1
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Folorunso AS, Mauger F, Hamer KA, Jayasinghe DD, Wahyutama IS, Ragains JR, Jones RR, DiMauro LF, Gaarde MB, Schafer KJ, Lopata K. Attochemistry Regulation of Charge Migration. J Phys Chem A 2023; 127:1894-1900. [PMID: 36791088 PMCID: PMC9986869 DOI: 10.1021/acs.jpca.3c00568] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/16/2023]
Abstract
Charge migration (CM) is a coherent attosecond process that involves the movement of localized holes across a molecule. To determine the relationship between a molecule's structure and the CM dynamics it exhibits, we perform systematic studies of para-functionalized bromobenzene molecules (X-C6H4-R) using real-time time-dependent density functional theory. We initiate valence-electron dynamics by emulating rapid strong-field ionization leading to a localized hole on the bromine atom. The resulting CM, which takes on the order of 1 fs, occurs via an X localized → C6H4 delocalized → R localized mechanism. Interestingly, the hole contrast on the acceptor functional group increases with increasing electron-donating strength. This trend is well-described by the Hammett σ value of the group, which is a commonly used metric for quantifying the effect of functionalization on the chemical reactivity of benzene derivatives. These results suggest that simple attochemistry principles and a density-based picture can be used to predict and understand CM.
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Affiliation(s)
| | | | | | | | | | | | - Robert R Jones
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, United States
| | - Louis F DiMauro
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, United States
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2
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Eschenbach P, Neugebauer J. Subsystem density-functional theory: A reliable tool for spin-density based properties. J Chem Phys 2022; 157:130902. [PMID: 36209003 DOI: 10.1063/5.0103091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Subsystem density-functional theory compiles a set of features that allow for efficiently calculating properties of very large open-shell radical systems such as organic radical crystals, proteins, or deoxyribonucleic acid stacks. It is computationally less costly than correlated ab initio wave function approaches and can pragmatically avoid the overdelocalization problem of Kohn-Sham density-functional theory without employing hard constraints on the electron-density. Additionally, subsystem density-functional theory calculations commonly start from isolated fragment electron densities, pragmatically preserving a priori specified subsystem spin-patterns throughout the calculation. Methods based on subsystem density-functional theory have seen a rapid development over the past years and have become important tools for describing open-shell properties. In this Perspective, we address open questions and possible developments toward challenging future applications in connection with subsystem density-functional theory for spin-dependent properties.
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Affiliation(s)
- Patrick Eschenbach
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Simulation, Westfälische Wilhelms-Universität Münster, Corrensstraße 36, 48149 Münster, Germany
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Simulation, Westfälische Wilhelms-Universität Münster, Corrensstraße 36, 48149 Münster, Germany
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3
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Toffoli D, Quarin M, Fronzoni G, Stener M. Accurate Vertical Excitation Energies of BODIPY/Aza-BODIPY Derivatives from Excited-State Mean-Field Calculations. J Phys Chem A 2022; 126:7137-7146. [PMID: 36173265 PMCID: PMC9574914 DOI: 10.1021/acs.jpca.2c04473] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
We report a benchmark study of vertical excitation energies
and
oscillator strengths for the HOMO → LUMO transitions of 17
boron–dipyrromethene (BODIPY) structures, showing a large variety
of ring sizes and substituents. Results obtained at the time-dependent
density functional theory (TDDFT) and at the delta-self-consistent-field
(ΔSCF) by using 13 different exchange correlation kernels (within
LDA, GGA, hybrid, and range-separated approximations) are benchmarked
against the experimental excitation energies when available. It is
found that the time-independent ΔSCF DFT method, when used in
combination with hybrid PBE0 and B3LYP functionals, largely outperforms
TDDFT and can be quite competitive, in terms of accuracy, with computationally
more costly wave function based methods such as CC2 and CASPT2.
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Affiliation(s)
- Daniele Toffoli
- Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Trieste, via L. Giorgieri 1, I-34127 Trieste, Italy.,CNR-IOM, Istituto Officina dei Materiali, I-34149, Trieste, Italy
| | - Matteo Quarin
- Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Trieste, via L. Giorgieri 1, I-34127 Trieste, Italy
| | - Giovanna Fronzoni
- Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Trieste, via L. Giorgieri 1, I-34127 Trieste, Italy
| | - Mauro Stener
- Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Trieste, via L. Giorgieri 1, I-34127 Trieste, Italy.,CNR-IOM, Istituto Officina dei Materiali, I-34149, Trieste, Italy
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4
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Sun H, Jiang H. Combined
DFT
and wave function theory approach to excited states of lanthanide luminescent materials: A case study of
LaF
3
:Ce
3+. J CHIN CHEM SOC-TAIP 2022. [DOI: 10.1002/jccs.202200348] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Affiliation(s)
- Huai‐Yang Sun
- Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering Peking University Beijing PR China
| | - Hong Jiang
- Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering Peking University Beijing PR China
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5
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de Sousa LE, de Silva P. Diabatic Decomposition Perspective on the Role of Charge Transfer and Local Excitations in Thermally Activated Delayed Fluorescence. J Chem Theory Comput 2022; 18:5459-5470. [PMID: 36007256 DOI: 10.1021/acs.jctc.2c00310] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Thermally activated delayed fluorescence (TADF) is a phenomenon that relies on the upconversion of triplet excitons to singlet excitons by means of reverse intersystem crossing (rISC). It has been shown both experimentally and theoretically that the TADF mechanism depends on the interplay between charge transfer and local excitations. However, the difference between the diabatic and adiabatic character of the involved excited states is rarely discussed in the literature. Here we develop a diabatization procedure to implement a four-state model Hamiltonian to a set of TADF molecules. We provide physical interpretations of the Hamiltonian elements and show their dependence on the electronic state of the equilibrium geometry. We also demonstrate how vibrations affect the TADF efficiency by modifying the diabatic decomposition of the molecule. Finally, we provide a simple model that connects the diabatic Hamiltonian to the electronic properties relevant to TADF and show how this relationship translates into different optimization strategies for rISC, fluorescence, and overall TADF performance.
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Affiliation(s)
- Leonardo Evaristo de Sousa
- Department of Energy Conversion and Storage, Technical University of Denmark, Anker Engelunds Vej 301, 2800 Kongens Lyngby, Denmark
| | - Piotr de Silva
- Department of Energy Conversion and Storage, Technical University of Denmark, Anker Engelunds Vej 301, 2800 Kongens Lyngby, Denmark
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6
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Schmerwitz YLA, Ivanov AV, Jónsson EÖ, Jónsson H, Levi G. Variational Density Functional Calculations of Excited States: Conical Intersection and Avoided Crossing in Ethylene Bond Twisting. J Phys Chem Lett 2022; 13:3990-3999. [PMID: 35481754 DOI: 10.1021/acs.jpclett.2c00741] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Theoretical studies of photochemical processes require a description of the energy surfaces of excited electronic states, especially near degeneracies, where transitions between states are most likely. Systems relevant to photochemical applications are typically too large for high-level multireference methods, and while time-dependent density functional theory (TDDFT) is efficient, it can fail to provide the required accuracy. A variational, time-independent density functional approach is applied to the twisting of the double bond and pyramidal distortion in ethylene, the quintessential model for photochemical studies. By allowing for symmetry breaking, the calculated energy surfaces exhibit the correct topology around the twisted-pyramidalized conical intersection even when using a semilocal functional approximation, and by including explicit self-interaction correction, the torsional energy curves are in close agreement with published multireference results. The findings of the present work point to the possibility of using a single determinant time-independent density functional approach to simulate nonadiabatic dynamics, even for large systems where multireference methods are impractical and TDDFT is often not accurate enough.
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Affiliation(s)
| | - Aleksei V Ivanov
- Science Institute of the University of Iceland, VR-III, 107 Reykjavík, Iceland
| | - Elvar Ö Jónsson
- Science Institute of the University of Iceland, VR-III, 107 Reykjavík, Iceland
| | - Hannes Jónsson
- Faculty of Physical Sciences, University of Iceland, VR-III, 107 Reykjavík, Iceland
- Department of Applied Physics, Aalto University, FI-00076 Espoo, Finland
| | - Gianluca Levi
- Science Institute of the University of Iceland, VR-III, 107 Reykjavík, Iceland
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7
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Stella M, Thapa K, Genovese L, Ratcliff LE. Transition-Based Constrained DFT for the Robust and Reliable Treatment of Excitations in Supramolecular Systems. J Chem Theory Comput 2022; 18:3027-3038. [PMID: 35471972 PMCID: PMC9097287 DOI: 10.1021/acs.jctc.1c00548] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2021] [Indexed: 11/28/2022]
Abstract
Despite the variety of available computational approaches, state-of-the-art methods for calculating excitation energies, such as time-dependent density functional theory (TDDFT), are computationally demanding and thus limited to moderate system sizes. Here, we introduce a new variation of constrained DFT (CDFT), wherein the constraint corresponds to a particular transition (T), or a combination of transitions, between occupied and virtual orbitals, rather than a region of the simulation space as in traditional CDFT. We compare T-CDFT with TDDFT and ΔSCF results for the low-lying excited states (S1 and T1) of a set of gas-phase acene molecules and OLED emitters and with reference results from the literature. At the PBE level of theory, T-CDFT outperforms ΔSCF for both classes of molecules, while also proving to be more robust. For the local excitations seen in the acenes, T-CDFT and TDDFT perform equally well. For the charge transfer (CT)-like excitations seen in the OLED molecules, T-CDFT also performs well, in contrast to the severe energy underestimation seen with TDDFT. In other words, T-CDFT is equally applicable to both local excitations and CT states, providing more reliable excitation energies at a much lower computational cost than TDDFT cost. T-CDFT is designed for large systems and has been implemented in the linear-scaling BigDFT code. It is therefore ideally suited for exploring the effects of explicit environments on excitation energies, paving the way for future simulations of excited states in complex realistic morphologies, such as those which occur in OLED materials.
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Affiliation(s)
- Martina Stella
- Department
of Materials, Imperial College London, London SW7 2AZ, U.K.
- The
Abdus Salam International Centre for Theoretical Physics, Condensed Matter and Statistical Physics, Trieste 34151, Italy
| | - Kritam Thapa
- Department
of Materials, Imperial College London, London SW7 2AZ, U.K.
| | - Luigi Genovese
- Université
Grenoble Alpes, CEA, IRIG-MEM-L_Sim, Grenoble 38000, France
| | - Laura E. Ratcliff
- Department
of Materials, Imperial College London, London SW7 2AZ, U.K.
- Centre
for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, U.K.
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8
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Kumar C, Luber S. Robust ΔSCF calculations with direct energy functional minimization methods and STEP for molecules and materials. J Chem Phys 2022; 156:154104. [PMID: 35459303 DOI: 10.1063/5.0075927] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The direct energy functional minimization method using the orbital transformation (OT) scheme in the program package CP2K has been employed for Δ self-consistent field (ΔSCF) calculations. The OT method for non-uniform molecular orbitals occupations allows us to apply the ΔSCF method for various kinds of molecules and periodic systems. Vertical excitation energies of heteroaromatic molecules and condensed phase systems, such as solvated ethylene and solvated uracil obeying periodic boundary conditions, are reported using the ΔSCF method. In addition, a Re-phosphate molecule attached to the surface of anatase (TiO2) has been investigated. Additionally, we have implemented a recently proposed state-targeted energy projection ΔSCF algorithm [K. Carter-Fenk and J. M. Herbert, J. Chem. Theory Comput. 16(8), 5067-5082 (2020)] for diagonalization based SCF in CP2K. It is found that the OT scheme provides a smooth and robust SCF convergence for all investigated excitation energies and (non-)periodic systems.
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Affiliation(s)
- Chandan Kumar
- Department of Chemistry, University of Zurich, Zurich, Switzerland
| | - Sandra Luber
- Department of Chemistry, University of Zurich, Zurich, Switzerland
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9
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Vandaele E, Mališ M, Luber S. The ΔSCF method for non-adiabatic dynamics of systems in the liquid phase. J Chem Phys 2022; 156:130901. [PMID: 35395890 DOI: 10.1063/5.0083340] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
Computational studies of ultrafast photoinduced processes give valuable insights into the photochemical mechanisms of a broad range of compounds. In order to accurately reproduce, interpret, and predict experimental results, which are typically obtained in a condensed phase, it is indispensable to include the condensed phase environment in the computational model. However, most studies are still performed in vacuum due to the high computational cost of state-of-the-art non-adiabatic molecular dynamics (NAMD) simulations. The quantum mechanical/molecular mechanical (QM/MM) solvation method has been a popular model to perform photodynamics in the liquid phase. Nevertheless, the currently used QM/MM embedding techniques cannot sufficiently capture all solute-solvent interactions. In this Perspective, we will discuss the efficient ΔSCF electronic structure method and its applications with respect to the NAMD of solvated compounds, with a particular focus on explicit quantum mechanical solvation. As more research is required for this method to reach its full potential, some challenges and possible directions for future research are presented as well.
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Affiliation(s)
- Eva Vandaele
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
| | - Momir Mališ
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
| | - Sandra Luber
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
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10
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Corzo HH, Abou Taka A, Pribram-Jones A, Hratchian HP. Using projection operators with maximum overlap methods to simplify challenging self-consistent field optimization. J Comput Chem 2021; 43:382-390. [PMID: 34936117 DOI: 10.1002/jcc.26797] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2021] [Revised: 10/30/2021] [Accepted: 11/28/2021] [Indexed: 02/04/2023]
Abstract
Maximum overlap methods are effective tools for optimizing challenging ground- and excited-state wave functions using self-consistent field models such as Hartree-Fock and Kohn-Sham density functional theory. Nevertheless, such models have shown significant sensitivity to the user-defined initial guess of the target wave function. In this work, a projection operator framework is defined and used to provide a metric for non-aufbau orbital selection in maximum-overlap-methods. The resulting algorithms, termed the Projection-based Maximum Overlap Method (PMOM) and Projection-based Initial Maximum Overlap Method (PIMOM), are shown to perform exceptionally well when using simple user-defined target solutions based on occupied/virtual molecular orbital permutations. This work also presents a new metric that provides a simple and conceptually convenient measure of agreement between the desired target and the current or final SCF results during a calculation employing a maximum-overlap method.
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Affiliation(s)
- Hector H Corzo
- Department of Chemistry and Biochemistry and Center for Chemical Computation and Theory, University of California, Merced, California, USA
| | - Ali Abou Taka
- Department of Chemistry and Biochemistry and Center for Chemical Computation and Theory, University of California, Merced, California, USA
| | - Aurora Pribram-Jones
- Department of Chemistry and Biochemistry and Center for Chemical Computation and Theory, University of California, Merced, California, USA
| | - Hrant P Hratchian
- Department of Chemistry and Biochemistry and Center for Chemical Computation and Theory, University of California, Merced, California, USA
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11
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Maitra NT. Double and Charge-Transfer Excitations in Time-Dependent Density Functional Theory. Annu Rev Phys Chem 2021; 73:117-140. [PMID: 34910562 DOI: 10.1146/annurev-physchem-082720-124933] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Time-dependent density functional theory has emerged as a method of choice for calculations of spectra and response properties in physics, chemistry, and biology, with its system-size scaling enabling computations on systems much larger than otherwise possible. While increasingly complex and interesting systems have been successfully tackled with relatively simple functional approximations, there has also been increasing awareness that these functionals tend to fail for certain classes of approximations. Here I review the fundamental challenges the approximate functionals have in describing double excitations and charge-transfer excitations, which are two of the most common impediments for the theory to be applied in a black-box way. At the same time, I describe the progress made in recent decades in developing functional approximations that give useful predictions for these excitations. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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Affiliation(s)
- Neepa T Maitra
- Department of Physics, Rutgers University at Newark, Newark, New Jersey, USA;
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12
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Ensemble Density Functional Theory of Neutral and Charged Excitations : Exact Formulations, Standard Approximations, and Open Questions. Top Curr Chem (Cham) 2021; 380:4. [PMID: 34825294 DOI: 10.1007/s41061-021-00359-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2021] [Accepted: 11/02/2021] [Indexed: 10/19/2022]
Abstract
Recent progress in the field of (time-independent) ensemble density-functional theory (DFT) for excited states are reviewed. Both Gross-Oliveira-Kohn (GOK) and N-centered ensemble formalisms, which are mathematically very similar and allow for an in-principle-exact description of neutral and charged electronic excitations, respectively, are discussed. Key exact results, for example, the equivalence between the infamous derivative discontinuity problem and the description of weight dependencies in the ensemble exchange-correlation density functional, are highlighted. The variational evaluation of orbital-dependent ensemble Hartree-exchange (Hx) energies is discussed in detail. We show in passing that state-averaging individual exact Hx energies can lead to severe (although solvable) v-representability issues. Finally, we explore the possibility of using the concept of density-driven correlation, which has been introduced recently and does not exist in regular ground-state DFT, for improving state-of-the-art correlation density-functional approximations for ensembles. The present review reflects the efforts of a growing community to turn ensemble DFT into a rigorous and reliable low-cost computational method for excited states. We hope that, in the near future, this contribution will stimulate new formal and practical developments in the field.
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13
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David G, Irons TJP, Fouda AEA, Furness JW, Teale AM. Self-Consistent Field Methods for Excited States in Strong Magnetic Fields: a Comparison between Energy- and Variance-Based Approaches. J Chem Theory Comput 2021; 17:5492-5508. [PMID: 34517708 DOI: 10.1021/acs.jctc.1c00236] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Self-consistent field methods for excited states offer an attractive low-cost route to study not only excitation energies but also properties of excited states. Here, we present the generalization of two self-consistent field methods, the maximum overlap method (MOM) and the σ-SCF method, to calculate excited states in strong magnetic fields and investigate their stability and accuracy in this context. These methods use different strategies to overcome the well-known variational collapse of energy-based optimizations to the lowest solution of a given symmetry. The MOM tackles this problem in the definition of the orbital occupations to constrain the self-consistent field procedure to converge on excited states, while the σ-SCF method is based on the minimization of the variance instead of the energy. To overcome the high computational cost of the variance minimization, we present a new implementation of the σ-SCF method with the resolution of identity approximation, allowing the use of large basis sets, which is an important requirement for calculations in strong magnetic fields. The accuracy of these methods is assessed by comparison with the benchmark literature data for He, H2, and CH+. The results reveal severe limitations of the variance-based scheme, which become more acute in large basis sets. In particular, many states are not accessible using variance optimization. Detailed analysis shows that this is a general feature of variance optimization approaches due to the masking of local minima in the optimization. In contrast, the MOM shows promising performance for computing excited states under these conditions, yielding results consistent with available benchmark data for a diverse range of electronic states.
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Affiliation(s)
- Grégoire David
- School of Chemistry, University of Nottingham, Nottingham NG7 2RD, U.K
| | - Tom J P Irons
- School of Chemistry, University of Nottingham, Nottingham NG7 2RD, U.K
| | - Adam E A Fouda
- School of Chemistry, University of Nottingham, Nottingham NG7 2RD, U.K.,Chemical Sciences and Engineering Division, Argonne National Laboratory, 9700 S Cass Avenue, Lemont, Illinois 60439, United States
| | - James W Furness
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, United States
| | - Andrew M Teale
- School of Chemistry, University of Nottingham, Nottingham NG7 2RD, U.K.,Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, Oslo N-0315, Norway
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14
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Ivanov AV, Levi G, Jónsson EÖ, Jónsson H. Method for Calculating Excited Electronic States Using Density Functionals and Direct Orbital Optimization with Real Space Grid or Plane-Wave Basis Set. J Chem Theory Comput 2021; 17:5034-5049. [PMID: 34227810 DOI: 10.1021/acs.jctc.1c00157] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A direct orbital optimization method is presented for density functional calculations of excited electronic states using either a real space grid or a plane-wave basis set. The method is variational, provides atomic forces in the excited states, and can be applied to Kohn-Sham (KS) functionals as well as orbital-density-dependent (ODD) functionals including explicit self-interaction correction. The implementation for KS functionals involves two nested loops: (1) An inner loop for finding a stationary point in a subspace spanned by the occupied and a few virtual orbitals corresponding to the excited state; (2) an outer loop for minimizing the energy in a tangential direction in the space of the orbitals. For ODD functionals, a third loop is used to find the unitary transformation that minimizes the energy functional among occupied orbitals only. Combined with the maximum overlap method, the algorithm converges in challenging cases where conventional self-consistent field algorithms tend to fail. The benchmark tests presented include two charge-transfer excitations in nitrobenzene and an excitation of CO to degenerate π* orbitals where the importance of complex orbitals is illustrated. The application of this method to several metal-to-ligand charge-transfer and metal-centered excited states of an FeII photosensitizer complex is described, and the results are compared to reported experimental estimates. This method is also used to study the effect of the Perdew-Zunger self-interaction correction on valence and Rydberg excited states of several molecules, both singlet and triplet states, and the performance compared to semilocal and hybrid functionals.
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Affiliation(s)
- Aleksei V Ivanov
- Science Institute and Faculty of Physical Sciences, University of Iceland, VR-III, 107 Reykjavík, Iceland
| | - Gianluca Levi
- Science Institute and Faculty of Physical Sciences, University of Iceland, VR-III, 107 Reykjavík, Iceland
| | - Elvar Ö Jónsson
- Science Institute and Faculty of Physical Sciences, University of Iceland, VR-III, 107 Reykjavík, Iceland
| | - Hannes Jónsson
- Science Institute and Faculty of Physical Sciences, University of Iceland, VR-III, 107 Reykjavík, Iceland
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15
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Hait D, Head-Gordon M. Orbital Optimized Density Functional Theory for Electronic Excited States. J Phys Chem Lett 2021; 12:4517-4529. [PMID: 33961437 DOI: 10.1021/acs.jpclett.1c00744] [Citation(s) in RCA: 70] [Impact Index Per Article: 23.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Density functional theory (DFT) based modeling of electronic excited states is of importance for investigation of the photophysical/photochemical properties and spectroscopic characterization of large systems. The widely used linear response time-dependent DFT (TDDFT) approach is, however, not effective at modeling many types of excited states, including (but not limited to) charge-transfer states, doubly excited states, and core-level excitations. In this perspective, we discuss state-specific orbital optimized (OO) DFT approaches as an alterative to TDDFT for electronic excited states. We motivate the use of OO-DFT methods and discuss reasons behind their relatively restricted historical usage (vs TDDFT). We subsequently highlight modern developments that address these factors and allow efficient and reliable OO-DFT computations. Several successful applications of OO-DFT for challenging electronic excitations are also presented, indicating their practical efficacy. OO-DFT approaches are thus increasingly becoming a useful route for computing excited states of large chemical systems. We conclude by discussing the limitations and challenges still facing OO-DFT methods, as well as some potential avenues for addressing them.
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Affiliation(s)
- Diptarka Hait
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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16
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Folorunso AS, Bruner A, Mauger F, Hamer KA, Hernandez S, Jones RR, DiMauro LF, Gaarde MB, Schafer KJ, Lopata K. Molecular Modes of Attosecond Charge Migration. PHYSICAL REVIEW LETTERS 2021; 126:133002. [PMID: 33861123 DOI: 10.1103/physrevlett.126.133002] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2020] [Accepted: 02/24/2021] [Indexed: 06/12/2023]
Abstract
First-principles calculations are employed to elucidate the modes of attosecond charge migration (CM) in halogenated hydrocarbon chains. We use constrained density functional theory (DFT) to emulate the creation of a localized hole on the halogen and follow the subsequent dynamics via time-dependent DFT. We find low-frequency CM modes (∼1 eV) that propagate across the molecule and study their dependence on length, bond order, and halogenation. We observe that the CM speed (∼4 Å/fs) is largely independent of molecule length, but is lower for triple-bonded versus double-bonded molecules. Additionally, as the halogen mass increases, the hole travels in a more particlelike manner as it moves across the molecule. These heuristics will be useful in identifying molecules and optimal CM detection methods for future experiments, especially for halogenated hydrocarbons which are promising targets for ionization-triggered CM.
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Affiliation(s)
- Aderonke S Folorunso
- Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - Adam Bruner
- Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - François Mauger
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - Kyle A Hamer
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - Samuel Hernandez
- Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - Robert R Jones
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - Louis F DiMauro
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| | - Mette B Gaarde
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - Kenneth J Schafer
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - Kenneth Lopata
- Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, USA
- Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA
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17
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Ramos P, Pavanello M. Nonadiabatic couplings from a variational excited state method based on constrained DFT. J Chem Phys 2021; 154:014110. [DOI: 10.1063/5.0028872] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Pablo Ramos
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA
| | - Michele Pavanello
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
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18
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Levi G, Ivanov AV, Jónsson H. Variational Density Functional Calculations of Excited States via Direct Optimization. J Chem Theory Comput 2020; 16:6968-6982. [DOI: 10.1021/acs.jctc.0c00597] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Gianluca Levi
- Science Institute and Faculty of Physical Sciences, University of Iceland, 107 Reykjavík, Iceland
| | - Aleksei V. Ivanov
- Science Institute and Faculty of Physical Sciences, University of Iceland, 107 Reykjavík, Iceland
- Saint Petersburg State University, 199034 Saint Petersburg, Russia
| | - Hannes Jónsson
- Science Institute and Faculty of Physical Sciences, University of Iceland, 107 Reykjavík, Iceland
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19
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Carter-Fenk K, Herbert JM. State-Targeted Energy Projection: A Simple and Robust Approach to Orbital Relaxation of Non-Aufbau Self-Consistent Field Solutions. J Chem Theory Comput 2020; 16:5067-5082. [DOI: 10.1021/acs.jctc.0c00502] [Citation(s) in RCA: 38] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- Kevin Carter-Fenk
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - John M. Herbert
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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20
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Neutral excitation density-functional theory: an efficient and variational first-principles method for simulating neutral excitations in molecules. Sci Rep 2020; 10:8947. [PMID: 32488196 PMCID: PMC7265560 DOI: 10.1038/s41598-020-65209-4] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2019] [Accepted: 04/17/2020] [Indexed: 11/08/2022] Open
Abstract
We introduce neutral excitation density-functional theory (XDFT), a computationally light, generally applicable, first-principles technique for calculating neutral electronic excitations. The concept is to generalise constrained density functional theory to free it from any assumptions about the spatial confinement of electrons and holes, but to maintain all the advantages of a variational method. The task of calculating the lowest excited state of a given symmetry is thereby simplified to one of performing a simple, low-cost sequence of coupled DFT calculations. We demonstrate the efficacy of the method by calculating the lowest single-particle singlet and triplet excitation energies in the well-known Thiel molecular test set, with results which are in good agreement with linear-response time-dependent density functional theory (LR-TDDFT). Furthermore, we show that XDFT can successfully capture two-electron excitations, in principle, offering a flexible approach to target specific effects beyond state-of-the-art adiabatic-kernel LR-TDDFT. Overall the method makes optical gaps and electron-hole binding energies readily accessible at a computational cost and scaling comparable to that of standard density functional theory. Owing to its multiple qualities beneficial to high-throughput studies where the optical gap is of particular interest; namely broad applicability, low computational demand, and ease of implementation and automation, XDFT presents as a viable candidate for research within materials discovery and informatics frameworks.
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21
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Pavošević F, Culpitt T, Hammes-Schiffer S. Multicomponent Quantum Chemistry: Integrating Electronic and Nuclear Quantum Effects via the Nuclear–Electronic Orbital Method. Chem Rev 2020; 120:4222-4253. [DOI: 10.1021/acs.chemrev.9b00798] [Citation(s) in RCA: 53] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Fabijan Pavošević
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
| | - Tanner Culpitt
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
| | - Sharon Hammes-Schiffer
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
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22
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Ramos P, Pavanello M. Erratum: “Low-lying excited states by constrained DFT” [J. Chem. Phys. 148, 144103 (2018)]. J Chem Phys 2020; 152:109902. [DOI: 10.1063/5.0004729] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Pablo Ramos
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA
| | - Michele Pavanello
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA
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23
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Xu X, Yang Y. Constrained nuclear-electronic orbital density functional theory: Energy surfaces with nuclear quantum effects. J Chem Phys 2020; 152:084107. [DOI: 10.1063/1.5143371] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Affiliation(s)
- Xi Xu
- Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706, USA
| | - Yang Yang
- Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706, USA
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24
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Hait D, Head-Gordon M. Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory. J Chem Theory Comput 2020; 16:1699-1710. [PMID: 32017554 DOI: 10.1021/acs.jctc.9b01127] [Citation(s) in RCA: 99] [Impact Index Per Article: 24.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present a general approach to converge excited state solutions to any quantum chemistry orbital optimization process, without the risk of variational collapse. The resulting square gradient minimization (SGM) approach only requires analytic energy/Lagrangian orbital gradients and merely costs 3 times as much as ground state orbital optimization (per iteration), when implemented via a finite difference approach. SGM is applied to both single determinant ΔSCF and spin-purified restricted open-shell Kohn-Sham (ROKS) approaches to study the accuracy of orbital optimized DFT excited states. It is found that SGM can converge challenging states where the maximum overlap method (MOM) or analogues either collapse to the ground state or fail to converge. We also report that ΔSCF/ROKS predict highly accurate excitation energies for doubly excited states (which are inaccessible via TDDFT). Singly excited states obtained via ROKS are also found to be quite accurate, especially for Rydberg states that frustrate (semi)local TDDFT. Our results suggest that orbital optimized excited state DFT methods can be used to push past the limitations of TDDFT to doubly excited, charge-transfer, or Rydberg states, making them a useful tool for the practical quantum chemist's toolbox for studying excited states in large systems.
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Affiliation(s)
- Diptarka Hait
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States.,Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States.,Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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25
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Smith B, Akimov AV. Modeling nonadiabatic dynamics in condensed matter materials: some recent advances and applications. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:073001. [PMID: 31661681 DOI: 10.1088/1361-648x/ab5246] [Citation(s) in RCA: 33] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This review focuses on recent developments in the field of nonadiabatic molecular dynamics (NA-MD), with particular attention given to condensed-matter systems. NA-MD simulations for small molecular systems can be performed using high-level electronic structure (ES) calculations, methods accounting for the quantization of nuclear motion, and using fewer approximations in the dynamical methodology itself. Modeling condensed-matter systems imposes many limitations on various aspects of NA-MD computations, requiring approximations at various levels of theory-from the ES, to the ways in which the coupling of electrons and nuclei are accounted for. Nonetheless, the approximate treatment of NA-MD in condensed-phase materials has gained a spin lately in many applied studies. A number of advancements of the methodology and computational tools have been undertaken, including general-purpose methods, as well as those tailored to nanoscale and condensed matter systems. This review summarizes such methodological and software developments, puts them into the broader context of existing approaches, and highlights some of the challenges that remain to be solved.
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Affiliation(s)
- Brendan Smith
- Department of Chemistry, University at Buffalo, The State University of New York, Buffalo, New York 14260-3000, United States of America
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26
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Levi G, Ivanov AV, Jónsson H. Variational calculations of excited states via direct optimization of the orbitals in DFT. Faraday Discuss 2020; 224:448-466. [DOI: 10.1039/d0fd00064g] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
A direct optimization method for obtaining excited electronic states using density functionals is presented.
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Affiliation(s)
- Gianluca Levi
- Science Institute and Faculty of Physical Sciences
- University of Iceland
- Iceland
| | - Aleksei V. Ivanov
- Science Institute and Faculty of Physical Sciences
- University of Iceland
- Iceland
- Saint Petersburg State University
- 199034 Saint Petersburg
| | - Hannes Jónsson
- Science Institute and Faculty of Physical Sciences
- University of Iceland
- Iceland
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27
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Mei Y, Yang W. Excited-State Potential Energy Surfaces, Conical Intersections, and Analytical Gradients from Ground-State Density Functional Theory. J Phys Chem Lett 2019; 10:2538-2545. [PMID: 31038964 PMCID: PMC7449530 DOI: 10.1021/acs.jpclett.9b00712] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
Kohn-Sham density functional theory (KS-DFT) has been a well-established theoretical foundation for ground-state electronic structure and has achieved great success in practical calculations. Recently, utilizing the eigenvalues from KS or generalized KS (GKS) calculations as an approximation to the quasiparticle energies, our group demonstrated a method to calculate the excitation energies from (G)KS calculation on the ground-state ( N - 1)-electron system. This method is now called QE-DFT (quasiparticle energies from DFT). In this work, we extend this QE-DFT method to describe excited-state potential energy surfaces (PESs), conical intersections, and the analytical gradients of excited-state PESs. The analytical gradients were applied to perform geometry optimization for excited states. In conjunction with several commonly used density functional approximations, QE-DFT can yield PESs in the vicinity of the equilibrium structure with accuracy similar to that from time-dependent DFT (TD-DFT). Furthermore, it describes conical intersection well, in contrast to TD-DFT. Good results for geometry optimization, especially bond length, of low-lying excitations for 14 small molecules are presented. The capability of describing excited-state PESs, conical intersections, and analytical gradients from QE-DFT and its efficiency based on just ground-state DFT calculations should be of great interest for describing photochemical and photophysical processes in complex systems.
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Affiliation(s)
- Yuncai Mei
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Key Laboratory of Theoretical Chemistry of Environment, School of Chemistry and Environment, South China Normal University, Guangzhou 510006, China
- Corresponding Author:
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28
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Barnsley JE, Shillito GE, Mapley JI, Larsen CB, Lucas NT, Gordon KC. Walking the Emission Tightrope: Spectral and Computational Analysis of Some Dual-Emitting Benzothiadiazole Donor–Acceptor Dyes. J Phys Chem A 2018; 122:7991-8006. [DOI: 10.1021/acs.jpca.8b05361] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
| | | | - Joseph I. Mapley
- Department of Chemistry, University of Otago, P.O. Box 56, Dunedin, New Zealand
| | | | - Nigel T. Lucas
- Department of Chemistry, University of Otago, P.O. Box 56, Dunedin, New Zealand
| | - Keith C. Gordon
- Department of Chemistry, University of Otago, P.O. Box 56, Dunedin, New Zealand
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