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Li J, Yang W. Chemical Potentials and the One-Electron Hamiltonian of the Second-Order Perturbation Theory from the Functional Derivative Approach. J Phys Chem A 2024; 128:4876-4885. [PMID: 38842399 DOI: 10.1021/acs.jpca.4c01574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2024]
Abstract
We develop a functional derivative approach to calculate the chemical potentials of second-order perturbation theory (MP2). In the functional derivative approach, the correlation part of the MP2 chemical potential, which is the derivative of the MP2 correlation energy with respect to the occupation number of frontier orbitals, is obtained from the chain rule via the noninteracting Green's function. First, the MP2 correlation energy is expressed in terms of the noninteracting Green's function, and its functional derivative to the noninteracting Green's function is the second-order self-energy. Then, the derivative of the noninteracting Green's function to the occupation number is obtained by including the orbital relaxation effect. We show that the MP2 chemical potentials obtained from the functional derivative approach agree with that obtained from the finite difference approach. The one-electron Hamiltonian, defined as the derivative of the MP2 energy with respect to the one particle density matrix, is also derived using the functional derivative approach, which can be used in the self-consistent calculations of MP2 and double-hybrid density functionals. The developed functional derivative approach is promising for calculating the chemical potentials and the one-electron Hamiltonian of approximate functionals and many-body perturbation approaches dependent explicitly on the noninteracting Green's function.
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Affiliation(s)
- Jiachen Li
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
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2
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Li J, Jin Y, Yu J, Yang W, Zhu T. Accurate Excitation Energies of Point Defects from Fast Particle-Particle Random Phase Approximation Calculations. J Phys Chem Lett 2024:2757-2764. [PMID: 38436573 DOI: 10.1021/acs.jpclett.4c00184] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/05/2024]
Abstract
We present an efficient particle-particle random phase approximation (ppRPA) approach that predicts accurate excitation energies of point defects, including the nitrogen-vacancy (NV-) and silicon-vacancy (SiV0) centers in diamond and the divacancy center (VV0) in 4H silicon carbide, with errors of ±0.2 eV compared with experimental values. Starting from the (N + 2)-electron ground state calculated with density functional theory (DFT), the ppRPA excitation energies of the N-electron system are calculated as the differences between the two-electron removal energies of the (N + 2)-electron system. We demonstrate that the ppRPA excitation energies converge rapidly with a few hundred canonical active-space orbitals. We also show that active-space ppRPA has weak DFT starting-point dependence and is significantly cheaper than the corresponding ground-state DFT calculation. This work establishes ppRPA as an accurate and low-cost tool for investigating excited-state properties of point defects and opens up new opportunities for applications of ppRPA to periodic bulk materials.
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Affiliation(s)
- Jiachen Li
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Yu Jin
- Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - Jincheng Yu
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Tianyu Zhu
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
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3
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Li J, Yu J, Chen Z, Yang W. Linear Scaling Calculations of Excitation Energies with Active-Space Particle-Particle Random-Phase Approximation. J Phys Chem A 2023; 127:7811-7822. [PMID: 37695567 DOI: 10.1021/acs.jpca.3c02834] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/12/2023]
Abstract
We developed an efficient active-space particle-particle random-phase approximation (ppRPA) approach to calculate accurate charge-neutral excitation energies of molecular systems. The active-space ppRPA approach constrains both indexes in particle and hole pairs in the ppRPA matrix, which only selects frontier orbitals with dominant contributions to low-lying excitation energies. It employs the truncation in both orbital indexes in the particle-particle and the hole-hole spaces. The resulting matrix, whose eigenvalues are excitation energies, has a dimension that is independent of the size of the systems. The computational effort for the excitation energy calculation, therefore, scales linearly with system size and is negligible compared with the ground-state calculation of the (N - 2)-electron system, where N is the electron number of the molecule. With the active space consisting of 30 occupied and 30 virtual orbitals, the active-space ppRPA approach predicts the excitation energies of valence, charge-transfer, Rydberg, double, and diradical excitations with the mean absolute errors (MAEs) smaller than 0.03 eV compared with the full-space ppRPA results. As a side product, we also applied the active-space ppRPA approach in the renormalized singles (RS) T-matrix approach. Combining the non-interacting pair approximation that approximates the contribution to the self-energy outside the active space, the active-space GRSTRS@PBE approach predicts accurate absolute and relative core-level binding energies with the MAEs around 1.58 and 0.3 eV, respectively. The developed linear scaling calculation of excitation energies is promising for applications to large and complex systems.
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Affiliation(s)
- Jiachen Li
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Jincheng Yu
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Zehua Chen
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
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4
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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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5
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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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6
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Li J, Chen Z, Yang W. Multireference Density Functional Theory for Describing Ground and Excited States with Renormalized Singles. J Phys Chem Lett 2022; 13:894-903. [PMID: 35049309 PMCID: PMC9365454 DOI: 10.1021/acs.jpclett.1c03913] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We applied renormalized singles (RS) in the multireference density functional theory (DFT) to calculate accurate energies of ground and excited states. The multireference DFT approach determines the total energy of the N-electron system as the sum of the (N - 2)-electron energy from a density functional approximation (DFA) and the two-electron addition energies from the particle-particle Tamm-Dancoff approximation (ppTDA), naturally including multireference description. The ppTDA@RS-DFA approach uses the RS Hamiltonian capturing all singles contributions in calculating two-electron addition energies, and its total energy is optimized with the optimized effective potential method. It significantly improves the original ppTDA@DFA. For ground states, ppTDA@RS-DFA properly describes dissociation curves tested and the double bond rotation of ethylene. For excited states, ppTDA@RS-DFA provides accurate excitation energies and largely eliminates the DFA dependence. ppTDA@RS-DFA thus provides an efficient multireference approach to systems with static correlation.
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Affiliation(s)
- Jiachen Li
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Zehua Chen
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
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7
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Li J, Chen Z, Yang W. Renormalized Singles Green's Function in the T-Matrix Approximation for Accurate Quasiparticle Energy Calculation. J Phys Chem Lett 2021; 12:6203-6210. [PMID: 34196553 PMCID: PMC8341309 DOI: 10.1021/acs.jpclett.1c01723] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We combine the renormalized singles (RS) Green's function with the T-matrix approximation for the single-particle Green's function to compute quasiparticle energies for valence and core states of molecular systems. The GRST0 method uses the RS Green's function that incorporates singles contributions as the initial Green's function. The GRSTRS method further calculates the generalized effective interaction with the RS Green's function by using RS eigenvalues in the T-matrix calculation through the particle-particle random phase approximation. The GRSTRS method provides significant improvements over one-shot methods G0T0 and G0W0 as demonstrated in calculations for GW100 and CORE65 test sets. It also systematically eliminates the dependence of G0T0 on the choice of density functional approximations. For valence states, the GRSTRS method provides excellent accuracy, which is better than that of G0T0 and G0W0. For core states, the GRSTRS method identifies correct peaks in the spectral function and significantly outperforms G0T0 on core-level binding energies (CLBEs) and relative CLBEs.
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Affiliation(s)
- Jiachen Li
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Zehua Chen
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
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8
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Bannwarth C, Yu JK, Hohenstein EG, Martínez TJ. Hole-hole Tamm-Dancoff-approximated density functional theory: A highly efficient electronic structure method incorporating dynamic and static correlation. J Chem Phys 2020; 153:024110. [PMID: 32668944 DOI: 10.1063/5.0003985] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The study of photochemical reaction dynamics requires accurate as well as computationally efficient electronic structure methods for the ground and excited states. While time-dependent density functional theory (TDDFT) is not able to capture static correlation, complete active space self-consistent field methods neglect much of the dynamic correlation. Hence, inexpensive methods that encompass both static and dynamic electron correlation effects are of high interest. Here, we revisit hole-hole Tamm-Dancoff approximated (hh-TDA) density functional theory for this purpose. The hh-TDA method is the hole-hole counterpart to the more established particle-particle TDA (pp-TDA) method, both of which are derived from the particle-particle random phase approximation (pp-RPA). In hh-TDA, the N-electron electronic states are obtained through double annihilations starting from a doubly anionic (N+2 electron) reference state. In this way, hh-TDA treats ground and excited states on equal footing, thus allowing for conical intersections to be correctly described. The treatment of dynamic correlation is introduced through the use of commonly employed density functional approximations to the exchange-correlation potential. We show that hh-TDA is a promising candidate to efficiently treat the photochemistry of organic and biochemical systems that involve several low-lying excited states-particularly those with both low-lying ππ* and nπ* states where inclusion of dynamic correlation is essential to describe the relative energetics. In contrast to the existing literature on pp-TDA and pp-RPA, we employ a functional-dependent choice for the response kernel in pp- and hh-TDA, which closely resembles the response kernels occurring in linear response and collinear spin-flip TDDFT.
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Affiliation(s)
- Christoph Bannwarth
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
| | - Jimmy K Yu
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
| | - Edward G Hohenstein
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
| | - Todd J Martínez
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
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9
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Zhang IY, Xu X. On the top rung of Jacob's ladder of density functional theory: Toward resolving the dilemma of
SIE
and
NCE. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2020. [DOI: 10.1002/wcms.1490] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Igor Ying Zhang
- Shanghai Key Laboratory of Molecular Catalysis and Innovation Materials, Collaborative Innovation Centre of Chemistry for Energy Materials, MOE Laboratory for Computational Physical Science, Department of Chemistry Fudan University Shanghai China
| | - Xin Xu
- Shanghai Key Laboratory of Molecular Catalysis and Innovation Materials, Collaborative Innovation Centre of Chemistry for Energy Materials, MOE Laboratory for Computational Physical Science, Department of Chemistry Fudan University Shanghai China
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10
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Mei Y, Yang W. Charge transfer excitation energies from ground state density functional theory calculations. J Chem Phys 2019; 150:144109. [PMID: 30981264 DOI: 10.1063/1.5087883] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Calculating charge transfer (CT) excitation energies with high accuracy and low computational cost is a challenging task. Kohn-Sham density functional theory (KS-DFT), due to its efficiency and accuracy, has achieved great success in describing ground state problems. To extend to excited state problems, our group recently demonstrated an approach with good numerical results to calculate low-lying and Rydberg excitation energies of an N-electron system from a ground state KS or generalized KS calculations of an (N - 1)-electron system via its orbital energies. In the present work, we explore further the same methodology to describe CT excitations. Numerical results from this work show that performance of conventional density functional approximations (DFAs) is not as good for CT excitations as for other excitations due to the delocalization error. Applying localized orbital scaling correction (LOSC) to conventional DFAs, a recently developed method in our group to effectively reduce the delocalization error, can improve the results. Overall, the performance of this methodology is better than time dependent DFT (TDDFT) with conventional DFAs. In addition, it shows that results from LOSC-DFAs in this method reach similar accuracy to other methods, such as ΔSCF, G0W0 with Bethe-Salpeter equations, particle-particle random phase approximation, and even high-level wavefunction methods like CC2. Our analysis shows that the correct 1/R trend for CT excitation can be captured from LOSC-DFA calculations, stressing that the application of DFAs with the minimal delocalization error is essential within this methodology. This work provides an efficient way to calculate CT excitation energies from ground state DFT.
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Affiliation(s)
- Yuncai Mei
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
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11
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Describing strong correlation with fractional-spin correction in density functional theory. Proc Natl Acad Sci U S A 2018; 115:9678-9683. [PMID: 30201706 DOI: 10.1073/pnas.1807095115] [Citation(s) in RCA: 38] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
An effective fractional-spin correction is developed to describe static/strong correlation in density functional theory. Combined with the fractional-charge correction from recently developed localized orbital scaling correction (LOSC), a functional, the fractional-spin LOSC (FSLOSC), is proposed. FSLOSC, a correction to commonly used functional approximations, introduces the explicit derivative discontinuity and largely restores the flat-plane behavior of electronic energy at fractional charges and fractional spins. In addition to improving results from conventional functionals for the prediction of ionization potentials, electron affinities, quasiparticle spectra, and reaction barrier heights, FSLOSC properly describes the dissociation of ionic species, single bonds, and multiple bonds without breaking space or spin symmetry and corrects the spurious fractional-charge dissociation of heteroatom molecules of conventional functionals. Thus, FSLOSC demonstrates success in reducing delocalization error and including strong correlation, within low-cost density functional approximation.
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12
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Sutton C, Yang Y, Zhang D, Yang W. Single, Double Electronic Excitations and Exciton Effective Conjugation Lengths in π-Conjugated Systems. J Phys Chem Lett 2018; 9:4029-4036. [PMID: 29939751 PMCID: PMC6205815 DOI: 10.1021/acs.jpclett.8b01366] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The 21Ag and 11Bu excited states of two prototypical π-conjugated compounds, polyacetylene and polydiacetylene, are investigated with the recently developed particle-particle random phase approximation (pp-RPA) method combined with the B3LYP functional. The polymer-limit transition energies are estimated as 1.38 and 1.72 eV for the 21Ag and 11Bu states, respectively, from an extrapolation of the computed excitation energies of model oligomers. These values increase to 1.95 and 2.24 eV for the same transitions when ground-state structures with ∼33% larger bond length alternation are adopted. Applying the pp-RPA to the vertical excitation energies in oligodiacetylene, the polymer-limit transition energies of the 21Ag and 11Bu states are computed to be 2.06 and 2.28 eV, respectively. These results are in good agreement with experimental values or theoretical best estimates, indicating that the pp-RPA method shows great promise for understanding many photophysical phenomena involving both single and double excitations.
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Affiliation(s)
- Christopher Sutton
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Yang Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Du Zhang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Department of Physics, 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 510631, China
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13
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Yang Y, Culpitt T, Hammes-Schiffer S. Multicomponent Time-Dependent Density Functional Theory: Proton and Electron Excitation Energies. J Phys Chem Lett 2018; 9:1765-1770. [PMID: 29553738 DOI: 10.1021/acs.jpclett.8b00547] [Citation(s) in RCA: 43] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The quantum mechanical treatment of both electrons and protons in the calculation of excited state properties is critical for describing nonadiabatic processes such as photoinduced proton-coupled electron transfer. Multicomponent density functional theory enables the consistent quantum mechanical treatment of more than one type of particle and has been implemented previously for studying ground state molecular properties within the nuclear-electronic orbital (NEO) framework, where all electrons and specified protons are treated quantum mechanically. To enable the study of excited state molecular properties, herein the linear response multicomponent time-dependent density functional theory (TDDFT) is derived and implemented within the NEO framework. Initial applications to FHF- and HCN illustrate that NEO-TDDFT provides accurate proton and electron excitation energies within a single calculation. As its computational cost is similar to that of conventional electronic TDDFT, the NEO-TDDFT approach is promising for diverse applications, particularly nonadiabatic proton transfer reactions, which may exhibit mixed electron-proton vibronic excitations.
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Affiliation(s)
- Yang Yang
- 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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14
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Pinter B, Chankisjijev A, Geerlings P, Harvey JN, De Proft F. Conceptual Insights into DFT Spin-State Energetics of Octahedral Transition-Metal Complexes through a Density Difference Analysis. Chemistry 2017; 24:5281-5292. [PMID: 29114944 DOI: 10.1002/chem.201704657] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2017] [Indexed: 11/08/2022]
Abstract
In this study, an intuitive concept is derived, which explains the characteristic dependence of spin-state energetics on the exact exchange admixture of DFT functionals in the case of octahedral transition metal complexes. The change in electron density distributions upon varying the admixture, c3 , in the B3LYP functional is analyzed for archetype ionic and covalent systems as well as for the Fe2+ ion in an ideal octahedral field. An understanding of how the DFT description of the electronic structure of octahedral complexes changes as a function of c3 is sought. A systematic spin-state energy analysis of 50 octahedral complexes of various metals and ligands with consistent experimental data is presented, allowing the derivation, in theory, of an optimal c3 value for each system. The notion that the admixture dependence of DFT spin-state energetics stems from the treatment of nondynamic electrons arising from the mixing of (M-Lz2 )0 (dz2 )2 and (M-Lx2-y2 )0 (dx2-y2 )2 configurations into the dominant (M-Lx2-y2 )2 (dx2-y2 )0 and (M-Lx2-y2 )2 (dx2-y2 )0 ones in the low(er) spin states is put forward. That is, in the effort to mimic such electron-electron interactions, ExLDA overestimates, whereas exact exchange downplays the contribution of this type of electron correlation to the stability of low(er) spin states, leading to the widespread practical observation that the higher the exact exchange admixture, the more stable the high-spin-state configuration.
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Affiliation(s)
- Balazs Pinter
- Eenheid Algemene Chemie, Vrije Universiteit Brussel, Faculteit Wetenschappen, Pleinlaan 2, 1050, Brussels, Belgium
| | - Artiom Chankisjijev
- Eenheid Algemene Chemie, Vrije Universiteit Brussel, Faculteit Wetenschappen, Pleinlaan 2, 1050, Brussels, Belgium
| | - Paul Geerlings
- Eenheid Algemene Chemie, Vrije Universiteit Brussel, Faculteit Wetenschappen, Pleinlaan 2, 1050, Brussels, Belgium
| | - Jeremy N Harvey
- Department of Chemistry, KU Leuven, Celestijnenlaan 200F, 3001, Leuven, Belgium
| | - Frank De Proft
- Eenheid Algemene Chemie, Vrije Universiteit Brussel, Faculteit Wetenschappen, Pleinlaan 2, 1050, Brussels, Belgium
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15
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Sinha Ray S, Manna S, Chaudhuri RK, Chattopadhyay S. Description of C2 dissociation using a naive treatment of dynamical correlation in the presence of quasidegeneracy of varying degree. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1323129] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Suvonil Sinha Ray
- Department of Chemistry, Indian Institute of Engineering Science and Technology, Howrah, India
| | - Shovan Manna
- Department of Chemistry, Indian Institute of Engineering Science and Technology, Howrah, India
| | | | - Sudip Chattopadhyay
- Department of Chemistry, Indian Institute of Engineering Science and Technology, Howrah, India
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16
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Chen GP, Voora VK, Agee MM, Balasubramani SG, Furche F. Random-Phase Approximation Methods. Annu Rev Phys Chem 2017; 68:421-445. [DOI: 10.1146/annurev-physchem-040215-112308] [Citation(s) in RCA: 88] [Impact Index Per Article: 12.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Guo P. Chen
- Department of Chemistry, University of California, Irvine, California 92697-2025;,
| | - Vamsee K. Voora
- Department of Chemistry, University of California, Irvine, California 92697-2025;,
| | - Matthew M. Agee
- Department of Chemistry, University of California, Irvine, California 92697-2025;,
| | | | - Filipp Furche
- Department of Chemistry, University of California, Irvine, California 92697-2025;,
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17
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Yang Y, Dominguez A, Zhang D, Lutsker V, Niehaus TA, Frauenheim T, Yang W. Charge transfer excitations from particle-particle random phase approximation—Opportunities and challenges arising from two-electron deficient systems. J Chem Phys 2017; 146:124104. [DOI: 10.1063/1.4977928] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yang Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Adriel Dominguez
- Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
| | - Du Zhang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Vitalij Lutsker
- Department of Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany
| | - Thomas A. Niehaus
- Université Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622 Villeurbanne, France
| | - Thomas Frauenheim
- Bremen Center for Computational Materials Science, Universität Bremen, Am Fallturm, 28359 Bremen, Germany
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
- Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education, School of Chemistry and Environment, South China Normal University, Guangzhou 510006, China
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18
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Kranz JJ, Elstner M, Aradi B, Frauenheim T, Lutsker V, Garcia AD, Niehaus TA. Time-Dependent Extension of the Long-Range Corrected Density Functional Based Tight-Binding Method. J Chem Theory Comput 2017; 13:1737-1747. [PMID: 28272887 DOI: 10.1021/acs.jctc.6b01243] [Citation(s) in RCA: 60] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
We present a consistent linear response formulation of the density functional based tight-binding method for long-range corrected exchange-correlation functionals (LC-DFTB). Besides a detailed account of derivation and implementation of the method, we also test the new scheme on a variety of systems considered to be problematic for conventional local/semilocal time-dependent density functional theory (TD-DFT). To this class belong the optical properties of polyacenes and nucleobases, as well as charge transfer excited states in molecular dimers. We find that the approximate LC-DFTB method exhibits the same general trends and similar accuracy as range-separated DFT methods at significantly reduced computational cost. The scheme should be especially useful in the determination of the electronic excited states of very large molecules, for which conventional TD-DFT is supposed to fail due to a multitude of artificial low energy states.
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Affiliation(s)
- Julian J Kranz
- Institute of Physical Chemistry and Institute of Biological Interfaces (IBG-2), Karlsruhe Institute of Technology , Kaiserstrasse 12, 76131 Karlsruhe, Germany
| | - Marcus Elstner
- Institute of Physical Chemistry and Institute of Biological Interfaces (IBG-2), Karlsruhe Institute of Technology , Kaiserstrasse 12, 76131 Karlsruhe, Germany
| | - Bálint Aradi
- BCCMS, University of Bremen , 28359 Bremen, Germany
| | | | - Vitalij Lutsker
- Department of Theoretical Physics, University of Regensburg , 93040 Regensburg, Germany
| | - Adriel Dominguez Garcia
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Thomas A Niehaus
- Université Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622 Lyon, France
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19
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Abstract
Higher acenes have drawn much attention as promising organic semiconductors with versatile electronic properties. However, the nature of their ground state and electronic excited states is still not fully clear. Their unusual chemical reactivity and instability are the main obstacles for experimental studies, and the potentially prominent diradical character, which might require a multireference description in such large systems, hinders theoretical investigations. Here, we provide a detailed answer with the particle-particle random-phase approximation calculation. The (1)Ag ground states of acenes up to decacene are on the closed-shell side of the diradical continuum, whereas the ground state of undecacene and dodecacene tilts more to the open-shell side with a growing polyradical character. The ground state of all acenes has covalent nature with respect to both short and long axes. The lowest triplet state (3)B2u is always above the singlet ground state even though the energy gap could be vanishingly small in the polyacene limit. The bright singlet excited state (1)B2u is a zwitterionic state to the short axis. The excited (1)Ag state gradually switches from a double-excitation state to another zwitterionic state to the short axis, but always keeps its covalent nature to the long axis. An energy crossing between the (1)B2u and excited (1)Ag states happens between hexacene and heptacene. Further energetic consideration suggests that higher acenes are likely to undergo singlet fission with a low photovoltaic efficiency; however, the efficiency might be improved if a singlet fission into multiple triplets could be achieved.
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20
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Yang Y, Burke K, Yang W. Accurate atomic quantum defects from particle–particle random phase approximation. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1123316] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Yang Yang
- Department of Chemistry, Duke University, Durham, NC, USA
| | - Kieron Burke
- Department of Chemistry, University of California, Irvine, CA, USA
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, NC, USA
- Department of Physics, Duke University, Durham, NC, USA
- Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education, School of Chemistry and Environment, South China Normal University, Guangzhou, China
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21
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Kong J, Proynov E. Density Functional Model for Nondynamic and Strong Correlation. J Chem Theory Comput 2015; 12:133-43. [DOI: 10.1021/acs.jctc.5b00801] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jing Kong
- Department of Chemistry and
Center for Computational Sciences, Middle Tennessee State University, 1301 Main Street, Murfreesboro, Tennessee 37130, United States
| | - Emil Proynov
- Department of Chemistry and
Center for Computational Sciences, Middle Tennessee State University, 1301 Main Street, Murfreesboro, Tennessee 37130, United States
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22
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Klimeš J, Kaltak M, Maggio E, Kresse G. Singles correlation energy contributions in solids. J Chem Phys 2015; 143:102816. [PMID: 26374009 DOI: 10.1063/1.4929346] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The random phase approximation to the correlation energy often yields highly accurate results for condensed matter systems. However, ways how to improve its accuracy are being sought and here we explore the relevance of singles contributions for prototypical solid state systems. We set out with a derivation of the random phase approximation using the adiabatic connection and fluctuation dissipation theorem, but contrary to the most commonly used derivation, the density is allowed to vary along the coupling constant integral. This yields results closely paralleling standard perturbation theory. We re-derive the standard singles of Görling-Levy perturbation theory [A. Görling and M. Levy, Phys. Rev. A 50, 196 (1994)], highlight the analogy of our expression to the renormalized singles introduced by Ren and coworkers [Phys. Rev. Lett. 106, 153003 (2011)], and introduce a new approximation for the singles using the density matrix in the random phase approximation. We discuss the physical relevance and importance of singles alongside illustrative examples of simple weakly bonded systems, including rare gas solids (Ne, Ar, Xe), ice, adsorption of water on NaCl, and solid benzene. The effect of singles on covalently and metallically bonded systems is also discussed.
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Affiliation(s)
- Jiří Klimeš
- Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, CZ-12116 Prague 2, Czech Republic
| | - Merzuk Kaltak
- Faculty of Physics and Center for Computational Materials Science, University of Vienna, Sensengasse 8/12, A-1090 Vienna, Austria
| | - Emanuele Maggio
- Faculty of Physics and Center for Computational Materials Science, University of Vienna, Sensengasse 8/12, A-1090 Vienna, Austria
| | - Georg Kresse
- Faculty of Physics and Center for Computational Materials Science, University of Vienna, Sensengasse 8/12, A-1090 Vienna, Austria
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23
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Peng D, Yang Y, Zhang P, Yang W. Restricted second random phase approximations and Tamm-Dancoff approximations for electronic excitation energy calculations. J Chem Phys 2015; 141:214102. [PMID: 25481124 DOI: 10.1063/1.4901716] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N(4)). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as ⟨Ŝ(2)⟩ are also developed and tested.
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Affiliation(s)
- Degao Peng
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Yang Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Peng Zhang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Weitao Yang
- Department of Chemistry and Department of Physics, Duke University, Durham, North Carolina 27708, USA
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24
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Yang Y, Peng D, Davidson ER, Yang W. Singlet–Triplet Energy Gaps for Diradicals from Particle–Particle Random Phase Approximation. J Phys Chem A 2015; 119:4923-32. [DOI: 10.1021/jp512727a] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Affiliation(s)
| | | | - Ernest R. Davidson
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Weitao Yang
- Key
Laboratory of Theoretical Chemistry of Environment, Ministry of Education,
School of Chemistry and Environment, South China Normal University, Guangzhou 510006, China
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25
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Affiliation(s)
- Aurora Pribram-Jones
- Department of Chemistry, University of California, Irvine, California 92697-2025;
| | - David A. Gross
- Department of Chemistry, University of California, Irvine, California 92697-2025;
| | - Kieron Burke
- Department of Chemistry, University of California, Irvine, California 92697-2025;
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26
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Yang Y, Peng D, Lu J, Yang W. Excitation energies from particle-particle random phase approximation: Davidson algorithm and benchmark studies. J Chem Phys 2014; 141:124104. [DOI: 10.1063/1.4895792] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yang Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Degao Peng
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Jianfeng Lu
- Department of Mathematics, Department of Chemistry, and Department of Physics, Duke University, Durham, North Carolina 27708, USA
| | - Weitao Yang
- Department of Chemistry and Department of Physics, Duke University, Durham, North Carolina 27708, USA and Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education, School of Chemistry and Environment, South China Normal University, Guangzhou 510006, China
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27
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Shenvi N, van Aggelen H, Yang Y, Yang W. Tensor hypercontracted ppRPA: Reducing the cost of the particle-particle random phase approximation from O(r 6) to O(r 4). J Chem Phys 2014; 141:024119. [DOI: 10.1063/1.4886584] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Affiliation(s)
- Neil Shenvi
- Department of Chemistry, Duke University, Durham, NC 27708, USA
| | - Helen van Aggelen
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - Yang Yang
- Department of Chemistry, Duke University, Durham, NC 27708, USA
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, NC 27708, USA
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