We compare the results obtained with the PBE, PBE0, non-tuned, and tuned LC-PBE functionals with available high-level CC reference values as well as experimental data. First, we compare ES geometrical parameters obtained for three different types of systems: molecules composed of a few atoms, 4-(dimethylamino)benzonitrile (DMABN), and conjugated dyes. To this end, we used wave-function results as benchmarks. Next, we evaluate the accuracy of the theoretically simulated spectra as compared to the experimental ones for five large dyes. Our results show that, besides small compact molecules for which tuning LC-PBE does not allow obtaining geometries more accurate than those computed with standard functionals, tuned range-separated functionals are clearly to be favored, not only for ES geometries but also for 0-0 energies, band shapes, and intensities for absorption and emission spectra. In particular, the results indicate that GW-tuned LC-PBE functionals provide improved matching with experimental spectra as compared to conventionally tuned functionals. It is an open question whether TD-DFT with GW-tuned functionals can qualitatively mimic the actual many-body Bethe-Salpeter (BSE/GW) formalism for which analytic ionic gradients remain to be developed.
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Affiliation(s)
- Iryna Knysh
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
| | - Denez Raimbault
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
| | - Ivan Duchemin
- Université Grenoble Alpes, CEA, IRIG-MEM-L_Sim, 38054 Grenoble, France
| | - Xavier Blase
- Université Grenoble Alpes, CNRS, Institut, Néel F-38042, Grenoble
| | - Denis Jacquemin
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
- Institut Universitaire de France, 75005 Paris, France
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7
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Rauwolf N, Klopper W, Holzer C. Non-linear light-matter interactions from the Bethe-Salpeter equation. J Chem Phys 2024; 160:061101. [PMID: 38341783 DOI: 10.1063/5.0191499] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2023] [Accepted: 01/15/2024] [Indexed: 02/13/2024] Open
Abstract
A route to assess non-linear light-matter interactions from the increasingly popular GW-Bethe-Salpeter equation (GW-BSE) method is outlined. In the present work, the necessary analytic expressions within the static-screened exchange approximation of the BSE are derived. This enables a straightforward implementation of the computation of the first hyperpolarizability as well as two-photon absorption processes for molecular systems. Benchmark calculations on small molecular systems reveal that the GW-BSE method is intriguingly accurate for predicting both first hyperpolarizabilities and two-photon absorption strengths. Using state-of-the-art Kohn-Sham references as a starting point, the accuracy of the GW-BSE method rivals that of the coupled-cluster singles-and-doubles method, outperforming both second-order coupled-cluster and time-dependent density-functional theory.
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Affiliation(s)
- Nina Rauwolf
- Institute of Physical Chemistry, Karlsruhe Institute of Technology, Kaiserstraße 12, 76131 Karlsruhe, Germany
| | - Wim Klopper
- Institute of Physical Chemistry, Karlsruhe Institute of Technology, Kaiserstraße 12, 76131 Karlsruhe, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, Kaiserstraße 12, 76131 Karlsruhe, Germany
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8
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Herbert JM. Visualizing and characterizing excited states from time-dependent density functional theory. Phys Chem Chem Phys 2024; 26:3755-3794. [PMID: 38226636 DOI: 10.1039/d3cp04226j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2024]
Abstract
Time-dependent density functional theory (TD-DFT) is the most widely-used electronic structure method for excited states, due to a favorable combination of low cost and semi-quantitative accuracy in many contexts, even if there are well recognized limitations. This Perspective describes various ways in which excited states from TD-DFT calculations can be visualized and analyzed, both qualitatively and quantitatively. This includes not just orbitals and densities but also well-defined statistical measures of electron-hole separation and of Frenkel-type exciton delocalization. Emphasis is placed on mathematical connections between methods that have often been discussed separately. Particular attention is paid to charge-transfer diagnostics, which provide indicators of when TD-DFT may not be trustworthy due to its categorical failure to describe long-range electron transfer. Measures of exciton size and charge separation that are directly connected to the underlying transition density are recommended over more ad hoc metrics for quantifying charge-transfer character.
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Affiliation(s)
- John M Herbert
- Department of Chemistry & Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA.
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9
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Knysh I, Villalobos-Castro JDJ, Duchemin I, Blase X, Jacquemin D. Excess and excited-state dipole moments of real-life dyes: a comparison between wave-function, BSE/ GW, and TD-DFT values. Phys Chem Chem Phys 2023; 25:29993-30004. [PMID: 37905396 DOI: 10.1039/d3cp04467j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2023]
Abstract
In this work, we assess the accuracy of the Bethe-Salpeter equation (BSE) many-body Green's function formalism, adopting the eigenvalue-self-consistent evGW exchange-correlation kernel, for the calculation of the excited-state (μES) and excess dipole moments (Δμ), the latter ones being the changes of dipole amplitude between the ground and excited states (ES), in organic dyes. We compare the results obtained with wave-function methods [ADC(2), CC2, and CCSD], time-dependent density functional theory (TD-DFT), and BSE/evGW levels of theory. First, we compute the evolution of the dipole moments of the two lowest singlet excited states of 4-(dimethylamino)benzonitrile (DMABN) upon twisting of the amino group. Next, we use a set of 25 dyes having ES characters ranging from locally excited to charge transfer to determine both μES and Δμ. For DMABN our results show that BSE/evGW provides Δμ values closer to the CCSD reference and more consistent trends than TD-DFT. Moreover, a statistical analysis of both Δμ and μES for the set of 25 dyes shows that the BSE/evGW accuracy is comparable or sometimes slightly better than that of TD-M06-2X and TD-CAM-B3LYP, BSE/evGW outperforming TD-DFT in challenging cases (zwitterionic and cyanine transitions). Finally, the starting point dependency of BSE/evGW seems to be larger for Δμ, ES dipoles, and oscillator strengths than for transition energies.
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Affiliation(s)
- Iryna Knysh
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France.
| | | | - Ivan Duchemin
- Université Grenoble Alpes, CEA, IRIG-MEM-L_Sim, 38054 Grenoble, France
| | - Xavier Blase
- Université Grenoble Alpes, CNRS, Institut Néel, F-38042 Grenoble, France.
| | - Denis Jacquemin
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France.
- Institut Universitaire de France, F-75005 Paris, France
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10
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Franzke Y, Holzer C, Andersen JH, Begušić T, Bruder F, Coriani S, Della Sala F, Fabiano E, Fedotov DA, Fürst S, Gillhuber S, Grotjahn R, Kaupp M, Kehry M, Krstić M, Mack F, Majumdar S, Nguyen BD, Parker SM, Pauly F, Pausch A, Perlt E, Phun GS, Rajabi A, Rappoport D, Samal B, Schrader T, Sharma M, Tapavicza E, Treß RS, Voora V, Wodyński A, Yu JM, Zerulla B, Furche F, Hättig C, Sierka M, Tew DP, Weigend F. TURBOMOLE: Today and Tomorrow. J Chem Theory Comput 2023; 19:6859-6890. [PMID: 37382508 PMCID: PMC10601488 DOI: 10.1021/acs.jctc.3c00347] [Citation(s) in RCA: 37] [Impact Index Per Article: 37.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Indexed: 06/30/2023]
Abstract
TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.
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Affiliation(s)
- Yannick
J. Franzke
- Fachbereich
Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
| | - Christof Holzer
- Institute
of Theoretical Solid State Physics, Karlsruhe
Institute of Technology (KIT), Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany
| | - Josefine H. Andersen
- DTU
Chemistry, Department of Chemistry, Technical
University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
| | - Tomislav Begušić
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Florian Bruder
- Fachbereich
Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
| | - Sonia Coriani
- DTU
Chemistry, Department of Chemistry, Technical
University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
| | - Fabio Della Sala
- Institute
for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for
Biomolecular Nanotechnologies @UNILE, Istituto
Italiano di Tecnologia, Via Barsanti, 73010 Arnesano, Italy
| | - Eduardo Fabiano
- Institute
for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for
Biomolecular Nanotechnologies @UNILE, Istituto
Italiano di Tecnologia, Via Barsanti, 73010 Arnesano, Italy
| | - Daniil A. Fedotov
- DTU
Chemistry, Department of Chemistry, Technical
University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
- Institute
of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Susanne Fürst
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17 Juni 135, 10623, Berlin, Germany
| | - Sebastian Gillhuber
- Institute
of Inorganic Chemistry, Karlsruhe Institute
of Technology (KIT), Engesserstr. 15, 76131 Karlsruhe, Germany
| | - Robin Grotjahn
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Martin Kaupp
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17 Juni 135, 10623, Berlin, Germany
| | - Max Kehry
- Institute
of Physical Chemistry, Karlsruhe Institute
of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Marjan Krstić
- Institute
of Theoretical Solid State Physics, Karlsruhe
Institute of Technology (KIT), Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany
| | - Fabian Mack
- Institute
of Physical Chemistry, Karlsruhe Institute
of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Sourav Majumdar
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Brian D. Nguyen
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Shane M. Parker
- Department
of Chemistry, Case Western Reserve University, 10900 Euclid Ave, Cleveland, Ohio 44106 United States
| | - Fabian Pauly
- Institute
of Physics, University of Augsburg, Universitätsstr. 1, 86159 Augsburg, Germany
| | - Ansgar Pausch
- Institute
of Physical Chemistry, Karlsruhe Institute
of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Eva Perlt
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - Gabriel S. Phun
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Ahmadreza Rajabi
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Dmitrij Rappoport
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Bibek Samal
- Department
of Chemical Sciences, Tata Institute of
Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Tim Schrader
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - Manas Sharma
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - Enrico Tapavicza
- Department
of Chemistry and Biochemistry, California
State University, Long Beach, 1250 Bellflower Boulevard, Long
Beach, California 90840-9507, United States
| | - Robert S. Treß
- Lehrstuhl
für Theoretische Chemie, Ruhr-Universität
Bochum, 44801 Bochum, Germany
| | - Vamsee Voora
- Department
of Chemical Sciences, Tata Institute of
Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Artur Wodyński
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17 Juni 135, 10623, Berlin, Germany
| | - Jason M. Yu
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Benedikt Zerulla
- Institute
of Nanotechnology, Karlsruhe Institute of
Technology (KIT), Hermann-von-Helmholtz-Platz
1, 76344 Eggenstein-Leopoldshafen Germany
| | - Filipp Furche
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Christof Hättig
- Lehrstuhl
für Theoretische Chemie, Ruhr-Universität
Bochum, 44801 Bochum, Germany
| | - Marek Sierka
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - David P. Tew
- Physical
and Theoretical Chemistry Laboratory, University
of Oxford, South Parks
Road, Oxford OX1 3QZ, United Kingdom
| | - Florian Weigend
- Fachbereich
Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
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11
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Förster A, van Lenthe E, Spadetto E, Visscher L. Two-Component GW Calculations: Cubic Scaling Implementation and Comparison of Vertex-Corrected and Partially Self-Consistent GW Variants. J Chem Theory Comput 2023; 19:5958-5976. [PMID: 37594901 PMCID: PMC10501001 DOI: 10.1021/acs.jctc.3c00512] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2023] [Indexed: 08/20/2023]
Abstract
We report an all-electron, atomic orbital (AO)-based, two-component (2C) implementation of the GW approximation (GWA) for closed-shell molecules. Our algorithm is based on the space-time formulation of the GWA and uses analytical continuation (AC) of the self-energy, and pair-atomic density fitting (PADF) to switch between AO and auxiliary basis. By calculating the dynamical contribution to the GW self-energy at a quasi-one-component level, our 2C-GW algorithm is only about a factor of 2-3 slower than in the scalar relativistic case. Additionally, we present a 2C implementation of the simplest vertex correction to the self-energy, the statically screened G3W2 correction. Comparison of first ionization potentials (IPs) of a set of 67 molecules with heavy elements (a subset of the SOC81 set) calculated with our implementation against results from the WEST code reveals mean absolute deviations (MAD) of around 70 meV for G0W0@PBE and G0W0@PBE0. We check the accuracy of our AC treatment by comparison to full-frequency GW calculations, which shows that in the absence of multisolution cases, the errors due to AC are only minor. This implies that the main sources of the observed deviations between both implementations are the different single-particle bases and the pseudopotential approximation in the WEST code. Finally, we assess the performance of some (partially self-consistent) variants of the GWA for the calculation of first IPs by comparison to vertical experimental reference values. G0W0@PBE0 (25% exact exchange) and G0W0@BHLYP (50% exact exchange) perform best with mean absolute deviations (MAD) of about 200 meV. Explicit treatment of spin-orbit effects at the 2C level is crucial for systematic agreement with experiment. On the other hand, eigenvalue-only self-consistent GW (evGW) and quasi-particle self-consistent GW (qsGW) significantly overestimate the IPs. Perturbative G3W2 corrections increase the IPs and therefore improve the agreement with experiment in cases where G0W0 alone underestimates the IPs. With a MAD of only 140 meV, 2C-G0W0@PBE0 + G3W2 is in best agreement with the experimental reference values.
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Affiliation(s)
- Arno Förster
- Theoretical
Chemistry, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Erik van Lenthe
- Software
for Chemistry and Materials NV, 1081 HV Amsterdam, The Netherlands
| | - Edoardo Spadetto
- Software
for Chemistry and Materials NV, 1081 HV Amsterdam, The Netherlands
| | - Lucas Visscher
- Theoretical
Chemistry, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
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12
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Marie A, Loos PF. A Similarity Renormalization Group Approach to Green's Function Methods. J Chem Theory Comput 2023. [PMID: 37311565 DOI: 10.1021/acs.jctc.3c00281] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
The family of Green's function methods based on the GW approximation has gained popularity in the electronic structure theory thanks to its accuracy in weakly correlated systems combined with its cost-effectiveness. Despite this, self-consistent versions still pose challenges in terms of convergence. A recent study [Monino and Loos J. Chem. Phys. 2022, 156, 231101.] has linked these convergence issues to the intruder-state problem. In this work, a perturbative analysis of the similarity renormalization group (SRG) approach is performed on Green's function methods. The SRG formalism enables us to derive, from first-principles, the expression of a naturally static and Hermitian form of the self-energy that can be employed in quasiparticle self-consistent GW (qsGW) calculations. The resulting SRG-based regularized self-energy significantly accelerates the convergence of qsGW calculations, slightly improves the overall accuracy, and is straightforward to implement in existing code.
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Affiliation(s)
- Antoine Marie
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31400 Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31400 Toulouse, France
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13
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Holzer C. Practical Post-Kohn-Sham Methods for Time-Reversal Symmetry Breaking References. J Chem Theory Comput 2023. [PMID: 37183702 DOI: 10.1021/acs.jctc.3c00156] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
The applicability of reduced scaling algorithms based on auxiliary subspace methods for the correlation energy from the random phase approximation (RPA) as well as the correlation part of the self-energy obtained from the GW method is outlined for time-reversal symmetry breaking Kohn-Sham (KS) references. The updated algorithms allow for an efficient evaluation of RPA energies and GW quasiparticle energies for molecular systems with KS references that break time-reversal symmetry. The latter occur, for example, in magnetic fields. Furthermore, KS references for relativistic open-shell molecules also break time-reversal symmetry due to the single determinant ansatz used. Errors of the updated reduced-scaling algorithms are shown to be negligible compared to reference implementations, while the overall computational scaling is reduced by 2 orders of magnitude. Ionization energies obtained from the GW approximation are shown to be robust even for the electronically complicated group of trivalent lanthanoid ions. Starting from GW quasiparticle energies, it is subsequently shown that light-matter interactions of these systems can be calculated using the Bethe-Salpeter equation (BSE). Using the combined GW-BSE method, the absorption and emission spectra of a molecular europium(III) complex can be obtained including spin-orbit coupling.
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Affiliation(s)
- Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany
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14
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Bruschi C, Gui X, Fuhr O, Klopper W, Bizzarri C. Reaching strong absorption up to 700 nm with new benzo[ g]quinoxaline-based heteroleptic copper(I) complexes for light-harvesting applications. Dalton Trans 2023. [PMID: 37157971 DOI: 10.1039/d3dt00902e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
Heteroleptic copper(I) complexes, with a diimine as a chromophoric unit and a bulky diphosphine as an ancillary ligand, have the advantage of a reduced pseudo Jahn-Teller effect in their excited state over the corresponding homoleptic bis(diimine) complexes. Nevertheless, their lowest absorption lies generally between 350 to 500 nm. Aiming at a strong absorption in the visible by stable heteroleptic Cu(I) complexes, we designed a novel diimine based on 4-(benzo[g]quinoxal-2'-yl)-1,2,3-triazole derivatives. The large π-conjugation of the benzoquinoxaline moiety shifted bathochromically the absorption with regard to other diimine-based Cu(I) complexes. Adding another Cu(I) core broadened the absorption and extended it to considerably longer wavelengths. Moreover, by fine-tuning the structure of the dichelating ligand, we achieved a panchromatic absorption up to 700 nm with a high molar extinction coefficient of 8000 M-1 cm-1 at maximum (λ = 570 nm), making this compound attractive for light-harvesting antennae.
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Affiliation(s)
- Cecilia Bruschi
- Institute of Organic Chemistry (IOC), Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 6, 76137 Karlsruhe, Germany.
| | - Xin Gui
- Institute of Physical Chemistry-Theoretical Chemistry, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Olaf Fuhr
- Institute of Nanotechnology (INT), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
- Karlsruhe Nano Micro Facility (KNMFi), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
| | - Wim Klopper
- Institute of Physical Chemistry-Theoretical Chemistry, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
- Institute of Nanotechnology (INT), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
| | - Claudia Bizzarri
- Institute of Organic Chemistry (IOC), Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 6, 76137 Karlsruhe, Germany.
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15
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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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16
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Knysh I, Villalobos-Castro JDJ, Duchemin I, Blase X, Jacquemin D. Exploring Bethe-Salpeter Excited-State Dipoles: The Challenging Case of Increasingly Long Push-Pull Oligomers. J Phys Chem Lett 2023; 14:3727-3734. [PMID: 37042642 DOI: 10.1021/acs.jpclett.3c00699] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
The change of molecular dipole moment induced by photon absorption is key to interpret the measured optical spectra. Except for compact molecules, time-dependent density functional theory (TD-DFT) remains the only theory allowing to quickly predict excited-state dipoles (μES), albeit with a strong dependency on the selected exchange-correlation functional. This Letter presents the first assessment of the performances of the many-body Green's function Bethe-Salpeter equation (BSE) formalism for the evaluation of the μES. We explore increasingly long push-pull oligomers as they present an excited-state nature evolving with system size. This work shows that BSE's μES do present the same evolution with oligomeric length as their CC2 and CCSD counterparts, with a dependency on the starting exchange-correlation functional that is strongly decreased as compared to TD-DFT. This Letter demonstrates that BSE is a valuable alternative to TD-DFT for properties related to the excited-state density and not only for transition energies and oscillator strengths.
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Affiliation(s)
- Iryna Knysh
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
| | | | - Ivan Duchemin
- Université Grenoble Alpes, CEA, IRIG-MEM-L Sim, 38054 Grenoble, France
| | - Xavier Blase
- Université Grenoble Alpes, CNRS, Institut NEEL, F-38042 Grenoble, France
| | - Denis Jacquemin
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
- Institut Universitaire de France, 75005 Paris, France
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17
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Knysh I, Letellier K, Duchemin I, Blase X, Jacquemin D. Excited state potential energy surfaces of N-phenylpyrrole upon twisting: reference values and comparison between BSE/ GW and TD-DFT. Phys Chem Chem Phys 2023; 25:8376-8385. [PMID: 36883347 DOI: 10.1039/d3cp00474k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/06/2023]
Abstract
The puzzling case of the mixing between the charge transfer (CT) and local excited (LE) characters upon twisting of the geometry of N-phenylpyrrole (N-PP) is investigated considering the six low-lying singlet excited states (ES). The theoretical calculations of the potential energy surfaces (PES) have been performed for these states using a Coupled Cluster method accounting for the impact of the contributions from the triples, many-body Green's function GW and Bethe-Salpeter equation (BSE) formalisms, as well as Time-Dependent Density Functional Theory (TD-DFT) using various exchange-correlation functionals. Our findings confirm that the BSE formalism is more reliable than TD-DFT for close-lying ES with mixed CT/LE nature. More specifically, BSE/GW yields a more accurate evolution of the excited state PES than TD-DFT when compared to the reference coupled cluster values. BSE/GW PES curves also show negligible exchange-correlation functional starting point dependency in sharp contrast with their TD-DFT counterparts.
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Affiliation(s)
- Iryna Knysh
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000, Nantes, France.
| | | | - Ivan Duchemin
- Université Grenoble Alpes, CEA, IRIG-MEM-L_Sim, 38054, Grenoble, France
| | - Xavier Blase
- Université Grenoble Alpes, CNRS, Institut Néel, F-38042, Grenoble, France.
| | - Denis Jacquemin
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000, Nantes, France.
- Institut Universitaire de France, 75005, Paris, France
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18
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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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19
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Chaudhuri D, Patterson CH. TDDFT versus GW/BSE Methods for Prediction of Light Absorption and Emission in a TADF Emitter. J Phys Chem A 2022; 126:9627-9643. [PMID: 36515973 PMCID: PMC9806837 DOI: 10.1021/acs.jpca.2c06403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Design concepts for organic light emitting diode (OLED) emitters, which exhibit thermally activated delayed fluorescence (TADF) and thereby achieve quantum yields exceeding 25%, depend on singlet-triplet splitting energies of order kT to allow reverse intersystem crossing at ambient temperatures. Simulation methods for these systems must be able to treat relatively large organic molecules, as well as predict their excited state energies, transition energies, singlet-triplet splittings, and absorption and emission cross sections with reasonable accuracy, in order to prove useful in the design process. Here we compare predictions of TDDFT with M06-2X and ωB97X-D exchange-correlation functionals and a GoWo@HF/BSE method for these quantities in the well-studied DPTZ-DBTO2 TADF emitter molecule. Geometry optimization is performed for ground state (GS) and lowest donor-acceptor charge transfer (CT) state for each functional. Optical absorption and emission cross sections and energies are calculated at these geometries. Relaxation energies are on the order of 0.5 eV, and the importance of obtaining excited state equilibrium geometries in predicting delayed fluorescence is demonstrated. There are clear trends in predictions of GoWo@HF/BSE, and TDDFT/ωB97X-D and M06-2X methods in which the former method favors local exciton (LE) states while the latter favors DA CT states and ωB97X-D makes intermediate predictions. GoWo@HF/BSE suffers from triplet instability for LE states but not CT states relevant for TADF. Shifts in HOMO and LUMO levels on adding a conductor-like polarizable continuum model dielectric background are used to estimate changes in excitation energies on going from the gas phase to a solvated molecule.
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20
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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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21
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Li J, Golze D, Yang W. Combining Renormalized Singles GW Methods with the Bethe-Salpeter Equation for Accurate Neutral Excitation Energies. J Chem Theory Comput 2022; 18:6637-6645. [PMID: 36279250 PMCID: PMC9972216 DOI: 10.1021/acs.jctc.2c00686] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We apply the renormalized singles (RS) Green's function in the Bethe-Salpeter equation (BSE)/GW approach to predict accurate neutral excitation energies of molecular systems. The BSE calculations are performed on top of the GRSWRS method, which uses the RS Green's function also for the computation of the screened Coulomb interaction W. We show that the BSE/GRSWRS approach significantly outperforms BSE/G0W0 for predicting excitation energies of valence, Rydberg, and charge-transfer (CT) excitations by benchmarking the Truhlar-Gagliardi set, Stein CT set, and an atomic Rydberg test set. For the Truhlar-Gagliardi test set, BSE/GRSWRS provides comparable accuracy to time-dependent density functional theory (TDDFT) and is slightly better than BSE starting from eigenvalue self-consistent GW (evGW). For the Stein CT test set, BSE/GRSWRS significantly outperforms BSE/G0W0 and TDDFT with the accuracy comparable to BSE/evGW. We also show that BSE/GRSWRS predicts Rydberg excitation energies of atomic systems well. Besides the excellent accuracy, BSE/GRSWRS largely eliminates the dependence on the choice of the density functional approximation. This work demonstrates that the BSE/GRSWRS approach is accurate and efficient for predicting excitation energies for a broad range of systems, which expands the applicability of the BSE/GW approach.
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Affiliation(s)
- Jiachen Li
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Dorothea Golze
- Faculty of Chemistry and Food Chemistry, Technische Universität Dresden, 01062 Dresden, Germany
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
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22
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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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23
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McKeon CA, Hamed SM, Bruneval F, Neaton JB. An optimally tuned range-separated hybrid starting point for ab initio GW plus Bethe–Salpeter equation calculations of molecules. J Chem Phys 2022; 157:074103. [DOI: 10.1063/5.0097582] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The ab initio GW plus Bethe–Salpeter equation (GW-BSE, where G is the one particle Green's function and W is the screened Coulomb interaction) approach has emerged as a leading method for predicting excitations in both solids and molecules with a predictive power contingent upon several factors. Among these factors are the (1) generalized Kohn–Sham eigensystem used to construct the GW self-energy and to solve the BSE and (2) the efficacy and suitability of the Tamm–Dancoff approximation. Here, we present a detailed benchmark study of low-lying singlet excitations from a generalized Kohn–Sham (gKS) starting point based on an optimally tuned range-separated hybrid (OTRSH) functional. We show that the use of this gKS starting point with one-shot G0W0 and G0W0-BSE leads to the lowest mean absolute errors (MAEs) and mean signed errors (MSEs), with respect to high-accuracy reference values, demonstrated in the literature thus far for the ionization potentials of the GW100 benchmark set and for low-lying neutral excitations of Thiel’s set molecules in the gas phase, without the need for self-consistency. The MSEs and MAEs of one-shot G0W0-BSE@OTRSH excitation energies are comparable to or lower than those obtained with other functional starting points after self-consistency. Additionally, we compare these results with linear-response time-dependent density functional theory (TDDFT) calculations and find GW-BSE to be superior to TDDFT when calculations are based on the same exchange-correlation functional. This work demonstrates tuned range-separated hybrids used in combination with GW and GW-BSE can greatly suppress starting point dependence for molecules, leading to accuracy similar to that for higher-order wavefunction-based theories for molecules without the need for costlier iterations to self-consistency.
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Affiliation(s)
- Caroline A. McKeon
- Department of Physics, University of California, Berkeley, California 94720, USA
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Natural Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Samia M. Hamed
- Department of Physics, University of California, Berkeley, California 94720, USA
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Natural Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Fabien Bruneval
- Université Paris-Saclay, CEA, Service de Recherches de Métallurgie Physique, 91191 Gif-sur-Yvette, France
| | - Jeffrey B. Neaton
- Department of Physics, University of California, Berkeley, California 94720, USA
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Natural Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Kavli ENSI, University of California, Berkeley, California 94720, USA
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24
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Loos PF, Lipparini F, Matthews DA, Blondel A, Jacquemin D. A Mountaineering Strategy to Excited States: Revising Reference Values with EOM-CC4. J Chem Theory Comput 2022; 18:4418-4427. [PMID: 35737466 DOI: 10.1021/acs.jctc.2c00416] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
In the framework of the computational determination of highly accurate vertical excitation energies in small organic compounds, we explore the possibilities offered by the equation-of-motion formalism relying on the approximate fourth-order coupled-cluster (CC) method, CC4. We demonstrate, using an extended set of more than 200 reference values based on CC including up to quadruples excitations (CCSDTQ), that CC4 is an excellent approximation to CCSDTQ for excited states with a dominant contribution from single excitations with an average deviation as small as 0.003 eV. We next assess the accuracy of several additive basis set correction schemes, in which vertical excitation energies obtained with a compact basis set and a high-order CC method are corrected with lower-order CC calculations performed in a larger basis set. Such strategies are found to be overall very beneficial, though their accuracy depends significantly on the actual scheme. Finally, CC4 is employed to improve several theoretical best estimates of the QUEST database for molecules containing between four and six (nonhydrogen) atoms, for which previous estimates were computed at the CCSDT level.
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Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Filippo Lipparini
- Dipartimento di Chimica e Chimica Industriale, University of Pisa, Via Moruzzi 3, 56124 Pisa, Italy
| | - Devin A Matthews
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States
| | - Aymeric Blondel
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
| | - Denis Jacquemin
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
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25
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Monino E, Loos PF. Unphysical discontinuities, intruder states and regularization in GW methods. J Chem Phys 2022; 156:231101. [PMID: 35732525 DOI: 10.1063/5.0089317] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
By recasting the non-linear frequency-dependent GW quasiparticle equation into a linear eigenvalue problem, we explain the appearance of multiple solutions and unphysical discontinuities in various physical quantities computed within the GW approximation. Considering the GW self-energy as an effective Hamiltonian, it is shown that these issues are key signatures of strong correlation in the (N ± 1)-electron states and can be directly related to the intruder state problem. A simple and efficient regularization procedure inspired by the similarity renormalization group is proposed to avoid such issues and speed up the convergence of partially self-consistent GW calculations.
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Affiliation(s)
- Enzo Monino
- 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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26
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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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27
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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] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [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 or better than the GW Green's function approach and with much less computational cost. The QP energies from LOSC instead of commonly used G0 W0 and ev GW 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 for Truhlar-Gagliardi test set containing valence, charge transfer (CT) and Rydberg excitations, BSE/LOSC with the Tamm-Dancoff approximation provides a comparable accuracy to time-dependent density functional theory (TDDFT) and BSE/ev GW. 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, United States of America
| | - Ye Jin
- Department of Chemistry, United States of America
| | | | - Weitao Yang
- Department of Chemistry, Duke University, United States of America
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28
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Krätschmer F, Gui X, Gamer MT, Klopper W, Roesky PW. Systematic investigation of the influence of electronic substituents on dinuclear gold(I) amidinates: synthesis, characterisation and photoluminescence studies. Dalton Trans 2022; 51:5471-5479. [PMID: 35266476 DOI: 10.1039/d1dt03795a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Dinuclear gold(I) compounds are of great interest due to their aurophilic interactions that influence their photophysical properties. Herein, we showcase that gold-gold interactions can be influenced by tuning the electronic properties of the ligands. Therefore, various para substituted (R) N,N'-bis(2,6-dimethylphenyl)formamidinate ligands (pRXylForm; Xyl = 2,6-dimethylphenyl and Form = formamidinate) were treated with Au(tht)Cl (tht = tetrahydrothiophene) to give via salt metathesis the corresponding gold(I) compounds [pRXylForm2Au2] (R = -OMe, -Me, -Ph, -H, -SMe, and -CO2Me). All complexes showed intense luminescence properties at low temperatures. Alignment with the Hammett parameter σp revealed the trends in the 1H and 13C NMR spectra. These results showed the influence of the donor-acceptor abilities of different substituents on the ligand system which were confirmed with calculated orbital energies. Photophysical investigations showed their lifetimes in the millisecond range indicating phosphorescence processes and revealed a redshift with the decreasing donor ability of the substituents in the solid state.
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Affiliation(s)
- Frederic Krätschmer
- Institute of Inorganic Chemistry, Karlsruhe Institute of Technology, Engesserstr. 15, 76131 Karlsruhe, Germany.
| | - Xin Gui
- Institute of Physical Chemistry, Karlsruhe Institute of Technology, Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Michael T Gamer
- Institute of Inorganic Chemistry, Karlsruhe Institute of Technology, Engesserstr. 15, 76131 Karlsruhe, Germany.
| | - Wim Klopper
- Institute of Physical Chemistry, Karlsruhe Institute of Technology, Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Peter W Roesky
- Institute of Inorganic Chemistry, Karlsruhe Institute of Technology, Engesserstr. 15, 76131 Karlsruhe, Germany.
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29
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Mester D, Kállay M. Charge-Transfer Excitations within Density Functional Theory: How Accurate Are the Most Recommended Approaches? J Chem Theory Comput 2022; 18:1646-1662. [PMID: 35200021 PMCID: PMC8908740 DOI: 10.1021/acs.jctc.1c01307] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
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The performance of
the most recent density functionals is assessed
for charge-transfer (CT) excitations using comprehensive intra- and
intermolecular CT benchmark sets with high-quality reference values.
For this comparison, the state-of-the-art range-separated (RS) and
long-range-corrected (LC) double hybrid (DH) approaches are selected,
and global DH and LC hybrid functionals are also inspected. The correct
long-range behavior of the exchange–correlation (XC) energy
is extensively studied, and various CT descriptors are compared as
well. Our results show that the most robust performance is attained
by RS-PBE-P86/SOS-ADC(2), as it is suitable to describe both types
of CT excitations with outstanding accuracy. Furthermore, concerning
the intramolecular transitions, unexpectedly excellent results are
obtained for most of the global DHs, but their limitations are also
demonstrated for bimolecular complexes. Despite the outstanding performance
of the LC-DH methods for common intramolecular excitations, serious
deficiencies are pointed out for intermolecular CT transitions, and
the wrong long-range behavior of the XC energy is revealed. The application
of LC hybrids to such transitions is not recommended in any respect.
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Affiliation(s)
- Dávid Mester
- Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
| | - Mihály Kállay
- Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
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30
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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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31
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Franzke YJ, Holzer C, Mack F. NMR Coupling Constants Based on the Bethe-Salpeter Equation in the GW Approximation. J Chem Theory Comput 2022; 18:1030-1045. [PMID: 34981925 DOI: 10.1021/acs.jctc.1c00999] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present the first steps to extend the Green's function GW method and the Bethe-Salpeter equation (BSE) to molecular response properties such as nuclear magnetic resonance (NMR) indirect spin-spin coupling constants. We discuss both a nonrelativistic one-component and a quasi-relativistic two-component formalism. The latter describes scalar-relativistic and spin-orbit effects and allows us to study heavy-element systems with reasonable accuracy. Efficiency is maintained by the application of the resolution of the identity approximation throughout. The performance is demonstrated using conventional central processing units (CPUs) and modern graphics processing units (GPUs) for molecules involving several thousand basis functions. Our results show that a large amount of Hartree-Fock exchange is vital to provide a sufficient Kohn-Sham starting point to compute the GW quasi-particle energies. As the GW-BSE approach is generally less accurate for triplet excitations or related properties such as the Fermi-contact interaction, the admixture of the Kohn-Sham correlation kernel through the contracted BSE (cBSE) method improves the results for NMR coupling constants. This leads to remarkable results when combined with the eigenvalue-only self-consistent variant (evGW) and Becke's half and half functional (BH&HLYP) or the CAM-QTP family. The developed methodology is used to calculate the Karplus curve of tin molecules, illustrating its applicability to extended chemically relevant molecules. Here, the GW-cBSE method improves upon the chosen BH&HLYP Kohn-Sham starting points.
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Affiliation(s)
- Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, 35032 Marburg, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
| | - Fabian Mack
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
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32
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Zwijnenburg M. The Effect of Particle Size and Composition on the Optical and Electronic Properties of CdO and CdS Rocksalt Nanoparticles. Phys Chem Chem Phys 2022; 24:21954-21965. [DOI: 10.1039/d2cp01342h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Quantum confinement like behaviour in CdO and CdS nanoparticles is demonstrated through explicit evGW-BSE many-body perturbation theory calculations on 0.6-1.4 nanometre particles of these materials. However, while the lowest optical...
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33
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inanlou S, Cortés-Mejía R, Özdemir AD, Höfener S, Klopper W, Wenzel W, Xie W, Elstner M. Understanding excited state properties of host materials in OLEDs: simulation of absorption spectrum of amorphous 4,4-bis(carbazol-9-yl)-2,2-biphenyl (CBP). Phys Chem Chem Phys 2022; 24:4576-4587. [DOI: 10.1039/d1cp04293a] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
4,4-bis(carbazol-9-yl)-2,2-biphenyl (CBP) is widely used as a host material in phosphorescent organic light-emitting diodes (PhOLEDs). In the present study, we simulate the absorption spectra of CBP in gas and condensed...
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34
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Holzer C, Pausch A, Klopper W. The GW/BSE Method in Magnetic Fields. Front Chem 2021; 9:746162. [PMID: 34900932 PMCID: PMC8655096 DOI: 10.3389/fchem.2021.746162] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2021] [Accepted: 10/19/2021] [Indexed: 11/16/2022] Open
Abstract
The GW approximation and the Bethe–Salpeter equation have been implemented into the Turbomole program package for computations of molecular systems in a strong, finite magnetic field. Complex-valued London orbitals are used as basis functions to ensure gauge-invariant computational results. The implementation has been benchmarked against triplet excitation energies of 36 small to medium-sized molecules against reference values obtained at the approximate coupled-cluster level (CC2 approximation). Finally, a spectacular change of colour from orange to green of the tetracene molecule is induced by applying magnetic fields between 0 and 9,000 T perpendicular to the molecular plane.
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Affiliation(s)
- Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Ansgar Pausch
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Wim Klopper
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.,Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), Eggenstein-Leopoldshafen, Germany
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35
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Grupe M, Boden P, Di Martino‐Fumo P, Gui X, Bruschi C, Israil R, Schmitt M, Nieger M, Gerhards M, Klopper W, Riehn C, Bizzarri C, Diller R. Time-Resolved Spectroscopy and Electronic Structure of Mono-and Dinuclear Pyridyl-Triazole/DPEPhos-Based Cu(I) Complexes. Chemistry 2021; 27:15251-15270. [PMID: 34550622 PMCID: PMC8597052 DOI: 10.1002/chem.202102760] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2021] [Indexed: 12/20/2022]
Abstract
Chemical and spectroscopic characterization of the mononuclear photosensitizers [(DPEPhos)Cu(I)(MPyrT)]0/+ (CuL, CuLH) and their dinuclear analogues (Cu2 L', Cu2 L'H2 ), backed by (TD)DFT and high-level GW-Bethe-Salpeter equation calculations, exemplifies the complex influence of charge, nuclearity and structural flexibility on UV-induced photophysical pathways. Ultrafast transient absorption and step-scan FTIR spectroscopy reveal flattening distortion in the triplet state of CuLH as controlled by charge, which also appears to have a large impact on the symmetry of the long-lived triplet states in Cu2 L' and Cu2 L'H2 . Time-resolved luminescence spectroscopy (solid state), supported by transient photodissociation spectroscopy (gas phase), confirm a lifetime of some tens of μs for the respective triplet states, as well as the energetics of thermally activated delayed luminescence, both being essential parameters for application of these materials based on earth-abundant copper in photocatalysis and luminescent devices.
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Affiliation(s)
- Merten Grupe
- Department of PhysicsTU KaiserslauternErwin-Schrödinger-Straße 4667663KaiserslauternGermany
| | - Pit Boden
- Department of ChemistryTU KaiserslauternErwin-Schrödinger-Straße 5267663KaiserslauternGermany
| | - Patrick Di Martino‐Fumo
- Department of ChemistryTU KaiserslauternErwin-Schrödinger-Straße 5267663KaiserslauternGermany
| | - Xin Gui
- Institute of Physical ChemistryKarlsruhe Institute of Technology (KIT)Fritz-Haber-Weg 276131KarlsruheGermany
| | - Cecilia Bruschi
- Institute of Organic Chemistry (IOC)Karlsruhe Institute of Technology (KIT)Fritz-Haber-Weg 676131KarlsruheGermany
| | - Roumany Israil
- Department of ChemistryTU KaiserslauternErwin-Schrödinger-Straße 5267663KaiserslauternGermany
| | - Marcel Schmitt
- Department of ChemistryTU KaiserslauternErwin-Schrödinger-Straße 5267663KaiserslauternGermany
| | - Martin Nieger
- Department of ChemistryUniversity of HelsinkiA.I. Virtasen aukio 100014HelsinkiFinland
| | - Markus Gerhards
- Department of ChemistryTU KaiserslauternErwin-Schrödinger-Straße 5267663KaiserslauternGermany
- Research Center OPTIMASErwin-Schrödinger-Straße 4667663KaiserslauternGermany
| | - Wim Klopper
- Institute of Physical ChemistryKarlsruhe Institute of Technology (KIT)Fritz-Haber-Weg 276131KarlsruheGermany
| | - Christoph Riehn
- Department of ChemistryTU KaiserslauternErwin-Schrödinger-Straße 5267663KaiserslauternGermany
- Research Center OPTIMASErwin-Schrödinger-Straße 4667663KaiserslauternGermany
| | - Claudia Bizzarri
- Institute of Organic Chemistry (IOC)Karlsruhe Institute of Technology (KIT)Fritz-Haber-Weg 676131KarlsruheGermany
| | - Rolf Diller
- Department of PhysicsTU KaiserslauternErwin-Schrödinger-Straße 4667663KaiserslauternGermany
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36
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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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37
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Bruschi C, Gui X, Salaeh‐arae N, Barchi T, Fuhr O, Lebedkin S, Klopper W, Bizzarri C. Versatile Heteroleptic Cu(I) Complexes Based on Quino(xa)‐line‐Triazole Ligands: from Visible‐Light Absorption and Cooperativity to Luminescence and Photoredox Catalysis. Eur J Inorg Chem 2021. [DOI: 10.1002/ejic.202100653] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Cecilia Bruschi
- Institute of Organic Chemistry Karlsruhe Institute of Technology Fritz-Haber-Weg 6 76137 Karlsruhe Germany
| | - Xin Gui
- Institute of Physical Chemistry-Theoretical Chemistry Karlsruhe Institute of Technology (KIT) Fritz-Haber-Weg 2 76131 Karlsruhe Germany
| | - Nasrin Salaeh‐arae
- Institute of Organic Chemistry Karlsruhe Institute of Technology Fritz-Haber-Weg 6 76137 Karlsruhe Germany
| | - Tobia Barchi
- Institute of Organic Chemistry Karlsruhe Institute of Technology Fritz-Haber-Weg 6 76137 Karlsruhe Germany
| | - Olaf Fuhr
- Institute of Nanotechnology Karlsruhe Institute of Technology Hermann-von-Helmholtz Platz 1 76344 Eggenstein-Leopoldshafen Germany
- Karlsruhe Nano MicroFacility (KNMF) Karlsruhe Institute of Technology Hermann-von Helmholtz-Platz 1 76344 Eggenstein-Leopoldshafen Germany
| | - Sergei Lebedkin
- Institute of Nanotechnology Karlsruhe Institute of Technology Hermann-von-Helmholtz Platz 1 76344 Eggenstein-Leopoldshafen Germany
| | - Wim Klopper
- Institute of Physical Chemistry-Theoretical Chemistry Karlsruhe Institute of Technology (KIT) Fritz-Haber-Weg 2 76131 Karlsruhe Germany
| | - Claudia Bizzarri
- Institute of Organic Chemistry Karlsruhe Institute of Technology Fritz-Haber-Weg 6 76137 Karlsruhe Germany
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38
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Wang X, Berkelbach TC. Absorption Spectra of Solids from Periodic Equation-of-Motion Coupled-Cluster Theory. J Chem Theory Comput 2021; 17:6387-6394. [PMID: 34559525 DOI: 10.1021/acs.jctc.1c00692] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present ab initio absorption spectra of six three-dimensional semiconductors and insulators calculated using Gaussian-based periodic equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD). The spectra are calculated efficiently by solving a system of linear equations at each frequency, giving access to an energy range of tens of electronvolts without explicit enumeration of excited states. We assess the impact of cost-saving approximations associated with Brillouin zone sampling, frozen orbitals, and the partitioned EOM-CCSD approximation. Although our most converged spectra exhibit line shapes that are in good agreement with experimental spectra, they are uniformly shifted to higher energies by about 1 eV, which is not explained by the remaining finite-size errors. We tentatively attribute this discrepancy to a combination of vibrational effects and the remaining electron correlation, i.e., triple excitations and above.
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Affiliation(s)
- Xiao Wang
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
| | - Timothy C Berkelbach
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States.,Department of Chemistry, Columbia University, New York, New York 10027, United States
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39
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Zwijnenburg MA. The effect of particle size on the optical and electronic properties of magnesium oxide nanoparticles. Phys Chem Chem Phys 2021; 23:21579-21590. [PMID: 34553204 DOI: 10.1039/d1cp02683f] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
The quasiparticle states, fundamental gaps, optical gaps, exciton binding energies and UV-vis spectra for a series of cuboidal nanoparticles of the prototypical oxide magnesium oxide (MgO), the largest of which has 216 atoms and edges of 1 nm, were predicted using many-body perturbation theory (evGW-BSE). The evolution of the properties with the particle size was explicitly studied. It was found that, while the highest occupied and lowest unoccupied quasiparticle states and fundamental gap change with the particle size, the optical gap remains essentially fixed for all but the smallest nanoparticles, in line with what was previously observed experimentally. The explanation for these observations is demonstrated to be that, while the optical gap is associated with an exciton that is highly localised around the particle's corner atoms, the highest occupied and lowest unoccupied quasiparticle states, while primarily localised on the oxygen corner atoms (hole) and magnesium corner atoms (electron), show significant delocalisation along the edges. The strong localisation of the exciton associated with the optical gap on the corner atoms is argued to also explain why the nanoparticles have much smaller optical gaps and red-shifted spectra compared to bulk MgO. Finally, it is discussed how this non-quantum confinement behaviour, where the properties of the nanoparticles arise from surface defects rather than differences in localisation of quasiparticle or exciton states, appears typical of alkaline earth oxide nanoparticles, and that the true optical gap of bulk crystals of such materials is also probably the result of surface defects, even if unobservable experimentally.
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Affiliation(s)
- Martijn A Zwijnenburg
- Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, UK.
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40
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Förster A, Visscher L. Low-Order Scaling Quasiparticle Self-Consistent GW for Molecules. Front Chem 2021; 9:736591. [PMID: 34540804 PMCID: PMC8446457 DOI: 10.3389/fchem.2021.736591] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2021] [Accepted: 08/13/2021] [Indexed: 11/13/2022] Open
Abstract
Low-order scaling GW implementations for molecules are usually restricted to approximations with diagonal self-energy. Here, we present an all-electron implementation of quasiparticle self-consistent GW for molecular systems. We use an efficient algorithm for the evaluation of the self-energy in imaginary time, from which a static non-local exchange-correlation potential is calculated via analytical continuation. By using a direct inversion of iterative subspace method, fast and stable convergence is achieved for almost all molecules in the GW100 database. Exceptions are systems which are associated with a breakdown of the single quasiparticle picture in the valence region. The implementation is proven to be starting point independent and good agreement of QP energies with other codes is observed. We demonstrate the computational efficiency of the new implementation by calculating the quasiparticle spectrum of a DNA oligomer with 1,220 electrons using a basis of 6,300 atomic orbitals in less than 4 days on a single compute node with 16 cores. We use then our implementation to study the dependence of quasiparticle energies of DNA oligomers consisting of adenine-thymine pairs on the oligomer size. The first ionization potential in vacuum decreases by nearly 1 electron volt and the electron affinity increases by 0.4 eV going from the smallest to the largest considered oligomer. This shows that the DNA environment stabilizes the hole/electron resulting from photoexcitation/photoattachment. Upon inclusion of the aqueous environment via a polarizable continuum model, the differences between the ionization potentials reduce to 130 meV, demonstrating that the solvent effectively compensates for the stabilizing effect of the DNA environment. The electron affinities of the different oligomers are almost identical in the aqueous environment.
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Affiliation(s)
- Arno Förster
- Theoretical Chemistry, Vrije Universiteit, Amsterdam, Netherlands
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41
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Patterson CH. Excited states of molecular and crystalline acetylene: application of TDHF and BSE via density fitting methods. Mol Phys 2021. [DOI: 10.1080/00268976.2020.1792568] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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42
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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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Loos PF, Comin M, Blase X, Jacquemin D. Reference Energies for Intramolecular Charge-Transfer Excitations. J Chem Theory Comput 2021; 17:3666-3686. [DOI: 10.1021/acs.jctc.1c00226] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, F-31400 Toulouse, France
| | | | - Xavier Blase
- Univ. Grenoble Alpes, CNRS, Inst NEEL, F-38042 Grenoble, France
| | - Denis Jacquemin
- Université de Nantes, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
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Holzer C, Franzke YJ, Kehry M. Assessing the Accuracy of Local Hybrid Density Functional Approximations for Molecular Response Properties. J Chem Theory Comput 2021; 17:2928-2947. [PMID: 33914504 DOI: 10.1021/acs.jctc.1c00203] [Citation(s) in RCA: 39] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A comprehensive overview of the performance of local hybrid functionals for molecular properties like excited states, ionization potentials within the GW framework, polarizabilities, magnetizabilities, NMR chemical shifts, and NMR spin-spin coupling constants is presented. We apply the generalization of the kinetic energy, τ, with the paramagnetic current density to all magnetic properties and the excitation energies from time-dependent density functional theory. This restores gauge invariance for these properties. Different ansätze for local mixing functions such as the iso-orbital indicator, the correlation length, the Görling-Levy second-order limit, and the spin polarization are compared. For the latter, we propose a modified version of the corresponding hyper-generalized gradient approximation functional of Perdew, Staroverov, Tao, and Scuseria (PSTS) [Phys. Rev. A 2008, 78, 052513] to allow for a numerically stable evaluation of the exchange-correlation kernel and hyperkernel. The PSTS functional leads to a very consistent improvement compared to the related TPSSh functional. It is further shown that the "best" choice of the local mixing function depends on the studied property and molecular class. While functionals based on the iso-orbital indicator lead to rather accurate excitation energies and ionization energies, the results are less impressive for NMR properties, for which a considerable dependence on the considered molecular test set and nuclei is observed. Johnson's local hybrid functional based on the correlation length yields remarkable results for NMR shifts of compounds featuring heavy elements and also for the excitation energies of organic compounds.
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Affiliation(s)
- Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
| | - Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, 35032 Marburg, Germany.,Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
| | - Max Kehry
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
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Wilhelm J, Seewald P, Golze D. Low-Scaling GW with Benchmark Accuracy and Application to Phosphorene Nanosheets. J Chem Theory Comput 2021; 17:1662-1677. [DOI: 10.1021/acs.jctc.0c01282] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Affiliation(s)
- Jan Wilhelm
- Institute of Theoretical Physics, University of Regensburg, D-93053 Regensburg, Germany
| | - Patrick Seewald
- Department of Chemistry, University of Zurich, CH-8057 Zurich, Switzerland
| | - Dorothea Golze
- Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
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46
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de Queiroz TB, de Figueroa ER, Coutinho-Neto MD, Maciel CD, Tapavicza E, Hashemi Z, Leppert L. First principles theoretical spectroscopy of methylene blue: Between limitations of time-dependent density functional theory approximations and its realistic description in the solvent. J Chem Phys 2021; 154:044106. [PMID: 33514105 DOI: 10.1063/5.0029727] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Methylene blue [3,7-Bis(di-methylamino) phenothiazin-5-ium chloride] is a phenothiazine dye with applications as a sensitizer for photodynamic therapy, photoantimicrobials, and dye-sensitized solar cells. Time-dependent density functional theory (TDDFT), based on (semi)local and global hybrid exchange-correlation functionals, fails to correctly describe its spectral features due to known limitations for describing optical excitations of π-conjugated systems. Here, we use TDDFT with a non-empirical optimally tuned range-separated hybrid functional to explore the optical excitations of gas phase and solvated methylene blue. We compute solvated configurations using molecular dynamics and an iterative procedure to account for explicit solute polarization. We rationalize and validate that by extrapolating the optimized range separation parameter to an infinite amount of solvating molecules, the optical gap of methylene blue is well described. Moreover, this method allows us to resolve contributions from solvent-solute intermolecular interactions and dielectric screening. We validate our results by comparing them to first-principles calculations based on the GW+Bethe-Salpeter equation approach and experiment. Vibronic calculations using TDDFT and the generating function method account for the spectra's subbands and bring the computed transition energies to within 0.15 eV of the experimental data. This methodology is expected to perform equivalently well for describing solvated spectra of π-conjugated systems.
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Affiliation(s)
- Thiago B de Queiroz
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Av. dos Estados 5001, 09510-580 Santo André-SP, Brazil
| | - Erick R de Figueroa
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Av. dos Estados 5001, 09510-580 Santo André-SP, Brazil
| | - Maurício D Coutinho-Neto
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Av. dos Estados 5001, 09510-580 Santo André-SP, Brazil
| | - Cleiton D Maciel
- Instituto Federal de Educação, Ciência e Tecnologia de São Paulo, Campus Itaquaquecetuba, Avenida Primeiro de Maio, 500, 08571-050 Itaquaquecetuba-SP, Brazil
| | - Enrico Tapavicza
- Department of Chemistry and Biochemistry, California State University, Long Beach, 1250 Bellflower Boulevard, Long Beach, California 90840, USA
| | - Zohreh Hashemi
- Institute of Physics, University of Bayreuth, Bayreuth 95440, Germany
| | - Linn Leppert
- Institute of Physics, University of Bayreuth, Bayreuth 95440, Germany
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Cortés-Mejía R, Höfener S, Klopper W. Effects of rotational conformation on electronic properties of 4,4′-bis(carbazol-9-yl)biphenyl (CBP): the single-molecule picture and beyond. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1876936] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Rodrigo Cortés-Mejía
- Theoretical Chemistry Group, Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Sebastian Höfener
- Theoretical Chemistry Group, Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Wim Klopper
- Theoretical Chemistry Group, Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
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48
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Kang MWC, Liu H, Kah JCY. Innate immune activation by conditioned medium of cancer cells following combined phototherapy with photosensitizer-loaded gold nanorods. JOURNAL OF MATERIALS CHEMISTRY. B 2020; 8:10812-10824. [PMID: 33174587 DOI: 10.1039/d0tc00044b] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
Nanoparticle-based phototherapy has evolved to include immunotherapy as an effective treatment combination for cancers through inducing anti-cancer immune activation leading to downstream adaptive responses and immune protection. However, most cancer phototherapy studies that claimed anti-cancer immunogenic effects often included exogenous immunostimulants to potentiate immune responses and did not clearly establish their effects on immune cells. In this study, we showed that combined photodynamic (PDT) and photothermal therapy (PTT) using gold nanorods (NRs) loaded with the photosensitizer chlorin e6 (Ce6) on endogenously formed mouse serum (MS) protein coronas (i.e., NR-MS-Ce6) on EMT6 murine mammary carcinoma cells could potentiate the activation of both J774A.1 macrophages and DC2.4 dendritic cells. The activation of these innate immune cells by the conditioned media from cancer cells treated with combined PDT + PTT was cell-type and number dependent. While treated B16-OVA murine melanoma cells induced lower activation levels for both immune cell types compared to EMT6, they caused higher pro-inflammatory cytokine secretion levels. Our study suggests the importance of immunological investigations to complement any nanoparticle-based therapeutic interventions to better evaluate their efficacy. This could be achieved through a simple approach to screen for the first line of immune responses arising from these therapies prior to in vivo studies.
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Affiliation(s)
- Malvin Wei Cherng Kang
- NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, University Hall, Tan Chin Tuan Wing, Level 04, #04-02, 21 Lower Kent Ridge, Singapore 119077, Singapore.
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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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50
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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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