1
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Gałyńska M, de Moraes MMF, Tecmer P, Boguslawski K. Delving into the catalytic mechanism of molybdenum cofactors: a novel coupled cluster study. Phys Chem Chem Phys 2024; 26:18918-18929. [PMID: 38952220 DOI: 10.1039/d4cp01500b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/03/2024]
Abstract
In this work, we use modern electronic structure methods to model the catalytic mechanism of different variants of the molybdenum cofactor (Moco). We investigate the dependence of various Moco model systems on structural relaxation and the importance of environmental effects for five critical points along the reaction coordinate with the DMSO and NO3- substrates. Furthermore, we scrutinize the performance of various coupled-cluster approaches for modeling the relative energies along the investigated reaction paths, focusing on several pair coupled cluster doubles (pCCD) flavors and conventional coupled cluster approximations. Moreover, we elucidate the Mo-O bond formation using orbital-based quantum information measures, which highlight the flow of σM-O bond formation and σN/S-O bond breaking. Our study shows that pCCD-based models are a viable alternative to conventional methods and offer us unique insights into the bonding situation along a reaction coordinate. Finally, this work highlights the importance of environmental effects or changes in the core and, consequently, in the model itself to elucidate the change in activity of different Moco variants.
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Affiliation(s)
- Marta Gałyńska
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
| | - Matheus Morato F de Moraes
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
| | - Paweł Tecmer
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
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2
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Chakraborty R, de Moraes MMF, Boguslawski K, Nowak A, Świerczyński J, Tecmer P. Toward Reliable Dipole Moments without Single Excitations: The Role of Orbital Rotations and Dynamical Correlation. J Chem Theory Comput 2024; 20:4689-4702. [PMID: 38809012 PMCID: PMC11171297 DOI: 10.1021/acs.jctc.4c00471] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2024] [Revised: 05/15/2024] [Accepted: 05/17/2024] [Indexed: 05/30/2024]
Abstract
The dipole moment is a crucial molecular property linked to a molecular system's bond polarity and overall electronic structure. To that end, the electronic dipole moment, which results from the electron density of a system, is often used to assess the accuracy and reliability of new electronic structure methods. This work analyses electronic dipole moments computed with the pair coupled cluster doubles (pCCD) ansätze and its linearized coupled cluster (pCCD-LCC) corrections using the canonical Hartree-Fock and pCCD-optimized (localized) orbital bases. The accuracy of pCCD-based dipole moments is assessed against experimental and CCSD(T) reference values using relaxed and unrelaxed density matrices and different basis set sizes. Our test set comprises molecules of various bonding patterns and electronic structures, exposing pCCD-based methods to a wide range of electron correlation effects. Additionally, we investigate the performance of pCCD-in-DFT dipole moments of some model complexes. Finally, our work indicates the importance of orbital relaxation in the pCCD model and shows the limitations of the linearized couple cluster corrections in predicting electronic dipole moments of multiple-bonded systems. Most importantly, pCCD with a linearized CCD correction can reproduce the dipole moment surfaces in singly bonded molecules, which are comparable to the multireference ones.
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Affiliation(s)
- Rahul Chakraborty
- Institute
of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland
| | - Matheus Morato F. de Moraes
- Institute
of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland
| | - Katharina Boguslawski
- Institute
of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland
| | - Artur Nowak
- Institute
of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland
| | - Julian Świerczyński
- Institute
of Engineering and Technology, Faculty of Physics, Astronomy, and
Informatics, Nicolaus Copernicus University
in Toruń, Grudzia̧dzka
5, 87-100 Toruń, Poland
| | - Paweł Tecmer
- Institute
of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland
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3
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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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4
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Miranda-Quintana RA, Kim TD, Lokhande RA, Richer M, Sánchez-Díaz G, Gaikwad PB, Ayers PW. Flexible Ansatz for N-Body Perturbation Theory. J Phys Chem A 2024; 128:3458-3467. [PMID: 38651558 DOI: 10.1021/acs.jpca.4c00855] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
We propose a new perturbation theory framework that can be used to help with the projective solution of the Schrödinger equation for arbitrary wave functions. This Flexible Ansatz for N-body Perturbation Theory (FANPT) is based on our previously proposed Flexible Ansatz for the N-body Configuration Interaction (FANCI). We derive recursive FANPT expressions, including arbitrary orders in the perturbation hierarchy. We show that the FANPT equations are well-behaved across a wide range of conditions, including static correlation-dominated configurations and highly nonlinear wave functions.
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Affiliation(s)
- Ramón Alain Miranda-Quintana
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, Florida 32603, United States
| | - Taewon D Kim
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, Florida 32603, United States
- 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, United States
| | - M Richer
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Gabriela Sánchez-Díaz
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Pratiksha B Gaikwad
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, Florida 32603, United States
| | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
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5
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Chan M, Verstraelen T, Tehrani A, Richer M, Yang XD, Kim TD, Vöhringer-Martinez E, Heidar-Zadeh F, Ayers PW. The tale of HORTON: Lessons learned in a decade of scientific software development. J Chem Phys 2024; 160:162501. [PMID: 38651814 DOI: 10.1063/5.0196638] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2024] [Accepted: 02/28/2024] [Indexed: 04/25/2024] Open
Abstract
HORTON is a free and open-source electronic-structure package written primarily in Python 3 with some underlying C++ components. While HORTON's development has been mainly directed by the research interests of its leading contributing groups, it is designed to be easily modified, extended, and used by other developers of quantum chemistry methods or post-processing techniques. Most importantly, HORTON adheres to modern principles of software development, including modularity, readability, flexibility, comprehensive documentation, automatic testing, version control, and quality-assurance protocols. This article explains how the principles and structure of HORTON have evolved since we started developing it more than a decade ago. We review the features and functionality of the latest HORTON release (version 2.3) and discuss how HORTON is evolving to support electronic structure theory research for the next decade.
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Affiliation(s)
- Matthew Chan
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S-4L8, Canada
| | - Toon Verstraelen
- Center for Molecular Modeling (CMM), Ghent University, Technologiepark-Zwijnaarde 46, B-9052 Ghent, Belgium
| | - Alireza Tehrani
- Department of Chemistry, Queen's University, Kingston, Ontario K7L-3N6, Canada
| | - Michelle Richer
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S-4L8, Canada
| | - Xiaotian Derrick Yang
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S-4L8, Canada
| | - Taewon David Kim
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S-4L8, Canada
| | - Esteban Vöhringer-Martinez
- Departamento de Físico Química, Facultad de Ciencias Químicas, Universidad de Concepción, 4070371 Concepción, Chile
| | - Farnaz Heidar-Zadeh
- Department of Chemistry, Queen's University, Kingston, Ontario K7L-3N6, Canada
| | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S-4L8, Canada
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6
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Gaikwad PB, Kim TD, Richer M, Lokhande RA, Sánchez-Díaz G, Limacher PA, Ayers PW, Miranda-Quintana RA. Coupled cluster-inspired geminal wavefunctions. J Chem Phys 2024; 160:144108. [PMID: 38597308 DOI: 10.1063/5.0202035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2024] [Accepted: 03/24/2024] [Indexed: 04/11/2024] Open
Abstract
Electron pairs have an illustrious history in chemistry, from powerful concepts to understanding structural stability and reactive changes to the promise of serving as building blocks of quantitative descriptions of the electronic structure of complex molecules and materials. However, traditionally, two-electron wavefunctions (geminals) have not enjoyed the popularity and widespread use of the more standard single-particle methods. This has changed recently, with a renewed interest in the development of geminal wavefunctions as an alternative to describing strongly correlated phenomena. Hence, there is a need to find geminal methods that are accurate, computationally tractable, and do not demand significant input from the user (particularly via cumbersome and often ill-behaved orbital optimization steps). Here, we propose new families of geminal wavefunctions inspired by the pair coupled cluster doubles ansatz. We present a new hierarchy of two-electron wavefunctions that extends the one-reference orbital idea to other geminals. Moreover, we show how to incorporate single-like excitations in this framework without leaving the quasiparticle picture. We explore the role of imposing seniority restrictions on these wavefunctions and benchmark these new methods on model strongly correlated systems.
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Affiliation(s)
- Pratiksha B Gaikwad
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, Florida 32603, USA
| | - Taewon D Kim
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, Florida 32603, USA
| | - M Richer
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Rugwed A Lokhande
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, Florida 32603, USA
| | - Gabriela Sánchez-Díaz
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Peter A Limacher
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
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7
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Johnson PA, DePrince AE. Single Reference Treatment of Strongly Correlated H 4 and H 10 Isomers with Richardson-Gaudin States. J Chem Theory Comput 2023; 19:8129-8146. [PMID: 37955440 DOI: 10.1021/acs.jctc.3c00807] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2023]
Abstract
Richardson-Gaudin (RG) states are employed as a variational wave function ansatz for strongly correlated isomers of H4 and H10. In each case, a single RG state describes the seniority-zero sector quite well. Simple natural orbital functionals offer a cheap and reasonable approximation of the outstanding weak correlation in the seniority-zero sector, while systematic improvement is achieved by performing a configuration interaction in terms of RG states.
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Affiliation(s)
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
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8
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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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9
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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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10
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Cassam-Chenaï P, Perez T, Accomasso D. 2D-block geminals: A non 1-orthogonal and non 0-seniority model with reduced computational complexity. J Chem Phys 2023; 158:074106. [PMID: 36813726 DOI: 10.1063/5.0133734] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/19/2023] Open
Abstract
We present a new geminal product wave function Ansatz where the geminals are not constrained to be strongly orthogonal or to be of seniority-zero. Instead, we introduce weaker orthogonality constraints between geminals that significantly lower the computational effort without sacrificing the indistinguishability of the electrons. That is to say, the electron pairs corresponding to the geminals are not fully distinguishable, and their product has yet to be antisymmetrized according to the Pauli principle to form a bona fide electronic wave function. Our geometrical constraints translate into simple equations involving the traces of products of our geminal matrices. In the simplest non-trivial model, a set of solutions is given by block-diagonal matrices where each block is 2 × 2 and consists of either a Pauli matrix or a normalized diagonal matrix multiplied by a complex parameter to be optimized. With this simplified Ansatz for geminals, the number of terms in the calculation of the matrix elements of quantum observables is considerably reduced. A proof of principle is reported and confirms that the Ansatz is more accurate than strongly orthogonal geminal products while remaining computationally affordable.
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Affiliation(s)
| | - Thomas Perez
- Université Côte d'Azur, LJAD, UMR 7351, 06100 Nice, France
| | - Davide Accomasso
- Dipartimento di Chimica e Chimica Industriale, Universita' di Pisa, via Moruzzi 13, 56124 Pisa, Italy
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11
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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: 4] [Impact Index Per Article: 4.0] [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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12
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Tecmer P, Boguslawski K. Geminal-based electronic structure methods in quantum chemistry. Toward a geminal model chemistry. Phys Chem Chem Phys 2022; 24:23026-23048. [PMID: 36149376 DOI: 10.1039/d2cp02528k] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this review, we discuss the recent progress in developing geminal-based theories for challenging problems in quantum chemistry. Specifically, we focus on the antisymmetrized geminal power, generalized valence bond, antisymmetrized product of strongly orthogonal geminals, singlet-type orthogonal geminals, the antisymmetric product of 1-reference orbital geminal, also known as the pair coupled cluster doubles ansatz, and geminals constructed from Richardson-Gaudin states. Furthermore, we review various corrections to account for the missing dynamical correlation effects in geminal models and possible extensions to target electronically excited states and open-shell species. Finally, we discuss some numerical examples and present-day challenges for geminal-based models, including a quantitative and qualitative analysis of wave functions, and software availability.
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Affiliation(s)
- Paweł Tecmer
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
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13
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Leszczyk A, Dome T, Tecmer P, Kedziera D, Boguslawski K. Resolving the π-assisted U-N σ f-bond formation using quantum information theory. Phys Chem Chem Phys 2022; 24:21296-21307. [PMID: 36043327 DOI: 10.1039/d2cp03377a] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We model the potential energy profiles of the UO2 (NCO)Cl2- → NUOCl2- + CO2 reaction pathway [Y. Gong, V. Vallet, M. del Carmen Michelini, D. Rios and J. K. Gibson, J. Phys. Chem. A, 2014, 118, 325-330] using different pair coupled-cluster doubles (pCCD) methods. Specifically, we focus on pCCD and pCCD-tailored coupled cluster models in predicting relative energies for the various intermediates and transition states along the reaction coordinate. Furthermore, we augment our study on energetics with an orbital-pair correlation analysis of the complete reaction pathway that features two distinct paths. Our analysis of orbital correlations sheds new light on the formation and breaking of respective bonds between the uranium, oxygen, and nitrogen atoms along the reaction coordinates where the "yl" bond is broken and a nitrido compound formed. Specifically, the strengthening of the U-N σf-bond is assisted by a π-type interaction that is delocalized over the C-N-U backbone of the UO2 (NCO)Cl2- complex.
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Affiliation(s)
- Aleksandra Leszczyk
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
| | - Tibor Dome
- Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland.,Institute of Astronomy, University of Cambridge, Madingley Road Cambridge, CB3 0HA, UK
| | - Paweł Tecmer
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
| | - Dariusz Kedziera
- Faculty of Chemistry, Nicolaus Copernicus University in Toruń, Gagarina 7, 87-100 Toruń, Poland
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
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14
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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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15
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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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16
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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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17
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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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18
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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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19
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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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20
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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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21
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Oña OB, Torre A, Lain L, Alcoba DR, Ríos E, Massaccesi GE. Variational determination of the two-electron reduced density matrix within the doubly occupied configuration interaction scheme: An extension to the study of open-shell systems. J Chem Phys 2020; 153:084101. [DOI: 10.1063/5.0020581] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ofelia B. Oña
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de La Plata, CCT La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, Diag. 113 y 64 (S/N), Sucursal 4, CC 16, 1900 La Plata, Argentina
| | - Alicia Torre
- Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain
| | - Luis Lain
- Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain
| | - Diego R. Alcoba
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
- Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Elías Ríos
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de La Plata, CCT La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, Diag. 113 y 64 (S/N), Sucursal 4, CC 16, 1900 La Plata, Argentina
| | - Gustavo E. Massaccesi
- Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
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22
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Larsson HR, Jiménez-Hoyos CA, Chan GKL. Minimal Matrix Product States and Generalizations of Mean-Field and Geminal Wave Functions. J Chem Theory Comput 2020; 16:5057-5066. [DOI: 10.1021/acs.jctc.0c00463] [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)
- Henrik R. Larsson
- Department of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | | | - Garnet Kin-Lic Chan
- Department of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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