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Marie A, Loos PF. Reference Energies for Valence Ionizations and Satellite Transitions. J Chem Theory Comput 2024; 20:4751-4777. [PMID: 38776293 PMCID: PMC11171335 DOI: 10.1021/acs.jctc.4c00216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2024] [Revised: 04/10/2024] [Accepted: 04/11/2024] [Indexed: 05/24/2024]
Abstract
Upon ionization of an atom or a molecule, another electron (or more) can be simultaneously excited. These concurrently generated states are called "satellites" (or shakeup transitions) as they appear in ionization spectra as higher-energy peaks with weaker intensity and larger width than the main peaks associated with single-particle ionizations. Satellites, which correspond to electronically excited states of the cationic species, are notoriously challenging to model using conventional single-reference methods due to their high excitation degree compared to the neutral reference state. This work reports 42 satellite transition energies and 58 valence ionization potentials (IPs) of full configuration interaction quality computed in small molecular systems. Following the protocol developed for the quest database [Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; and Loos, P.-F. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], these reference energies are computed using the configuration interaction using a perturbative selection made iteratively (CIPSI) method. In addition, the accuracy of the well-known coupled-cluster (CC) hierarchy (CC2, CCSD, CC3, CCSDT, CC4, and CCSDTQ) is gauged against these new accurate references. The performances of various approximations based on many-body Green's functions (GW, GF2, and T-matrix) for IPs are also analyzed. Their limitations in correctly modeling satellite transitions are discussed.
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Affiliation(s)
- Antoine Marie
- Laboratoire de Chimie et Physique
Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse 31062, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique
Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse 31062, France
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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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Yang X, Zheng X, Yang W. Density Functional Prediction of Quasiparticle, Excitation, and Resonance Energies of Molecules With a Global Scaling Correction Approach. Front Chem 2020; 8:588808. [PMID: 33425848 PMCID: PMC7793789 DOI: 10.3389/fchem.2020.588808] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2020] [Accepted: 09/23/2020] [Indexed: 11/13/2022] Open
Abstract
Molecular quasiparticle and excitation energies determine essentially the spectral characteristics measured in various spectroscopic experiments. Accurate prediction of these energies has been rather challenging for ground-state density functional methods, because the commonly adopted density function approximations suffer from delocalization error. In this work, by presuming a quantitative correspondence between the quasiparticle energies and the generalized Kohn–Sham orbital energies, and employing a previously developed global scaling correction approach, we achieve substantially improved prediction of molecular quasiparticle and excitation energies. In addition, we also extend our previous study on temporary anions in resonant states, which are associated with negative molecular electron affinities. The proposed approach does not require any explicit self-consistent field calculation on the excited-state species, and is thus highly efficient and convenient for practical purposes.
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Affiliation(s)
- Xiaolong Yang
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, China
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, NC, United States.,Key Laboratory of Theoretical Chemistry of Environment, School of Chemistry and Environment, South China Normal University, Guangzhou, China
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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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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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Muchová E, Slavíček P. Beyond Koopmans' theorem: electron binding energies in disordered materials. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:043001. [PMID: 30524069 DOI: 10.1088/1361-648x/aaf130] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The topical review focuses on calculating ionization energies (IE), or electronic polarons in quasi-particle terminology, in large disordered systems, e.g. for a solute dissolved in a molecular solvent. The simplest estimate of the ionization energy is provided by one-electron energies in the Hartree-Fock theory, but the calculated quantities are not accurate. Density functional theory as many-body theory provides a principal opportunity for calculating one-electron energies including correlation and relaxation effects, i.e. the true energies of electronic polarons. We argue that such a principal possibility materializes within the concept of optimally tuned range-separated hybrid functionals (OT-RSH). We describe various schemes for optimal tuning. Importantly, the OT-RSH scheme is investigated for systems capped with dielectric continuum, providing a consistent picture on the QM/dielectric boundary. Finally, some limitations and open issues of the OT-RSH approach are addressed.
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Affiliation(s)
- Eva Muchová
- Department of Physical Chemistry, University of Chemistry and Technology, Prague, Czech Republic
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Solov'ev VP, Ustynyuk YA, Zhokhova NI, Karpov KV. Predictive Models for HOMO and LUMO Energies of N-Donor Heterocycles as Ligands for Lanthanides Separation. Mol Inform 2018; 37:e1800025. [PMID: 29971949 DOI: 10.1002/minf.201800025] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2018] [Accepted: 06/20/2018] [Indexed: 11/11/2022]
Abstract
Quantum chemical calculations combined with QSPR methodology reveal challenging perspectives for the solution of a number of fundamental and applied problems. In this work, we performed the PM7 and DFT calculations and QSPR modeling of HOMO and LUMO energies for polydentate N-heterocyclic ligands promising for the extraction separation of lanthanides because these values are related to the ligands selectivity in the respect to the target cations. Data for QSPR modeling comprised the PM7 calculated HOMO and LUMO energies of N-donor heterocycles, including several types of both known and virtual undescribed polydentate ligands. Ensemble modeling included various molecular fragments as descriptors and different variable selection techniques to build consensus models (CMs) on a training set of 388 ligands using external cross-validation. CMs were then verified to make predictions for two external test sets: 45 ligands (T1) that were similar to the ligands of the training set, and 1546 structures (T2), which were substantially different from the ligands of the training set. The consensus models predict well in 5-fold cross-validation (RMSEHOMO =0.097 eV, RMSELUMO =0.064 eV), and on the external test sets (T1: RMSEHOMO =0.26 eV, RMSELUMO =0.24 eV; T2: RMSEHOMO =0.26 eV, RMSELUMO =0.17 eV). An analysis of the results reveals that substituents in heteroaromatic rings of the ligands and at the amide nitrogens can deeply influence their metal binding properties.
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Affiliation(s)
- Vitaly P Solov'ev
- A.N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Leninskiy prosp., 31, 119071, Moscow, Russia
| | - Yuri A Ustynyuk
- Chemistry Department, M.V. Lomonosov Moscow State University, 119991, Moscow, Russia
| | - Nelly I Zhokhova
- Faculty of Physics, M.V. Lomonosov Moscow State University, 119991, Moscow, Russia
| | - Kirill V Karpov
- Faculty of Physics, M.V. Lomonosov Moscow State University, 119991, Moscow, Russia
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Coons MP, Herbert JM. Quantum chemistry in arbitrary dielectric environments: Theory and implementation of nonequilibrium Poisson boundary conditions and application to compute vertical ionization energies at the air/water interface. J Chem Phys 2018; 148:222834. [DOI: 10.1063/1.5023916] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Affiliation(s)
- Marc P. Coons
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - John M. Herbert
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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