1
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Bartlett RJ. Perspective on Coupled-cluster Theory. The evolution toward simplicity in quantum chemistry. Phys Chem Chem Phys 2024; 26:8013-8037. [PMID: 38390989 DOI: 10.1039/d3cp03853j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/24/2024]
Abstract
Coupled-cluster theory has revolutionized quantum chemistry. It has provided the framework to effectively solve the problem of electron correlation, the main focus of the field for over 60 years. This has enabled ab initio quantum chemistry to provide predictive quality results for most quantities of interest that are obtainable from first-principle calculations. The best that one can do in a basis is the 'full CI,' the exact solution of the non-relativistic Schrödinger equation or, if need be, the relativistic Dirac equation. With due regard to converging the basis set and adequate consideration of higher clusters and relativity in a calculation, virtually predictive results can be obtained. But in addition to its numerical performance, coupled-cluster theory also offers a conceptually new, many-body foundation for the theory that should be appreciated by all practitioners. The latter is emphasized in this perspective, leading to the 'evolution toward simplicity' in the title. The ultimate theory will benefit from the several features that are uniquely exact in coupled-cluster theory and its equation-of-motion (EOM-CC) extensions.
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Affiliation(s)
- Rodney J Bartlett
- Quantum Theory Project, Department of Chemistry, University of Florida, P. O. Box 117200, Gainesville, Florida, USA.
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2
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Kanungo B, Kaplan AD, Shahi C, Gavini V, Perdew JP. Unconventional Error Cancellation Explains the Success of Hartree-Fock Density Functional Theory for Barrier Heights. J Phys Chem Lett 2024; 15:323-328. [PMID: 38170179 DOI: 10.1021/acs.jpclett.3c03088] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2024]
Abstract
Energy barriers, which control the rates of chemical reactions, are seriously underestimated by computationally efficient semilocal approximations for the exchange-correlation energy. The accuracy of a semilocal density functional approximation is strongly boosted for reaction barrier heights by evaluating that approximation non-self-consistently on Hartree-Fock electron densities, which has been known for ∼30 years. The conventional explanation is that the Hartree-Fock theory yields the more accurate density. This work presents a benchmark Kohn-Sham inversion of accurate coupled-cluster densities for the reaction H2 + F → HHF → H + HF and finds a strong, understandable cancellation between positive (excessively overcorrected) density-driven and large negative functional-driven errors (expected from stretched radical bonds in the transition state) within this Hartree-Fock density functional theory. This confirms earlier conclusions (Kaplan, A. D., et al. J. Chem. Theory Comput. 2023, 19, 532-543) based on 76 barrier heights and three less reliable, but less expensive, fully nonlocal density functional proxies for the exact density.
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Affiliation(s)
- Bikash Kanungo
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Aaron D Kaplan
- Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Chandra Shahi
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, United States
| | - Vikram Gavini
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - John P Perdew
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, United States
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3
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Pavlicek A, Windom ZW, Perera A, Bartlett RJ. A comparison of QTP functionals against coupled-cluster methods for EAs of small organic molecules. J Chem Phys 2024; 160:014106. [PMID: 38180255 DOI: 10.1063/5.0177136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2023] [Accepted: 12/19/2023] [Indexed: 01/06/2024] Open
Abstract
EA-EOM-CCSD electron affinities and LUMO energies of various Kohn-Sham density functional theory (DFT) methods are calculated for an a priori IP benchmark set of 64 small, closed-shell molecules. The purpose of these calculations was to investigate whether the QTP KS-DFT functionals can emulate EA-EOM-CC with only a mean-field approximation. We show that the accuracy of DFT-relative to CCSD-improves significantly when elements of correlated orbital theory are introduced into the parameterization to define the QTP family of functionals. In particular, QTP(02), which has only a single range separation parameter, provides results accurate to a MAD of <0.15 eV for the whole set of 64 molecules compared to EA-EOM-CCSD, far exceeding the results from the non-QTP family of density functionals.
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Affiliation(s)
- Abigail Pavlicek
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Zachary W Windom
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Ajith Perera
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Rodney J Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
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Manzhos S, Tsuda S, Ihara M. Machine learning in computational chemistry: interplay between (non)linearity, basis sets, and dimensionality. Phys Chem Chem Phys 2023; 25:1546-1555. [PMID: 36562317 DOI: 10.1039/d2cp04155c] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Machine learning (ML) based methods and tools have now firmly established themselves in physical chemistry and in particular in theoretical and computational chemistry and in materials chemistry. The generality of popular ML techniques such as neural networks or kernel methods (Gaussian process and kernel ridge regression and their flavors) permitted their application to diverse problems from prediction of properties of functional materials (catalysts, solid state ionic conductors, etc.) from descriptors to the building of interatomic potentials (where ML is currently routinely used in applications) and electron density functionals. These ML techniques are assumed to have superior expressive power of nonlinear methods, and are often used "as is", with concepts such as "non-parametric" or "deep learning" used without a clear justification for their need or advantage over simpler and more robust alternatives. In this Perspective, we highlight some interrelations between popular ML techniques and traditional linear regressions and basis expansions and demonstrate that in certain regimes (such as a very high dimensionality) these approximations might collapse. We also discuss ways to recover the expressive power of a nonlinear approach and to help select hyperparameters with the help of high-dimensional model representation and to obtain elements of insight while preserving the generality of the method.
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Affiliation(s)
- Sergei Manzhos
- School of Materials and Chemical Technology, Tokyo Institute of Technology, Ookayama 2-12-1, Meguro-ku, Tokyo 152-8552, Japan.
| | - Shunsaku Tsuda
- School of Materials and Chemical Technology, Tokyo Institute of Technology, Ookayama 2-12-1, Meguro-ku, Tokyo 152-8552, Japan.
| | - Manabu Ihara
- School of Materials and Chemical Technology, Tokyo Institute of Technology, Ookayama 2-12-1, Meguro-ku, Tokyo 152-8552, Japan.
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5
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Park YC, Perera A, Bartlett RJ. Density functionals for core excitations. J Chem Phys 2022; 157:094107. [PMID: 36075732 DOI: 10.1063/5.0111095] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The core excitation energies and related principal ionization energies are obtained for selected molecules using several density functionals and compared with benchmark equation-of-motion coupled cluster (EOM-CC) results. Both time-dependent and time-independent formulations of excitation spectra in the time-dependent density functional theory and the EOM-CC are employed to obtain excited states that are not always easily accessible with the time-independent method. Among those functionals, we find that the QTP(00) functional, which is only parameterized to reproduce the five IPs of water, provides excellent core IPs and core excitation energies, consistently yielding better excitation and ionization energies. We show that orbital eigenvalues of KS density functional theory play an important role in determining the accuracy of the excitation and photoelectron spectra.
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Affiliation(s)
- Young Choon Park
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435, USA
| | - Ajith Perera
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435, USA
| | - Rodney J Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435, USA
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6
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Hirao K, Bae HS, Song JW, Chan B. Vertical ionization potential benchmarks from Koopmans prediction of Kohn-Sham theory with long-range corrected (LC) functional. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:194001. [PMID: 35158348 DOI: 10.1088/1361-648x/ac54e3] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2021] [Accepted: 02/14/2022] [Indexed: 06/14/2023]
Abstract
The Kohn-Sham density functional theory (KS-DFT) with the long-range corrected (LC) functional is applied to the benchmark dataset of 401 valence ionization potentials (IPs) of 63 small molecules of Chong, Gritsenko and Baerends (the CGB set). The vertical IP of the CGB set are estimated as negative orbital energies within the context of the Koopmans' prediction using the LCgau-core range-separation scheme in combination with PW86-PW91 exchange-correlation functional. The range separation parameterμof the functional is tuned to minimize the error of the negative HOMO orbital energy from experimental IP. The results are compared with literature data, includingab initioIP variant of the equation-of-motion coupled cluster theory with singles and doubles (IP-EOM-CCSD), the negative orbital energies calculated by KS-DFT with the statistical averaging of orbital potential, and those with the QTP family of functionals. The optimally tuned LC functional performs better than other functionals for the estimation of valence level IP. The mean absolute deviations (MAD) from experiment and from IP-EOM-CCSD are 0.31 eV (1.77%) and 0.25 eV (1.46%), respectively. LCgau-core performs quite well even with fixedμ(not system-dependent). Aμvalue around 0.36 bohr-1gives MAD of 0.40 eV (2.42%) and 0.33 eV (1.96%) relative to experiment and IP-EOM-CCSD, respectively. The LCgau-core-PW86-PW91 functional is an efficient alternative to IP-EOM-CCSD and it is reasonably accurate for outer valence orbitals. We have also examined its application to core ionization energies of C(1s), N(1s), O(1s) and F(1s). The C(1s) core ionization energies are reproduced reasonably [MAD of 46 cases is 0.76 eV (0.26%)] but N(1s), O(1s) and F(1s) core ionization energies are predicted less accurately.
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Affiliation(s)
- Kimihiko Hirao
- Fukui Institute for Fundamental Chemistry, Kyoto University, Takano, Nishihiraki-cho 34-4, Sakyo-ku, Kyoto, 606-8103, Japan
- RIKEN Center for Computational Science, 7-1-26, Minatojima-minami-machi, Chuo-ku, Kobe, 650-0047, Japan
| | - Han-Seok Bae
- Department of Chemistry Education, Daegu University, Gyeongsan, 113-8656, Korea
| | - Jong-Won Song
- Department of Chemistry Education, Daegu University, Gyeongsan, 113-8656, Korea
| | - Bun Chan
- Graduate School of Engineering, Nagasaki University, Bunkyo 1-14, Nagasaki 852-8521, Japan
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7
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Mendes RA, Haiduke RLA, Bartlett RJ. The Devil's Triangle of Kohn-Sham density functional theory and excited states. J Chem Phys 2021; 154:074106. [PMID: 33607901 DOI: 10.1063/5.0035446] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Exchange-correlation (XC) functionals from Density Functional Theory (DFT) developed under the rigorous arguments of Correlated Orbital Theory (COT) address the Devil's Triangle of prominent errors in Kohn-Sham (KS) DFT. At the foundation of this triangle lie the incorrect one-particle spectrum, the lack of integer discontinuity, and the self-interaction error. At the top level, these failures manifest themselves in incorrect charge transfer and Rydberg excitation energies, along with poor activation barriers. Accordingly, the Quantum Theory Project (QTP) XC functionals have been created to address several of the long-term issues encountered in KS theory and its Time Dependent DFT (TDDFT) variant for electronic excitations. Recognizing that COT starts with a correct one-particle spectrum, a condition imposed on the QTP functionals by means of minimum parameterization, the question that arises is how does this affect the electronically excited states? Among up to 28 XC functionals considered, the QTP family provides one of the smallest mean absolute deviations for charge-transfer excitations while also showing excellent results for Rydberg states. However, there is some room for improvement in the case of excitation energies to valence states, which are systematically underestimated by all functionals investigated. An alternative path for better treatment of excitation energies, mainly for valence states, is offered by using orbital energies from QTP functionals, especially by CAM-QTP-02 and LC-QTP. In this case, the deviations from the reference data can be reduced approximately by half.
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Affiliation(s)
- Rodrigo A Mendes
- Departamento de Química e Física Molecular, Instituto de Química de São Carlos, Universidade de São Paulo, CP 780, 13560-970 São Carlos, SP, Brazil
| | - Roberto L A Haiduke
- Departamento de Química e Física Molecular, Instituto de Química de São Carlos, Universidade de São Paulo, CP 780, 13560-970 São Carlos, SP, Brazil
| | - Rodney J Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435, USA
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8
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Husch T, Sun J, Cheng L, Lee SJR, Miller TF. Improved accuracy and transferability of molecular-orbital-based machine learning: Organics, transition-metal complexes, non-covalent interactions, and transition states. J Chem Phys 2021; 154:064108. [DOI: 10.1063/5.0032362] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Affiliation(s)
- Tamara Husch
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Jiace Sun
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Lixue Cheng
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Sebastian J. R. Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Thomas F. Miller
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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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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Szepieniec MS, Greer JC. Electrode-molecule energy level offsets in a gold-benzene diamine-gold single molecule tunnel junction. J Chem Phys 2020; 153:174104. [PMID: 33167633 DOI: 10.1063/5.0024567] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
One means for describing electron transport across single molecule tunnel junctions (MTJs) is to use density functional theory (DFT) in conjunction with a nonequilibrium Green's function formalism. This description relies on interpreting solutions to the Kohn-Sham (KS) equations used to solve the DFT problem as quasiparticle (QP) states. Many practical DFT implementations suffer from electron self-interaction errors and an inability to treat charge image potentials for molecules near metal surfaces. For MTJs, the overall effect of these errors is typically manifested as an overestimation of electronic currents. Correcting KS energies for self-interaction and image potential errors results in MTJ current-voltage characteristics in close agreement with measured currents. An alternative transport approach foregoes a QP picture and solves for a many-electron wavefunction on the MTJ subject to open system boundary conditions. It is demonstrated that this many-electron method provides similar results to the corrected QP picture for electronic current. The analysis of these two distinct approaches is related through corrections to a junction's electronic structure beyond the KS energies for the case of a benzene diamine molecule bonded between two gold electrodes.
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Affiliation(s)
- Mark S Szepieniec
- Tyndall National Institute, University College Cork, Lee Maltings, Dyke Parade, Cork T12 R5CP, Ireland
| | - James C Greer
- Department of Electrical and Electronic Engineering, Nottingham Ningbo New Materials Institute, University of Nottingham Ningbo China, 199 Taikang East Road, Ningbo 315100, China
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Abstract
The attraction density functional theory (DFT) has for electronic structure theory is that it is easier to do computationally than ab initio, correlated wavefunction methods, due to its effective one-particle structure. On the contrary, ab initio theorists insist on the ability to converge to the right answer in appropriate limits, but this requires a treatment of the reduced two-particle density matrix. DFT avoids that by appealing to an "existence" theorem (not a constructive one) that all its effects are subsummed into a DFT functional of the one-particle density. However, the existence of thousands of DFT functionals emphasizes that there is no satisfactory way to systematically improve the Kohn-Sham (KS) version as most changes in parameterization or formulation seldom lead to a new functional that is genuinely better than others. Some researchers in the DFT community try to address this issue by imposing conditions rigorously derived from exact DFT considerations, but to date, no one has shown how this route will ever lead to converged results even for the ground state, much less for all the other electronic states obtained from time-dependent DFT that are critically important for chemistry. On the contrary, coupled-cluster (CC) theory and its equation-of-motion extensions provide rigorous results for both that KS-DFT methods are attempting to emulate. How to use them and their exact formal properties to tie CC theory to an effective one-particle form is the target of this perspective. This route addresses the devil's triangle of KS-DFT problems: the one-particle spectrum, self-interaction, and the integer discontinuity.
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Affiliation(s)
- Rodney J Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435, USA
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12
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Dittmer A, Izsák R, Neese F, Maganas D. Accurate Band Gap Predictions of Semiconductors in the Framework of the Similarity Transformed Equation of Motion Coupled Cluster Theory. Inorg Chem 2019; 58:9303-9315. [PMID: 31240911 PMCID: PMC6750750 DOI: 10.1021/acs.inorgchem.9b00994] [Citation(s) in RCA: 40] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
![]()
In
this work, we present a detailed comparison between wave-function-based
and particle/hole techniques for the prediction of band gap energies
of semiconductors. We focus on the comparison of the back-transformed
Pair Natural Orbital Similarity Transformed Equation of Motion Coupled-Cluster
(bt-PNO-STEOM-CCSD) method with Time Dependent Density Functional
Theory (TD-DFT) and Delta Self Consistent Field/DFT (Δ-SCF/DFT)
that are employed to calculate the band gap energies in a test set
of organic and inorganic semiconductors. Throughout, we have used
cluster models for the calculations that were calibrated by comparing
the results of the cluster calculations to periodic DFT calculations
with the same functional. These calibrations were run with cluster
models of increasing size until the results agreed closely with the
periodic calculation. It is demonstrated that bt-PNO-STEOM-CC yields
accurate results that are in better than 0.2 eV agreement with the
experiment. This holds for both organic and inorganic semiconductors.
The efficiency of the employed computational protocols is thoroughly
discussed. Overall, we believe that this study is an important contribution
that can aid future developments and applications of excited state
coupled cluster methods in the field of solid-state chemistry and
heterogeneous catalysis. In this work, it is shown
that a combination of the embedded cluster approach with wave-function-based
ab initio methods in the framework of the Similarity Transformed Equation
of Motion Coupled Cluster (bt-PNO STEOM-CC) provides an accurate protocol
for band gap energy predictions in classes of organic and inorganic
semiconductors.
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Affiliation(s)
- Anneke Dittmer
- Max-Planck-Institut für Kohlenforschung , Kaiser-Wilhelm-Platz 1 , 45470 Mülheim an der Ruhr , Germany
| | - Róbert Izsák
- Max-Planck-Institut für Kohlenforschung , Kaiser-Wilhelm-Platz 1 , 45470 Mülheim an der Ruhr , Germany
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung , Kaiser-Wilhelm-Platz 1 , 45470 Mülheim an der Ruhr , Germany
| | - Dimitrios Maganas
- Max-Planck-Institut für Kohlenforschung , Kaiser-Wilhelm-Platz 1 , 45470 Mülheim an der Ruhr , Germany
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Margraf JT, Dral PO. What is semiempirical molecular orbital theory approximating? J Mol Model 2019; 25:119. [DOI: 10.1007/s00894-019-4005-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2019] [Accepted: 03/21/2019] [Indexed: 01/13/2023]
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14
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Ranasinghe DS, Margraf JT, Perera A, Bartlett RJ. Vertical valence ionization potential benchmarks from equation-of-motion coupled cluster theory and QTP functionals. J Chem Phys 2019; 150:074108. [DOI: 10.1063/1.5084728] [Citation(s) in RCA: 34] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Duminda S. Ranasinghe
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Johannes T. Margraf
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
- Chair for Theoretical Chemistry, Technische Universität München, Lichtenbergstrasse 4, 85747 Garching, Germany
| | - Ajith Perera
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Rodney J. Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
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15
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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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16
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Pohl MN, Muchová E, Seidel R, Ali H, Sršeň Š, Wilkinson I, Winter B, Slavíček P. Do water's electrons care about electrolytes? Chem Sci 2019; 10:848-865. [PMID: 30774880 PMCID: PMC6346409 DOI: 10.1039/c8sc03381a] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2018] [Accepted: 11/01/2018] [Indexed: 01/01/2023] Open
Abstract
Ions have a profound effect on the geometrical structure of liquid water and an aqueous environment is known to change the electronic structure of ions. Here we combine photoelectron spectroscopy measurements from liquid microjets with molecular dynamical and quantum chemical calculations to address the reverse question, to what extent do ions affect the electronic structure of liquid water? We study aqueous solutions of sodium iodide (NaI) over a wide concentration range, from nearly pure water to 8 M solutions, recording spectra in the 5 to 60 eV binding energy range to include all water valence and the solute Na+ 2p, I- 4d, and I- 5p orbital ionization peaks. We observe that the electron binding energies of the solute ions change only slightly as a function of electrolyte concentration, less than 150 ± 60 meV over an ∼8 M range. Furthermore, the photoelectron spectrum of liquid water is surprisingly mildly affected as we transform the sample from a dilute aqueous salt solution to a viscous, crystalline-like phase. The most noticeable spectral changes are a negative binding energy shift of the water 1b2 ionizing transition (up to -370 ± 60 meV) and a narrowing of the flat-top shape water 3a1 ionization feature (up to 450 ± 90 meV). A novel computationally efficient technique is introduced to calculate liquid-state photoemission spectra using small clusters from molecular dynamics (MD) simulations embedded in dielectric continuum. This theoretical treatment captured the characteristic positions and structures of the aqueous photoemission peaks, reproducing the experimentally observed narrowing of the water 3a1 feature and weak sensitivity of the water binding energies to electrolyte concentration. The calculations allowed us to attribute the small binding energy shifts to ion-induced disruptions of intermolecular electronic interactions. Furthermore, they demonstrate the importance of considering concentration-dependent screening lengths for a correct description of the electronic structure of solvated systems. Accounting for electronic screening, the calculations highlight the minimal effect of electrolyte concentration on the 1b1 binding energy reference, in accord with the experiments. This leads us to a key finding that the isolated, lowest-binding-energy, 1b1, photoemission feature of liquid water is a robust energetic reference for aqueous liquid microjet photoemission studies.
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Affiliation(s)
- Marvin N Pohl
- Fritz-Haber-Institut der Max-Planck-Gesellschaft , Faradayweg 4-6 , D-14195 Berlin , Germany .
- Fachbereich Physik , Freie Universität Berlin , Arnimallee 14 , D-14195 Berlin , Germany
| | - Eva Muchová
- Department of Physical Chemistry , University of Chemistry and Technology , Technická 5 , 16628 Prague , Czech Republic .
| | - Robert Seidel
- Helmholtz-Zentrum Berlin für Materialien und Energie , Hahn-Meitner-Platz 1 , D-14109 Berlin , Germany .
- Humboldt-Universität zu Berlin , Department of Chemistry , Brook-Taylor-Str. 2 , D-12489 Berlin , Germany
| | - Hebatallah Ali
- Fritz-Haber-Institut der Max-Planck-Gesellschaft , Faradayweg 4-6 , D-14195 Berlin , Germany .
- Fachbereich Physik , Freie Universität Berlin , Arnimallee 14 , D-14195 Berlin , Germany
| | - Štěpán Sršeň
- Department of Physical Chemistry , University of Chemistry and Technology , Technická 5 , 16628 Prague , Czech Republic .
| | - Iain Wilkinson
- Helmholtz-Zentrum Berlin für Materialien und Energie , Hahn-Meitner-Platz 1 , D-14109 Berlin , Germany .
| | - Bernd Winter
- Fritz-Haber-Institut der Max-Planck-Gesellschaft , Faradayweg 4-6 , D-14195 Berlin , Germany .
| | - Petr Slavíček
- Department of Physical Chemistry , University of Chemistry and Technology , Technická 5 , 16628 Prague , Czech Republic .
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17
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Mei Y, Li C, Su NQ, Yang W. Approximating Quasiparticle and Excitation Energies from Ground State Generalized Kohn-Sham Calculations. J Phys Chem A 2019; 123:666-673. [PMID: 30589546 DOI: 10.1021/acs.jpca.8b10380] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Quasiparticle energies and fundamental band gaps in particular are critical properties of molecules and materials. It was rigorously established that the generalized Kohn-Sham HOMO and LUMO orbital energies are the chemical potentials of electron removal and addition and thus good approximations to band edges and fundamental gaps from a density functional approximation (DFA) with minimal delocalization error. For other quasiparticle energies, their connection to the generalized Kohn-Sham orbital energies has not been established but remains highly interesting. We provide the comparison of experimental quasiparticle energies for many finite systems with calculations from the GW Green function and localized orbitals scaling correction (LOSC), a recently developed correction to semilocal DFAs, which has minimal delocalization error. Extensive results with over 40 systems clearly show that LOSC orbital energies achieve slightly better accuracy than the GW calculations with little dependence on the semilocal DFA, supporting the use of LOSC DFA orbital energies to predict quasiparticle energies. This also leads to the calculations of excitation energies of the N-electron systems from the ground state DFA calculations of the ( N - 1)-electron systems. Results show good performance with accuracy similar to TDDFT and the delta SCF approach for valence excitations with commonly used DFAs with or without LOSC. For Rydberg states, good accuracy was obtained only with the use of LOSC DFA. This work highlights the pathway to quasiparticle and excitation energies from ground density functional calculations.
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Affiliation(s)
- Yuncai Mei
- Department of Chemistry , Duke University , Durham , North Carolina 27708 , United States
| | - Chen Li
- 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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18
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Mostafanejad M, Haney J, DePrince AE. Kinetic-energy-based error quantification in Kohn–Sham density functional theory. Phys Chem Chem Phys 2019; 21:26492-26501. [DOI: 10.1039/c9cp04595c] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present a basis-independent metric to assess the quality of the electron density obtained from Kohn–Sham (KS) density functional theory (DFT).
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Affiliation(s)
| | - Jessica Haney
- Department of Chemistry and Biochemistry
- Florida State University
- Tallahassee
- USA
| | - A. Eugene DePrince
- Department of Chemistry and Biochemistry
- Florida State University
- Tallahassee
- USA
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19
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Park YC, Perera A, Bartlett RJ. Low scaling EOM-CCSD and EOM-MBPT(2) method with natural transition orbitals. J Chem Phys 2018; 149:184103. [DOI: 10.1063/1.5045340] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Young Choon Park
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Ajith Perera
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Rodney J. Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
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20
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Jin Y, Bartlett RJ. Accurate computation of X-ray absorption spectra with ionization potential optimized global hybrid functional. J Chem Phys 2018; 149:064111. [DOI: 10.1063/1.5038434] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yifan Jin
- Quantum Theory Project, Departments of Chemistry and Physics, University of Florida, Gainesville, Florida 32611, USA
| | - Rodney J. Bartlett
- Quantum Theory Project, Departments of Chemistry and Physics, University of Florida, Gainesville, Florida 32611, USA
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21
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Ghosh S, Verma P, Cramer CJ, Gagliardi L, Truhlar DG. Combining Wave Function Methods with Density Functional Theory for Excited States. Chem Rev 2018; 118:7249-7292. [PMID: 30044618 DOI: 10.1021/acs.chemrev.8b00193] [Citation(s) in RCA: 135] [Impact Index Per Article: 22.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.
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Affiliation(s)
- Soumen Ghosh
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Pragya Verma
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Christopher J Cramer
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Laura Gagliardi
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
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22
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Margraf JT, Bartlett R. Communication: Coupled cluster and many-body perturbation theory for fractional charges and spins. J Chem Phys 2018; 148:221103. [DOI: 10.1063/1.5040164] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Johannes T. Margraf
- Chair for Theoretical Chemistry, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany
| | - Rodney Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
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23
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Haiduke RLA, Bartlett RJ. Non-empirical exchange-correlation parameterizations based on exact conditions from correlated orbital theory. J Chem Phys 2018; 148:184106. [DOI: 10.1063/1.5025723] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Roberto Luiz A. Haiduke
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435, USA
- São Carlos Institute of Chemistry, University of São Paulo, CP 780, 13560-970 São Carlos, SP, Brazil
| | - Rodney J. Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435, USA
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24
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Lutz JJ, Duan XF, Ranasinghe DS, Jin Y, Margraf JT, Perera A, Burggraf LW, Bartlett RJ. Valence and charge-transfer optical properties for some Si nC m( m, n≤ 12) clusters: Comparing TD-DFT, complete-basis-limit EOMCC, and benchmarks from spectroscopy. J Chem Phys 2018; 148:174309. [DOI: 10.1063/1.5022701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Jesse J. Lutz
- Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio 45433, USA
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Xiaofeng F. Duan
- Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio 45433, USA
- Air Force Research Laboratory DoD Supercomputing Resource Center, Wright-Patterson Air Force Base, Ohio 45433, USA
| | | | - Yifan Jin
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Johannes T. Margraf
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Ajith Perera
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Larry W. Burggraf
- Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio 45433, USA
| | - Rodney J. Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
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25
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Bienvenu AV, Knizia G. Efficient Treatment of Local Meta-generalized Gradient Density Functionals via Auxiliary Density Expansion: The Density Fitting J + X Approximation. J Chem Theory Comput 2018; 14:1297-1303. [DOI: 10.1021/acs.jctc.7b01083] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Alyssa V. Bienvenu
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Gerald Knizia
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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26
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Ranasinghe DS, Perera A, Bartlett RJ. A note on the accuracy of KS-DFT densities. J Chem Phys 2017; 147:204103. [DOI: 10.1063/1.5001939] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Ajith Perera
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Rodney J. Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
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27
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Ranasinghe DS, Margraf JT, Jin Y, Bartlett RJ. Does the ionization potential condition employed in QTP functionals mitigate the self-interaction error? J Chem Phys 2017; 146:034102. [PMID: 28109216 DOI: 10.1063/1.4973727] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Though contrary to conventional wisdom, the interpretation of all occupied Kohn-Sham eigenvalues as vertical ionization potentials is justified by several formal and numerical arguments. Similarly, the performance of density functional approximations (DFAs) for fractionally charged systems has been extensively studied as a measure of one- and many-electron self-interaction errors (MSIEs). These complementary perspectives (initially recognized in ab initio dft) are shown to lead to the unifying concept that satisfying Bartlett's IP theorem in DFA's mitigates self-interaction errors. In this contribution, we show that the IP-optimized QTP functionals (reparameterization of CAM-B3LYP where all eigenvalues are approximately equal to vertical IPs) display reduced self-interaction errors in a variety of tests including the He2+ potential curve. Conversely, the MSIE-optimized rCAM-B3LYP functional also displays accurate orbital eigenvalues. It is shown that the CAM-QTP and rCAM-B3LYP functionals show improved dissociation limits, fundamental gaps and thermochemical accuracy compared to their parent functional CAM-B3LYP.
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Affiliation(s)
| | - Johannes T Margraf
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Yifan Jin
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Rodney J Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
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28
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Rishi V, Perera A, Nooijen M, Bartlett RJ. Excited states from modified coupled cluster methods: Are they any better than EOM CCSD? J Chem Phys 2017; 146:144104. [DOI: 10.1063/1.4979078] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Affiliation(s)
- Varun Rishi
- Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32611, USA
| | - Ajith Perera
- Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32611, USA
| | - Marcel Nooijen
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Rodney J. Bartlett
- Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32611, USA
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29
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Interpreting Bonding and Spectra With Correlated, One-Electron Concepts From Electron Propagator Theory. ANNUAL REPORTS IN COMPUTATIONAL CHEMISTRY 2017. [DOI: 10.1016/bs.arcc.2017.06.002] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
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30
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Margraf JT, Ranasinghe DS, Bartlett RJ. Automatic generation of reaction energy databases from highly accurate atomization energy benchmark sets. Phys Chem Chem Phys 2017; 19:9798-9805. [DOI: 10.1039/c7cp00757d] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We describe the automatic generation of reaction energy benchmark sets from arbitrary atomization energy reference data.
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