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Drontschenko V, Ochsenfeld C. Low-Scaling, Efficient and Memory Optimized Computation of Nuclear Magnetic Resonance Shieldings within the Random Phase Approximation Using Cholesky-Decomposed Densities and an Attenuated Coulomb Metric. J Phys Chem A 2024. [PMID: 39239944 DOI: 10.1021/acs.jpca.4c02773] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/07/2024]
Abstract
An efficient method for the computation of nuclear magnetic resonance (NMR) shielding tensors within the random phase approximation (RPA) is presented based on our recently introduced resolution-of-the-identity (RI) atomic orbital RPA NMR method [Drontschenko, V. J. Chem. Theory Comput. 2023, 19, 7542-7554] utilizing Cholesky decomposed density type matrices and employing an attenuated Coulomb RI metric. The introduced sparsity is efficiently exploited using sparse matrix algebra. This allows for an efficient and low-scaling computation of RPA NMR shielding tensors. Furthermore, we introduce a batching method for the computation of memory demanding intermediates that accounts for their sparsity. This extends the applicability of our method to even larger systems that would have been out of reach before, such as, e.g., a DNA strand with 260 atoms and 3408 atomic orbital basis functions.
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Affiliation(s)
- Viktoria Drontschenko
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
- Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany
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2
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Tecmer P, Boguslawski K. Geminal-based electronic structure methods in quantum chemistry. Toward a geminal model chemistry. Phys Chem Chem Phys 2022; 24:23026-23048. [PMID: 36149376 DOI: 10.1039/d2cp02528k] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this review, we discuss the recent progress in developing geminal-based theories for challenging problems in quantum chemistry. Specifically, we focus on the antisymmetrized geminal power, generalized valence bond, antisymmetrized product of strongly orthogonal geminals, singlet-type orthogonal geminals, the antisymmetric product of 1-reference orbital geminal, also known as the pair coupled cluster doubles ansatz, and geminals constructed from Richardson-Gaudin states. Furthermore, we review various corrections to account for the missing dynamical correlation effects in geminal models and possible extensions to target electronically excited states and open-shell species. Finally, we discuss some numerical examples and present-day challenges for geminal-based models, including a quantitative and qualitative analysis of wave functions, and software availability.
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Affiliation(s)
- Paweł Tecmer
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
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3
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Abraham V, Mayhall NJ. Cluster many-body expansion: A many-body expansion of the electron correlation energy about a cluster mean field reference. J Chem Phys 2021; 155:054101. [PMID: 34364343 DOI: 10.1063/5.0057752] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
The many-body expansion (MBE) is an efficient tool that has a long history of use for calculating interaction energies, binding energies, lattice energies, and so on. In the past, applications of MBE to correlation energy have been unfeasible for large systems, but recent improvements to computing resources have sparked renewed interest in capturing the correlation energy using the generalized nth order Bethe-Goldstone equation. In this work, we extend this approach, originally proposed for a Slater determinant, to a tensor product state (TPS) based wavefunction. By partitioning the active space into smaller orbital clusters, our approach starts from a cluster mean field reference TPS configuration and includes the correlation contribution of the excited TPSs using the MBE. This method, named cluster MBE (cMBE), improves the convergence of MBE at lower orders compared to directly doing a block-based MBE from a RHF reference. We present numerical results for strongly correlated systems, such as the one- and two-dimensional Hubbard models and the chromium dimer. The performance of the cMBE method is also tested by partitioning the extended π space of several large π-conjugated systems, including a graphene nano-sheet with a very large active space of 114 electrons in 114 orbitals, which would require 1066 determinants for the exact FCI solution.
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Affiliation(s)
- Vibin Abraham
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, USA
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4
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Margócsy Á, Szabados Á. Ring coupled cluster doubles at the multireference level. J Chem Phys 2020; 152:204114. [PMID: 32486660 DOI: 10.1063/5.0005075] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A ring approximation within an internally contracted multireference (MR) Coupled Cluster (CC) framework is worked out and tested. Derivation of equations utilizes MR based, generalized normal ordering and the corresponding generalized Wick-theorem (MR-GWT). Contractions among cluster operators are avoided by adopting a normal ordered exponential ansatz. The original version of the MR ring CC doubles (MR-rCCD) equations [Á. Szabados and Á. Margócsy, Mol. Phys. 115, 2731 (2017)] is rectified in two aspects. On the one hand, over-completeness of double excitations is treated by relying on the concept of frames. On the other hand, restriction on the maximal cumulant rank is lifted from two to four. This is found essential for obtaining reliable correlation corrections to the energy. The MR function underlying the approach is provided by the Generalized Valence Bond (GVB) model. The pair structure of the reference ensures a fragment structure of GVB cumulants. This represents a benefit when evaluating cumulant contractions appearing as a consequence of MR-GWT. In particular, cumulant involving terms remain less expensive than their traditional, pair-contracted counterpart, facilitating an O(N6) eventual scaling of the proposed MR-rCCD method. Pilot applications are presented for covalent bond breaking, deprotonation energies, and torsional potentials.
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Affiliation(s)
- Á Margócsy
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Faculty of Science, ELTE Eötvös Loránd University, Budapest, Hungary
| | - Á Szabados
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Faculty of Science, ELTE Eötvös Loránd University, Budapest, Hungary
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5
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Pastorczak E, Jensen HJA, Kowalski PH, Pernal K. Generalized Valence Bond Perfect-Pairing Made Versatile Through Electron-Pairs Embedding. J Chem Theory Comput 2019; 15:4430-4439. [PMID: 31287698 DOI: 10.1021/acs.jctc.9b00384] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Ewa Pastorczak
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | | | - Piotr H. Kowalski
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
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6
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Lee J, Small DW, Head-Gordon M. Open-shell coupled-cluster valence-bond theory augmented with an independent amplitude approximation for three-pair correlations: Application to a model oxygen-evolving complex and single molecular magnet. J Chem Phys 2018; 149:244121. [DOI: 10.1063/1.5052667] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Joonho Lee
- Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - David W. Small
- Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Martin Head-Gordon
- Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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7
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Margócsy Á, Kowalski P, Pernal K, Szabados Á. Multiple bond breaking with APSG-based correlation methods: comparison of two approaches. Theor Chem Acc 2018. [DOI: 10.1007/s00214-018-2355-4] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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8
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Azar RJ, Head-Gordon M. Similarity-transformed perturbation theory on top of truncated local coupled cluster solutions: Theory and applications to intermolecular interactions. J Chem Phys 2015; 142:204101. [DOI: 10.1063/1.4921377] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Richard Julian Azar
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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9
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Small DW, Lawler KV, Head-Gordon M. Coupled Cluster Valence Bond Method: Efficient Computer Implementation and Application to Multiple Bond Dissociations and Strong Correlations in the Acenes. J Chem Theory Comput 2014; 10:2027-40. [DOI: 10.1021/ct500112y] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Affiliation(s)
- David W. Small
- Department
of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical
Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Keith V. Lawler
- Department
of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical
Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Martin Head-Gordon
- Department
of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical
Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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11
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Piris M. Interpair electron correlation by second-order perturbative corrections to PNOF5. J Chem Phys 2013; 139:064111. [DOI: 10.1063/1.4817946] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.2] [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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Parkhill JA, Azar J, Head-Gordon M. The formulation and performance of a perturbative correction to the perfect quadruples model. J Chem Phys 2011; 134:154112. [DOI: 10.1063/1.3582729] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
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13
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Parkhill JA, Head-Gordon M. A truncation hierarchy of coupled cluster models of strongly correlated systems based on perfect-pairing references: The singles+doubles models. J Chem Phys 2010; 133:124102. [DOI: 10.1063/1.3483556] [Citation(s) in RCA: 30] [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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14
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Parkhill JA, Head-Gordon M. A tractable and accurate electronic structure method for static correlations: The perfect hextuples model. J Chem Phys 2010; 133:024103. [DOI: 10.1063/1.3456001] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
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15
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Valdes H, Pluhackova K, Hobza P. Phenylalanyl-Glycyl-Phenylalanine Tripeptide: A Model System for Aromatic−Aromatic Side Chain Interactions in Proteins. J Chem Theory Comput 2009; 5:2248-56. [DOI: 10.1021/ct900174f] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- H. Valdes
- Dpto. Química Física y Analítica, Universidad de Oviedo, C/Julián Clavería, 8, 33006 (Oviedo) Asturias, Spain, Center for Biomolecules and Complex Molecular Systems, Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, 16610 Prague 6, Czech Republic, and Department of Physical Chemistry, Palacky University, 771 42 Olomouc, Czech Republic
| | - K. Pluhackova
- Dpto. Química Física y Analítica, Universidad de Oviedo, C/Julián Clavería, 8, 33006 (Oviedo) Asturias, Spain, Center for Biomolecules and Complex Molecular Systems, Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, 16610 Prague 6, Czech Republic, and Department of Physical Chemistry, Palacky University, 771 42 Olomouc, Czech Republic
| | - P. Hobza
- Dpto. Química Física y Analítica, Universidad de Oviedo, C/Julián Clavería, 8, 33006 (Oviedo) Asturias, Spain, Center for Biomolecules and Complex Molecular Systems, Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, 16610 Prague 6, Czech Republic, and Department of Physical Chemistry, Palacky University, 771 42 Olomouc, Czech Republic
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16
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Parkhill JA, Lawler K, Head-Gordon M. The perfect quadruples model for electron correlation in a valence active space. J Chem Phys 2009; 130:084101. [DOI: 10.1063/1.3086027] [Citation(s) in RCA: 59] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
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17
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Thom AJW, Head-Gordon M. Locating multiple self-consistent field solutions: an approach inspired by metadynamics. PHYSICAL REVIEW LETTERS 2008; 101:193001. [PMID: 19113263 DOI: 10.1103/physrevlett.101.193001] [Citation(s) in RCA: 63] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2008] [Indexed: 05/27/2023]
Abstract
We propose a method to locate the solutions to the self-consistent field (SCF) equations, using an approach based upon metadynamics. We define a distance function between density matrices. Within an SCF calculation, when a solution is found, a biasing potential based on distance from the solution is added to the energy to avoid reconvergence to the same solution. Multiple solutions can therefore be relatively easily found. Using this method we locate all known solutions and one unknown solution of the H4 model. The set of restricted Hartree-Fock (RHF) solutions for the nitrogen molecule is located, and a broken-symmetry solution lower in energy than the symmetric RHF solution is found corresponding to dissociation into doublet fragments.
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Affiliation(s)
- Alex J W Thom
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA.
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18
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Shen J, Fang T, Hua W, Li S. Spectroscopic Constants of Single-Bond Diatomic Molecules and Singlet−Triplet Gaps of Diradicals by the Block-Correlated Coupled Cluster Theory. J Phys Chem A 2008; 112:4703-9. [DOI: 10.1021/jp7118907] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Affiliation(s)
- Jun Shen
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing, 210093, Peopleʼs Republic of China
| | - Tao Fang
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing, 210093, Peopleʼs Republic of China
| | - Weijie Hua
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing, 210093, Peopleʼs Republic of China
| | - Shuhua Li
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing, 210093, Peopleʼs Republic of China
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19
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Lawler KV, Beran GJO, Head-Gordon M. Symmetry breaking in benzene and larger aromatic molecules within generalized valence bond coupled cluster methods. J Chem Phys 2008; 128:024107. [DOI: 10.1063/1.2817600] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
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20
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Valdes H, Pluháčková K, Pitonák M, Řezáč J, Hobza P. Benchmark database on isolated small peptides containing an aromatic side chain: comparison between wave function and density functional theory methods and empirical force field. Phys Chem Chem Phys 2008; 10:2747-57. [DOI: 10.1039/b719294k] [Citation(s) in RCA: 135] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
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21
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Valdés H, Klusák V, Pitoňák M, Exner O, Starý I, Hobza P, Rulíšek L. Evaluation of the intramolecular basis set superposition error in the calculations of larger molecules: [n]helicenes and Phe-Gly-Phe tripeptide. J Comput Chem 2008; 29:861-70. [DOI: 10.1002/jcc.20841] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
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22
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Fang T, Li S. Block correlated coupled cluster theory with a complete active-space self-consistent-field reference function: The formulation and test applications for single bond breaking. J Chem Phys 2007; 127:204108. [DOI: 10.1063/1.2800027] [Citation(s) in RCA: 53] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
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23
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Cullen J. An approximate diatomics in molecules formulation of generalized valence bond theory. J Comput Chem 2007; 29:497-504. [PMID: 17663438 DOI: 10.1002/jcc.20808] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
The slow computational speed of the generalized valence bond perfect pairing method (GVB-PP) has been an impediment to its routine use. We have addressed this problem by employing a diatomics in molecules Hamiltonian derived from a second quantization perturbation approach. This results in all three- and four-centered two-electron integrals being dropped from the traditional GVB-PP calculation. For moderate sized molecules, as for example C20 computed with a double zeta + polarization basis, there is on average a fifty-fold decrease in computational times. In this article, we present the theory behind our approach and analyze the accuracy and speed of this approximate GVB-PP method for several cases where density functional methods have produced ambivalent results.
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Affiliation(s)
- John Cullen
- Department of Chemistry, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2.
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24
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Rassolov VA, Xu F. Geminal model chemistry. IV. Variational and size consistent pure spin states. J Chem Phys 2007; 127:044104. [PMID: 17672678 DOI: 10.1063/1.2755738] [Citation(s) in RCA: 53] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
We present a computationally inexpensive method that yields ground state wave functions of pure spin symmetry. The method is variational and rigorously size consistent, free from adjustable parameters, and has a favorable scaling with system size. It is based on the recently introduced partially spin restricted geminal wave functions with limited spin contamination. Computations of a bond breaking, a transition metal compound, and a symmetric hydrogen cluster confirm the properties of this method.
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Affiliation(s)
- Vitaly A Rassolov
- Department of Chemistry and Biochemistry, University of South Carolina, 631 Sumter Street, Columbia, South Carolina 29208, USA.
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25
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Abstract
The authors define an ab initio electronic structure model that uses partial spin restriction. It is an intermediate case between the so-called spin-restricted and spin-unrestricted formulations, which are popular in electronic structure methodology. Partial spin restriction arises naturally when the wave function is represented as an antisymmetrized product of two-electron functions, as it is done in generalized valence bond and antisymmetrized product of strongly orthogonal geminal theories. The authors show that the new model is size consistent, and it improves the description of transition metal compounds.
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Affiliation(s)
- Vitaly A Rassolov
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA.
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26
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Cerný J, Jurecka P, Hobza P, Valdés H. Resolution of Identity Density Functional Theory Augmented with an Empirical Dispersion Term (RI-DFT-D): A Promising Tool for Studying Isolated Small Peptides. J Phys Chem A 2007; 111:1146-54. [PMID: 17253667 DOI: 10.1021/jp066504m] [Citation(s) in RCA: 65] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
Resolution of identity standard density functional theory augmented with a damped empirical dispersion term (RI-DFT-D) calculations have been carried out on a set of lowest energy minima of tryptophyl-glycine (Trp-Gly) and tryptophyl-glycyl-glycine (Trp-Gly-Gly) peptides. RI-DFT-D (TPSS/TZVP) results are in excellent agreement with benchmark data based on the CCSD(T) method. Experimental spectra could be assigned according to the calculated IR frequencies. Central processing unit (CPU) time requirements are only slightly higher than those needed for the DFT calculations. Consequently, RI-DFT-D theory seems to be a promising methodology for studying oligopeptides with accuracy comparable to ab initio quantum chemical calculations.
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Affiliation(s)
- Jirí Cerný
- Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic and Center for Biomolecules and Complex Molecular Systems, 166 10 Prague 6, Czech Republic
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27
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Hachmann J, Cardoen W, Chan GKL. Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group. J Chem Phys 2006; 125:144101. [PMID: 17042573 DOI: 10.1063/1.2345196] [Citation(s) in RCA: 135] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Abstract
We have devised a local ab initio density matrix renormalization group algorithm to describe multireference correlations in large systems. For long molecules that are extended in one of their spatial dimensions, we can obtain an exact characterization of correlation, in the given basis, with a cost that scales only quadratically with the size of the system. The reduced scaling is achieved solely through integral screening and without the construction of correlation domains. We demonstrate the scaling, convergence, and robustness of the algorithm in polyenes and hydrogen chains. We converge to exact correlation energies (in the sense of full configuration interaction, with 1-10 microE(h) precision) in all cases and correlate up to 100 electrons in 100 active orbitals. We further use our algorithm to obtain exact energies for the metal-insulator transition in hydrogen chains and compare and contrast our results with those from conventional quantum chemical methods.
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Affiliation(s)
- Johannes Hachmann
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, USA.
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28
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Bochevarov AD, Temelso B, Sherrill CD. Hybrid correlation models based on active-space partitioning: Seeking accurate O(N5) ab initio methods for bond breaking. J Chem Phys 2006; 125:054109. [PMID: 16942205 DOI: 10.1063/1.2222350] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Moller-Plesset second-order (MP2) perturbation theory remains the least expensive standard ab initio method that includes electron correlation, scaling as O(N5) with the number of molecular orbitals N. Unfortunately, when restricted Hartree-Fock orbitals are employed, the potential energy curves calculated with this method are of little use at large interatomic separations because of the divergent behavior of MP2 in these regions. In our previous study [J. Chem. Phys. 122, 234110 (2005)] we combined the MP2 method with the singles and doubles coupled cluster (CCSD) method to produce a hybrid method that retains the computational scaling of MP2 and improves dramatically the shape of the MP2 curves. In this work we expand the hybrid methodology to several other schemes. We investigate a new, improved MP2-CCSD method as well as a few other O(N5) methods related to the Epstein-Nesbet pair correlation theory. Nonparallelity errors across the dissociation curve as well as several spectroscopic constants are computed for BH, HF, H2O, CH+, CH4, and Li2 molecules with the 6-31G* basis set and compared with the corresponding full configuration interaction results. We show that among the O(N5) methods considered, our new hybrid MP2-CCSD method is the most accurate and significantly outperforms MP2 not only at large interatomic separations, but also near equilibrium geometries.
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Affiliation(s)
- Arteum D Bochevarov
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA
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29
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Beran GJ, Head-Gordon M. On the Nature of Unrestricted Orbitals in Variational Active Space Wave Functions. J Phys Chem A 2006; 110:9915-20. [PMID: 16898694 DOI: 10.1021/jp061814q] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
Active space coupled cluster methods exhibit unusual, nonsmooth spin symmetry-breaking behavior where the unrestricted minimum lies higher in energy at short bond distances and crosses below the restricted solution at longer distances. The restricted solution is also observed to be a stable minimum slightly beyond the symmetry-breaking point. This behavior arises due to differences in the optimal active spaces defining the restricted and unrestricted wave functions and results in unrestricted wave functions that are not strictly size consistent. We suggest a new, size-consistent model that allows the orbitals to break spin symmetry only within the active space.
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Affiliation(s)
- Gregory J Beran
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
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30
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Abstract
This essay provides a perspective on several issues in valence bond theory: the physical significance of semilocal bonding orbitals, the capability of valence bond concepts to explain systems with multireferences character, the use of valence bond theory to provide analytical representations of potential energy surfaces for chemical dynamics by the method of semiempirical valence bond potential energy surfaces (an early example of specific reaction parameters), by multiconfiguration molecular mechanics, by the combined valence bond-molecular mechanics method, and by the use of valence bond states as coupled diabatic states for describing electronically nonadiabatic processes (photochemistry). The essay includes both ab initio and semiempirical approaches.
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Affiliation(s)
- Donald G Truhlar
- Department of Chemistry and Supercomputing Institute, University of Minnesota, 207 Pleasant Street S.E., Minneapolis, Minnesota 55455-0431, USA.
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