1
|
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.
Collapse
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
| |
Collapse
|
2
|
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.
Collapse
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
| |
Collapse
|
3
|
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
| |
Collapse
|
4
|
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
| |
Collapse
|
5
|
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.
Collapse
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
| |
Collapse
|
6
|
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.
Collapse
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
| |
Collapse
|
7
|
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.
Collapse
|
8
|
Affiliation(s)
- Neil Qiang Su
- Collaborative Innovation Center of Chemistry for Energy Materials, Fudan University, Shanghai 200433, China
- Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Fudan University, Shanghai 200433, China
- MOE Key Laboratory of Computational Physical Sciences, Fudan University, Shanghai 200433, China
- Department of Chemistry, Fudan University, Shanghai 200433, China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Fudan University, Shanghai 200433, China
- Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Fudan University, Shanghai 200433, China
- MOE Key Laboratory of Computational Physical Sciences, Fudan University, Shanghai 200433, China
- Department of Chemistry, Fudan University, Shanghai 200433, China
| |
Collapse
|
9
|
Śmiga S, Franck O, Mussard B, Buksztel A, Grabowski I, Luppi E, Toulouse J. Self-consistent double-hybrid density-functional theory using the optimized-effective-potential method. J Chem Phys 2017; 145:144102. [PMID: 27782500 DOI: 10.1063/1.4964319] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We introduce an orbital-optimized double-hybrid (DH) scheme using the optimized-effective-potential (OEP) method. The orbitals are optimized using a local potential corresponding to the complete exchange-correlation energy expression including the second-order Møller-Plesset correlation contribution. We have implemented a one-parameter version of this OEP-based self-consistent DH scheme using the BLYP density-functional approximation and compared it to the corresponding non-self-consistent DH scheme for calculations on a few closed-shell atoms and molecules. While the OEP-based self-consistency does not provide any improvement for the calculations of ground-state total energies and ionization potentials, it does improve the accuracy of electron affinities and restores the meaning of the LUMO orbital energy as being connected to a neutral excitation energy. Moreover, the OEP-based self-consistent DH scheme provides reasonably accurate exchange-correlation potentials and correlated densities.
Collapse
Affiliation(s)
- Szymon Śmiga
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, 87-100 Torun, Poland
| | - Odile Franck
- Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, CNRS, Sorbonne Universités, F-75005 Paris, France
| | - Bastien Mussard
- Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, CNRS, Sorbonne Universités, F-75005 Paris, France
| | - Adam Buksztel
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, 87-100 Torun, Poland
| | - Ireneusz Grabowski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, 87-100 Torun, Poland
| | - Eleonora Luppi
- Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, CNRS, Sorbonne Universités, F-75005 Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, CNRS, Sorbonne Universités, F-75005 Paris, France
| |
Collapse
|
10
|
Su NQ, Pernot P, Xu X, Savin A. When does a functional correctly describe both the structure and the energy of the transition state? J Mol Model 2017; 23:65. [PMID: 28185112 DOI: 10.1007/s00894-017-3229-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2016] [Accepted: 01/12/2017] [Indexed: 11/30/2022]
Abstract
Requiring that several properties are well reproduced is a severe test on density functional approximations. This can be assessed through the estimation of joint and conditional success probabilities. An example is provided for a small set of molecules, for properties characterizing the transition states (geometries and energies).
Collapse
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
| | - Pascal Pernot
- CNRS, UMR8000, Laboratoire de Chimie Physique, F-91405, Orsay, France.,Univ. Paris-Sud, UMR8000, Laboratoire de Chimie Physique, F-91405, Orsay, France
| | - 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
| | - Andreas Savin
- CNRS, UMR7616, Laboratoire de Chimie Théorique, F-75005, Paris, France. .,UPMC Univ Paris 06, UMR7616, Laboratoire de Chimie Théorique, F-75005, Paris, France.
| |
Collapse
|
11
|
Mussard B, Toulouse J. Fractional-charge and fractional-spin errors in range-separated density-functional theory. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1213910] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Bastien Mussard
- Institut des sciences du calcul et des données, Université Pierre et Marie Curie, Sorbonne Universités, Paris, France
- Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, Sorbonne Universités, CNRS, Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, Sorbonne Universités, CNRS, Paris, France
| |
Collapse
|
12
|
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
| |
Collapse
|
13
|
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
| |
Collapse
|
14
|
Su NQ, Xu X. A comparative study of the xDH-PBE0 and DSD-PBEPBE-D3BJ doubly hybrid density functionals. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1129462] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Neil Qiang Su
- Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Laboratory for Computational Physical Science, Collaborative Innovation Center of Chemistry for Energy Materials, Department of Chemistry, Fudan University, Shanghai, China
| | - Xin Xu
- Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Laboratory for Computational Physical Science, Collaborative Innovation Center of Chemistry for Energy Materials, Department of Chemistry, Fudan University, Shanghai, China
| |
Collapse
|