1
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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. [PMID: 38809012 DOI: 10.1021/acs.jctc.4c00471] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [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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2
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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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3
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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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4
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Dutta R, Gao F, Khamoshi A, Henderson TM, Scuseria GE. Correlated pair ansatz with a binary tree structure. J Chem Phys 2024; 160:084113. [PMID: 38421064 DOI: 10.1063/5.0185375] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Accepted: 02/02/2024] [Indexed: 03/02/2024] Open
Abstract
We develop an efficient algorithm to implement the recently introduced binary tree state (BTS) ansatz on a classical computer. BTS allows a simple approximation to permanents arising from the computationally intractable antisymmetric product of interacting geminals and respects size-consistency. We show how to compute BTS overlap and reduced density matrices efficiently. We also explore two routes for developing correlated BTS approaches: Jastrow coupled cluster on BTS and linear combinations of BT states. The resulting methods show great promise in benchmark applications to the reduced Bardeen-Cooper-Schrieffer Hamiltonian and the one-dimensional XXZ Heisenberg Hamiltonian.
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Affiliation(s)
- Rishab Dutta
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Fei Gao
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Armin Khamoshi
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Thomas M Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Gustavo E Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
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5
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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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6
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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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7
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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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8
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Motta M, Sung KJ, Whaley KB, Head-Gordon M, Shee J. Bridging physical intuition and hardware efficiency for correlated electronic states: the local unitary cluster Jastrow ansatz for electronic structure. Chem Sci 2023; 14:11213-11227. [PMID: 37860666 PMCID: PMC10583744 DOI: 10.1039/d3sc02516k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2023] [Accepted: 09/20/2023] [Indexed: 10/21/2023] Open
Abstract
A prominent goal in quantum chemistry is to solve the molecular electronic structure problem for ground state energy with high accuracy. While classical quantum chemistry is a relatively mature field, the accurate and scalable prediction of strongly correlated states found, e.g., in bond breaking and polynuclear transition metal compounds remains an open problem. Within the context of a variational quantum eigensolver, we propose a new family of ansatzes which provides a more physically appropriate description of strongly correlated electrons than a unitary coupled cluster with single and double excitations (qUCCSD), with vastly reduced quantum resource requirements. Specifically, we present a set of local approximations to the unitary cluster Jastrow wavefunction motivated by Hubbard physics. As in the case of qUCCSD, exactly computing the energy scales factorially with system size on classical computers but polynomially on quantum devices. The local unitary cluster Jastrow ansatz removes the need for SWAP gates, can be tailored to arbitrary qubit topologies (e.g., square, hex, and heavy-hex), and is well-suited to take advantage of continuous sets of quantum gates recently realized on superconducting devices with tunable couplers. The proposed family of ansatzes demonstrates that hardware efficiency and physical transparency are not mutually exclusive; indeed, chemical and physical intuition regarding electron correlation can illuminate a useful path towards hardware-friendly quantum circuits.
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Affiliation(s)
- Mario Motta
- IBM Quantum, IBM Research - Almaden San Jose CA 95120 USA
| | - Kevin J Sung
- IBM Quantum, IBM T. J. Watson Research Center Yorktown Heights NY 10598 USA
| | - K Birgitta Whaley
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Berkeley Quantum Information and Computation Center, University of California Berkeley CA 94720 USA
- Challenge Institute for Quantum Computation, University of California Berkeley CA 94720 USA
| | - Martin Head-Gordon
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory Berkeley CA 94720 USA
| | - James Shee
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Department of Chemistry, Rice University Houston TX 77005 USA
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9
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Ravi M, Perera A, Park YC, Bartlett RJ. Excited states with pair coupled cluster doubles tailored coupled cluster theory. J Chem Phys 2023; 159:094101. [PMID: 37655762 DOI: 10.1063/5.0161368] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2023] [Accepted: 08/11/2023] [Indexed: 09/02/2023] Open
Abstract
It is known that some non-dynamic effects of electron correlation can be included in coupled cluster theory using a tailoring technique that separates the effects of non-dynamic and dynamic correlations. Recently, the simple pCCD (pair coupled cluster doubles) wavefunction was shown to provide good results for some non-dynamic correlation problems, such as bond-breaking, in a spin-adapted way with no active space selection. In this paper, we report a study of excited states using "tailored coupled cluster singles and doubles," to attempt to use pCCD as a kernel for more complete coupled-cluster singles and doubles (CCSD) results for excited states. Several excited states are explored from those primarily due to single excitations to those dominated by doubly excited states and from singlet-triplet splittings for some diradical states. For the first two situations, tailored pCCD-TCCSD offers no improvement over equation of motion-CCSD. However, when we explore the singlet-triplet gap of diradical molecules that are manifestly multi-reference, a pCCD kernel provides improved results, particularly with generalized valence bond orbitals.
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Affiliation(s)
- Moneesha Ravi
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435, USA
| | - Ajith Perera
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435, USA
| | - Young Choon Park
- Korea Institute of Fusion Energy, 37 Dongjangsan-ro, Gunsan, Jeollabuk-do 54004, Republic of Korea
| | - Rodney J Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435, USA
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10
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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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11
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Izsák R, Ivanov AV, Blunt NS, Holzmann N, Neese F. Measuring Electron Correlation: The Impact of Symmetry and Orbital Transformations. J Chem Theory Comput 2023; 19:2703-2720. [PMID: 37022051 PMCID: PMC10210250 DOI: 10.1021/acs.jctc.3c00122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Indexed: 04/07/2023]
Abstract
In this perspective, the various measures of electron correlation used in wave function theory, density functional theory and quantum information theory are briefly reviewed. We then focus on a more traditional metric based on dominant weights in the full configuration solution and discuss its behavior with respect to the choice of the N-electron and the one-electron basis. The impact of symmetry is discussed, and we emphasize that the distinction among determinants, configuration state functions and configurations as reference functions is useful because the latter incorporate spin-coupling into the reference and should thus reduce the complexity of the wave function expansion. The corresponding notions of single determinant, single spin-coupling and single configuration wave functions are discussed and the effect of orbital rotations on the multireference character is reviewed by analyzing a simple model system. In molecular systems, the extent of correlation effects should be limited by finite system size and in most cases the appropriate choices of one-electron and N-electron bases should be able to incorporate these into a low-complexity reference function, often a single configurational one.
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Affiliation(s)
- Róbert Izsák
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Aleksei V. Ivanov
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Nick S. Blunt
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Nicole Holzmann
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Frank Neese
- Max-Planck
Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
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12
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Khamoshi A, Dutta R, Scuseria GE. State Preparation of Antisymmetrized Geminal Power on a Quantum Computer without Number Projection. J Phys Chem A 2023; 127:4005-4014. [PMID: 37129503 DOI: 10.1021/acs.jpca.3c00525] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
The antisymmetrized geminal power (AGP) is equivalent to the number projected Bardeen-Cooper-Schrieffer (PBCS) wave function. It is also an elementary symmetric polynomial (ESP) state. We generalize previous research on deterministically implementing the Dicke state to a state preparation algorithm for an ESP state, or equivalently AGP, on a quantum computer. Our method is deterministic and has polynomial cost, and it does not rely on number symmetry breaking and restoration. We also show that our circuit is equivalent to a disentangled unitary paired coupled cluster operator and a layer of unitary Jastrow operator acting on a single Slater determinant. The method presented herein highlights the ability of disentangled unitary coupled cluster to capture nontrivial entanglement properties that are hardly accessible with traditional Hartree-Fock based electronic structure methods.
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Affiliation(s)
- Armin Khamoshi
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Rishab Dutta
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
| | - Gustavo E Scuseria
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
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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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Kim TD, Richer M, Sánchez-Díaz G, Miranda-Quintana RA, Verstraelen T, Heidar-Zadeh F, Ayers PW. Fanpy: A python library for prototyping multideterminant methods in ab initio quantum chemistry. J Comput Chem 2023; 44:697-709. [PMID: 36440947 DOI: 10.1002/jcc.27034] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2022] [Accepted: 09/05/2022] [Indexed: 11/30/2022]
Abstract
Fanpy is a free and open-source Python library for developing and testing multideterminant wavefunctions and related ab initio methods in electronic structure theory. The main use of Fanpy is to quickly prototype new methods by making it easier to convert the mathematical formulation of a new wavefunction ansätze to a working implementation. Fanpy is designed based on our recently introduced Flexible Ansatz for N-electron Configuration Interaction (FANCI) framework, where multideterminant wavefunctions are represented by their overlaps with Slater determinants of orthonormal spin-orbitals. In the simplest case, a new wavefunction ansatz can be implemented by simply writing a function for evaluating its overlap with an arbitrary Slater determinant. Fanpy is modular in both implementation and theory: the wavefunction model, the system's Hamiltonian, and the choice of objective function are all independent modules. This modular structure makes it easy for users to mix and match different methods and for developers to quickly explore new ideas. Fanpy is written purely in Python with standard dependencies, making it accessible for various operating systems. In addition, it adheres to principles of modern software development, including comprehensive documentation, extensive testing, quality assurance, and continuous integration and delivery protocols. This article is considered to be the official release notes for the Fanpy library.
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Affiliation(s)
- Taewon D Kim
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario, Canada.,Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, Florida, USA
| | - M Richer
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario, Canada
| | - Gabriela Sánchez-Díaz
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario, Canada
| | | | - Toon Verstraelen
- Center for Molecular Modeling (CMM), Ghent University, Ghent, Belgium
| | | | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario, Canada
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15
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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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16
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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: 0] [Impact Index Per Article: 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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17
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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: 0] [Impact Index Per Article: 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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18
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Ríos E, Alcoba DR, Lain L, Torre A, Oña OB, Massaccesi GE. Variational determination of the two-electron reduced density matrix within the doubly occupied configuration interaction framework: Treatments of triplet N-electron systems. J Chem Phys 2022; 157:014102. [DOI: 10.1063/5.0088125] [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
This work performs variational determinations of two-electron reduced density matrices corresponding to open-shell N-electron systems within the framework of the doubly occupied configuration interaction treatment, traditionally limited to studies of closed-shell systems. The procedure has allowed us to describe satisfactorily molecular systems in triplet states following two methods. One of them adds hydrogen atoms at an infinite distance of the triplet system studied, constituting a singlet supersystem. Energies and reduced density matrices of the triplet system are obtained by removing the contributions of the added atoms from the singlet supersystem results. The second procedure determines variationally the two-electron reduced density matrices corresponding to the triplet systems by means of adequate couplings of basis-set functions. Both models have been managed by imposing N-representability conditions on the reduced density matrix calculations. Results obtained from these methods for molecular systems in triplet ground states are reported and compared with those provided by benchmark methods.
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Affiliation(s)
| | - Diego Ricardo Alcoba
- Departmento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina
| | - Luis Lain
- Quimica Fisica, Universidad del Pais Vasco Facultad de Ciencia y Tecnologia, Spain
| | - Alicia Torre
- Quimica Fisica, Universidad del Pais Vasco, Spain
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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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Magoulas I, Shen J, Piecuch P. Addressing strong correlation by approximate coupled-pair methods with active-space and full treatments of three-body clusters. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2057365] [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)
- Ilias Magoulas
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
| | - Jun Shen
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
| | - Piotr Piecuch
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
- Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA
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23
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Elayan IA, Gupta R, Hollett JW. ΔNO and the complexities of electron correlation in simple hydrogen clusters. J Chem Phys 2022; 156:094102. [DOI: 10.1063/5.0073227] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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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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Damour Y, Véril M, Kossoski F, Caffarel M, Jacquemin D, Scemama A, Loos PF. Accurate full configuration interaction correlation energy estimates for five- and six-membered rings. J Chem Phys 2021; 155:134104. [PMID: 34624964 DOI: 10.1063/5.0065314] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Following our recent work on the benzene molecule [P.-F. Loos, Y. Damour, and A. Scemama, J. Chem. Phys. 153, 176101 (2020)], motivated by the blind challenge of Eriksen et al. [J. Phys. Chem. Lett. 11, 8922 (2020)] on the same system, we report accurate full configuration interaction (FCI) frozen-core correlation energy estimates for 12 five- and six-membered ring molecules (cyclopentadiene, furan, imidazole, pyrrole, thiophene, benzene, pyrazine, pyridazine, pyridine, pyrimidine, s-tetrazine, and s-triazine) in the standard correlation-consistent double-ζ Dunning basis set (cc-pVDZ). Our FCI correlation energy estimates, with an estimated error smaller than 1 millihartree, are based on energetically optimized-orbital selected configuration interaction calculations performed with the configuration interaction using a perturbative selection made iteratively algorithm. Having at our disposal these accurate reference energies, the respective performance and convergence properties of several popular and widely used families of single-reference quantum chemistry methods are investigated. In particular, we study the convergence properties of (i) the Møller-Plesset perturbation series up to fifth-order (MP2, MP3, MP4, and MP5), (ii) the iterative approximate coupled-cluster series CC2, CC3, and CC4, and (iii) the coupled-cluster series CCSD, CCSDT, and CCSDTQ. The performance of the ground-state gold standard CCSD(T) as well as the completely renormalized CC model, CR-CC(2,3), is also investigated. We show that MP4 provides an interesting accuracy/cost ratio, while MP5 systematically worsens the correlation energy estimates. In addition, CC3 outperforms CCSD(T) and CR-CC(2,3), as well as its more expensive parent CCSDT. A similar trend is observed for the methods including quadruple excitations, where the CC4 model is shown to be slightly more accurate than CCSDTQ, both methods providing correlation energies within 2 millihartree of the FCI limit.
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Affiliation(s)
- Yann Damour
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Mickaël Véril
- 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
| | - Michel Caffarel
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Denis Jacquemin
- Université de Nantes, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
| | - Anthony Scemama
- 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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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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28
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Lemmens L, De Vriendt X, Tolstykh D, Huysentruyt T, Bultinck P, Acke G. GQCP: The Ghent Quantum Chemistry Package. J Chem Phys 2021; 155:084802. [PMID: 34470369 DOI: 10.1063/5.0057515] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
The Ghent Quantum Chemistry Package (GQCP) is an open-source electronic structure software package that aims to provide an intuitive and expressive software framework for electronic structure software development. Its high-level interfaces (accessible through C++ and Python) have been specifically designed to correspond to theoretical concepts, while retaining access to lower-level intermediates and allowing structural run-time modifications of quantum chemical solvers. GQCP focuses on providing quantum chemical method developers with the computational "building blocks" that allow them to flexibly develop proof of principle implementations for new methods and applications up to the level of two-component spinor bases.
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Affiliation(s)
- Laurent Lemmens
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
| | - Xeno De Vriendt
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
| | - Daria Tolstykh
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
| | - Tobias Huysentruyt
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
| | - Patrick Bultinck
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
| | - Guillaume Acke
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
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29
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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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30
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Kim TD, Miranda-Quintana RA, Richer M, Ayers PW. Flexible ansatz for N-body configuration interaction. COMPUT THEOR CHEM 2021. [DOI: 10.1016/j.comptc.2021.113187] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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31
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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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32
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Dutta R, Chen GP, Henderson TM, Scuseria GE. Construction of linearly independent non-orthogonal AGP states. J Chem Phys 2021; 154:114112. [DOI: 10.1063/5.0045006] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Rishab Dutta
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Guo P. Chen
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
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33
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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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34
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Khamoshi A, Chen GP, Henderson TM, Scuseria GE. Exploring non-linear correlators on AGP. J Chem Phys 2021; 154:074113. [DOI: 10.1063/5.0039618] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Armin Khamoshi
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Guo P. Chen
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Thomas M. Henderson
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E. Scuseria
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
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35
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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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36
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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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37
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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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38
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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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39
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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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40
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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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41
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Sokolov IO, Barkoutsos PK, Ollitrault PJ, Greenberg D, Rice J, Pistoia M, Tavernelli I. Quantum orbital-optimized unitary coupled cluster methods in the strongly correlated regime: Can quantum algorithms outperform their classical equivalents? J Chem Phys 2020; 152:124107. [PMID: 32241157 DOI: 10.1063/1.5141835] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Coupled Cluster (CC) method is used to compute the electronic correlation energy in atoms and molecules and often leads to highly accurate results. However, due to its single-reference nature, standard CC in its projected form fails to describe quantum states characterized by strong electronic correlations and multi-reference projective methods become necessary. On the other hand, quantum algorithms for the solution of many-electron problems have also emerged recently. The quantum unitary variant of CC (UCC) with singles and doubles (q-UCCSD) is a popular wavefunction Ansatz for the variational quantum eigensolver algorithm. The variational nature of this approach can lead to significant advantages compared to its classical equivalent in the projected form, in particular, for the description of strong electronic correlation. However, due to the large number of gate operations required in q-UCCSD, approximations need to be introduced in order to make this approach implementable in a state-of-the-art quantum computer. In this work, we evaluate several variants of the standard q-UCCSD Ansatz in which only a subset of excitations is included. In particular, we investigate the singlet and pair q-UCCD approaches combined with orbital optimization. We show that these approaches can capture the dissociation/distortion profiles of challenging systems, such as H4, H2O, and N2 molecules, as well as the one-dimensional periodic Fermi-Hubbard chain. These results promote the future use of q-UCC methods for the solution of challenging electronic structure problems in quantum chemistry.
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Affiliation(s)
- Igor O Sokolov
- Zurich Research Laboratory, IBM Research GmbH, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | | | - Pauline J Ollitrault
- Zurich Research Laboratory, IBM Research GmbH, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Donny Greenberg
- IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - Julia Rice
- IBM Almaden Research Center, San Jose, California 95120, USA
| | - Marco Pistoia
- IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - Ivano Tavernelli
- Zurich Research Laboratory, IBM Research GmbH, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
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42
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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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43
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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: 10] [Impact Index Per Article: 2.0] [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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44
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Gomez JA, Molla M, Garza AJ, Henderson TM, Scuseria GE. Assessing combinations of singlet-paired coupled cluster and density functional theory for treating electron correlation in closed and open shells. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1615144] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- John A. Gomez
- Department of Chemistry, Rice University, Houston, TX, USA
- Applied Physics Graduate Program, Rice University, Houston, TX, USA
| | - Mahlet Molla
- Department of Chemistry, Rice University, Houston, TX, USA
| | | | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, TX, USA
- Department of Physics and Astronomy, Rice University, Houston, TX, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, TX, USA
- Department of Physics and Astronomy, Rice University, Houston, TX, USA
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45
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Gomez JA, Henderson TM, Scuseria GE. Polynomial-product states: A symmetry-projection-based factorization of the full coupled cluster wavefunction in terms of polynomials of double excitations. J Chem Phys 2019; 150:144108. [PMID: 30981260 DOI: 10.1063/1.5085314] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Our goal is to remedy the failure of symmetry-adapted coupled-cluster theory in the presence of strong correlation. Previous work along these lines has taken us from a diagram-level analysis of the coupled-cluster equations to an understanding of the collective modes which can occur in various channels of the coupled-cluster equations to the exploration of non-exponential wavefunctions in efforts to combine coupled-cluster theory with symmetry projection. In this manuscript, we extend these efforts by introducing a new, polynomial product wavefunction ansatz that incorporates information from symmetry projection into standard coupled-cluster theory in a way that attempts to mitigate the effects of the lack of size extensivity and size consistency characteristic of symmetry-projected methods. We describe the new approach in detail within the context of our previous efforts, explore some illustrative calculations, and consider one route for reducing the computational cost of the new method.
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Affiliation(s)
- John A Gomez
- Applied Physics Graduate Program, Rice University, Houston, Texas 77005, USA
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46
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Faulstich FM, Máté M, Laestadius A, Csirik MA, Veis L, Antalik A, Brabec J, Schneider R, Pittner J, Kvaal S, Legeza Ö. Numerical and Theoretical Aspects of the DMRG-TCC Method Exemplified by the Nitrogen Dimer. J Chem Theory Comput 2019; 15:2206-2220. [PMID: 30802406 PMCID: PMC7002028 DOI: 10.1021/acs.jctc.8b00960] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
![]()
In
this article, we investigate the numerical and theoretical aspects
of the coupled-cluster method tailored by matrix-product states. We
investigate formal properties of the used method, such as energy size
consistency and the equivalence of linked and unlinked formulation.
The existing mathematical analysis is here elaborated in a quantum
chemical framework. In particular, we highlight the use of what we
have defined as a complete active space-external space gap describing
the basis splitting between the complete active space and the external
part generalizing the concept of a HOMO–LUMO gap. Furthermore,
the behavior of the energy error for an optimal basis splitting, i.e.,
an active space choice minimizing the density matrix renormalization
group-tailored coupled-cluster singles doubles error, is discussed.
We show numerical investigations on the robustness with respect to
the bond dimensions of the single orbital entropy and the mutual information,
which are quantities that are used to choose a complete active space.
Moreover, the dependence of the ground-state energy error on the complete
active space has been analyzed numerically in order to find an optimal
split between the complete active space and external space by minimizing
the density matrix renormalization group-tailored coupled-cluster
error.
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Affiliation(s)
- Fabian M Faulstich
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Oslo , P.O. Box 1033 Blindern, N-0315 Oslo , Norway
| | - Mihály Máté
- Strongly Correlated Systems "Lendület" Research Group , Wigner Research Center for Physics , H-1525 , P.O. Box 49, Budapest , Hungary.,Department of Physics of Complex Systems , Eötvös Loránd University , Pf. 32 , H-1518 Budapest , Hungary
| | - Andre Laestadius
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Oslo , P.O. Box 1033 Blindern, N-0315 Oslo , Norway
| | - Mihály András Csirik
- Strongly Correlated Systems "Lendület" Research Group , Wigner Research Center for Physics , H-1525 , P.O. Box 49, Budapest , Hungary
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic , v.v.i., Dolejškova 3 , 18223 Prague 8 , Czech Republic
| | - Andrej Antalik
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic , v.v.i., Dolejškova 3 , 18223 Prague 8 , Czech Republic.,Faculty of Mathematics and Physics , Charles University , 11636 Prague , Czech Republic
| | - Jiří Brabec
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic , v.v.i., Dolejškova 3 , 18223 Prague 8 , Czech Republic
| | - Reinhold Schneider
- Modeling, Simulation and Optimization in Science, Department of Mathematics , Technische Universität Berlin , Sekretariat MA 5-3, Straße des 17. Juni 136 , 10623 Berlin , Germany
| | - Jiří Pittner
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic , v.v.i., Dolejškova 3 , 18223 Prague 8 , Czech Republic
| | - Simen Kvaal
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Oslo , P.O. Box 1033 Blindern, N-0315 Oslo , Norway
| | - Örs Legeza
- Strongly Correlated Systems "Lendület" Research Group , Wigner Research Center for Physics , H-1525 , P.O. Box 49, Budapest , Hungary
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47
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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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48
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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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49
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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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Bytautas L, Dukelsky J. Seniority based energy renormalization group (Ω-ERG) approach in quantum chemistry: Initial formulation and application to potential energy surfaces. COMPUT THEOR CHEM 2018. [DOI: 10.1016/j.comptc.2018.08.011] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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