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Alcoba DR, Lain L, Torre A, Ayala TR, Oña OB, Massaccesi GE, Peralta JE, Melo JI. Generalized Spin in the Variance-Based Wave Function Optimization Method within the Doubly Occupied Configuration Interaction Framework. J Phys Chem A 2024. [PMID: 39140833 DOI: 10.1021/acs.jpca.4c02742] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/15/2024]
Abstract
In this work, we implement a generalized spin formulation of the doubly occupied configuration interaction methodology using the energy variance of the N-electron Hamiltonian. We perform the optimization of the N-electron wave functions and calculate their corresponding energies, using a unified variational treatment for ground and excited states based on the energy variance, which allows us to describe the entire energy spectra on an equal footing. We analyze the effects produced by the breakdown of the Ŝ2 and Ŝz symmetries in the spectra of model hydrogenic clusters in terms of energies and spin-related quantities, arising from the restricted, unrestricted, and generalized spin methods. The results are compared with other related methods as well as full configuration interaction.
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Affiliation(s)
- Diego R Alcoba
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Ciudad Universitaria, 1428 Buenos Aires, Argentina
- CONICET─Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Luis Lain
- Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain
| | - Alicia Torre
- Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain
| | - Tomás R Ayala
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Ofelia B Oña
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de 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
- Instituto de Investigaciones Matemáticas "Luis A. Santaló" (IMAS), Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Juan E Peralta
- Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, United States
| | - Juan I Melo
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Ciudad Universitaria, 1428 Buenos Aires, Argentina
- CONICET─Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Ciudad Universitaria, 1428 Buenos Aires, Argentina
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2
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Johnson PA. Beyond a Richardson-Gaudin Mean-Field: Slater-Condon Rules and Perturbation Theory. J Phys Chem A 2024; 128:6033-6045. [PMID: 39007410 DOI: 10.1021/acs.jpca.4c02857] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/16/2024]
Abstract
Richardson-Gaudin states provide a basis of the Hilbert space for strongly correlated electrons. In this study, optimal expressions for the transition density matrix elements between Richardson-Gaudin states are obtained with a cost comparable with the corresponding reduced density matrix elements. Analogues of the Slater-Condon rules are identified based on the number of near-zero singular values of the RG state overlap matrix. Finally, a perturbative approach is shown to be close in quality to a configuration interaction of Richardson-Gaudin states while being feasible to compute.
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Affiliation(s)
- Paul A Johnson
- Département de Chimie, Université Laval, Québec, Québec G1V 0A6, Canada
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3
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Alcoba DR, Oña OB, Torre A, Lain L, Sierra G, Massaccesi GE. A variance-based optimization for determining ground and excited N-electron wave functions within the doubly occupied configuration interaction scheme. J Chem Phys 2024; 160:164107. [PMID: 38656446 DOI: 10.1063/5.0191857] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2023] [Accepted: 04/07/2024] [Indexed: 04/26/2024] Open
Abstract
This work describes optimizations of N-electron system wave functions by means of the simulated annealing technique within the doubly occupied configuration interaction framework. Using that technique, we minimize the energy variance of a Hamiltonian, providing determinations of wave functions corresponding to ground or excited states in an identical manner. The procedure that allows us to determine electronic spectra can be performed using treatments of restricted or unrestricted types. The results found in selected systems, described in terms of energy, spin, and wave function, are analyzed, showing the performance of each method. We also compare these results with those arising from more traditional approaches that minimize the energy, in both restricted and unrestricted versions, and with those obtained from the full configuration interaction treatment.
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Affiliation(s)
- Diego R Alcoba
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Ciudad Universitaria, 1428 Buenos Aires, Argentina
- CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Ofelia B Oña
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de La Plata, Consejo Nacional de Investigaciones Cientıficas y Tócnicas, 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
| | - Guadalupe Sierra
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Gustavo E Massaccesi
- Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
- Instituto de Investigaciones Matemáticas Luis Santaló, Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
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4
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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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5
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Kim K, Lim S, Shin K, Lee G, Jung Y, Kyoung W, Rhee JKK, Rhee YM. Variational quantum eigensolver for closed-shell molecules with non-bosonic corrections. Phys Chem Chem Phys 2024; 26:8390-8396. [PMID: 38406868 DOI: 10.1039/d3cp05570a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/27/2024]
Abstract
The realization of quantum advantage with noisy-intermediate-scale quantum (NISQ) machines has become one of the major challenges in computational sciences. Maintaining coherence of a physical system with more than ten qubits is a critical challenge that motivates research on compact system representations to reduce algorithm complexity. Toward this end, the variational quantum eigensolver (VQE) used to perform quantum simulations is considered to be one of the most promising algorithms for quantum chemistry in the NISQ era. We investigate reduced mapping of one spatial orbital to a single qubit to analyze the ground state energy in a way that the Pauli operators of qubits are mapped to the creation/annihilation of singlet pairs of electrons. To include the effect of non-bosonic (or non-paired) excitations, we introduce a simple correction scheme in the electron correlation model approximated by the geometrical mean of the bosonic (or paired) terms. Employing it in a VQE algorithm, we assess ground state energies of H2O, N2, and Li2O in good agreement with full configuration interaction (FCI) models respectively, using only 6, 8, and 12 qubits with quantum gate depths proportional to the squares of the qubit counts. With the adopted seniority-zero approximation that uses only one half of the qubit counts of a conventional VQE algorithm, we find that our non-bosonic correction method reaches reliable quantum chemistry simulations at least for the tested systems.
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Affiliation(s)
- Kyungmin Kim
- Department of Chemistry, KAIST, Daejeon, 34141, Republic of Korea.
| | - Sumin Lim
- Department of Physics, KAIST, Daejeon, 34141, Republic of Korea
| | - Kyujin Shin
- Materials Research & Engineering Center, CTO Division, Hyundai Motor Company, Uiwang 16082, Republic of Korea
| | - Gwonhak Lee
- School of Electrical Engineering, KAIST, Daejeon, 34141, Republic of Korea.
| | - Yousung Jung
- Department of Chemical Engineering, Seoul National University, Seoul, 08826, Republic of Korea
| | - Woomin Kyoung
- Materials Research & Engineering Center, CTO Division, Hyundai Motor Company, Uiwang 16082, Republic of Korea
| | - June-Koo Kevin Rhee
- School of Electrical Engineering, KAIST, Daejeon, 34141, Republic of Korea.
- KAIST ITRC of Quantum Computing for AI, KAIST, Daejeon, 34141, Republic of Korea
- KAIST Institute for IT Convergence, KAIST, Daejeon, 34141, Republic of Korea
| | - Young Min Rhee
- Department of Chemistry, KAIST, Daejeon, 34141, Republic of Korea.
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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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Kossoski F, Loos PF. Seniority and Hierarchy Configuration Interaction for Radicals and Excited States. J Chem Theory Comput 2023. [PMID: 37965728 DOI: 10.1021/acs.jctc.3c00946] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2023]
Abstract
Hierarchy configuration interaction (hCI) has recently been introduced as an alternative configuration interaction (CI) route combining excitation degree and seniority number and has been shown to efficiently recover both dynamic and static correlations for closed-shell molecular systems [ J. Phys. Chem. Lett. 2022, 13, 4342]. Here we generalize hCI for an arbitrary reference determinant, allowing calculations for radicals and excited states in a state-specific way. We gauge this route against excitation-based CI (eCI) and seniority-based CI (sCI) by evaluating how different ground-state properties of radicals converge to the full CI limit. We find that hCI outperforms or matches eCI, whereas sCI is far less accurate, in line with previous observations for closed-shell molecules. Employing second-order Epstein-Nesbet (EN2) perturbation theory as a correction significantly accelerates the convergence of hCI and eCI. We further explore various hCI and sCI models to calculate the excitation energies of closed- and open-shell systems. Our results underline that the choice of both the reference determinant and the set of orbitals drives the fine balance between correlation of ground and excited states. State-specific hCI2 and higher-order models perform similarly to their eCI counterparts, whereas lower orders of hCI deliver poor results unless supplemented by the EN2 correction, which substantially improves their accuracy. In turn, sCI1 produces decent excitation energies for radicals, encouraging the development of related seniority-based coupled-cluster methods.
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Affiliation(s)
- Fábris Kossoski
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, F-31062 Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, F-31062 Toulouse, France
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8
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Garros A, Alcoba DR, Capuzzi P, Lain L, Torre A, Oña OB, Dukelsky J. Determination of electronic excitation energies within the doubly occupied configuration interaction space by means of the Hermitian operator method. J Chem Phys 2023; 159:124107. [PMID: 38127377 DOI: 10.1063/5.0168585] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2023] [Accepted: 09/06/2023] [Indexed: 12/23/2023] Open
Abstract
In this work, we formulate the equations of motion corresponding to the Hermitian operator method in the framework of the doubly occupied configuration interaction space. The resulting algorithms turn out to be considerably simpler than the equations provided by that method in more conventional spaces, enabling the determination of excitation energies in N-electron systems under an affordable polynomial computational cost. The implementation of this technique only requires to know the elements of low-order reduced density matrices of an N-electron reference state, which can be obtained from any approximate method. We contrast our procedure against the reduced Bardeen-Cooper-Schrieffer and Richardson-Gaudin-Kitaev integrable models, pointing out the reliability of our proposal.
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Affiliation(s)
- Adán Garros
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Ciudad Universitaria, 1428 Buenos Aires, Argentina
- CONICET-Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Diego R Alcoba
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Ciudad Universitaria, 1428 Buenos Aires, Argentina
- CONICET-Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Pablo Capuzzi
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Ciudad Universitaria, 1428 Buenos Aires, Argentina
- CONICET-Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Luis Lain
- Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain
| | - Alicia Torre
- Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain
| | - Ofelia B Oña
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, Diag. 113 y 64 (S/N), Sucursal 4, CC 16, 1900 La Plata, Argentina
| | - Jorge Dukelsky
- Instituto de Estructura de la Materia, CSIC, Serrano 123, E-28006 Madrid, Spain
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9
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Khamoshi A, Dutta R, Scuseria GE. State Preparation of Antisymmetrized Geminal Power on a Quantum Computer without Number Projection. J Phys Chem A 2023; 127:4005-4014. [PMID: 37129503 DOI: 10.1021/acs.jpca.3c00525] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
The antisymmetrized geminal power (AGP) is equivalent to the number projected Bardeen-Cooper-Schrieffer (PBCS) wave function. It is also an elementary symmetric polynomial (ESP) state. We generalize previous research on deterministically implementing the Dicke state to a state preparation algorithm for an ESP state, or equivalently AGP, on a quantum computer. Our method is deterministic and has polynomial cost, and it does not rely on number symmetry breaking and restoration. We also show that our circuit is equivalent to a disentangled unitary paired coupled cluster operator and a layer of unitary Jastrow operator acting on a single Slater determinant. The method presented herein highlights the ability of disentangled unitary coupled cluster to capture nontrivial entanglement properties that are hardly accessible with traditional Hartree-Fock based electronic structure methods.
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Affiliation(s)
- Armin Khamoshi
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Rishab Dutta
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
| | - Gustavo E Scuseria
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
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10
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Kossoski F, Loos PF. State-Specific Configuration Interaction for Excited States. J Chem Theory Comput 2023; 19:2258-2269. [PMID: 37024102 PMCID: PMC10134430 DOI: 10.1021/acs.jctc.3c00057] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/08/2023]
Abstract
We introduce and benchmark a systematically improvable route for excited-state calculations, labeled state-specific configuration interaction (ΔCI), which is a particular realization of multiconfigurational self-consistent field and multireference configuration interaction. Starting with a reference built from optimized configuration state functions, separate CI calculations are performed for each targeted state (hence, state-specific orbitals and determinants). Accounting for single and double excitations produces the ΔCISD model, which can be improved with second-order Epstein-Nesbet perturbation theory (ΔCISD+EN2) or a posteriori Davidson corrections (ΔCISD+Q). These models were gauged against a vast and diverse set of 294 reference excitation energies. We have found that ΔCI is significantly more accurate than standard ground-state-based CI, whereas close performances were found between ΔCISD and EOM-CC2 and between ΔCISD+EN2 and EOM-CCSD. For larger systems, ΔCISD+Q delivers more accurate results than EOM-CC2 and EOM-CCSD. The ΔCI route can handle challenging multireference problems, singly and doubly excited states, from closed- and open-shell species, with overall comparable accuracy and thus represents a promising alternative to more established methodologies. In its current form, however, it is reliable only for relatively low-lying excited states.
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Affiliation(s)
- Fábris Kossoski
- 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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11
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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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12
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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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13
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Damour Y, Quintero-Monsebaiz R, Caffarel M, Jacquemin D, Kossoski F, Scemama A, Loos PF. Ground- and Excited-State Dipole Moments and Oscillator Strengths of Full Configuration Interaction Quality. J Chem Theory Comput 2023; 19:221-234. [PMID: 36548519 DOI: 10.1021/acs.jctc.2c01111] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
We report ground- and excited-state dipole moments and oscillator strengths (computed in different "gauges" or representations) of full configuration interaction (FCI) quality using the selected configuration interaction method known as Configuration Interaction using a Perturbative Selection made Iteratively (CIPSI). Thanks to a set encompassing 35 ground- and excited-state properties computed in 11 small molecules, the present near-FCI estimates allow us to assess the accuracy of high-order coupled-cluster (CC) calculations including up to quadruple excitations. In particular, we show that incrementing the excitation degree of the CC expansion (from CC with singles and doubles (CCSD) to CC with singles, doubles, and triples (CCSDT) or from CCSDT to CC with singles, doubles, triples, and quadruples (CCSDTQ)) reduces the average error with respect to the near-FCI reference values by approximately 1 order of magnitude.
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Affiliation(s)
- Yann Damour
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Raúl Quintero-Monsebaiz
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Michel Caffarel
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Denis Jacquemin
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France.,Institut Universitaire de France (IUF), F-75005 Paris, France
| | - Fábris Kossoski
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
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14
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Cioslowski J, Strasburger K. A Universal Power Law Governing the Accuracy of Wave Function-Based Electronic Structure Calculations. J Phys Chem Lett 2022; 13:8055-8061. [PMID: 35994623 DOI: 10.1021/acs.jpclett.2c01987] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
A universal power law governing the accuracy of wave function-based electronic structure calculations is derived from first principles. The resulting expression ΔE(N,N)N≳19π2gNN, where g is a system-specific factor assuming values between zero and one and ≳ stands for asymptotic inequality at the limit of N→∞, allows facile estimation of the error ΔE(N,N) in the electronic energy of a singlet state of an N-electron system computed with a basis set of N one-electron functions. Several approaches to the estimation of the factor g, which depends on the on-top two-electron density, are presented.
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Affiliation(s)
- Jerzy Cioslowski
- Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
| | - Krzysztof Strasburger
- Department of Physical and Quantum Chemistry, Faculty of Chemistry, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
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15
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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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16
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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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17
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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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18
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Fecteau CÉ, Cloutier S, Moisset JD, Boulay J, Bultinck P, Faribault A, Johnson PA. Near-exact treatment of seniority-zero ground and excited states with a Richardson-Gaudin mean-field. J Chem Phys 2022; 156:194103. [PMID: 35597662 DOI: 10.1063/5.0091338] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Eigenvectors of the reduced Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, Richardson-Gaudin (RG) states, are used as a variational wavefunction ansatz for strongly correlated electronic systems. These states are geminal products whose coefficients are solutions of non-linear equations. Previous results showed an un-physical apparent avoided crossing in ground state dissociation curves for hydrogen chains. In this paper, it is shown that each seniority-zero state of the molecular Coulomb Hamiltonian corresponds directly to an RG state. However, the seniority-zero ground state does not correspond to the ground state of a reduced BCS Hamiltonian. The difficulty is in choosing the correct RG state. The systems studied showed a clear choice, and we expect that it should always be possible to reason physically which state to choose.
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Affiliation(s)
- Charles-Émile Fecteau
- Département de chimie, Université Laval, 1045 Avenue de la Médecine, bureau 1220, Québec, Québec G1V 0A6, Canada
| | - Samuel Cloutier
- Département de chimie, Université Laval, 1045 Avenue de la Médecine, bureau 1220, Québec, Québec G1V 0A6, Canada
| | - Jean-David Moisset
- Département de chimie, Université Laval, 1045 Avenue de la Médecine, bureau 1220, Québec, Québec G1V 0A6, Canada
| | - Jérémy Boulay
- Département de chimie, Université Laval, 1045 Avenue de la Médecine, bureau 1220, Québec, Québec G1V 0A6, Canada
| | - Patrick Bultinck
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 S3, B-9000 Ghent, Belgium
| | | | - Paul A Johnson
- Département de chimie, Université Laval, 1045 Avenue de la Médecine, bureau 1220, Québec, Québec G1V 0A6, Canada
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19
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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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20
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Abstract
Quantum embedding schemes are a promising way to extend multireference computations to large molecules with strong correlation effects localized on a small number of atoms. This work introduces a second-order active-space embedding theory [ASET(2)] which improves upon mean-field frozen embedding by treating fragment-environment interactions via an approximate canonical transformation. The canonical transformation employed in ASET(2) is formulated using the driven similarity renormalization group. The ASET(2) scheme is benchmarked on the N═N bond dissociation in pentyldiazene, the S0 to S1 excitation in 1-octene, and the interaction energy of the O2-benzene complex. The ASET(2) explicit treatment of fragment-environment interactions beyond the mean-field level generally improves the accuracy of embedded computations, and it becomes necessary to achieve an accurate description of excitation energies of 1-octene and the singlet-triplet gap of the O2-benzene complex.
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Affiliation(s)
- Nan He
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Chenyang Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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21
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Elayan IA, Gupta R, Hollett JW. ΔNO and the complexities of electron correlation in simple hydrogen clusters. J Chem Phys 2022; 156:094102. [DOI: 10.1063/5.0073227] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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22
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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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23
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Kossoski F, Marie A, Scemama A, Caffarel M, Loos PF. Excited States from State-Specific Orbital-Optimized Pair Coupled Cluster. J Chem Theory Comput 2021; 17:4756-4768. [PMID: 34310140 PMCID: PMC8359009 DOI: 10.1021/acs.jctc.1c00348] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2021] [Indexed: 01/31/2023]
Abstract
The pair coupled cluster doubles (pCCD) method (where the excitation manifold is restricted to electron pairs) has a series of interesting features. Among others, it provides ground-state energies very close to what is obtained with doubly occupied configuration interaction (DOCI), but with a polynomial cost (compared with the exponential cost of the latter). Here, we address whether this similarity holds for excited states by exploring the symmetric dissociation of the linear H4 molecule. When ground-state Hartree-Fock (HF) orbitals are employed, pCCD and DOCI excited-state energies do not match, a feature that is assigned to the poor HF reference. In contrast, by optimizing the orbitals at the pCCD level (oo-pCCD) specifically for each excited state, the discrepancies between pCCD and DOCI decrease by 1 or 2 orders of magnitude. Therefore, the pCCD and DOCI methodologies still provide comparable energies for excited states, but only if suitable, state-specific orbitals are adopted. We also assessed whether a pCCD approach could be used to directly target doubly excited states, without having to resort to the equation-of-motion (EOM) formalism. In our Δoo-pCCD model, excitation energies are extracted from the energy difference between separate oo-pCCD calculations for the ground state and the targeted excited state. For a set comprising the doubly excited states of CH+, BH, nitroxyl, nitrosomethane, and formaldehyde, we found that Δoo-pCCD provides quite accurate excitation energies, with root-mean-square deviations (with respect to full configuration interaction results) lower than those of CC3 and comparable to those of EOM-CCSDT, two methods with a much higher computational cost.
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Affiliation(s)
- Fábris Kossoski
- Laboratoire de Chimie et Physique Quantiques
(UMR 5626), Université de Toulouse,
CNRS, UPS, 31062 Toulouse, France
| | - Antoine Marie
- Laboratoire de Chimie et Physique Quantiques
(UMR 5626), Université de Toulouse,
CNRS, UPS, 31062 Toulouse, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques
(UMR 5626), Université de Toulouse,
CNRS, UPS, 31062 Toulouse, France
| | - Michel Caffarel
- Laboratoire de Chimie et Physique Quantiques
(UMR 5626), Université de Toulouse,
CNRS, UPS, 31062 Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques
(UMR 5626), Université de Toulouse,
CNRS, UPS, 31062 Toulouse, France
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24
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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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25
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Alcoba DR, Oña OB, Lain L, Torre A, Capuzzi P, Massaccesi GE, Ríos E, Rubio-García A, Dukelsky J. Variational determination of ground and excited-state two-electron reduced density matrices in the doubly occupied configuration space: A dispersion operator approach. J Chem Phys 2021; 154:224104. [PMID: 34241224 DOI: 10.1063/5.0051793] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This work implements a variational determination of the elements of two-electron reduced density matrices corresponding to the ground and excited states of N-electron interacting systems based on the dispersion operator technique. The procedure extends the previously reported proposal [Nakata et al., J. Chem. Phys. 125, 244109 (2006)] to two-particle interaction Hamiltonians and N-representability conditions for the two-, three-, and four-particle reduced density matrices in the doubly occupied configuration interaction space. The treatment has been applied to describe electronic spectra using two benchmark exactly solvable pairing models: reduced Bardeen-Cooper-Schrieffer and Richardson-Gaudin-Kitaev Hamiltonians. The dispersion operator combined with N-representability conditions up to the four-particle reduced density matrices provides excellent results.
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Affiliation(s)
- Diego R Alcoba
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Ofelia B Oña
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad de la Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, Diag. 113 y 64 (S/N), Sucursal 4, CC 16, 1900 La Plata, Argentina
| | - Luis Lain
- Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain
| | - Alicia Torre
- Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain
| | - Pablo Capuzzi
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Gustavo E Massaccesi
- Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Elías Ríos
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad de la Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, Diag. 113 y 64 (S/N), Sucursal 4, CC 16, 1900 La Plata, Argentina
| | - Alvaro Rubio-García
- Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain
| | - Jorge Dukelsky
- Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain
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26
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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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27
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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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28
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Kedžuch S, Šimunek J, Veis M, Noga J. Doubly Occupied Pair Coupled Cluster F12 Approach. J Chem Theory Comput 2020; 16:7372-7380. [PMID: 32866010 DOI: 10.1021/acs.jctc.0c00659] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Inspired by reports of the good performance of the doubly occupied pair coupled cluster (pCCD) theory in describing static electron correlation, we have introduced and implemented a variant thereof that includes single excitations and explicitly treats the dynamic electron correlation using the F12 methodology (pCCSD-F12). This drastically reduces the computation scaling with respect to the standard method using the full double-excitation operator (CCSD-F12). Slater-type geminals as a correlation factor, together with fixed cusp conditions, were used, which is known as the SP-ansatz. For sample model systems, we have investigated the performance of reference states constructed from either canonical or localized molecular orbitals. Finaly, the employment of Brueckner orbitals has been tested, which causes the single excitations to naturally vanish from the wave function expansion (B-pCCD-F12). Our test systems include different-sized rings of hydrogen atoms and dissociation curves for small molecules such as HF, N2, and CO2; and comparison with CCSD-F12 is presented for a series of reaction enthalpies.
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Affiliation(s)
- Stanislav Kedžuch
- Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University, Mlynská dolina, Ilkovičova 6, SK-84215 Bratislava, Slovakia.,RIKEN Center for Computational Science, 7-1-26 Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
| | - Ján Šimunek
- Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University, Mlynská dolina, Ilkovičova 6, SK-84215 Bratislava, Slovakia
| | - Matej Veis
- Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University, Mlynská dolina, Ilkovičova 6, SK-84215 Bratislava, Slovakia
| | - Jozef Noga
- Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University, Mlynská dolina, Ilkovičova 6, SK-84215 Bratislava, Slovakia.,Computing Centre, Centre of Operations of the Slovak Academy of Sciences, Dúbravská cesta 9, SK-84535 Bratislava, Slovakia
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29
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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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30
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Chen Z, Wu W. Ab initio valence bond theory: A brief history, recent developments, and near future. J Chem Phys 2020; 153:090902. [PMID: 32891101 DOI: 10.1063/5.0019480] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
This Perspective presents a survey of several issues in ab initio valence bond (VB) theory with a primary focus on recent advances made by the Xiamen VB group, including a brief review of the earlier history of the ab initio VB methods, in-depth discussion of algorithms for nonorthogonal orbital optimization in the VB self-consistent field method and VB methods incorporating dynamic electron correlation, along with a concise overview of VB methods for complex systems and VB models for chemical bonding and reactivity, and an outlook of opportunities and challenges for the near future of the VB theory.
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Affiliation(s)
- Zhenhua Chen
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, The State Key Laboratory of Physical Chemistry of Solid Surfaces, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
| | - Wei Wu
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, The State Key Laboratory of Physical Chemistry of Solid Surfaces, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
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31
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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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32
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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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33
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Vu N, DePrince AE. Size-extensive seniority-zero energy functionals derived from configuration interaction with double excitations. J Chem Phys 2020; 152:244103. [DOI: 10.1063/5.0011637] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Affiliation(s)
- Nam Vu
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
| | - A. Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
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34
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Head-Marsden K, Mazziotti DA. Active-Space Pair Two-Electron Reduced Density Matrix Theory for Strong Correlation. J Phys Chem A 2020; 124:4848-4854. [DOI: 10.1021/acs.jpca.0c01937] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Kade Head-Marsden
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, United States
| | - David A. Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, United States
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35
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Fales BS, Martínez TJ. Fast transformations between configuration state function and Slater determinant bases for direct configuration interaction. J Chem Phys 2020; 152:164111. [PMID: 32357800 DOI: 10.1063/5.0005155] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A hybrid configuration state function (CSF) and Slater determinant (SD) basis full configuration interaction (CI) program was developed to simultaneously take advantage of fast SD basis algorithms for σ = Hc formation and the smaller CI vector length and more robust convergence offered by a CSF basis. Graphical processing unit acceleration of the direct CSF-SD and SD-CSF basis transformation algorithms ensures that the combined transformation time per iteration relative to σ formation is small (∼15%). In addition to the obvious benefits of reducing the memory footprint of the CI vector, additional computational savings are demonstrated that rely directly on the size of the CI basis, in one particular case reducing the CI time-to-solution of a HF-CAS-(16,16)-CI/6-31G calculation of ethylene from 1954.79 s to 956 s by using a CSF basis, a 2.0× speedup.
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Affiliation(s)
- B Scott Fales
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
| | - Todd J Martínez
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
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36
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He N, Evangelista FA. A zeroth-order active-space frozen-orbital embedding scheme for multireference calculations. J Chem Phys 2020; 152:094107. [PMID: 33480706 DOI: 10.1063/1.5142481] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Multireference computations of large-scale chemical systems are typically limited by the computational cost of quantum chemistry methods. In this work, we develop a zeroth-order active space embedding theory [ASET(0)], a simple and automatic approach for embedding any multireference dynamical correlation method based on a frozen-orbital treatment of the environment. ASET(0) is combined with the second-order multireference driven similarity renormalization group and tested on several benchmark problems, including the excitation energy of 1-octene and bond-breaking in ethane and pentyldiazene. Finally, we apply ASET(0) to study the singlet-triplet gap of p-benzyne and 9,10-anthracyne diradicals adsorbed on a NaCl surface. Our results show that despite its simplicity, ASET(0) is a powerful and sufficiently accurate embedding scheme applicable when the coupling between the fragment and the environment is in the weak to medium regime.
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Affiliation(s)
- Nan He
- Department of Chemistry, Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Francesco A Evangelista
- Department of Chemistry, Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
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37
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Zhang N, Liu W, Hoffmann MR. Iterative Configuration Interaction with Selection. J Chem Theory Comput 2020; 16:2296-2316. [DOI: 10.1021/acs.jctc.9b01200] [Citation(s) in RCA: 43] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Ning Zhang
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Beijing 100871, China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong 266237, China
| | - Mark R. Hoffmann
- Chemistry Department, University of North Dakota, Grand Forks, North Dakota 58202-9024, United States
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38
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Hollett JW, Loos PF. Capturing static and dynamic correlation with ΔNO-MP2 and ΔNO-CCSD. J Chem Phys 2020; 152:014101. [PMID: 31914756 DOI: 10.1063/1.5140669] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The ΔNO method for static correlation is combined with second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster singles and doubles (CCSD) to account for dynamic correlation. The MP2 and CCSD expressions are adapted from finite-temperature CCSD, which includes orbital occupancies and vacancies, and expanded orbital summations. Correlation is partitioned with the aid of damping factors incorporated into the MP2 and CCSD residual equations. Potential energy curves for a selection of diatomics are in good agreement with extrapolated full configuration interaction results and on par with conventional multireference approaches.
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Affiliation(s)
- Joshua W Hollett
- Department of Chemistry, University of Winnipeg, Winnipeg, Manitoba R3B 2G3, Canada
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
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39
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Vu N, Mitxelena I, DePrince AE. An adiabatic connection for doubly-occupied configuration interaction wave functions. J Chem Phys 2019; 151:244121. [PMID: 31893894 DOI: 10.1063/1.5130660] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Abstract
An adiabatic connection (AC) is developed as an electron correlation correction for doubly occupied configuration interaction (DOCI) wave functions. Following the work of Pernal [Phys. Rev. Lett. 120, 013001 (2018)], the working equations of the approach, termed AC-DOCI, are rooted in the extended random phase approximation (ERPA) and require knowledge of only the ground-state two-electron reduced density matrix (2RDM) from the DOCI. As such, the AC is naturally suited to modeling electron correlation in variational 2RDM (v2RDM)-based approximations to the DOCI. The v2RDM-driven AC-DOCI is applied to the dissociation of molecular nitrogen and the double dissociation of water; the approach yields energies that are similar in quality to those from second-order multireference perturbation theory near equilibrium, but the quality of the AC-DOCI energy degrades at stretched geometries. The exact adiabatic connection path suggests the assumption that the one-electron reduced-density matrix is constant along the AC path is invalid at stretched geometries, but this deficiency alone cannot explain the observed behavior. Rather, it appears that the ERPA's single-particle-transition ansatz cannot, in general, provide good approximations to the 2RDM along the AC path. The AC-DOCI is also applied to a set of 45 reaction energies; for these systems, the approach has an average accuracy that is comparable to that of single-reference second-order many-body perturbation theory.
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Affiliation(s)
- Nam Vu
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
| | - Ion Mitxelena
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), P.K. 1072, 20080 Donostia, Euskadi, Spain
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
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40
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Zhou C, Zeng C, Ma B, Ying F, Chen Z, Wu W. Novel implementation of seniority number truncated valence bond methods with applications to H22 chain. J Chem Phys 2019; 151:194107. [DOI: 10.1063/1.5123197] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] 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
| | - Chenyu Zeng
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
| | - Bo Ma
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
| | - Fuming Ying
- 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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41
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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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42
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Rubio-García A, Dukelsky J, Alcoba DR, Capuzzi P, Oña OB, Ríos E, Torre A, Lain L. Variational reduced density matrix method in the doubly-occupied configuration interaction space using four-particle N-representability conditions: Application to the XXZ model of quantum magnetism. J Chem Phys 2019; 151:154104. [PMID: 31640387 DOI: 10.1063/1.5118899] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This work deals with the variational determination of the two-particle reduced density matrix (2-RDM) and the energy corresponding to the ground state of N-particle systems within the doubly occupied configuration interaction (DOCI) space. Here, we impose for the first time up to four-particle N-representability constraint conditions in the variational determination of the 2-RDM matrix elements using the standard semidefinite programming algorithms. The energies and 2-RDMs obtained from this treatment and the corresponding computational costs are compared with those arisen from previously reported less restrictive variational methods [D. R. Alcoba et al., J. Chem. Phys. 149, 194105 (2018)] as well as with the exact DOCI values. We apply the different approximations to the one-dimensional XXZ model of quantum magnetism, which has a rich phase diagram with one critical phase and constitutes a stringent test for the method. The numerical results show the usefulness of our treatment to achieve a high degree of accuracy.
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Affiliation(s)
- A Rubio-García
- Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain
| | - J Dukelsky
- Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain
| | - D R Alcoba
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - P Capuzzi
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - O 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
| | - E 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
| | - A Torre
- Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain
| | - L Lain
- Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain
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43
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Cioslowski J, Mihálka ZÉ, Szabados Á. Bilinear Constraints upon the Correlation Contribution to the Electron-Electron Repulsion Energy as a Functional of the One-Electron Reduced Density Matrix. J Chem Theory Comput 2019; 15:4862-4872. [PMID: 31294976 DOI: 10.1021/acs.jctc.9b00443] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Perturbative analysis of the functional U[n, ψ] that yields the correlation component U of the electron-electron repulsion energy in terms of the vectors ψ(1) and n of the natural spinorbitals and their occupation numbers (the 1-matrix functional) facilitates examination of the flaws inherent to the present implementations of the density matrix functional theory. Recognizing that the practical usefulness of any approximate 1-matrix functional hinges upon its capability of exactly reproducing the leading contribution to U at the limit of vanishing electron-electron interactions gives rise to asymptotic bilinear constraints for the (exact or model) 2-cumulant G2 that enters the expression for U. The asymptotic behavior of certain blocks of G2 is found to be equally important. These identities, which are obtained for both the single-determinantal and a model multideterminantal cases, take precedence over the linear constraints commonly enforced in the course of approximate construction of such functionals. This observation reveals the futility of designing sophisticated approximations tailored for the second-order contribution to G2 while neglecting proper formulation of the respective first-order contribution that in the case of the so-called JKL-only functionals requires abandoning the JK-dependence altogether. It has its repercussions not only for the functionals of the PNOF family but also for the expressions involving only the L-type two-electron repulsion integrals (in the guise of their exchange counterparts) that account only for the correlation effects due to electrons with antiparallel spins and are well-defined only for spin-unpolarized and high-spin systems (yielding vanishing U for the latter).
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Affiliation(s)
- Jerzy Cioslowski
- Institute of Physics , University of Szczecin , Wielkopolska 15 , 70-451 Szczecin , Poland
| | - Zsuzsanna É Mihálka
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Faculty of Science , ELTE Eötvös Loránd University , POB 32, H-1518 Budapest , Hungary.,Hevesy György Ph.D. School of Chemistry, Faculty of Science , ELTE Eötvös Loránd University , POB 32, H-1518 Budapest , Hungary
| | - Ágnes Szabados
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Faculty of Science , ELTE Eötvös Loránd University , POB 32, H-1518 Budapest , Hungary
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44
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Benavides-Riveros CL, Marques MAL. On the time evolution of fermionic occupation numbers. J Chem Phys 2019; 151:044112. [DOI: 10.1063/1.5109009] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Miguel A. L. Marques
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06120 Halle (Saale), Germany
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45
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Alcoba DR, Torre A, Lain L, Massaccesi GE, Oña OB, Ríos E. Unrestricted treatment for the direct variational determination of the two-electron reduced density matrix for doubly occupied-configuration-interaction wave functions. J Chem Phys 2019; 150:164106. [PMID: 31042927 DOI: 10.1063/1.5092182] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This work extends to the unrestricted orbital approach the procedure described in our previous report [Alcoba et al., J. Chem. Phys. 148, 024105 (2018)] for determining variationally the two-electron reduced density matrix arising from doubly occupied-configuration-interaction wave functions by imposing two- and three-index N-representability conditions. An analysis of the numerical results obtained in selected systems, from both restricted and unrestricted treatments, allows one to assess the performance of these methodologies as well as to show the influence of the P, Q, G, T1, and T2 positivity conditions. We highlight the satisfactory results obtained within the unrestricted scheme.
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Affiliation(s)
- 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
| | - 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
| | - 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
| | - 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
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46
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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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47
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Zhang H, Zhou C, Mo Y, Wu W. Performance of the VBSCF method for pericyclic and π bond shift reactions. J Comput Chem 2018; 40:1123-1129. [DOI: 10.1002/jcc.25729] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2018] [Revised: 08/27/2018] [Accepted: 09/27/2018] [Indexed: 11/06/2022]
Affiliation(s)
- Huaiyu Zhang
- Institute of Computational Quantum Chemistry; College of Chemistry and Material Science, Hebei Normal University; Shijiazhuang 050024 China
- The State Key Laboratory of Physical Chemistry of Solid Surfaces; Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, iChEM, and College of Chemistry and Chemical Engineering, Xiamen University; Xiamen 361005 China
| | - Chen Zhou
- The State Key Laboratory of Physical Chemistry of Solid Surfaces; Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, iChEM, and College of Chemistry and Chemical Engineering, Xiamen University; Xiamen 361005 China
| | - Yirong Mo
- The State Key Laboratory of Physical Chemistry of Solid Surfaces; Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, iChEM, and College of Chemistry and Chemical Engineering, Xiamen University; Xiamen 361005 China
- Department of Chemistry; Western Michigan University; Kalamazoo Michigan 49008 USA
| | - Wei Wu
- The State Key Laboratory of Physical Chemistry of Solid Surfaces; Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, iChEM, and College of Chemistry and Chemical Engineering, Xiamen University; Xiamen 361005 China
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48
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Alcoba DR, Capuzzi P, Rubio-García A, Dukelsky J, Massaccesi GE, Oña OB, Torre A, Lain L. Variational reduced density matrix method in the doubly occupied configuration interaction space using three-particleN-representability conditions. J Chem Phys 2018; 149:194105. [DOI: 10.1063/1.5056247] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- 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
| | - Pablo Capuzzi
- 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
| | - Alvaro Rubio-García
- Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain
| | - Jorge Dukelsky
- Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain
| | - Gustavo E. Massaccesi
- Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - 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
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49
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Breaking the curse of dimension for the electronic Schrödinger equation with functional analysis. COMPUT THEOR CHEM 2018. [DOI: 10.1016/j.comptc.2018.08.017] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Bytautas L, Dukelsky J. Seniority based energy renormalization group (Ω-ERG) approach in quantum chemistry: Initial formulation and application to potential energy surfaces. COMPUT THEOR CHEM 2018. [DOI: 10.1016/j.comptc.2018.08.011] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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