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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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Mester D, Kállay M. Vertical Ionization Potentials and Electron Affinities at the Double-Hybrid Density Functional Level. J Chem Theory Comput 2023; 19:3982-3995. [PMID: 37326360 PMCID: PMC10339736 DOI: 10.1021/acs.jctc.3c00363] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Indexed: 06/17/2023]
Abstract
The double-hybrid (DH) time-dependent density functional theory is extended to vertical ionization potentials (VIPs) and electron affinities (VEAs). Utilizing the density fitting approximation, efficient implementations are presented for the genuine DH ansatz relying on the perturbative second-order correction, while an iterative analogue is also elaborated using our second-order algebraic-diagrammatic construction [ADC(2)]-based DH approach. The favorable computational requirements of the present schemes are discussed in detail. The performance of the recently proposed spin-component-scaled and spin-opposite-scaled (SOS) range-separated (RS) and long-range corrected (LC) DH functionals is comprehensively assessed, while popular hybrid and global DH approaches are also discussed. For the benchmark calculations, up-to-date test sets are selected with high-level coupled-cluster references. Our results show that the ADC(2)-based SOS-RS-PBE-P86 approach is the most accurate and robust functional. This method consistently outperforms the excellent SOS-ADC(2) approach for VIPs, although the results are somewhat less satisfactory for VEAs. Among the genuine DH functionals, the SOS-ωPBEPP86 approach is also recommended for describing ionization processes, but its performance is even less reliable for electron-attached states. In addition, surprisingly good results are attained by the LC hybrid ωB97X-D functional, where the corresponding occupied (unoccupied) orbital energies are retrieved as VIPs (VEAs) within the present formalism.
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Affiliation(s)
- Dávid Mester
- Department
of Physical Chemistry and Materials Science, Faculty of Chemical Technology
and Biotechnology, Budapest University of
Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- ELKH-BME
Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- MTA-BME
Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
| | - Mihály Kállay
- Department
of Physical Chemistry and Materials Science, Faculty of Chemical Technology
and Biotechnology, Budapest University of
Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- ELKH-BME
Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- MTA-BME
Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
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3
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Su NQ, Xu X. Perturbation theory made efficient and effective for predictions of ionization potential and electron affinity. J Chem Phys 2021; 154:174101. [PMID: 34241082 DOI: 10.1063/5.0047956] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
Ionization potential and electron affinity are essential molecular properties. The most straightforward method is to calculate them by taking the total energy differences of the initial and final states according to the definition. However, it often suffers from a serious convergence problem due to the requirement of the self-consistent field (SCF) calculations for the ionic states with non-Aufbau choices of occupations. In the present work, we have constructed a theoretical framework in view of perturbation theory to bypass the SCF calculations of the ionic states. To address the imbalance issue that arises from the precisely treated neutral ground state followed by the truncated perturbative treatment of the ionic states, an accurate yet effective method has been developed here, which adds back some terms from the higher order perturbations into the lower order to cancel out the most computationally cost terms in the truncated expansion, thus reaching a better convergence with less computation. The validity of the present methodology has been tested out by applying it to the Hartree-Fock (HF) method in combination with the correlation effect described at the second-order Møller-Plesset level in a frozen-orbital approximation. All the derivations in this work are given in a general framework, which are applicable not only to HF but also to a wide range of density functional theory methods from semi-local functionals to hybrid and doubly hybrid functionals.
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Affiliation(s)
- Neil Qiang Su
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, China
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4
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Gu Y, Xu X. Extended Koopmans’ theorem in the adiabatic connection formalism: Applied to doubly hybrid density functionals. J Chem Phys 2020; 153:044109. [DOI: 10.1063/5.0010743] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yonghao Gu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, China
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5
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Gu Y, Xu X. Extended Koopmans' theorem at the second‐order perturbation theory. J Comput Chem 2020; 41:1165-1174. [DOI: 10.1002/jcc.26163] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2019] [Revised: 01/12/2020] [Accepted: 01/18/2020] [Indexed: 11/09/2022]
Affiliation(s)
- Yonghao Gu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative MaterialsMinistry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University Shanghai China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative MaterialsMinistry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University Shanghai China
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6
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Amati M, Stoia S, Baerends EJ. The Electron Affinity as the Highest Occupied Anion Orbital Energy with a Sufficiently Accurate Approximation of the Exact Kohn-Sham Potential. J Chem Theory Comput 2020; 16:443-452. [PMID: 31794657 PMCID: PMC6964414 DOI: 10.1021/acs.jctc.9b00981] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
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Negative ions are not accurately represented in density
functional
approximations (DFAs) such as (semi)local density functionals (LDA
or GGA or meta-GGA). This is caused by the much too high orbital energies
(not negative enough) with these DFAs compared to the exact Kohn–Sham
values. Negative ions very often have positive DFA HOMO energies,
hence they are unstable. These problems do not occur with the exact
Kohn–Sham potential, the anion HOMO energy then being equal
to minus the electron affinity. It is therefore desirable to develop
sufficiently accurate approximations to the exact Kohn–Sham
potential. There are further beneficial effects on the orbital shapes
and the density of using a good approximation to the exact KS potential.
Notably the unoccupied orbitals are not unduly diffuse, as they are
in the Hartree–Fock model, with hybrid functionals, and even
with (semi)local density functional approximations (LDFAs). We show
that the recently developed B-GLLB-VWN approximation [Gritsenko et
al. J. Chem. Phys.2016, 144, 204114] to the exact KS potential affords stable negative ions
with HOMO orbital energy close to minus the electron affinity.
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Affiliation(s)
- M Amati
- Università degli Studi della Basilicata , Viale dell'Ateneo Lucano 10 , 85100 Potenza , Italy
| | - S Stoia
- Università degli Studi della Basilicata , Viale dell'Ateneo Lucano 10 , 85100 Potenza , Italy
| | - E J Baerends
- Sectie Theoretische Chemie, FEW , Vrije Universiteit , De Boelelaan 1083 , 1081 HV Amsterdam , The Netherlands
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Gu Y, Xu X. A correlation–relaxation-balanced direct method at the second order perturbation theory for accurate ionization potential predictions. Phys Chem Chem Phys 2020; 22:22342-22348. [DOI: 10.1039/d0cp03430d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
With almost no extra computational cost after a normal MP2 procedure, the CRB-MP2 method proposed here yields high quality valence and core IPs for a wide range of species.
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Affiliation(s)
- Yonghao Gu
- Collaborative Innovation Center of Chemistry for Energy Materials
- Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials
- Ministry of Education Key Laboratory of Computational Physical Sciences
- Department of Chemistry
- Fudan University
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials
- Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials
- Ministry of Education Key Laboratory of Computational Physical Sciences
- Department of Chemistry
- Fudan University
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8
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Su NQ, Xu X. Insights into Direct Methods for Predictions of Ionization Potential and Electron Affinity in Density Functional Theory. J Phys Chem Lett 2019; 10:2692-2699. [PMID: 31059262 DOI: 10.1021/acs.jpclett.9b01052] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Vertical ionization potential (IP) and electron affinity (EA) are fundamental molecular properties, while the Δ method and the direct method are the widely used approaches to compute these properties. The Δ method is calculated by taking the total energy difference of the initial and final states, whose reliability is seriously affected by the issue associated with the imbalanced treatment of these two states. The direct method based on the derivatives involving only one single-state calculation can yield a quasi-particle spectrum whose accuracy, on the other hand, is mostly affected by the levels of approximate molecular structure theories. Because of the aforementioned issues, EA prediction can be particularly problematic. Here we present, for the first time, an analytic theory on the derivation and realization of generalized Kohn-Sham (KS) eigenvalues of doubly hybrid (DH) functionals that depend on both occupied and unoccupied orbitals. The method based on the KS eigenvalues of neutral systems, termed the NKS method, is found to suffer little from the imbalance issue, while it is only the NKS method that can offer accurate EA prediction from a good functional approximation, such as the XYG3 type of DH functionals. Being less sensitive to the size of basis sets, the NKS method is of great significance for its application to large systems. The insights gained in this work are useful for the calculation of properties associated with small energy differences while emphasizing the importance of the development of generalized functionals that rely on both occupied and unoccupied orbitals.
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Affiliation(s)
- Neil Qiang Su
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry , Fudan University , Shanghai 200433 , China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry , Fudan University , Shanghai 200433 , China
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9
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Hirata S, Doran AE, Knowles PJ, Ortiz JV. One-particle many-body Green’s function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms. J Chem Phys 2017; 147:044108. [DOI: 10.1063/1.4994837] [Citation(s) in RCA: 44] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Alexander E. Doran
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Peter J. Knowles
- School of Chemistry, Cardiff University, Park Place, Cardiff CF10 3AT, United Kingdom
| | - J. V. Ortiz
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, USA
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10
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Zhang D, Su NQ, Yang W. Accurate Quasiparticle Spectra from the T-Matrix Self-Energy and the Particle-Particle Random Phase Approximation. J Phys Chem Lett 2017; 8:3223-3227. [PMID: 28654275 DOI: 10.1021/acs.jpclett.7b01275] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The GW self-energy, especially G0W0 based on the particle-hole random phase approximation (phRPA), is widely used to study quasiparticle (QP) energies. Motivated by the desirable features of the particle-particle (pp) RPA compared to the conventional phRPA, we explore the pp counterpart of GW, that is, the T-matrix self-energy, formulated with the eigenvectors and eigenvalues of the ppRPA matrix. We demonstrate the accuracy of the T-matrix method for molecular QP energies, highlighting the importance of the pp channel for calculating QP spectra.
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Affiliation(s)
- Du Zhang
- Department of Chemistry, Duke University , Durham, North Carolina 27708, United States
| | - Neil Qiang Su
- 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
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11
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Su NQ, Xu X. The XYG3 type of doubly hybrid density functionals. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2016. [DOI: 10.1002/wcms.1274] [Citation(s) in RCA: 43] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Neil Qiang Su
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry; Fudan University; Shanghai 200433 China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry; Fudan University; Shanghai 200433 China
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12
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Su NQ, Xu X. Second-Order Perturbation Theory for Fractional Occupation Systems: Applications to Ionization Potential and Electron Affinity Calculations. J Chem Theory Comput 2016; 12:2285-97. [DOI: 10.1021/acs.jctc.6b00197] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Neil Qiang Su
- Collaborative Innovation
Center of Chemistry for Energy Materials, Shanghai Key Laboratory
of Molecular Catalysis and Innovative Materials, MOE Laboratory for
Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200433, China
| | - Xin Xu
- Collaborative Innovation
Center of Chemistry for Energy Materials, Shanghai Key Laboratory
of Molecular Catalysis and Innovative Materials, MOE Laboratory for
Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200433, China
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13
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Su NQ, Xu X. Integration Approach at the Second-Order Perturbation Theory: Applications to Ionization Potential and Electron Affinity Calculations. J Chem Theory Comput 2015; 11:4677-88. [DOI: 10.1021/acs.jctc.5b00591] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Neil Qiang Su
- Collaborative Innovation
Center of Chemistry for Energy Materials, Shanghai Key Laboratory
of Molecular Catalysis and Innovative Materials, MOE Laboratory for
Computational Physical Science, Department of Chemistry, Fudan University, Shanghai, 200433, China
| | - Xin Xu
- Collaborative Innovation
Center of Chemistry for Energy Materials, Shanghai Key Laboratory
of Molecular Catalysis and Innovative Materials, MOE Laboratory for
Computational Physical Science, Department of Chemistry, Fudan University, Shanghai, 200433, China
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14
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Zhang D, Steinmann SN, Yang W. Dynamical second-order Bethe-Salpeter equation kernel: A method for electronic excitation beyond the adiabatic approximation. J Chem Phys 2013; 139:154109. [DOI: 10.1063/1.4824907] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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15
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Steinmann SN, Yang W. Wave function methods for fractional electrons. J Chem Phys 2013; 139:074107. [DOI: 10.1063/1.4817849] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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