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; 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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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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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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4
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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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5
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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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6
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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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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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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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9
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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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10
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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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11
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Nishida M, Akama T, Kobayashi M, Taketsugu T. Time-dependent Hartree–Fock–Bogoliubov method for molecular systems: An alternative excited-state methodology including static electron correlation. Chem Phys Lett 2023. [DOI: 10.1016/j.cplett.2023.140386] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/22/2023]
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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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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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15
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Johnson PA, Ayers PW, Baerdemacker SD, Limacher PA, Neck DV. Bivariational Principle for an Antisymmetrized Product of Nonorthogonal Geminals Appropriate for Strong Electron Correlation. COMPUT THEOR CHEM 2022. [DOI: 10.1016/j.comptc.2022.113718] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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16
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Margócsy Á, Szabados Á. Dressing of Vertices by Cumulants in Multi-Reference Coupled Cluster. J Chem Theory Comput 2021; 17:6947-6964. [PMID: 34643380 DOI: 10.1021/acs.jctc.1c00730] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A new scheme is introduced in Multi-Reference (MR) Coupled Cluster (CC) based on the MR Generalized Normal Ordering (MRGNO) and the corresponding MR Generalized Wick Theorem (MRGWT) of Kutzelnigg and Mukherjee. The key element is the identification of a structure in MRGWT generated terms, facilitated by Goldstone diagram techniques. This allows for bundling the many terms of the MRGWT expansion and introduces a hierarchy in the equations that can be harnessed in devising approximations. One- and two-particle interaction vertices are found to be uniformly substituted for their counterpart dressed by density cumulants. This allows for a straightforward rewriting of the ordinary energy expression of CC with interaction dressed (id) one- and two-particle terms and reveals the presence of three- and higher-rank dressed interaction vertices too. Cumulants appearing out of dressed interaction vertices contribute to the amplitude equations and can be interpreted to have an amplitude dressing role. Dressing of one- and two-particle interaction vertices is the most straightforward to implement and does not hinder computational feasibility, provided that the reference function involves strictly limited active space sizes. The Generalized Valence Bond wave function, underlying pilot numerical tests, fulfills this criterion. Results on multiple bond breaking scenarios point to the need of stepping beyond one- and two-particle id. An extremely simple version of incorporating amplitude dressing in addition to one- and two-particle id is seen to cure the potential energy curves remarkably, stimulating further investigations along this line.
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Affiliation(s)
- Ádám Margócsy
- ELTE Eötvös Loránd University, Faculty of Science, Institute of Chemistry Laboratory of Theoretical Chemistry Hevesy György PhD School of Chemistry, P.O. Box 32, Budapest 1518, Hungary
| | - Ágnes Szabados
- ELTE Eötvös Loránd University, Faculty of Science, Institute of Chemistry Laboratory of Theoretical Chemistry, P.O. Box 32, Budapest 1518, Hungary
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17
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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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18
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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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19
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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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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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Dutta R, Henderson TM, Scuseria GE. Geminal Replacement Models Based on AGP. J Chem Theory Comput 2020; 16:6358-6367. [DOI: 10.1021/acs.jctc.0c00807] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Rishab Dutta
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
| | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
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22
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Mihálka ZÉ, Surján PR, Szabados Á. Half-Projection of the Strongly Orthogonal Unrestricted Geminals’ Product Wave Function. J Chem Theory Comput 2019; 16:892-903. [DOI: 10.1021/acs.jctc.9b00858] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Zs. É. Mihálka
- Faculty of Science, Institute of Chemistry, Laboratory of Theoretical Chemistry, ELTE Eötvös Loránd University, Budapest, Hungary
- Hevesy György Ph.D. School of Chemistry, ELTE, Budapest, Hungary
| | - P. R. Surján
- Faculty of Science, Institute of Chemistry, Laboratory of Theoretical Chemistry, ELTE Eötvös Loránd University, Budapest, Hungary
| | - Á. Szabados
- Faculty of Science, Institute of Chemistry, Laboratory of Theoretical Chemistry, ELTE Eötvös Loránd University, Budapest, Hungary
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23
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Khamoshi A, Henderson TM, Scuseria GE. Efficient evaluation of AGP reduced density matrices. J Chem Phys 2019; 151:184103. [DOI: 10.1063/1.5127850] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [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
| | - 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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24
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Rishi V, Valeev EF. Can the distinguishable cluster approximation be improved systematically by including connected triples? J Chem Phys 2019. [DOI: 10.1063/1.5097150] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Varun Rishi
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
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25
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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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26
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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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27
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Földvári D, Tóth Z, Surján PR, Szabados Á. Geminal perturbation theory based on the unrestricted Hartree-Fock wavefunction. J Chem Phys 2019; 150:034103. [PMID: 30660159 DOI: 10.1063/1.5060731] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A perturbative correction exploiting natural orbitals and the pair function structure of the unrestricted Hartree-Fock (UHF) wavefunction is devised. The method offers a simple framework for describing multireference systems where static correlation is captured by UHF. The UHF wavefunction is built of two-electron fragments (geminals), involving both singlet and triplet (ms = 0) parts. At order zero of the perturbative treatment, configuration interaction coefficients of UHF geminals are relaxed. The zero order Hamiltonian is of the Dyall-type, including explicit two-electron interaction within geminals and leading to a formal 6th power scaling. Adopting an effective one-electron zero order Hamiltonian term for the subset of virtual orbitals reduces scaling of the correction step to 4th power. Formal properties of the proposed schemes are discussed. Energetic data and natural occupation numbers of illustrative test systems are used to assess the new approach. The cases where the wavefunction becomes essentially spin pure at the level of reference show good performance. Spin contamination remaining at order zero is found to undermine the perturbative correction.
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Affiliation(s)
- D Földvári
- Laboratory of Theoretical Chemistry, Faculty of Science, Institute of Chemistry, ELTE Eötvös Loránd University, Budapest, Hungary
| | - Zs Tóth
- Laboratory of Theoretical Chemistry, Faculty of Science, Institute of Chemistry, ELTE Eötvös Loránd University, Budapest, Hungary
| | - P R Surján
- Laboratory of Theoretical Chemistry, Faculty of Science, Institute of Chemistry, ELTE Eötvös Loránd University, Budapest, Hungary
| | - Á Szabados
- Laboratory of Theoretical Chemistry, Faculty of Science, Institute of Chemistry, ELTE Eötvös Loránd University, Budapest, Hungary
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28
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Margócsy Á, Kowalski P, Pernal K, Szabados Á. Multiple bond breaking with APSG-based correlation methods: comparison of two approaches. Theor Chem Acc 2018. [DOI: 10.1007/s00214-018-2355-4] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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29
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Zhou C, Chen Z, Wu W. Reciprocal transformation of seniority number restricted wave function. J Chem Phys 2018; 149:044111. [DOI: 10.1063/1.5032129] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Affiliation(s)
- Chen Zhou
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
| | - Zhenhua Chen
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
| | - Wei Wu
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, iChem and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
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30
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Lanssens C, Ayers PW, Van Neck D, De Baerdemacker S, Gunst K, Bultinck P. Method for making 2-electron response reduced density matrices approximately N-representable. J Chem Phys 2018; 148:084104. [PMID: 29495792 DOI: 10.1063/1.4994618] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In methods like geminal-based approaches or coupled cluster that are solved using the projected Schrödinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based on response theory. However, the 2-RDMs from response theory are not N-representable. That is, the response 2-RDM does not correspond to an actual physical N-electron wave function. We present a new algorithm for making these non-N-representable 2-RDMs approximately N-representable, i.e., it has the right symmetry and normalization and it fulfills the P-, Q-, and G-conditions. Next to an algorithm which can be applied to any 2-RDM, we have also developed a 2-RDM optimization procedure specifically for seniority-zero 2-RDMs. We aim to find the 2-RDM with the right properties which is the closest (in the sense of the Frobenius norm) to the non-N-representable 2-RDM by minimizing the square norm of the difference between this initial response 2-RDM and the targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM, Q-matrix, and G-matrix are positive semidefinite, i.e., their eigenvalues are non-negative. Our method is suitable for fixing non-N-representable 2-RDMs which are close to being N-representable. Through the N-representability optimization algorithm we add a small correction to the initial 2-RDM such that it fulfills the most important N-representability conditions.
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Affiliation(s)
- Caitlin Lanssens
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4L8, Canada
| | - Dimitri Van Neck
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | - Stijn De Baerdemacker
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | - Klaas Gunst
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | - Patrick Bultinck
- Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Ghent, Belgium
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31
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Johnson PA, Limacher PA, Kim TD, Richer M, Miranda-Quintana RA, Heidar-Zadeh F, Ayers PW, Bultinck P, De Baerdemacker S, Van Neck D. Strategies for extending geminal-based wavefunctions: Open shells and beyond. COMPUT THEOR CHEM 2017. [DOI: 10.1016/j.comptc.2017.05.010] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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32
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A comparative study on seniority-based MO and VB calculations of the singlet and triplet energy gaps of open-shell molecules. COMPUT THEOR CHEM 2017. [DOI: 10.1016/j.comptc.2017.03.031] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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33
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Head-Marsden K, Mazziotti DA. Pair 2-electron reduced density matrix theory using localized orbitals. J Chem Phys 2017; 147:084101. [PMID: 28863513 DOI: 10.1063/1.4999423] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Full configuration interaction (FCI) restricted to a pairing space yields size-extensive correlation energies but its cost scales exponentially with molecular size. Restricting the variational two-electron reduced-density-matrix (2-RDM) method to represent the same pairing space yields an accurate lower bound to the pair FCI energy at a mean-field-like computational scaling of O(r3) where r is the number of orbitals. In this paper, we show that localized molecular orbitals can be employed to generate an efficient, approximately size-extensive pair 2-RDM method. The use of localized orbitals eliminates the substantial cost of optimizing iteratively the orbitals defining the pairing space without compromising accuracy. In contrast to the localized orbitals, the use of canonical Hartree-Fock molecular orbitals is shown to be both inaccurate and non-size-extensive. The pair 2-RDM has the flexibility to describe the spectra of one-electron RDM occupation numbers from all quantum states that are invariant to time-reversal symmetry. Applications are made to hydrogen chains and their dissociation, n-acene from naphthalene through octacene, and cadmium telluride 2-, 3-, and 4-unit polymers. For the hydrogen chains, the pair 2-RDM method recovers the majority of the energy obtained from similar calculations that iteratively optimize the orbitals. The localized-orbital pair 2-RDM method with its mean-field-like computational scaling and its ability to describe multi-reference correlation has important applications to a range of strongly correlated phenomena in chemistry and physics.
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Affiliation(s)
- Kade Head-Marsden
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - David A Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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34
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Rishi V, Perera A, Nooijen M, Bartlett RJ. Excited states from modified coupled cluster methods: Are they any better than EOM CCSD? J Chem Phys 2017; 146:144104. [DOI: 10.1063/1.4979078] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Affiliation(s)
- Varun Rishi
- Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32611, USA
| | - Ajith Perera
- Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32611, USA
| | - Marcel Nooijen
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Rodney J. Bartlett
- Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32611, USA
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35
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Sharma S, Knizia G, Guo S, Alavi A. Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory. J Chem Theory Comput 2017; 13:488-498. [DOI: 10.1021/acs.jctc.6b00898] [Citation(s) in RCA: 46] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Affiliation(s)
- Sandeep Sharma
- Max Planck Institute
for Solid State Research, Heisenbergstraße
1, 70569 Stuttgart, Germany
- Department
of Chemistry and Biochemistry, University of Colorado Boulder, Boulder, Colorado 80302, United States
| | - Gerald Knizia
- Department
of Chemistry, Pennsylvania State University, 401A Chemistry Building, University Park, Pennsylvania 16802, United States
| | - Sheng Guo
- Department
of Chemistry, Princeton University, Princeton, New Jersey 08544, United States
| | - Ali Alavi
- Max Planck Institute
for Solid State Research, Heisenbergstraße
1, 70569 Stuttgart, Germany
- Department
of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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36
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Affiliation(s)
- Peter A. Limacher
- Institute of Physical Chemistry, Karlsruhe Institute of Technology, Karlsruhe, Germany
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37
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Senjean B, Tsuchiizu M, Robert V, Fromager E. Local density approximation in site-occupation embedding theory. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1182224] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Bruno Senjean
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, Strasbourg, France
| | | | - Vincent Robert
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, Strasbourg, France
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, Strasbourg, France
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38
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Boguslawski K, Ayers PW. Linearized Coupled Cluster Correction on the Antisymmetric Product of 1-Reference Orbital Geminals. J Chem Theory Comput 2015; 11:5252-61. [DOI: 10.1021/acs.jctc.5b00776] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Katharina Boguslawski
- Institute
of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Torun, Poland
| | - Paul W. Ayers
- Department
of Chemistry and Chemical Biology, McMaster University, 1280 Main
Street West, Hamilton, ON, L8S 4M1, Canada
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39
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Van Raemdonck M, Alcoba DR, Poelmans W, De Baerdemacker S, Torre A, Lain L, Massaccesi GE, Van Neck D, Bultinck P. Polynomial scaling approximations and dynamic correlation corrections to doubly occupied configuration interaction wave functions. J Chem Phys 2015; 143:104106. [PMID: 26374017 DOI: 10.1063/1.4930260] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
A class of polynomial scaling methods that approximate Doubly Occupied Configuration Interaction (DOCI) wave functions and improve the description of dynamic correlation is introduced. The accuracy of the resulting wave functions is analysed by comparing energies and studying the overlap between the newly developed methods and full configuration interaction wave functions, showing that a low energy does not necessarily entail a good approximation of the exact wave function. Due to the dependence of DOCI wave functions on the single-particle basis chosen, several orbital optimisation algorithms are introduced. An energy-based algorithm using the simulated annealing method is used as a benchmark. As a computationally more affordable alternative, a seniority number minimising algorithm is developed and compared to the energy based one revealing that the seniority minimising orbital set performs well. Given a well-chosen orbital basis, it is shown that the newly developed DOCI based wave functions are especially suitable for the computationally efficient description of static correlation and to lesser extent dynamic correlation.
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Affiliation(s)
- Mario Van Raemdonck
- Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium
| | - Diego R Alcoba
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Ward Poelmans
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | - Stijn De Baerdemacker
- Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium
| | - 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
| | - Gustavo E Massaccesi
- Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Dimitri Van Neck
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | - Patrick Bultinck
- Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium
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40
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Bytautas L, Scuseria GE, Ruedenberg K. Seniority number description of potential energy surfaces: Symmetric dissociation of water, N2, C2, and Be2. J Chem Phys 2015; 143:094105. [DOI: 10.1063/1.4929904] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Laimutis Bytautas
- Department of Chemistry, Galveston College, 4015 Ave. Q, Galveston, Texas 77550, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Chemistry Department, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
| | - Klaus Ruedenberg
- Department of Chemistry, Iowa State University, Ames, Iowa 50011, USA
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41
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Poelmans W, Van Raemdonck M, Verstichel B, De Baerdemacker S, Torre A, Lain L, Massaccesi GE, Alcoba DR, Bultinck P, Van Neck D. Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function. J Chem Theory Comput 2015; 11:4064-76. [DOI: 10.1021/acs.jctc.5b00378] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ward Poelmans
- Center
for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | - Mario Van Raemdonck
- Department
of Inorganic and Physical Chemistry, Ghent University, Krijgslaan
281 (S3), 9000 Gent, Belgium
| | - Brecht Verstichel
- Center
for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | - Stijn De Baerdemacker
- Center
for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
- Department
of Inorganic and Physical Chemistry, Ghent University, Krijgslaan
281 (S3), 9000 Gent, Belgium
| | - 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
| | - Gustavo E. Massaccesi
- Departamento
de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Diego R. Alcoba
- Departamento
de Física, Facultad de Ciencias Exactas y Naturales, Universidad
de Buenos Aires and Instituto de Física de Buenos Aires, Consejo
Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Patrick Bultinck
- Department
of Inorganic and Physical Chemistry, Ghent University, Krijgslaan
281 (S3), 9000 Gent, Belgium
| | - Dimitri Van Neck
- Center
for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
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42
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Abstract
A new single-pair operator for seniority-zero wave functions is introduced closely related to the single-particle Fock operator from conventional Hartree-Fock theory. This allows one to ascribe orbital energies in the context of model Hamiltonians, for which no single-particle operators exist. Several applications demonstrate the usefulness of these orbital energies. In analogy to Koopmans' theorem, atomic double ionization potentials are successfully predicted. A computationally efficient second-order perturbation scheme for seniority-zero wave functions scaling quadratically with system size is defined and applied to the dissociation of nitrogen and to strongly correlated two-dimensional Heisenberg lattices. An extension of the method for full seniority is presented leading to an intruder-free single reference perturbation theory with improved asymptotic convergence.
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Affiliation(s)
- Peter A Limacher
- Institute of Physical Chemistry, Karlsruhe Institute of Technology , D-76131 Karlsruhe, Germany
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43
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Affiliation(s)
- Zhenhua Chen
- The State Key Laboratory
of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial
Key Laboratory of Theoretical and Computational Chemistry and College
of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
| | - Chen Zhou
- The State Key Laboratory
of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial
Key Laboratory of Theoretical and Computational Chemistry and College
of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
| | - Wei Wu
- The State Key Laboratory
of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial
Key Laboratory of Theoretical and Computational Chemistry and College
of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
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44
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45
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46
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Verstraelen T, Vandenbrande S, Ayers PW. Direct computation of parameters for accurate polarizable force fields. J Chem Phys 2015; 141:194114. [PMID: 25416881 DOI: 10.1063/1.4901513] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
We present an improved electronic linear response model to incorporate polarization and charge-transfer effects in polarizable force fields. This model is a generalization of the Atom-Condensed Kohn-Sham Density Functional Theory (DFT), approximated to second order (ACKS2): it can now be defined with any underlying variational theory (next to KS-DFT) and it can include atomic multipoles and off-center basis functions. Parameters in this model are computed efficiently as expectation values of an electronic wavefunction, obviating the need for their calibration, regularization, and manual tuning. In the limit of a complete density and potential basis set in the ACKS2 model, the linear response properties of the underlying theory for a given molecular geometry are reproduced exactly. A numerical validation with a test set of 110 molecules shows that very accurate models can already be obtained with fluctuating charges and dipoles. These features greatly facilitate the development of polarizable force fields.
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Affiliation(s)
- Toon Verstraelen
- Center for Molecular Modeling (CMM), Member of the QCMM Ghent-Brussels Alliance, Ghent University, Technologiepark 903, B9000 Ghent, Belgium
| | - Steven Vandenbrande
- Center for Molecular Modeling (CMM), Member of the QCMM Ghent-Brussels Alliance, Ghent University, Technologiepark 903, B9000 Ghent, Belgium
| | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4M1, Canada
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47
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Jeszenszki P, Surján PR, Szabados Á. Spin Symmetry and Size Consistency of Strongly Orthogonal Geminals. J Chem Theory Comput 2015; 11:3096-103. [DOI: 10.1021/acs.jctc.5b00333] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Péter Jeszenszki
- Laboratory of Theoretical
Chemistry, Institute of Chemistry, Loránd Eötvös University, 1518 Budapest, POB 32, Hungary
| | - Péter R. Surján
- Laboratory of Theoretical
Chemistry, Institute of Chemistry, Loránd Eötvös University, 1518 Budapest, POB 32, Hungary
| | - Ágnes Szabados
- Laboratory of Theoretical
Chemistry, Institute of Chemistry, Loránd Eötvös University, 1518 Budapest, POB 32, Hungary
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48
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van Aggelen H, Yang Y, Yang W. Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random phase approximation. J Chem Phys 2015; 140:18A511. [PMID: 24832319 DOI: 10.1063/1.4865816] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Despite their unmatched success for many applications, commonly used local, semi-local, and hybrid density functionals still face challenges when it comes to describing long-range interactions, static correlation, and electron delocalization. Density functionals of both the occupied and virtual orbitals are able to address these problems. The particle-hole (ph-) Random Phase Approximation (RPA), a functional of occupied and virtual orbitals, has recently known a revival within the density functional theory community. Following up on an idea introduced in our recent communication [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013)], we formulate more general adiabatic connections for the correlation energy in terms of pairing matrix fluctuations described by the particle-particle (pp-) propagator. With numerical examples of the pp-RPA, the lowest-order approximation to the pp-propagator, we illustrate the potential of density functional approximations based on pairing matrix fluctuations. The pp-RPA is size-extensive, self-interaction free, fully anti-symmetric, describes the strong static correlation limit in H2, and eliminates delocalization errors in H2(+) and other single-bond systems. It gives surprisingly good non-bonded interaction energies--competitive with the ph-RPA--with the correct R(-6) asymptotic decay as a function of the separation R, which we argue is mainly attributable to its correct second-order energy term. While the pp-RPA tends to underestimate absolute correlation energies, it gives good relative energies: much better atomization energies than the ph-RPA, as it has no tendency to underbind, and reaction energies of similar quality. The adiabatic connection in terms of pairing matrix fluctuation paves the way for promising new density functional approximations.
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Affiliation(s)
- Helen van Aggelen
- Department of Inorganic and Physical Chemistry, Ghent University, Ghent, Belgium
| | - Yang Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Weitao Yang
- Department of Chemistry and Department of Physics, Duke University, Durham, North Carolina 27708, USA
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49
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Small DW, Sundstrom EJ, Head-Gordon M. A simple way to test for collinearity in spin symmetry broken wave functions: General theory and application to generalized Hartree Fock. J Chem Phys 2015; 142:094112. [DOI: 10.1063/1.4913740] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- David W. Small
- Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Eric J. Sundstrom
- Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Martin Head-Gordon
- Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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50
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Small DW, Sundstrom EJ, Head-Gordon M. Restricted Hartree Fock using complex-valued orbitals: A long-known but neglected tool in electronic structure theory. J Chem Phys 2015; 142:024104. [DOI: 10.1063/1.4905120] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- David W. Small
- Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Eric J. Sundstrom
- Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Martin Head-Gordon
- Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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