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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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2
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Jones GM, Li RR, DePrince AE, Vogiatzis KD. Data-Driven Refinement of Electronic Energies from Two-Electron Reduced-Density-Matrix Theory. J Phys Chem Lett 2023:6377-6385. [PMID: 37418691 DOI: 10.1021/acs.jpclett.3c01382] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/09/2023]
Abstract
The exponential computational cost of describing strongly correlated electrons can be mitigated by adopting a reduced-density matrix (RDM)-based description of the electronic structure. While variational two-electron RDM (v2RDM) methods can enable large-scale calculations on such systems, the quality of the solution is limited by the fact that only a subset of known necessary N-representability constraints can be applied to the 2RDM in practical calculations. Here, we demonstrate that violations of partial three-particle (T1 and T2) N-representability conditions, which can be evaluated with knowledge of only the 2RDM, can serve as physics-based features in a machine-learning (ML) protocol for improving energies from v2RDM calculations that consider only two-particle (PQG) conditions. Proof-of-principle calculations demonstrate that the model yields substantially improved energies relative to reference values from configuration-interaction-based calculations.
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Affiliation(s)
- Grier M Jones
- Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Run R Li
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
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3
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Li RR, Rubin NC, DePrince AE. Challenges for Variational Reduced-Density-Matrix Theory: Total Angular Momentum Constraints. J Chem Theory Comput 2022; 18:5966-5977. [PMID: 36150206 DOI: 10.1021/acs.jctc.2c00402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The variational two-electron reduced density matrix (v2RDM) method is generalized for the description of total angular momentum (J) and projection of total angular momentum (MJ) states in atomic systems described by nonrelativistic Hamiltonians, and it is shown that the approach exhibits serious deficiencies. Under ensemble N-representability constraints, v2RDM theory fails to retain the appropriate degeneracies among various J states for fixed spin (S) and orbital angular momentum (L), and for fixed L, S, and J, the manifold of MJ states is not necessarily degenerate. Moreover, a substantial energy error is observed for a system for which the two-electron reduced density matrix is exactly ensemble N-representable; in this case, the error stems from violations in pure-state N-representability conditions. Unfortunately, such violations do not appear to be good indicators of the reliability of energies from v2RDM theory in general. Several states are identified for which energy errors are near zero and yet pure-state conditions are clearly violated.
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Affiliation(s)
- Run R Li
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | | | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
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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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5
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Li RR, Liebenthal MD, DePrince AE. Challenges for variational reduced-density-matrix theory with three-particle N-representability conditions. J Chem Phys 2021; 155:174110. [PMID: 34742213 DOI: 10.1063/5.0066404] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The direct variational optimization of the two-electron reduced density matrix (2RDM) can provide a reference-independent description of the electronic structure of many-electron systems that naturally capture strong or nondynamic correlation effects. Such variational 2RDM approaches can often provide a highly accurate description of strong electron correlation, provided that the 2RDMs satisfy at least partial three-particle N-representability conditions (e.g., the T2 condition). However, recent benchmark calculations on hydrogen clusters [N. H. Stair and F. A. Evangelista, J. Chem. Phys. 153, 104108 (2020)] suggest that even the T2 condition leads to unacceptably inaccurate results in the case of two- and three-dimensional clusters. We demonstrate that these failures persist under the application of full three-particle N-representability conditions (3POS). A variety of correlation metrics are explored in order to identify regimes under which 3POS calculations become unreliable, and we find that the relative squared magnitudes of the cumulant three- and two-particle reduced density matrices correlate reasonably well with the energy error in these systems. However, calculations on other molecular systems reveal that this metric is not a universal indicator for the reliability of the reduced-density-matrix theory with 3POS conditions.
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Affiliation(s)
- Run R Li
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
| | - Marcus D Liebenthal
- 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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6
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Affiliation(s)
| | - A. Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, FL, USA
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7
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Head-Marsden K, Flick J, Ciccarino CJ, Narang P. Quantum Information and Algorithms for Correlated Quantum Matter. Chem Rev 2020; 121:3061-3120. [PMID: 33326218 DOI: 10.1021/acs.chemrev.0c00620] [Citation(s) in RCA: 35] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.
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Affiliation(s)
- Kade Head-Marsden
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Johannes Flick
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
| | - Christopher J Ciccarino
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States.,Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Prineha Narang
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
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8
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Chaykin D, Jansson C, Keil F, Lange M, Ohlhus KT, Rump SM. Rigorous Lower Bounds for the Ground State Energy of Molecules by Employing Necessary N-Representability Conditions. J Chem Theory Comput 2020; 16:7342-7356. [PMID: 33185448 DOI: 10.1021/acs.jctc.0c00497] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Electronic structure calculations, in particular the computation of the ground state energy, lead to challenging problems in optimization. These problems are of enormous importance in quantum chemistry for calculations of properties of solids and molecules. Minimization methods for computing the ground state energy can be developed by employing a variational approach, where the second-order reduced density matrix defines the variable. This concept leads to large-scale semidefinite programming problems that provide a lower bound for the ground state energy. Upper bounds of the ground state energy can be calculated for example with the Hartree-Fock method or numerically more exact for a given basis set by full CI. However, Nakata et al. ( J. Chem. Phys.200111482828292) observed that due to numerical errors the semidefinite solver produced erroneous results with a lower bound significantly larger than the full CI energy. For the LiH, CH-, NH-, OH, OH-, and HF molecules violations within one mhartree were observed. We applied the software VSDP which takes all numerical errors due to floating-point arithmetic operations into consideration. For two test libraries VSDP provides tight rigorous error bounds lower than full CI energies reported with an accuracy of 0.1 to 0.01 mhartree. Only little computation work must be spent in order to compute close rigorous error bounds for the ground state energy.
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Affiliation(s)
- Denis Chaykin
- Institute of Chemical Reaction Engineering, Hamburg University of Technology, Eißendorfer Strasse 38, Hamburg 21073, Germany
| | - Christian Jansson
- Institute for Reliable Computing, Hamburg University of Technology, Am Schwarzenberg-Campus 3, Hamburg 21073, Germany
| | - Frerich Keil
- Institute of Chemical Reaction Engineering, Hamburg University of Technology, Eißendorfer Strasse 38, Hamburg 21073, Germany
| | - Marko Lange
- Institute for Reliable Computing, Hamburg University of Technology, Am Schwarzenberg-Campus 3, Hamburg 21073, Germany
| | - Kai Torben Ohlhus
- Institute for Reliable Computing, Hamburg University of Technology, Am Schwarzenberg-Campus 3, Hamburg 21073, Germany.,Graduate School of Science, Tokyo Woman's Christian University, 2-6-1 Zempukuji, Suginami-ku, Tokyo 167-8585, Japan
| | - Siegfried M Rump
- Institute for Reliable Computing, Hamburg University of Technology, Am Schwarzenberg-Campus 3, Hamburg 21073, Germany.,Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
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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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10
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Maradzike E, Hapka M, Pernal K, DePrince AE. Reduced Density Matrix-Driven Complete Active Apace Self-Consistent Field Corrected for Dynamic Correlation from the Adiabatic Connection. J Chem Theory Comput 2020; 16:4351-4360. [PMID: 32538086 DOI: 10.1021/acs.jctc.0c00324] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
The recently proposed multireference adiabatic connection (AC) formalism [Pernal, Phys. Rev. Lett. 120, 013001 (2018)] is applied to recover dynamic electron correlation effects lacking in variational two-electron reduced density matrix (v2RDM)-driven complete active space self-consistent field theory (CASSCF). The AC approach is validated by computing potential energy curves for the dissociation of molecular nitrogen and the symmetric double dissociation of H2O while enforcing two sets of approximate N-representability conditions in the underlying v2RDM-driven CASSCF calculations (either two-particle or two-particle plus partial three-particle conditions). The AC yields smaller absolute errors than second-order N-electron perturbation theory (NEVPT2) at all molecular geometries for both sets of the N-representability conditions considered. The efficacy of the approach for thermochemistry is also assessed for a set of 31 small-molecule reactions. When imposing partial three-particle N-representability conditions, mean and maximum unsigned errors in reaction energies from the AC are superior to those from NEVPT2.
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Affiliation(s)
- Elvis Maradzike
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - Michał Hapka
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland.,Faculty of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland
| | - Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
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11
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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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12
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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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13
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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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14
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Mullinax JW, Maradzike E, Koulias LN, Mostafanejad M, Epifanovsky E, Gidofalvi G, DePrince AE. Heterogeneous CPU + GPU Algorithm for Variational Two-Electron Reduced-Density Matrix-Driven Complete Active-Space Self-Consistent Field Theory. J Chem Theory Comput 2019; 15:6164-6178. [DOI: 10.1021/acs.jctc.9b00768] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- J. Wayne Mullinax
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306, United States
| | - Elvis Maradzike
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306, United States
| | - Lauren N. Koulias
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306, United States
| | - Mohammad Mostafanejad
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306, United States
| | - Evgeny Epifanovsky
- Q-Chem, Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588, United States
| | - Gergely Gidofalvi
- Department of Chemistry and Biochemistry, Gonzaga University, Spokane, Washington 99258, United States
| | - A. Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306, United States
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15
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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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16
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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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17
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Rubio-García A, Alcoba DR, Capuzzi P, Dukelsky J. Benchmarking the Variational Reduced Density Matrix Theory in the Doubly Occupied Configuration Interaction Space with Integrable Pairing Models. J Chem Theory Comput 2018; 14:4183-4192. [PMID: 29906104 DOI: 10.1021/acs.jctc.8b00387] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The variational reduced density matrix theory has been recently applied with great success to models within the truncated doubly occupied configuration interaction space, which corresponds to the seniority zero subspace. Conservation of the seniority quantum number restricts the Hamiltonians to be based on the SU(2) algebra. Among them there is a whole family of exactly solvable Richardson-Gaudin pairing Hamiltonians. We benchmark the variational theory against two different exactly solvable models, the Richardson-Gaudin-Kitaev and the reduced BCS Hamiltonians. We obtain exact numerical results for the so-called [Formula: see text] N-representability conditions in both cases for systems that go from 10 to 100 particles. However, when random single-particle energies as appropriate for small superconducting grains are considered, the exactness is lost but still a high accuracy is obtained.
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Affiliation(s)
- A Rubio-García
- 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.,Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas , 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.,Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas , Ciudad Universitaria , 1428 Buenos Aires , Argentina
| | - J Dukelsky
- Instituto de Estructura de la Materia, CSIC, Serrano 123 , 28006 Madrid , Spain
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18
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Alcoba DR, Torre A, Lain L, Massaccesi GE, Oña OB, Honoré EM, Poelmans W, Van Neck D, Bultinck P, De Baerdemacker S. Direct variational determination of the two-electron reduced density matrix for doubly occupied-configuration-interaction wave functions: The influence of three-index N-representability conditions. J Chem Phys 2018; 148:024105. [PMID: 29331147 DOI: 10.1063/1.5008811] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This work proposes the variational determination of two-electron reduced density matrices corresponding to the ground state of N-electron systems within the doubly occupied-configuration-interaction methodology. The P, Q, and G two-index N-representability conditions have been extended to the T1 and T2 (T2') three-index ones and the resulting optimization problem has been addressed using a standard semidefinite program. We report results obtained from the doubly occupied-configuration-interaction method, from the two-index constraint variational procedure and from the two- and three-index constraint variational treatment. The discussion of these results along with a study of the computational cost demanded shows the usefulness of our proposal.
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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
| | - 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
| | - Eduardo M Honoré
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Ward Poelmans
- Center for Molecular Modeling, Ghent University, Technologiepark 903, B-9052 Zwijnaarde, Belgium
| | - Dimitri Van Neck
- Center for Molecular Modeling, Ghent University, Technologiepark 903, B-9052 Zwijnaarde, Belgium
| | - Patrick Bultinck
- Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium
| | - Stijn De Baerdemacker
- Center for Molecular Modeling, Ghent University, Technologiepark 903, B-9052 Zwijnaarde, Belgium
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