1
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Ludovicy J, Dahl R, Lüchow A. Toward Compact Selected Configuration Interaction Wave Functions with Quantum Monte Carlo─A Case Study of C 2. J Chem Theory Comput 2023; 19:2792-2803. [PMID: 37130194 DOI: 10.1021/acs.jctc.2c01229] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
The 1Σg+ ground state of C2 is investigated using truncated CIPSI-Jastrow CSF wave functions with Hartree-Fock orbitals within the framework of variational and diffusion quantum Monte Carlo. The truncation is performed based on the absolute value of the CI coefficients, and the Jastrow, molecular orbitals, and CI parameters are either partially or fully reoptimized with respect to the variational energy. Excellent absolute as well as bond dissociation energies are obtained at DMC level with very compact, fully optimized wave functions. By studying the expansions in more detail, we observe a change in the CI picture when reoptimizing the antisymmetric part of the CIPSI-Jastrow wave functions. Furthermore, we demonstrate that a decrease in the VMC energy as well as an improvement of the nodal surface quality can be achieved─with the same expansion size─if the CSFs are selected in the presence of a Jastrow correlation function, laying the foundation for a Jastrow selected CI scheme with quantum Monte Carlo.
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Affiliation(s)
- Jil Ludovicy
- Institute of Physical Chemistry, RWTH Aachen University, Landoltweg 2, 52074 Aachen, Germany
| | - Robin Dahl
- Institute of Physical Chemistry, RWTH Aachen University, Landoltweg 2, 52074 Aachen, Germany
| | - Arne Lüchow
- Institute of Physical Chemistry, RWTH Aachen University, Landoltweg 2, 52074 Aachen, Germany
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2
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Gerasimov IS, Losev TV, Epifanov EY, Rudenko I, Bushmarinov IS, Ryabov AA, Zhilyaev PA, Medvedev MG. Comment on "Pushing the frontiers of density functionals by solving the fractional electron problem". Science 2022; 377:eabq3385. [PMID: 35926034 DOI: 10.1126/science.abq3385] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Abstract
Kirkpatrick et al. (Reports, 9 December 2021, p. 1385) trained a neural network-based DFT functional, DM21, on fractional-charge (FC) and fractional-spin (FS) systems, and they claim that it has outstanding accuracy for chemical systems exhibiting strong correlation. Here, we show that the ability of DM21 to generalize the behavior of such systems does not follow from the published results and requires revisiting.
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Affiliation(s)
- Igor S Gerasimov
- Department of Chemistry, Kyungpook National University, Daegu 41566, South Korea
| | - Timofey V Losev
- N. D. Zelinsky Institute of Organic Chemistry of Russian Academy of Sciences, 119991 Moscow, Russian Federation.,Department of Chemistry, Lomonosov Moscow State University, 119991 Moscow, Russian Federation
| | - Evgeny Yu Epifanov
- N. D. Zelinsky Institute of Organic Chemistry of Russian Academy of Sciences, 119991 Moscow, Russian Federation.,National Research University Higher School of Economics, 101000 Moscow, Russian Federation
| | - Irina Rudenko
- Yandex, 119021 Moscow, Russian Federation.,Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Region 141700, Russian Federation
| | | | - Alexander A Ryabov
- Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Region 141700, Russian Federation.,Center for Materials Technologies, Skolkovo Institute of Science and Technology, Moscow 143026, Russian Federation
| | - Petr A Zhilyaev
- Center for Materials Technologies, Skolkovo Institute of Science and Technology, Moscow 143026, Russian Federation
| | - Michael G Medvedev
- N. D. Zelinsky Institute of Organic Chemistry of Russian Academy of Sciences, 119991 Moscow, Russian Federation.,National Research University Higher School of Economics, 101000 Moscow, Russian Federation
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3
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Boyn JN, Mazziotti DA. Elucidating the molecular orbital dependence of the total electronic energy in multireference problems. J Chem Phys 2022; 156:194104. [PMID: 35597644 DOI: 10.1063/5.0090342] [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
The accurate resolution of the chemical properties of strongly correlated systems, such as biradicals, requires the use of electronic structure theories that account for both multi-reference and dynamic correlation effects. A variety of methods exist that aim to resolve the dynamic correlation in multi-reference problems, commonly relying on an exponentially scaling complete-active-space self-consistent-field (CASSCF) calculation to generate reference molecular orbitals (MOs). However, while CASSCF orbitals provide the optimal solution for a selected set of correlated (active) orbitals, their suitability in the quest for the resolution of the total correlation energy has not been thoroughly investigated. Recent research has shown the ability of Kohn-Shan density functional theory to provide improved orbitals for coupled cluster (CC) and Møller-Plesset perturbation theory (MP) calculations. Here, we extend the search for optimal and more cost effective MOs to post-configuration-interaction [post-(CI)] methods, surveying the ability of the MOs obtained with various density functional theory (DFT) functionals, as well as Hartree-Fock and CC and MP calculations to accurately capture the total electronic correlation energy. Applying the anti-Hermitian contracted Schrödinger equation to the dissociation of N2, the calculation of biradical singlet-triplet gaps, and the transition states of bicylobutane isomerization, we demonstrate that DFT provides a cost-effective alternative to CASSCF in providing reference orbitals for post-CI dynamic correlation calculations.
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Affiliation(s)
- Jan-Niklas Boyn
- The James Franck Institute and The Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA
| | - David A Mazziotti
- The James Franck Institute and The Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA
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4
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Kirkpatrick J, McMorrow B, Turban DHP, Gaunt AL, Spencer JS, Matthews AGDG, Obika A, Thiry L, Fortunato M, Pfau D, Castellanos LR, Petersen S, Nelson AWR, Kohli P, Mori-Sánchez P, Hassabis D, Cohen AJ. Pushing the frontiers of density functionals by solving the fractional electron problem. Science 2021; 374:1385-1389. [PMID: 34882476 DOI: 10.1126/science.abj6511] [Citation(s) in RCA: 116] [Impact Index Per Article: 38.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
[Figure: see text].
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Affiliation(s)
| | | | | | | | | | | | | | - Louis Thiry
- Département d'informatique, ENS, CNRS, PSL University, Paris, France
| | | | - David Pfau
- DeepMind, 6 Pancras Square, London N1C 4AG, UK
| | | | | | | | | | | | | | - Aron J Cohen
- DeepMind, 6 Pancras Square, London N1C 4AG, UK.,Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany
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5
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Peng Y, Zhou X, Wang Z, Wang F. Diffusion Monte Carlo method on small boron clusters using single- and multi- determinant-Jastrow trial wavefunctions. J Chem Phys 2021; 154:024301. [PMID: 33445915 DOI: 10.1063/5.0031051] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Multireference character in some small boron clusters could be significant, and a previous all-electron fixed-node diffusion quantum Monte Carlo (FN-DMC) calculation with the single-determinant-Jastrow (SDJ) trial wavefunction shows that the atomization energy (AE) of B4 + is overestimated by about 1.4 eV compared with the coupled cluster method with single, doubles, and perturbative triples [CCSD(T)] results. All-electron FN-DMC calculations and those with the pseudopotential (PP) using SDJ and multi-determinant-Jastrow (MDJ) trial wavefunctions with B3LYP orbitals as well as CC calculations at different levels are carried out on Bn Q (n = 1-5, Q = -1, 0, 1) clusters. The obtained FN-DMC energies indicate that the node error of the employed SDJ trial wavefunction in all-electron calculations is different from that with the PP for some clusters. The error of AEs and dissociation energies (DEs) from all-electron FN-DMC calculations is larger than that with the PP when the SDJ trial wavefunction is employed, while errors of CC methods do not depend on whether the PP is used. AEs and DEs of the boron clusters are improved significantly when MDJ trial wavefunctions are used in both all-electron calculations and those with the PP, and their error is similar to that of CCSD(T) compared with CCSDT(Q) results. On the other hand, reasonable adiabatic electron detachment energies (ADEs) and ionization potentials (AIPs) are achieved with FN-DMC using SDJ trial wavefunctions and MDJ is less effective on ADEs and AIPs. Furthermore, the relative energy between two structures of B9 - is predicted reliably with FN-DMC using the SDJ trial wavefunction and the effect of MDJ is negligible, while density functional theory results using different exchange-correlation functionals differ significantly.
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Affiliation(s)
- Yun Peng
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu 610065, People's Republic of China
| | - Xiaojun Zhou
- Department of Physics, Shaanxi University of Science and Technology, Xi'an 710021, People's Republic of China
| | - Zhifan Wang
- School of Electronic Engineering, Chengdu Technological University, Chengdu 610064, People's Republic of China
| | - Fan Wang
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu 610065, People's Republic of China
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6
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Nukazawa T, Iwamoto T. Interconversion between a planar 1,3-dichlorobicyclo[1.1.0]tetrasilane and a (chloro)(chlorosilyl)cyclotrisilene. Dalton Trans 2020; 49:16728-16735. [DOI: 10.1039/d0dt03408h] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A 1,3-dichlorotetrasilabicyclo[1.1.0]butane with a π-type bridgehead Si–Si bond undergoes a skeletal isomerisation to a 1-chloro-2-(chlorosilyl)cyclotrisilene.
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Affiliation(s)
- Takumi Nukazawa
- Department of Chemistry
- Graduate School of Science
- Tohoku University
- Sendai 980-8578
- Japan
| | - Takeaki Iwamoto
- Department of Chemistry
- Graduate School of Science
- Tohoku University
- Sendai 980-8578
- Japan
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7
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Dubecký M. Bias cancellation in one-determinant fixed-node diffusion Monte Carlo: Insights from fermionic occupation numbers. Phys Rev E 2017; 95:033308. [PMID: 28415179 DOI: 10.1103/physreve.95.033308] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2016] [Indexed: 06/07/2023]
Abstract
The accuracy of the fixed-node diffusion Monte Carlo (FNDMC) depends on the node location of the supplied trial state Ψ_{T}. The practical FNDMC approaches available for large systems rely on compact yet effective Ψ_{T}, most often containing an explicitly correlated single Slater determinant (SD). However, SD nodes may be better suited to one system than to another, which may possibly lead to inaccurate FNDMC energy differences. It remains a challenge how to estimate nonequivalence or appropriateness of SDs. Here we use the differences of a measure based on the Euclidean distance between the natural orbital occupation number (NOON) vector of the SD and the exact solution in the NOON vector space, which can be viewed as a measure of SD nonequivalence and as a qualitative measure of the expected degree of nondynamic-correlation-related bias in FNDMC energy differences. This is explored on a set of small noncovalent complexes and covalent bond breaking of Si_{2} vs N_{2}. It turns out that NOON-based measures well reflect the magnitude and sign of the bias present in the data available, thus providing insights into the nature of bias cancellation in SD FNDMC energy differences.
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Affiliation(s)
- Matúš Dubecký
- Department of Physics, Faculty of Science, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic and ATRI, Faculty of Materials Science and Technology, Slovak University of Technology, Paulínska 16, 917 24 Trnava, Slovakia
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8
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Bertels LW, Mazziotti DA. Accurate prediction of diradical chemistry from a single-reference density-matrix method: Model application to the bicyclobutane to gauche-1,3-butadiene isomerization. J Chem Phys 2014; 141:044305. [PMID: 25084908 DOI: 10.1063/1.4890117] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Multireference correlation in diradical molecules can be captured by a single-reference 2-electron reduced-density-matrix (2-RDM) calculation with only single and double excitations in the 2-RDM parametrization. The 2-RDM parametrization is determined by N-representability conditions that are non-perturbative in their treatment of the electron correlation. Conventional single-reference wave function methods cannot describe the entanglement within diradical molecules without employing triple- and potentially even higher-order excitations of the mean-field determinant. In the isomerization of bicyclobutane to gauche-1,3-butadiene the parametric 2-RDM (p2-RDM) method predicts that the diradical disrotatory transition state is 58.9 kcal/mol above bicyclobutane. This barrier is in agreement with previous multireference calculations as well as recent Monte Carlo and higher-order coupled cluster calculations. The p2-RDM method predicts the Nth natural-orbital occupation number of the transition state to be 0.635, revealing its diradical character. The optimized geometry from the p2-RDM method differs in important details from the complete-active-space self-consistent-field geometry used in many previous studies including the Monte Carlo calculation.
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Affiliation(s)
- Luke W Bertels
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - David A Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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9
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Melnichuk A, Bartlett RJ. Relaxed active space: Fixing tailored-CC with high order coupled cluster. II. J Chem Phys 2014; 140:064113. [DOI: 10.1063/1.4862676] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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10
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Shen J, Piecuch P. Combining active-space coupled-cluster methods with moment energy corrections via the CC(P;Q) methodology, with benchmark calculations for biradical transition states. J Chem Phys 2012; 136:144104. [PMID: 22502498 DOI: 10.1063/1.3700802] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We have recently suggested the CC(P;Q) methodology that can correct energies obtained in the active-space coupled-cluster (CC) or equation-of-motion (EOM) CC calculations, which recover much of the nondynamical and some dynamical electron correlation effects, for the higher-order, mostly dynamical, correlations missing in the active-space CC/EOMCC considerations. It is shown that one can greatly improve the description of biradical transition states, both in terms of the resulting energy barriers and total energies, by combining the CC approach with singles, doubles, and active-space triples, termed CCSDt, with the CC(P;Q)-style correction due to missing triple excitations defining the CC(t;3) approximation.
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Affiliation(s)
- Jun Shen
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
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11
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Nedd SA, DeYonker NJ, Wilson AK, Piecuch P, Gordon MS. Incorporating a completely renormalized coupled cluster approach into a composite method for thermodynamic properties and reaction paths. J Chem Phys 2012; 136:144109. [DOI: 10.1063/1.3700801] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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Affiliation(s)
- Brian M. Austin
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, United States
| | - Dmitry Yu. Zubarev
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, United States
| | - William A. Lester
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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