1
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Johnson PA. Beyond a Richardson-Gaudin Mean-Field: Slater-Condon Rules and Perturbation Theory. J Phys Chem A 2024. [PMID: 39007410 DOI: 10.1021/acs.jpca.4c02857] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/16/2024]
Abstract
Richardson-Gaudin states provide a basis of the Hilbert space for strongly correlated electrons. In this study, optimal expressions for the transition density matrix elements between Richardson-Gaudin states are obtained with a cost comparable with the corresponding reduced density matrix elements. Analogues of the Slater-Condon rules are identified based on the number of near-zero singular values of the RG state overlap matrix. Finally, a perturbative approach is shown to be close in quality to a configuration interaction of Richardson-Gaudin states while being feasible to compute.
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Affiliation(s)
- Paul A Johnson
- Département de Chimie, Université Laval, Québec, Québec G1V 0A6, Canada
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2
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Gałyńska M, de Moraes MMF, Tecmer P, Boguslawski K. Delving into the catalytic mechanism of molybdenum cofactors: a novel coupled cluster study. Phys Chem Chem Phys 2024; 26:18918-18929. [PMID: 38952220 DOI: 10.1039/d4cp01500b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/03/2024]
Abstract
In this work, we use modern electronic structure methods to model the catalytic mechanism of different variants of the molybdenum cofactor (Moco). We investigate the dependence of various Moco model systems on structural relaxation and the importance of environmental effects for five critical points along the reaction coordinate with the DMSO and NO3- substrates. Furthermore, we scrutinize the performance of various coupled-cluster approaches for modeling the relative energies along the investigated reaction paths, focusing on several pair coupled cluster doubles (pCCD) flavors and conventional coupled cluster approximations. Moreover, we elucidate the Mo-O bond formation using orbital-based quantum information measures, which highlight the flow of σM-O bond formation and σN/S-O bond breaking. Our study shows that pCCD-based models are a viable alternative to conventional methods and offer us unique insights into the bonding situation along a reaction coordinate. Finally, this work highlights the importance of environmental effects or changes in the core and, consequently, in the model itself to elucidate the change in activity of different Moco variants.
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Affiliation(s)
- Marta Gałyńska
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
| | - Matheus Morato F de Moraes
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
| | - Paweł Tecmer
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
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3
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Chakraborty R, de Moraes MMF, Boguslawski K, Nowak A, Świerczyński J, Tecmer P. Toward Reliable Dipole Moments without Single Excitations: The Role of Orbital Rotations and Dynamical Correlation. J Chem Theory Comput 2024; 20:4689-4702. [PMID: 38809012 PMCID: PMC11171297 DOI: 10.1021/acs.jctc.4c00471] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2024] [Revised: 05/15/2024] [Accepted: 05/17/2024] [Indexed: 05/30/2024]
Abstract
The dipole moment is a crucial molecular property linked to a molecular system's bond polarity and overall electronic structure. To that end, the electronic dipole moment, which results from the electron density of a system, is often used to assess the accuracy and reliability of new electronic structure methods. This work analyses electronic dipole moments computed with the pair coupled cluster doubles (pCCD) ansätze and its linearized coupled cluster (pCCD-LCC) corrections using the canonical Hartree-Fock and pCCD-optimized (localized) orbital bases. The accuracy of pCCD-based dipole moments is assessed against experimental and CCSD(T) reference values using relaxed and unrelaxed density matrices and different basis set sizes. Our test set comprises molecules of various bonding patterns and electronic structures, exposing pCCD-based methods to a wide range of electron correlation effects. Additionally, we investigate the performance of pCCD-in-DFT dipole moments of some model complexes. Finally, our work indicates the importance of orbital relaxation in the pCCD model and shows the limitations of the linearized couple cluster corrections in predicting electronic dipole moments of multiple-bonded systems. Most importantly, pCCD with a linearized CCD correction can reproduce the dipole moment surfaces in singly bonded molecules, which are comparable to the multireference ones.
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Affiliation(s)
- Rahul Chakraborty
- Institute
of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland
| | - Matheus Morato F. de Moraes
- Institute
of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland
| | - Katharina Boguslawski
- Institute
of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland
| | - Artur Nowak
- Institute
of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland
| | - Julian Świerczyński
- Institute
of Engineering and Technology, Faculty of Physics, Astronomy, and
Informatics, Nicolaus Copernicus University
in Toruń, Grudzia̧dzka
5, 87-100 Toruń, Poland
| | - Paweł Tecmer
- Institute
of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland
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4
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Gałyńska M, Boguslawski K. Benchmarking Ionization Potentials from pCCD Tailored Coupled Cluster Models. J Chem Theory Comput 2024; 20:4182-4195. [PMID: 38752491 PMCID: PMC11137826 DOI: 10.1021/acs.jctc.4c00172] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2024] [Revised: 05/04/2024] [Accepted: 05/07/2024] [Indexed: 05/29/2024]
Abstract
The ionization potential (IP) is an important parameter providing essential insights into the reactivity of chemical systems. IPs are also crucial for designing, optimizing, and understanding the functionality of modern technological devices. We recently showed that limiting the CC ansatz to the seniority-zero sector proves insufficient in predicting reliable and accurate ionization potentials within an IP equation-of-motion coupled-cluster formalism. Specifically, the absence of dynamical correlation in the seniority-zero pair coupled cluster doubles (pCCD) model led to unacceptably significant errors of approximately 1.5 eV. In this work, we aim to explore the impact of dynamical correlation and the choice of the molecular orbital basis (canonical vs localized) in CC-type methods targeting 230 ionized states in 70 molecules, comprising small organic molecules, medium-sized organic acceptors, and nucleobases. We focus on pCCD-based approaches as well as the conventional IP-EOM-CCD and IP-EOM-CCSD. Their performance is compared to the CCSD(T) or CCSDT equivalent and experimental reference data. Our statistical analysis reveals that all investigated frozen-pair coupled cluster methods exhibit similar performance, with differences in errors typically within chemical accuracy (1 kcal/mol or 0.05 eV). Notably, the effect of the molecular orbital basis, such as canonical Hartree-Fock or natural pCCD-optimized orbitals, on the IPs is marginal if dynamical correlation is accounted for. Our study suggests that triple excitations are crucial in achieving chemical accuracy in IPs when modeling electron detachment processes with pCCD-based methods.
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Affiliation(s)
- Marta Gałyńska
- Institute of Physics, Faculty of Physics,
Astronomy, and Informatics, Nicolaus Copernicus
University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics,
Astronomy, and Informatics, Nicolaus Copernicus
University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland
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5
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Chan M, Verstraelen T, Tehrani A, Richer M, Yang XD, Kim TD, Vöhringer-Martinez E, Heidar-Zadeh F, Ayers PW. The tale of HORTON: Lessons learned in a decade of scientific software development. J Chem Phys 2024; 160:162501. [PMID: 38651814 DOI: 10.1063/5.0196638] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2024] [Accepted: 02/28/2024] [Indexed: 04/25/2024] Open
Abstract
HORTON is a free and open-source electronic-structure package written primarily in Python 3 with some underlying C++ components. While HORTON's development has been mainly directed by the research interests of its leading contributing groups, it is designed to be easily modified, extended, and used by other developers of quantum chemistry methods or post-processing techniques. Most importantly, HORTON adheres to modern principles of software development, including modularity, readability, flexibility, comprehensive documentation, automatic testing, version control, and quality-assurance protocols. This article explains how the principles and structure of HORTON have evolved since we started developing it more than a decade ago. We review the features and functionality of the latest HORTON release (version 2.3) and discuss how HORTON is evolving to support electronic structure theory research for the next decade.
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Affiliation(s)
- Matthew Chan
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S-4L8, Canada
| | - Toon Verstraelen
- Center for Molecular Modeling (CMM), Ghent University, Technologiepark-Zwijnaarde 46, B-9052 Ghent, Belgium
| | - Alireza Tehrani
- Department of Chemistry, Queen's University, Kingston, Ontario K7L-3N6, Canada
| | - Michelle Richer
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S-4L8, Canada
| | - Xiaotian Derrick Yang
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S-4L8, Canada
| | - Taewon David Kim
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S-4L8, Canada
| | - Esteban Vöhringer-Martinez
- Departamento de Físico Química, Facultad de Ciencias Químicas, Universidad de Concepción, 4070371 Concepción, Chile
| | - Farnaz Heidar-Zadeh
- Department of Chemistry, Queen's University, Kingston, Ontario K7L-3N6, Canada
| | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S-4L8, Canada
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6
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Gaikwad PB, Kim TD, Richer M, Lokhande RA, Sánchez-Díaz G, Limacher PA, Ayers PW, Miranda-Quintana RA. Coupled cluster-inspired geminal wavefunctions. J Chem Phys 2024; 160:144108. [PMID: 38597308 DOI: 10.1063/5.0202035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2024] [Accepted: 03/24/2024] [Indexed: 04/11/2024] Open
Abstract
Electron pairs have an illustrious history in chemistry, from powerful concepts to understanding structural stability and reactive changes to the promise of serving as building blocks of quantitative descriptions of the electronic structure of complex molecules and materials. However, traditionally, two-electron wavefunctions (geminals) have not enjoyed the popularity and widespread use of the more standard single-particle methods. This has changed recently, with a renewed interest in the development of geminal wavefunctions as an alternative to describing strongly correlated phenomena. Hence, there is a need to find geminal methods that are accurate, computationally tractable, and do not demand significant input from the user (particularly via cumbersome and often ill-behaved orbital optimization steps). Here, we propose new families of geminal wavefunctions inspired by the pair coupled cluster doubles ansatz. We present a new hierarchy of two-electron wavefunctions that extends the one-reference orbital idea to other geminals. Moreover, we show how to incorporate single-like excitations in this framework without leaving the quasiparticle picture. We explore the role of imposing seniority restrictions on these wavefunctions and benchmark these new methods on model strongly correlated systems.
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Affiliation(s)
- Pratiksha B Gaikwad
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, Florida 32603, USA
| | - Taewon D Kim
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, Florida 32603, USA
| | - M Richer
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Rugwed A Lokhande
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, Florida 32603, USA
| | - Gabriela Sánchez-Díaz
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Peter A Limacher
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
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7
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Johnson PA, DePrince AE. Single Reference Treatment of Strongly Correlated H 4 and H 10 Isomers with Richardson-Gaudin States. J Chem Theory Comput 2023; 19:8129-8146. [PMID: 37955440 DOI: 10.1021/acs.jctc.3c00807] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2023]
Abstract
Richardson-Gaudin (RG) states are employed as a variational wave function ansatz for strongly correlated isomers of H4 and H10. In each case, a single RG state describes the seniority-zero sector quite well. Simple natural orbital functionals offer a cheap and reasonable approximation of the outstanding weak correlation in the seniority-zero sector, while systematic improvement is achieved by performing a configuration interaction in terms of RG states.
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Affiliation(s)
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
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8
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Kossoski F, Loos PF. Seniority and Hierarchy Configuration Interaction for Radicals and Excited States. J Chem Theory Comput 2023. [PMID: 37965728 DOI: 10.1021/acs.jctc.3c00946] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2023]
Abstract
Hierarchy configuration interaction (hCI) has recently been introduced as an alternative configuration interaction (CI) route combining excitation degree and seniority number and has been shown to efficiently recover both dynamic and static correlations for closed-shell molecular systems [ J. Phys. Chem. Lett. 2022, 13, 4342]. Here we generalize hCI for an arbitrary reference determinant, allowing calculations for radicals and excited states in a state-specific way. We gauge this route against excitation-based CI (eCI) and seniority-based CI (sCI) by evaluating how different ground-state properties of radicals converge to the full CI limit. We find that hCI outperforms or matches eCI, whereas sCI is far less accurate, in line with previous observations for closed-shell molecules. Employing second-order Epstein-Nesbet (EN2) perturbation theory as a correction significantly accelerates the convergence of hCI and eCI. We further explore various hCI and sCI models to calculate the excitation energies of closed- and open-shell systems. Our results underline that the choice of both the reference determinant and the set of orbitals drives the fine balance between correlation of ground and excited states. State-specific hCI2 and higher-order models perform similarly to their eCI counterparts, whereas lower orders of hCI deliver poor results unless supplemented by the EN2 correction, which substantially improves their accuracy. In turn, sCI1 produces decent excitation energies for radicals, encouraging the development of related seniority-based coupled-cluster methods.
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Affiliation(s)
- Fábris Kossoski
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, F-31062 Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, F-31062 Toulouse, France
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9
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Tecmer P, Gałyńska M, Szczuczko L, Boguslawski K. Geminal-Based Strategies for Modeling Large Building Blocks of Organic Electronic Materials. J Phys Chem Lett 2023; 14:9909-9917. [PMID: 37903084 PMCID: PMC10641881 DOI: 10.1021/acs.jpclett.3c02434] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2023] [Revised: 10/09/2023] [Accepted: 10/24/2023] [Indexed: 11/01/2023]
Abstract
We elaborate on unconventional electronic structure methods based on geminals and their potential to advance the rapidly developing field of organic photovoltaics (OPVs). Specifically, we focus on the computational advantages of geminal-based methods over standard approaches and identify the critical aspects of OPV development. Examples are reliable and efficient computations of orbital energies, electronic spectra, and van der Waals interactions. Geminal-based models can also be combined with quantum embedding techniques and a quantum information analysis of orbital interactions to gain a fundamental understanding of the electronic structures and properties of realistic OPV building blocks. Furthermore, other organic components present in, for instance, dye-sensitized solar cells (DSSCs) represent another promising scope of application. Finally, we provide numerical examples predicting the properties of a small building block of OPV components and two carbazole-based dyes proposed as possible DSSC sensitizers.
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Affiliation(s)
- Paweł Tecmer
- Institute of Physics, Faculty of Physics,
Astronomy, and Informatics, Nicolaus Copernicus
University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland
| | - Marta Gałyńska
- Institute of Physics, Faculty of Physics,
Astronomy, and Informatics, Nicolaus Copernicus
University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland
| | - Lena Szczuczko
- Institute of Physics, Faculty of Physics,
Astronomy, and Informatics, Nicolaus Copernicus
University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics,
Astronomy, and Informatics, Nicolaus Copernicus
University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland
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10
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Chakraborty R, Boguslawski K, Tecmer P. Static embedding with pair coupled cluster doubles based methods. Phys Chem Chem Phys 2023; 25:25377-25388. [PMID: 37705409 DOI: 10.1039/d3cp02502k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/15/2023]
Abstract
Quantum embedding methods have recently been significantly developed to model large molecular structures. This work proposes a novel wave function theory in a density functional theory (WTF-in-DFT) embedding scheme based on pair-coupled cluster doubles (pCCD)-type methods. While pCCD can reliably describe strongly-correlated systems with mean-field-like computational cost, the large extent of the dynamic correlation can be accounted for by (linearized) coupled-cluster corrections on top of the pCCD wave function. Here we focus on the linearized coupled-cluster singles and doubles (LCCSD) ansatz for electronic ground states and its extension to excited states within the equation of motion (EOM) formalism. We test our EOM-pCCD-LCCSD-in-DFT approach for the vertical excitation energies of the hydrogen-bonded water-ammonia complex, micro-solvated thymine, and uranyl tetrahalides (UO2X42-, X = F, Cl, Br). Furthermore, we assess the quality of the embedding potential using an orbital entanglement and correlation analysis. The approximate embedding models successfully capture changes in the excitation energies going from bare fragments to supramolecular structures and represent a promising computational method for excited states in large molecular systems.
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Affiliation(s)
- Rahul Chakraborty
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
| | - Paweł Tecmer
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
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11
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Jahani S, Boguslawski K, Tecmer P. The relationship between structure and excited-state properties in polyanilines from geminal-based methods. RSC Adv 2023; 13:27898-27911. [PMID: 37736567 PMCID: PMC10509596 DOI: 10.1039/d3ra05621j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2023] [Accepted: 09/04/2023] [Indexed: 09/23/2023] Open
Abstract
We employ state-of-the-art quantum chemistry methods to study the structure-to-property relationship in polyanilines (PANIs) of different lengths and oxidation states. Specifically, we focus on leucoemeraldine, emeraldine, and pernigraniline in their tetramer and octamer forms. We scrutinize their structural properties, HOMO and LUMO energies, HOMO-LUMO gaps, and vibrational and electronic spectroscopy using various Density Functional Approximations (DFAs). Furthermore, the accuracy of DFAs is assessed by comparing them to experimental and wavefunction-based reference data. We perform large-scale orbital-optimized pair-Coupled Cluster Doubles (oo-pCCD) calculations for ground and electronically excited states and conventional Configuration Interaction Singles (CIS) calculations for electronically excited states in all investigated systems. The EOM-pCCD+S approach with pCCD-optimized orbitals allows us to unambiguously identify charge transfer and local transitions across the investigated PANI systems-an analysis not possible within a delocalized canonical molecular orbital basis obtained, for instance, by DFAs. We show that the low-lying part of the emeraldine and pernigraniline spectrum is dominated by charge transfer excitations and that polymer elongation changes the character of the leading transitions. Furthermore, we augment our study with a quantum informational analysis of orbital correlations in various forms of PANIs.
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Affiliation(s)
- Seyedehdelaram Jahani
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń Grudziadzka 5 87-100 Toruń Poland
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń Grudziadzka 5 87-100 Toruń Poland
| | - Paweł Tecmer
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń Grudziadzka 5 87-100 Toruń Poland
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12
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Mamache S, Gałyńska M, Boguslawski K. Benchmarking ionization potentials using the simple pCCD model. Phys Chem Chem Phys 2023. [PMID: 37378457 DOI: 10.1039/d3cp01963b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/29/2023]
Abstract
The electron-detachment energy is measured by the ionization potential (IP). As a result, it is a fundamental, observable and important molecular electronic signature in photoelectron spectroscopy. A precise theoretical prediction of electron-detachment energies or ionization potentials is essential for organic optoelectronic systems like transistors, solar cells, or light-emitting diodes. In this work, we benchmark the performance of the recently presented IP variant of the equation-of-motion pair coupled cluster doubles (IP-EOM-pCCD) model to determine IPs. Specifically, the predicted ionization energies are compared to experimental results and higher-order coupled cluster theories based on statistically assessing 201 electron-detached states of 41 organic molecules for three different molecular orbital basis sets and two sets of particle-hole operators. While IP-EOM-pCCD features a reasonable spread and skewness of ionization energies, its mean error and standard deviation differ by up to 1.5 eV from reference data. Our study, thus, highlights the importance of dynamical correlation to reliably predict IPs from a pCCD reference function in small organic molecules.
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Affiliation(s)
- Saddem Mamache
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
| | - Marta Gałyńska
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
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13
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Nowak A, Boguslawski K. A configuration interaction correction on top of pair coupled cluster doubles. Phys Chem Chem Phys 2023; 25:7289-7301. [PMID: 36810525 DOI: 10.1039/d2cp05171k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
Numerous numerical studies have shown that geminal-based methods are a promising direction to model strongly correlated systems with low computational costs. Several strategies have been introduced to capture the missing dynamical correlation effects, which typically exploit a posteriori corrections to account for correlation effects associated with broken-pair states or inter-geminal correlations. In this article, we scrutinize the accuracy of the pair coupled cluster doubles (pCCD) method extended by configuration interaction (CI) theory. Specifically, we benchmark various CI models, including, at most double excitations against selected CC corrections as well as conventional single-reference CC methods. A simple Davidson correction is also tested. The accuracy of the proposed pCCD-CI approaches is assessed for challenging small model systems such as the N2 and F2 dimers and various di- and triatomic actinide-containing compounds. In general, the proposed CI methods considerably improve spectroscopic constants compared to the conventional CCSD approach, provided a Davidson correction is included in the theoretical model. At the same time, their accuracy lies between those of the linearized frozen pCCD and frozen pCCD variants.
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Affiliation(s)
- Artur Nowak
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
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14
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Cassam-Chenaï P, Perez T, Accomasso D. 2D-block geminals: A non 1-orthogonal and non 0-seniority model with reduced computational complexity. J Chem Phys 2023; 158:074106. [PMID: 36813726 DOI: 10.1063/5.0133734] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/19/2023] Open
Abstract
We present a new geminal product wave function Ansatz where the geminals are not constrained to be strongly orthogonal or to be of seniority-zero. Instead, we introduce weaker orthogonality constraints between geminals that significantly lower the computational effort without sacrificing the indistinguishability of the electrons. That is to say, the electron pairs corresponding to the geminals are not fully distinguishable, and their product has yet to be antisymmetrized according to the Pauli principle to form a bona fide electronic wave function. Our geometrical constraints translate into simple equations involving the traces of products of our geminal matrices. In the simplest non-trivial model, a set of solutions is given by block-diagonal matrices where each block is 2 × 2 and consists of either a Pauli matrix or a normalized diagonal matrix multiplied by a complex parameter to be optimized. With this simplified Ansatz for geminals, the number of terms in the calculation of the matrix elements of quantum observables is considerably reduced. A proof of principle is reported and confirms that the Ansatz is more accurate than strongly orthogonal geminal products while remaining computationally affordable.
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Affiliation(s)
| | - Thomas Perez
- Université Côte d'Azur, LJAD, UMR 7351, 06100 Nice, France
| | - Davide Accomasso
- Dipartimento di Chimica e Chimica Industriale, Universita' di Pisa, via Moruzzi 13, 56124 Pisa, Italy
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15
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Żuchowski PS, Moszynski R. Dispersion Energy from the Time-Independent Coupled-Cluster Polarization Propagator. J Chem Theory Comput 2023; 19:1177-1185. [PMID: 36734970 PMCID: PMC9979596 DOI: 10.1021/acs.jctc.2c00902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
We present a new method of calculation of the dispersion energy in the second-order symmetry-adapted perturbation theory. Using the Longuet-Higgins integral and time-independent coupled-cluster response theory, one shows that the general expression for the dispersion energy can be written in terms of cluster amplitudes and the excitation operators σ, which can be obtained by solving a linear equation. We introduced an approximate scheme dubbed CCPP2(T) for the dispersion energy accurate to the second order of intramonomer correlation, which includes certain classes to be summed to infinity. Assessment of the accuracy of the CCPP2(T) dispersion energy against the FCI dispersion for He2 demonstrates its high accuracy. For more complex systems, CCPP2(T) matches the accuracy of the best methods introduced for calculations of dispersion so far. The method can be extended to higher-order levels of excitations, providing a systematically improvable theory of dispersion interaction.
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Affiliation(s)
- Piotr S. Żuchowski
- Faculty
of Physics, Astronomy and Applied Informatics, Institute of Physics, Nicolas Copernicus University in Torun, Grudziadzka 5/7, Torun87-100, Poland,E-mail:
| | - Robert Moszynski
- Quantum
Chemistry Laboratory, Faculty of Chemistry, University of Warsaw, Pasteura 1, Warsaw02-093, Poland,E-mail:
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16
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Faribault A, Dimo C, Moisset JD, Johnson PA. Reduced density matrices/static correlation functions of Richardson–Gaudin states without rapidities. J Chem Phys 2022; 157:214104. [DOI: 10.1063/5.0123911] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/02/2022] Open
Abstract
Seniority-zero geminal wavefunctions are known to capture bond-breaking correlation. Among this class of wavefunctions, Richardson–Gaudin states stand out as they are eigenvectors of a model Hamiltonian. This provides a clear physical picture, clean expressions for reduced density matrix (RDM) elements, and systematic improvement (with a complete set of eigenvectors). Known expressions for the RDM elements require the computation of rapidities, which are obtained by first solving for the so-called eigenvalue based variables (EBV) and then root-finding a Lagrange interpolation polynomial. In this paper, we obtain expressions for the RDM elements directly in terms of the EBV. The final expressions can be computed at the same cost as the rapidity expressions. Therefore, except, in particular, circumstances, it is entirely unnecessary to compute rapidities at all. The RDM elements require numerically inverting a matrix, and while this is usually undesirable, we demonstrate that it is stable, except when there is degeneracy in the single-particle energies. In such cases, a different construction would be required.
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Affiliation(s)
| | - Claude Dimo
- Physics Department and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | | | - Paul A. Johnson
- Département de Chimie, Université Laval, Québec, Québec G1V 0A6, Canada
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17
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Tecmer P, Boguslawski K. Geminal-based electronic structure methods in quantum chemistry. Toward a geminal model chemistry. Phys Chem Chem Phys 2022; 24:23026-23048. [PMID: 36149376 DOI: 10.1039/d2cp02528k] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this review, we discuss the recent progress in developing geminal-based theories for challenging problems in quantum chemistry. Specifically, we focus on the antisymmetrized geminal power, generalized valence bond, antisymmetrized product of strongly orthogonal geminals, singlet-type orthogonal geminals, the antisymmetric product of 1-reference orbital geminal, also known as the pair coupled cluster doubles ansatz, and geminals constructed from Richardson-Gaudin states. Furthermore, we review various corrections to account for the missing dynamical correlation effects in geminal models and possible extensions to target electronically excited states and open-shell species. Finally, we discuss some numerical examples and present-day challenges for geminal-based models, including a quantitative and qualitative analysis of wave functions, and software availability.
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Affiliation(s)
- Paweł Tecmer
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
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18
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Leszczyk A, Dome T, Tecmer P, Kedziera D, Boguslawski K. Resolving the π-assisted U-N σ f-bond formation using quantum information theory. Phys Chem Chem Phys 2022; 24:21296-21307. [PMID: 36043327 DOI: 10.1039/d2cp03377a] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We model the potential energy profiles of the UO2 (NCO)Cl2- → NUOCl2- + CO2 reaction pathway [Y. Gong, V. Vallet, M. del Carmen Michelini, D. Rios and J. K. Gibson, J. Phys. Chem. A, 2014, 118, 325-330] using different pair coupled-cluster doubles (pCCD) methods. Specifically, we focus on pCCD and pCCD-tailored coupled cluster models in predicting relative energies for the various intermediates and transition states along the reaction coordinate. Furthermore, we augment our study on energetics with an orbital-pair correlation analysis of the complete reaction pathway that features two distinct paths. Our analysis of orbital correlations sheds new light on the formation and breaking of respective bonds between the uranium, oxygen, and nitrogen atoms along the reaction coordinates where the "yl" bond is broken and a nitrido compound formed. Specifically, the strengthening of the U-N σf-bond is assisted by a π-type interaction that is delocalized over the C-N-U backbone of the UO2 (NCO)Cl2- complex.
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Affiliation(s)
- Aleksandra Leszczyk
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
| | - Tibor Dome
- Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland.,Institute of Astronomy, University of Cambridge, Madingley Road Cambridge, CB3 0HA, UK
| | - Paweł Tecmer
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
| | - Dariusz Kedziera
- Faculty of Chemistry, Nicolaus Copernicus University in Toruń, Gagarina 7, 87-100 Toruń, Poland
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
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19
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Moisset JD, Fecteau CÉ, Johnson PA. Density matrices of seniority-zero geminal wavefunctions. J Chem Phys 2022; 156:214110. [DOI: 10.1063/5.0088602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
Scalar products and density matrix elements of closed-shell pair geminal wavefunctions are evaluated directly in terms of the pair amplitudes, resulting in an analog of Wick’s theorem for fermions or bosons. This expression is, in general, intractable, but it is shown how it becomes feasible in three distinct ways for Richardson–Gaudin (RG) states, the antisymmetrized geminal power, and the antisymmetrized product of strongly orthogonal geminals. Dissociation curves for hydrogen chains are computed with off-shell RG states and the antisymmetrized product of interacting geminals. Both are near exact, suggesting that the incorrect results observed with ground state RG states (a local maximum rather than smooth dissociation) may be fixable using a different RG state.
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Affiliation(s)
| | | | - Paul A. Johnson
- Département de Chimie, Université Laval, Québec, Québec G1V 0A6, Canada
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20
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Fecteau CÉ, Cloutier S, Moisset JD, Boulay J, Bultinck P, Faribault A, Johnson PA. Near-exact treatment of seniority-zero ground and excited states with a Richardson-Gaudin mean-field. J Chem Phys 2022; 156:194103. [PMID: 35597662 DOI: 10.1063/5.0091338] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Eigenvectors of the reduced Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, Richardson-Gaudin (RG) states, are used as a variational wavefunction ansatz for strongly correlated electronic systems. These states are geminal products whose coefficients are solutions of non-linear equations. Previous results showed an un-physical apparent avoided crossing in ground state dissociation curves for hydrogen chains. In this paper, it is shown that each seniority-zero state of the molecular Coulomb Hamiltonian corresponds directly to an RG state. However, the seniority-zero ground state does not correspond to the ground state of a reduced BCS Hamiltonian. The difficulty is in choosing the correct RG state. The systems studied showed a clear choice, and we expect that it should always be possible to reason physically which state to choose.
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Affiliation(s)
- Charles-Émile Fecteau
- Département de chimie, Université Laval, 1045 Avenue de la Médecine, bureau 1220, Québec, Québec G1V 0A6, Canada
| | - Samuel Cloutier
- Département de chimie, Université Laval, 1045 Avenue de la Médecine, bureau 1220, Québec, Québec G1V 0A6, Canada
| | - Jean-David Moisset
- Département de chimie, Université Laval, 1045 Avenue de la Médecine, bureau 1220, Québec, Québec G1V 0A6, Canada
| | - Jérémy Boulay
- Département de chimie, Université Laval, 1045 Avenue de la Médecine, bureau 1220, Québec, Québec G1V 0A6, Canada
| | - Patrick Bultinck
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 S3, B-9000 Ghent, Belgium
| | | | - Paul A Johnson
- Département de chimie, Université Laval, 1045 Avenue de la Médecine, bureau 1220, Québec, Québec G1V 0A6, Canada
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21
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Kossoski F, Damour Y, Loos PF. Hierarchy Configuration Interaction: Combining Seniority Number and Excitation Degree. J Phys Chem Lett 2022; 13:4342-4349. [PMID: 35537704 PMCID: PMC9125689 DOI: 10.1021/acs.jpclett.2c00730] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2022] [Accepted: 04/13/2022] [Indexed: 06/14/2023]
Abstract
We propose a novel partitioning of the Hilbert space, hierarchy configuration interaction (hCI), where the excitation degree (with respect to a given reference determinant) and the seniority number (i.e., the number of unpaired electrons) are combined in a single hierarchy parameter. The key appealing feature of hCI is that each hierarchy level accounts for all classes of determinants whose number shares the same scaling with system size. By surveying the dissociation of multiple molecular systems, we found that the overall performance of hCI usually exceeds or, at least, parallels that of excitation-based CI. For higher orders of hCI and excitation-based CI, the additional computational burden related to orbital optimization usually does not compensate the marginal improvements compared with results obtained with Hartree-Fock orbitals. The exception is orbital-optimized CI with single excitations, a minimally correlated model displaying the qualitatively correct description of single bond breaking at a very modest computational cost.
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Affiliation(s)
- Fábris Kossoski
- Laboratoire
de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Yann Damour
- Laboratoire
de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Pierre-François Loos
- Laboratoire
de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
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22
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Johnson PA, Ayers PW, Baerdemacker SD, Limacher PA, Neck DV. Bivariational Principle for an Antisymmetrized Product of Nonorthogonal Geminals Appropriate for Strong Electron Correlation. COMPUT THEOR CHEM 2022. [DOI: 10.1016/j.comptc.2022.113718] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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23
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Sørensen LK. On the size consistency problem for anti-symmetrised geminal power wave function ansatz. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2049385] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- L. K. Sørensen
- Department of Theoretical Chemistry and Biology, School of Engineering Sciences in Chemistry, Biotechnology and Health, Royal Institute of Technology, Stockholm, SE, Sweden
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24
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Leszczyk A, Máté M, Legeza Ö, Boguslawski K. Assessing the Accuracy of Tailored Coupled Cluster Methods Corrected by Electronic Wave Functions of Polynomial Cost. J Chem Theory Comput 2021; 18:96-117. [PMID: 34965121 DOI: 10.1021/acs.jctc.1c00284] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Tailored coupled cluster theory represents a computationally inexpensive way to describe static and dynamical electron correlation effects. In this work, we scrutinize the performance of various coupled cluster methods tailored by electronic wave functions of polynomial cost. Specifically, we focus on frozen-pair coupled cluster (fpCC) methods, which are tailored by pair-coupled cluster doubles (pCCD), and coupled cluster theory tailored by matrix product state wave functions optimized by the density matrix renormalization group (DMRG) algorithm. As test system, we selected a set of various small- and medium-sized molecules containing diatomics (N2, F2, C2, CN+, CO, BN, BO+, and Cr2) and molecules (ammonia, ethylene, cyclobutadiene, benzene, hydrogen chains, rings, and cuboids) for which the conventional single-reference coupled cluster singles and doubles (CCSD) method is not able to produce accurate results for spectroscopic constants, potential energy surfaces, and barrier heights. Most importantly, DMRG-tailored and pCCD-tailored approaches yield similar errors in spectroscopic constants and potential energy surfaces compared to accurate theoretical and/or experimental reference data. Although fpCC methods provide a reliable description for the dissociation pathway of molecules featuring single and quadruple bonds, they fail in the description of triple or hextuple bond-breaking processes or avoided crossing regions.
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Affiliation(s)
- Aleksandra Leszczyk
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, ul. Grudzia̧dzka 5, 87-100 Toruń, Poland
| | - Mihály Máté
- Strongly Correlated Systems "Lendület" Research Group, Wigner Research Center for Physics, H-1525 Budapest, Hungary.,Department of Physics of Complex Systems, Eötvös Loránd University, Pf. 32, H-1518 Budapest, Hungary
| | - Örs Legeza
- Strongly Correlated Systems "Lendület" Research Group, Wigner Research Center for Physics, H-1525 Budapest, Hungary.,Institute for Advanced Study, Technical University of Munich, 80333 Munich, Germany
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, ul. Grudzia̧dzka 5, 87-100 Toruń, Poland
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25
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Abstract
The pair coupled cluster doubles (pCCD) ansatz represents an inexpensive but accurate single-reference method to describe multi-reference problems. By construction, pCCD remains, however, applicable to closed-shell systems. For the first time, we present extensions to pCCD that allow us to target open-shell molecules with up to 4 unpaired electrons. Although requiring only modest computational cost, our methods approach chemical accuracy for some challenging cases, while their performance is comparable to more expensive models like DMRG or CCSD(T).
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Affiliation(s)
- Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, ul. Grudziądzka 5, 87-100 Toruń, Poland.
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26
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Marie A, Kossoski F, Loos PF. Variational coupled cluster for ground and excited states. J Chem Phys 2021; 155:104105. [PMID: 34525834 DOI: 10.1063/5.0060698] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In single-reference coupled-cluster (CC) methods, one has to solve a set of non-linear polynomial equations in order to determine the so-called amplitudes that are then used to compute the energy and other properties. Although it is of common practice to converge to the (lowest-energy) ground-state solution, it is also possible, thanks to tailored algorithms, to access higher-energy roots of these equations that may or may not correspond to genuine excited states. Here, we explore the structure of the energy landscape of variational CC and we compare it with its (projected) traditional version in the case where the excitation operator is restricted to paired double excitations (pCCD). By investigating two model systems (the symmetric stretching of the linear H4 molecule and the continuous deformation of the square H4 molecule into a rectangular arrangement) in the presence of weak and strong correlations, the performance of variational pCCD (VpCCD) and traditional pCCD is gauged against their configuration interaction (CI) equivalent, known as doubly occupied CI, for reference Slater determinants made of ground- or excited-state Hartree-Fock orbitals or state-specific orbitals optimized directly at the VpCCD level. The influence of spatial symmetry breaking is also investigated.
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Affiliation(s)
- Antoine Marie
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Fábris Kossoski
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
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27
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Kossoski F, Marie A, Scemama A, Caffarel M, Loos PF. Excited States from State-Specific Orbital-Optimized Pair Coupled Cluster. J Chem Theory Comput 2021; 17:4756-4768. [PMID: 34310140 PMCID: PMC8359009 DOI: 10.1021/acs.jctc.1c00348] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
![]()
The pair coupled
cluster doubles (pCCD) method (where the excitation
manifold is restricted to electron pairs) has a series of interesting
features. Among others, it provides ground-state energies very close
to what is obtained with doubly occupied configuration interaction
(DOCI), but with a polynomial cost (compared with the exponential
cost of the latter). Here, we address whether this similarity holds
for excited states by exploring the symmetric dissociation of the
linear H4 molecule. When ground-state Hartree–Fock
(HF) orbitals are employed, pCCD and DOCI excited-state energies do
not match, a feature that is assigned to the poor HF reference. In
contrast, by optimizing the orbitals at the pCCD level (oo-pCCD) specifically
for each excited state, the discrepancies between pCCD and DOCI decrease
by 1 or 2 orders of magnitude. Therefore, the pCCD and DOCI methodologies
still provide comparable energies for excited states, but only if
suitable, state-specific orbitals are adopted. We also assessed whether
a pCCD approach could be used to directly target doubly excited states,
without having to resort to the equation-of-motion (EOM) formalism.
In our Δoo-pCCD model, excitation energies are extracted from
the energy difference between separate oo-pCCD calculations for the
ground state and the targeted excited state. For a set comprising
the doubly excited states of CH+, BH, nitroxyl, nitrosomethane,
and formaldehyde, we found that Δoo-pCCD provides quite accurate
excitation energies, with root-mean-square deviations (with respect
to full configuration interaction results) lower than those of CC3
and comparable to those of EOM-CCSDT, two methods with a much higher
computational cost.
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Affiliation(s)
- Fábris Kossoski
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Antoine Marie
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Michel Caffarel
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
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28
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Johnson PA, Fortin H, Cloutier S, Fecteau CÉ. Transition density matrices of Richardson-Gaudin states. J Chem Phys 2021; 154:124125. [PMID: 33810647 DOI: 10.1063/5.0041051] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Recently, ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, Richardson-Gaudin (RG) states, have been employed as a wavefunction ansatz for strong correlation. This wavefunction physically represents a mean-field of pairs of electrons (geminals) with a constant pairing strength. To move beyond the mean-field, one must develop the wavefunction on the basis of all the RG states. This requires both practical expressions for transition density matrices and an idea of which states are most important in the expansion. In this contribution, we present expressions for the transition density matrix elements and calculate them numerically for half-filled picket-fence models (reduced BCS models with constant energy spacing). There are no Slater-Condon rules for RG states, though an analog of the aufbau principle proves to be useful in choosing which states are important.
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Affiliation(s)
- Paul A Johnson
- Département de Chimie, Université Laval, Québec, Québec G1V 0A6, Canada
| | - Hubert Fortin
- Département de Chimie, Université Laval, Québec, Québec G1V 0A6, Canada
| | - Samuel Cloutier
- Département de Chimie, Université Laval, Québec, Québec G1V 0A6, Canada
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29
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Nowak A, Legeza Ö, Boguslawski K. Orbital entanglement and correlation from pCCD-tailored coupled cluster wave functions. J Chem Phys 2021; 154:084111. [DOI: 10.1063/5.0038205] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Affiliation(s)
- Artur Nowak
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Torun, Poland
| | - Örs Legeza
- Strongly Correlated Systems “Lendület" Research Group, Wigner Research Center for Physics, H-1525 Budapest, Hungary
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Torun, Poland
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30
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Kedžuch S, Šimunek J, Veis M, Noga J. Doubly Occupied Pair Coupled Cluster F12 Approach. J Chem Theory Comput 2020; 16:7372-7380. [PMID: 32866010 DOI: 10.1021/acs.jctc.0c00659] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Inspired by reports of the good performance of the doubly occupied pair coupled cluster (pCCD) theory in describing static electron correlation, we have introduced and implemented a variant thereof that includes single excitations and explicitly treats the dynamic electron correlation using the F12 methodology (pCCSD-F12). This drastically reduces the computation scaling with respect to the standard method using the full double-excitation operator (CCSD-F12). Slater-type geminals as a correlation factor, together with fixed cusp conditions, were used, which is known as the SP-ansatz. For sample model systems, we have investigated the performance of reference states constructed from either canonical or localized molecular orbitals. Finaly, the employment of Brueckner orbitals has been tested, which causes the single excitations to naturally vanish from the wave function expansion (B-pCCD-F12). Our test systems include different-sized rings of hydrogen atoms and dissociation curves for small molecules such as HF, N2, and CO2; and comparison with CCSD-F12 is presented for a series of reaction enthalpies.
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Affiliation(s)
- Stanislav Kedžuch
- Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University, Mlynská dolina, Ilkovičova 6, SK-84215 Bratislava, Slovakia.,RIKEN Center for Computational Science, 7-1-26 Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
| | - Ján Šimunek
- Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University, Mlynská dolina, Ilkovičova 6, SK-84215 Bratislava, Slovakia
| | - Matej Veis
- Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University, Mlynská dolina, Ilkovičova 6, SK-84215 Bratislava, Slovakia
| | - Jozef Noga
- Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University, Mlynská dolina, Ilkovičova 6, SK-84215 Bratislava, Slovakia.,Computing Centre, Centre of Operations of the Slovak Academy of Sciences, Dúbravská cesta 9, SK-84535 Bratislava, Slovakia
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31
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Fecteau CÉ, Fortin H, Cloutier S, Johnson PA. Reduced density matrices of Richardson-Gaudin states in the Gaudin algebra basis. J Chem Phys 2020; 153:164117. [PMID: 33138426 DOI: 10.1063/5.0027393] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian have recently been employed as a variational wavefunction ansatz in quantum chemistry. This wavefunction is a mean-field of pairs of electrons (geminals). In this contribution, we report optimal expressions for their reduced density matrices in both the original physical basis and the basis of the Richardson-Gaudin pairs. Physical basis expressions were originally reported by Gorohovsky and Bettelheim [Phys. Rev. B 84, 224503 (2011)]. In each case, the expressions scale like O(N4), with the most expensive step being the solution of linear equations. Analytic gradients are also reported in the physical basis. These expressions are an important step toward practical mean-field methods to treat strongly correlated electrons.
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Affiliation(s)
| | - Hubert Fortin
- Département de chimie, Université Laval, Québec, Québec G1V 0A6, Canada
| | - Samuel Cloutier
- Département de chimie, Université Laval, Québec, Québec G1V 0A6, Canada
| | - Paul A Johnson
- Département de chimie, Université Laval, Québec, Québec G1V 0A6, Canada
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32
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Johnson PA, Fecteau CÉ, Berthiaume F, Cloutier S, Carrier L, Gratton M, Bultinck P, De Baerdemacker S, Van Neck D, Limacher P, Ayers PW. Richardson–Gaudin mean-field for strong correlation in quantum chemistry. J Chem Phys 2020; 153:104110. [DOI: 10.1063/5.0022189] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Affiliation(s)
- Paul A. Johnson
- Département de Chimie, Université Laval, Québec, Québec G1V 0A6, Canada
| | | | | | - Samuel Cloutier
- Département de Chimie, Université Laval, Québec, Québec G1V 0A6, Canada
| | - Laurie Carrier
- Département de Chimie, Université Laval, Québec, Québec G1V 0A6, Canada
| | - Marianne Gratton
- Département de Chimie, Université Laval, Québec, Québec G1V 0A6, Canada
| | | | - Stijn De Baerdemacker
- Department of Chemistry, University of New Brunswick, Fredericton, New Brunswick E3B 5A3, Canada
| | - Dimitri Van Neck
- Center for Molecular Modeling, Ghent University, Zwijnaarde, Belgium
| | | | - Paul W. Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
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33
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Vu N, DePrince AE. Size-extensive seniority-zero energy functionals derived from configuration interaction with double excitations. J Chem Phys 2020; 152:244103. [DOI: 10.1063/5.0011637] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Affiliation(s)
- Nam Vu
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
| | - A. Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
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34
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Kowalski K, Bauman NP. Sub-system quantum dynamics using coupled cluster downfolding techniques. J Chem Phys 2020; 152:244127. [DOI: 10.1063/5.0008436] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Karol Kowalski
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, USA
| | - Nicholas P. Bauman
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, USA
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35
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Head-Marsden K, Mazziotti DA. Active-Space Pair Two-Electron Reduced Density Matrix Theory for Strong Correlation. J Phys Chem A 2020; 124:4848-4854. [DOI: 10.1021/acs.jpca.0c01937] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Kade Head-Marsden
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, United States
| | - David A. Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, United States
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36
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Bauman NP, Bylaska EJ, Krishnamoorthy S, Low GH, Wiebe N, Granade CE, Roetteler M, Troyer M, Kowalski K. Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms. J Chem Phys 2019; 151:014107. [PMID: 31272173 DOI: 10.1063/1.5094643] [Citation(s) in RCA: 32] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper, we discuss the extension of the recently introduced subsystem embedding subalgebra coupled cluster (SES-CC) formalism to unitary CC formalisms. In analogy to the standard single-reference SES-CC formalism, its unitary CC extension allows one to include the dynamical (outside the active space) correlation effects in an SES induced complete active space (CAS) effective Hamiltonian. In contrast to the standard single-reference SES-CC theory, the unitary CC approach results in a Hermitian form of the effective Hamiltonian. Additionally, for the double unitary CC (DUCC) formalism, the corresponding CAS eigenvalue problem provides a rigorous separation of external cluster amplitudes that describe dynamical correlation effects-used to define the effective Hamiltonian-from those corresponding to the internal (inside the active space) excitations that define the components of eigenvectors associated with the energy of the entire system. The proposed formalism can be viewed as an efficient way of downfolding many-electron Hamiltonian to the low-energy model represented by a particular choice of CAS. In principle, this technique can be extended to any type of CAS representing an arbitrary energy window of a quantum system. The Hermitian character of low-dimensional effective Hamiltonians makes them an ideal target for several types of full configuration interaction type eigensolvers. As an example, we also discuss the algebraic form of the perturbative expansions of the effective DUCC Hamiltonians corresponding to composite unitary CC theories and discuss possible algorithms for hybrid classical and quantum computing. Given growing interest in quantum computing, we provide energies for H2 and Be systems obtained with the quantum phase estimator algorithm available in the Quantum Development Kit for the approximate DUCC Hamiltonians.
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Affiliation(s)
- Nicholas P Bauman
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
| | - Eric J Bylaska
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
| | - Sriram Krishnamoorthy
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
| | - Guang Hao Low
- Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
| | - Nathan Wiebe
- Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
| | - Christopher E Granade
- Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
| | - Martin Roetteler
- Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
| | - Matthias Troyer
- Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
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37
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Brzęk F, Boguslawski K, Tecmer P, Żuchowski PS. Benchmarking the Accuracy of Seniority-Zero Wave Function Methods for Noncovalent Interactions. J Chem Theory Comput 2019; 15:4021-4035. [PMID: 31136703 DOI: 10.1021/acs.jctc.9b00189] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Filip Brzęk
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun, Grudziadzka 5, 87-100 Torun, Poland
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun, Grudziadzka 5, 87-100 Torun, Poland
- Faculty of Chemistry, Nicolaus Copernicus University in Torun, Gagarina 7, 87-100 Torun, Poland
| | - Paweł Tecmer
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun, Grudziadzka 5, 87-100 Torun, Poland
| | - Piotr Szymon Żuchowski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun, Grudziadzka 5, 87-100 Torun, Poland
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38
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Nowak A, Tecmer P, Boguslawski K. Assessing the accuracy of simplified coupled cluster methods for electronic excited states in f0 actinide compounds. Phys Chem Chem Phys 2019; 21:19039-19053. [DOI: 10.1039/c9cp03678d] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We scrutinize the performance of different variants of equation of motion coupled cluster (EOM-CC) methods to predict electronic excitation energies and excited state potential energy surfaces in closed-shell actinide species.
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Affiliation(s)
- Artur Nowak
- Institute of Physics
- Faculty of Physics
- Astronomy, and Informatics
- Nicolaus Copernicus University in Toruń
- 87-100 Toruń
| | - Paweł Tecmer
- Institute of Physics
- Faculty of Physics
- Astronomy, and Informatics
- Nicolaus Copernicus University in Toruń
- 87-100 Toruń
| | - Katharina Boguslawski
- Institute of Physics
- Faculty of Physics
- Astronomy, and Informatics
- Nicolaus Copernicus University in Toruń
- 87-100 Toruń
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39
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Boguslawski K. Targeting Doubly Excited States with Equation of Motion Coupled Cluster Theory Restricted to Double Excitations. J Chem Theory Comput 2018; 15:18-24. [DOI: 10.1021/acs.jctc.8b01053] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun, Grudziadzka 5, 87-100 Torun, Poland
- Faculty of Chemistry, Nicolaus Copernicus University in Torun, Gagarina 7, 87-100 Torun, Poland
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40
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Kats D, Tew DP. Orbital-Optimized Distinguishable Cluster Theory with Explicit Correlation. J Chem Theory Comput 2018; 15:13-17. [DOI: 10.1021/acs.jctc.8b01047] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Daniel Kats
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - David P. Tew
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
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41
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Zhou C, Chen Z, Wu W. Reciprocal transformation of seniority number restricted wave function. J Chem Phys 2018; 149:044111. [DOI: 10.1063/1.5032129] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Affiliation(s)
- Chen Zhou
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
| | - Zhenhua Chen
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
| | - Wei Wu
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, iChem and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
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42
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Kowalski K. Properties of coupled-cluster equations originating in excitation sub-algebras. J Chem Phys 2018. [DOI: 10.1063/1.5010693] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
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43
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Lanssens C, Ayers PW, Van Neck D, De Baerdemacker S, Gunst K, Bultinck P. Method for making 2-electron response reduced density matrices approximately N-representable. J Chem Phys 2018; 148:084104. [PMID: 29495792 DOI: 10.1063/1.4994618] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In methods like geminal-based approaches or coupled cluster that are solved using the projected Schrödinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based on response theory. However, the 2-RDMs from response theory are not N-representable. That is, the response 2-RDM does not correspond to an actual physical N-electron wave function. We present a new algorithm for making these non-N-representable 2-RDMs approximately N-representable, i.e., it has the right symmetry and normalization and it fulfills the P-, Q-, and G-conditions. Next to an algorithm which can be applied to any 2-RDM, we have also developed a 2-RDM optimization procedure specifically for seniority-zero 2-RDMs. We aim to find the 2-RDM with the right properties which is the closest (in the sense of the Frobenius norm) to the non-N-representable 2-RDM by minimizing the square norm of the difference between this initial response 2-RDM and the targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM, Q-matrix, and G-matrix are positive semidefinite, i.e., their eigenvalues are non-negative. Our method is suitable for fixing non-N-representable 2-RDMs which are close to being N-representable. Through the N-representability optimization algorithm we add a small correction to the initial 2-RDM such that it fulfills the most important N-representability conditions.
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Affiliation(s)
- Caitlin Lanssens
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4L8, Canada
| | - Dimitri Van Neck
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | - Stijn De Baerdemacker
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | - Klaas Gunst
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | - Patrick Bultinck
- Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Ghent, Belgium
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44
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Hybrid Treatments Based on Determinant Seniority Numbers and Spatial Excitation Levels in the Configuration Interaction Framework. ADVANCES IN QUANTUM CHEMISTRY 2018. [DOI: 10.1016/bs.aiq.2017.05.003] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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45
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Boguslawski K, Tecmer P. Benchmark of Dynamic Electron Correlation Models for Seniority-Zero Wave Functions and Their Application to Thermochemistry. J Chem Theory Comput 2017; 13:5966-5983. [DOI: 10.1021/acs.jctc.6b01134] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Katharina Boguslawski
- Institute
of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun, Grudziadzka 5, 87-100 Torun, Poland
- Faculty
of Chemistry, Nicolaus Copernicus University in Torun, Gagarina 7, 87-100 Torun, Poland
| | - Paweł Tecmer
- Institute
of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun, Grudziadzka 5, 87-100 Torun, Poland
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46
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Johnson PA, Limacher PA, Kim TD, Richer M, Miranda-Quintana RA, Heidar-Zadeh F, Ayers PW, Bultinck P, De Baerdemacker S, Van Neck D. Strategies for extending geminal-based wavefunctions: Open shells and beyond. COMPUT THEOR CHEM 2017. [DOI: 10.1016/j.comptc.2017.05.010] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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47
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A comparative study on seniority-based MO and VB calculations of the singlet and triplet energy gaps of open-shell molecules. COMPUT THEOR CHEM 2017. [DOI: 10.1016/j.comptc.2017.03.031] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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48
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Head-Marsden K, Mazziotti DA. Pair 2-electron reduced density matrix theory using localized orbitals. J Chem Phys 2017; 147:084101. [PMID: 28863513 DOI: 10.1063/1.4999423] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Full configuration interaction (FCI) restricted to a pairing space yields size-extensive correlation energies but its cost scales exponentially with molecular size. Restricting the variational two-electron reduced-density-matrix (2-RDM) method to represent the same pairing space yields an accurate lower bound to the pair FCI energy at a mean-field-like computational scaling of O(r3) where r is the number of orbitals. In this paper, we show that localized molecular orbitals can be employed to generate an efficient, approximately size-extensive pair 2-RDM method. The use of localized orbitals eliminates the substantial cost of optimizing iteratively the orbitals defining the pairing space without compromising accuracy. In contrast to the localized orbitals, the use of canonical Hartree-Fock molecular orbitals is shown to be both inaccurate and non-size-extensive. The pair 2-RDM has the flexibility to describe the spectra of one-electron RDM occupation numbers from all quantum states that are invariant to time-reversal symmetry. Applications are made to hydrogen chains and their dissociation, n-acene from naphthalene through octacene, and cadmium telluride 2-, 3-, and 4-unit polymers. For the hydrogen chains, the pair 2-RDM method recovers the majority of the energy obtained from similar calculations that iteratively optimize the orbitals. The localized-orbital pair 2-RDM method with its mean-field-like computational scaling and its ability to describe multi-reference correlation has important applications to a range of strongly correlated phenomena in chemistry and physics.
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Affiliation(s)
- Kade Head-Marsden
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - David A Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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49
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Boguslawski K. Targeting excited states in all-trans polyenes with electron-pair states. J Chem Phys 2016; 145:234105. [DOI: 10.1063/1.4972053] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun, Grudziadzka 5, 87-100 Torun, Poland and Faculty of Chemistry, Nicolaus Copernicus University in Torun, Gagarina 7, 87-100 Torun, Poland
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50
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Zhao L, Neuscamman E. Amplitude Determinant Coupled Cluster with Pairwise Doubles. J Chem Theory Comput 2016; 12:5841-5850. [DOI: 10.1021/acs.jctc.6b00812] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Luning Zhao
- Department
of Chemistry, University of California, Berkeley, California 94720, United States
| | - Eric Neuscamman
- Department
of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical
Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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