1
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Bartlett RJ. Perspective on Coupled-cluster Theory. The evolution toward simplicity in quantum chemistry. Phys Chem Chem Phys 2024; 26:8013-8037. [PMID: 38390989 DOI: 10.1039/d3cp03853j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/24/2024]
Abstract
Coupled-cluster theory has revolutionized quantum chemistry. It has provided the framework to effectively solve the problem of electron correlation, the main focus of the field for over 60 years. This has enabled ab initio quantum chemistry to provide predictive quality results for most quantities of interest that are obtainable from first-principle calculations. The best that one can do in a basis is the 'full CI,' the exact solution of the non-relativistic Schrödinger equation or, if need be, the relativistic Dirac equation. With due regard to converging the basis set and adequate consideration of higher clusters and relativity in a calculation, virtually predictive results can be obtained. But in addition to its numerical performance, coupled-cluster theory also offers a conceptually new, many-body foundation for the theory that should be appreciated by all practitioners. The latter is emphasized in this perspective, leading to the 'evolution toward simplicity' in the title. The ultimate theory will benefit from the several features that are uniquely exact in coupled-cluster theory and its equation-of-motion (EOM-CC) extensions.
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Affiliation(s)
- Rodney J Bartlett
- Quantum Theory Project, Department of Chemistry, University of Florida, P. O. Box 117200, Gainesville, Florida, USA.
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2
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Hansen AS, Aurbakken E, Pedersen TB. Smooth potential-energy surfaces in fragmentation-based local correlation methods for periodic systems. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1896046] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- A. S. Hansen
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, Oslo, Norway
| | - E. Aurbakken
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, Oslo, Norway
| | - T. B. Pedersen
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, Oslo, Norway
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3
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Song C, Martínez TJ. Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units. J Chem Phys 2017; 147:161723. [DOI: 10.1063/1.4997997] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Chenchen Song
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA and SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Todd J. Martínez
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA and SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
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4
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Huang C. Patching the Exchange-Correlation Potential in Density Functional Theory. J Chem Theory Comput 2016; 12:2224-33. [DOI: 10.1021/acs.jctc.6b00051] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Chen Huang
- Department
of Scientific
Computing, Florida State University, Tallahassee, Florida 32306-4120, United States
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5
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Rybkin VV, VandeVondele J. Spin-Unrestricted Second-Order Møller–Plesset (MP2) Forces for the Condensed Phase: From Molecular Radicals to F-Centers in Solids. J Chem Theory Comput 2016; 12:2214-23. [DOI: 10.1021/acs.jctc.6b00015] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Vladimir V. Rybkin
- Nanoscale Simulations, Department
of Materials, ETH Zürich, Wolfgang-Pauli-Str. 27, CH-8093 Zürich, Switzerland
| | - Joost VandeVondele
- Nanoscale Simulations, Department
of Materials, ETH Zürich, Wolfgang-Pauli-Str. 27, CH-8093 Zürich, Switzerland
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6
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Abstract
Interest in molecular crystals has grown thanks to their relevance to pharmaceuticals, organic semiconductor materials, foods, and many other applications. Electronic structure methods have become an increasingly important tool for modeling molecular crystals and polymorphism. This article reviews electronic structure techniques used to model molecular crystals, including periodic density functional theory, periodic second-order Møller-Plesset perturbation theory, fragment-based electronic structure methods, and diffusion Monte Carlo. It also discusses the use of these models for predicting a variety of crystal properties that are relevant to the study of polymorphism, including lattice energies, structures, crystal structure prediction, polymorphism, phase diagrams, vibrational spectroscopies, and nuclear magnetic resonance spectroscopy. Finally, tools for analyzing crystal structures and intermolecular interactions are briefly discussed.
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Affiliation(s)
- Gregory J O Beran
- Department of Chemistry, University of California , Riverside, California 92521, United States
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7
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Huang W, Xing DH, Lu JB, Long B, Schwarz WHE, Li J. How Much Can Density Functional Approximations (DFA) Fail? The Extreme Case of the FeO4 Species. J Chem Theory Comput 2016; 12:1525-33. [PMID: 26938575 DOI: 10.1021/acs.jctc.5b01040] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A thorough theoretical study of the relative energies of various molecular Fe·4O isomers with different oxidation states of both Fe and O atoms is presented, comparing simple Hartree-Fock through many Kohn-Sham approximations up to extended coupled cluster and DMRG multiconfiguration benchmark methods. The ground state of Fe·4O is a singlet, hexavalent iron(VI) complex (1)C2v-[Fe(VI)O2](2+)(O2)(2-), with isomers of oxidation states Fe(II), Fe(III), Fe(IV), Fe(V), and Fe(VIII) all lying slightly higher within the range of 1 eV. The disputed existence of oxidation state Fe(VIII) is discussed for isolated FeO4 molecules. Density functional theory (DFT) at various DF approximation (DFA) levels of local and gradient approaches, Hartree-Fock exchange and meta hybrids, range dependent, DFT-D and DFT+U models do not perform better for the relative stabilities of the geometric and electronic Fe·4O isomers than within 1-5 eV. The Fe·4O isomeric species are an excellent testing and validation ground for the development of density functional and wave function methods for strongly correlated multireference states, which do not seem to always follow chemical intuition.
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Affiliation(s)
- Wei Huang
- Department of Chemistry and Key Laboratory of Organic Optoelectronics & Molecular Engineering of the Ministry of Education, Tsinghua University , Beijing 100084, China
| | - Deng-Hui Xing
- Department of Chemistry and Key Laboratory of Organic Optoelectronics & Molecular Engineering of the Ministry of Education, Tsinghua University , Beijing 100084, China
| | - Jun-Bo Lu
- Department of Chemistry and Key Laboratory of Organic Optoelectronics & Molecular Engineering of the Ministry of Education, Tsinghua University , Beijing 100084, China
| | - Bo Long
- Department of Chemistry and Key Laboratory of Organic Optoelectronics & Molecular Engineering of the Ministry of Education, Tsinghua University , Beijing 100084, China
| | - W H Eugen Schwarz
- Department of Chemistry and Key Laboratory of Organic Optoelectronics & Molecular Engineering of the Ministry of Education, Tsinghua University , Beijing 100084, China
| | - Jun Li
- Department of Chemistry and Key Laboratory of Organic Optoelectronics & Molecular Engineering of the Ministry of Education, Tsinghua University , Beijing 100084, China
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8
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Del Ben M, Hutter J, VandeVondele J. Forces and stress in second order Møller-Plesset perturbation theory for condensed phase systems within the resolution-of-identity Gaussian and plane waves approach. J Chem Phys 2015; 143:102803. [DOI: 10.1063/1.4919238] [Citation(s) in RCA: 50] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Mauro Del Ben
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Jürg Hutter
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Joost VandeVondele
- Department of Materials, ETH Zürich, Wolfgang-Pauli-Strasse 27, CH-8093 Zürich, Switzerland
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9
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Bulik IW, Chen W, Scuseria GE. Electron correlation in solids via density embedding theory. J Chem Phys 2014; 141:054113. [DOI: 10.1063/1.4891861] [Citation(s) in RCA: 68] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Affiliation(s)
| | - Weibing Chen
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
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10
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Beran GJO, Wen S, Nanda K, Huang Y, Heit Y. Accurate and Robust Molecular Crystal Modeling Using Fragment-Based Electronic Structure Methods. Top Curr Chem (Cham) 2013; 345:59-93. [DOI: 10.1007/128_2013_502] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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11
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Nanda KD, Beran GJO. Prediction of organic molecular crystal geometries from MP2-level fragment quantum mechanical/molecular mechanical calculations. J Chem Phys 2012; 137:174106. [DOI: 10.1063/1.4764063] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.5] [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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Del Ben M, Hutter J, VandeVondele J. Second-Order Møller–Plesset Perturbation Theory in the Condensed Phase: An Efficient and Massively Parallel Gaussian and Plane Waves Approach. J Chem Theory Comput 2012; 8:4177-88. [DOI: 10.1021/ct300531w] [Citation(s) in RCA: 111] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Affiliation(s)
- Mauro Del Ben
- Institute of Physical Chemistry, University of Zürich, Winterthurerstrasse 190,
CH-8057 Zürich,
| | - Jürg Hutter
- Institute of Physical Chemistry, University of Zürich, Winterthurerstrasse 190,
CH-8057 Zürich,
| | - Joost VandeVondele
- Department of Materials, ETH Zürich, Wolfgang-Pauli-Strasse 27, CH-8093
Zürich, Switzerland
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13
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Helgaker T, Coriani S, Jørgensen P, Kristensen K, Olsen J, Ruud K. Recent Advances in Wave Function-Based Methods of Molecular-Property Calculations. Chem Rev 2012; 112:543-631. [DOI: 10.1021/cr2002239] [Citation(s) in RCA: 463] [Impact Index Per Article: 38.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Trygve Helgaker
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Sonia Coriani
- Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Trieste, Via Giorgieri 1, I-34127 Trieste, Italy
| | - Poul Jørgensen
- Lundbeck Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
| | - Kasper Kristensen
- Lundbeck Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
| | - Jeppe Olsen
- Lundbeck Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
| | - Kenneth Ruud
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø, N-9037 Tromsø, Norway
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14
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Wen S, Nanda K, Huang Y, Beran GJO. Practical quantum mechanics-based fragment methods for predicting molecular crystal properties. Phys Chem Chem Phys 2012; 14:7578-90. [DOI: 10.1039/c2cp23949c] [Citation(s) in RCA: 100] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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15
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Katouda M, Nagase S. Application of second-order Møller–Plesset perturbation theory with resolution-of-identity approximation to periodic systems. J Chem Phys 2010; 133:184103. [DOI: 10.1063/1.3503153] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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17
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Stoyanova A, Hozoi L, Fulde P, Stoll H. Correlation-induced corrections to the band structure of boron nitride: A wave-function-based approach. J Chem Phys 2009; 131:044119. [DOI: 10.1063/1.3177010] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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18
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19
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20
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Pisani C, Maschio L, Casassa S, Halo M, Schütz M, Usvyat D. Periodic local MP2 method for the study of electronic correlation in crystals: Theory and preliminary applications. J Comput Chem 2008; 29:2113-24. [DOI: 10.1002/jcc.20975] [Citation(s) in RCA: 205] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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21
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Piris M, Otto P. Natural orbital functional for correlation in polymers. INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 2005; 102:90-97. [DOI: 10.1002/qua.20291] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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22
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Hirata S, Podeszwa R, Tobita M, Bartlett RJ. Coupled-cluster singles and doubles for extended systems. J Chem Phys 2004; 120:2581-92. [PMID: 15268402 DOI: 10.1063/1.1637577] [Citation(s) in RCA: 96] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Coupled-cluster theory with connected single and double excitation operators (CCSD) and related approximations, such as linearized CCSD, quadratic configuration interaction with single and double excitation operators, coupled-cluster with connected double excitation operator (CCD), linearized CCD, approximate CCD, and second- and third-order many-body perturbation theories, are formulated and implemented for infinitely extended one-dimensional systems (polymers), on the basis of the periodic boundary conditions and distance-based screening of integrals, density matrix elements, and excitation amplitudes. The variation of correlation energies with the truncation radii of short- and long-range lattice sums and with the number of wave vector sampling points in the first Brillouin zone is examined for polyethylene, polyacetylene, and polyyne, and is shown to be a function of the degree of pi-electron conjugation or the fundamental band gaps. The t2 and t1 amplitudes in the atomic orbital (AO) basis are obtained by first computing the t amplitudes in the Bloch-orbital basis and subsequently back-transforming them into the AO basis. The plot of these AO-based t amplitudes as a function of unit cells also indicates that the t2 amplitudes of polyacetylene and polyyne exhibit appreciably slower decay than those of polyethylene, although the asymptotic decay behavior is invariably 1/r3. The AO-based t1 amplitudes appear to correlate strongly with the electronic structure, and they decay seemingly exponentially for polyethylene whereas they stay at a constant magnitude across the seventh nearest neighbors of polyacetylene and polyyne, which attests to far reaching effects of nondynamical electron correlation mediated by orbital rotation. Nonetheless, the unit cell contributions to the correlation energies taper below 10(-6) hartree after 15 A for all three polymers. The basis set dependence of the decay behavior of t2 amplitudes is also examined for linear hydrogen fluoride polymer (HF)infinity and linear beryllium polymer (Be)infinity employing the STO-3G, 6-31G, and 6-31G* basis sets, and proves to be rather small.
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Affiliation(s)
- So Hirata
- William R. Wiley Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352, USA.
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23
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Pino R, Scuseria GE. Importance of chain–chain interactions on the band gap of trans-polyacetylene as predicted by second-order perturbation theory. J Chem Phys 2004; 121:8113-9. [PMID: 15485275 DOI: 10.1063/1.1798991] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We employ the Laplace-transformed second-order Moller-Plesset perturbation theory for periodic systems in its atomic orbital basis formulation to determine the geometric structure and band gap of interacting polyacetylene chains. We have studied single, double, and triple chains, and also two-dimensional crystals. We estimate from first principles the equilibrium interchain distance and setting angle, along with binding energy between trans-polyacetylene chains due to dispersion interactions. The dependence of the correlation corrected quasiparticle band gap on the intrachain and interchain geometric parameters is studied, obtaining that the gap of the compound structures is substantially reduced with respect to the single chain polymer.
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Affiliation(s)
- Ramiro Pino
- Department of Chemistry, Rice University, Houston, TX 77005-1892, USA.
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24
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Jacquemin D, André JM, Champagne B. Analytic ab initio determination of the elastic modulus in stereoregular polymers: Analytical integral derivatives, long-range effects, implementation, and examples. J Chem Phys 2003. [DOI: 10.1063/1.1523909] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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25
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Jacquemin D, Champagne B, André JM, Deumens E, Ohrn Y. Integral algorithm and density matrix integration scheme for ab initio band structure calculations on polymeric systems. J Comput Chem 2002; 23:1430-44. [PMID: 12370945 DOI: 10.1002/jcc.10146] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
A new program for band structure calculations of periodic one-dimensional systems has been constructed. It is distinguishable from other codes by the efficient two-electron integral evaluation and the integration schemes of the density matrix in the first Brillouin zone. The computation of polymeric two-electron integrals is based on the McMurchie Davidson algorithm and builds batches of the different cell indices included in the polymeric system. Consequently it presents efficient scaling with respect to the number of unit cells taken into account. Our algorithm takes into account fully the polymeric symmetry rather than the molecular symmetry. A semidirect procedure where only exchange integrals are computed at each SCF cycle is proposed in order to maintain balance between computation time and disk space. In addition, the integration of the density matrix over a large number of cell indices can be performed by different methods, such as Gauss-Legendre, Clenshaw-Curtis, Filon, and Alaylioglu-Evans-Hyslop. This last scheme is able to obtain an accuracy of 10(-13) a.u. on each individual density matrix element for all cell indices with only 48 k-points.
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Affiliation(s)
- Denis Jacquemin
- Laboratoire de Chimie Théorique Appliquée, Facultés Universitaires Notre-Dame de la Paix, rue de Bruxelles, 61, B-5000 Namur, Belgium.
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26
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Ayala PY, Kudin KN, Scuseria GE. Atomic orbital Laplace-transformed second-order Møller–Plesset theory for periodic systems. J Chem Phys 2001. [DOI: 10.1063/1.1414369] [Citation(s) in RCA: 181] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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27
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Highly accurate treatment of electron correlation in polymers: coupled-cluster and many-body perturbation theories. Chem Phys Lett 2001. [DOI: 10.1016/s0009-2614(01)00897-1] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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28
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Poulsen TD, Mikkelsen KV, Fripiat JG, Jacquemin D, Champagne B. MP2 correlation effects upon the electronic and vibrational properties of polyyne. J Chem Phys 2001. [DOI: 10.1063/1.1353550] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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29
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Hirata S, Bartlett RJ. Many-body Green’s-function calculations on the electronic excited states of extended systems. J Chem Phys 2000. [DOI: 10.1063/1.481372] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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30
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Ab initio and semi-empirical studies of the static polarizability and the second hyperpolarizability of diamond: finite Td symmetry models from CH4 to C281H172. Chem Phys Lett 2000. [DOI: 10.1016/s0009-2614(99)01337-8] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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31
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Hirata S, Head-Gordon M, Bartlett RJ. Configuration interaction singles, time-dependent Hartree–Fock, and time-dependent density functional theory for the electronic excited states of extended systems. J Chem Phys 1999. [DOI: 10.1063/1.480443] [Citation(s) in RCA: 172] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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32
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Jacquemin D, André JM, Champagne B. Long-range effects in optimizing the geometry of stereoregular polymers. II. Hydrogen fluoride chains as a working example. J Chem Phys 1999. [DOI: 10.1063/1.479791] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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33
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Jacquemin D, André JM, Champagne B. Long-range effects in optimizing the geometry of stereoregular polymers. I. Formalism. J Chem Phys 1999. [DOI: 10.1063/1.479790] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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34
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Modern Correlation Theories for Extended, Periodic Systems. Top Curr Chem (Cham) 1999. [DOI: 10.1007/3-540-48972-x_7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/07/2023]
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