1
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Reliability and performances of real-time time-dependent auxiliary density functional theory. Theor Chem Acc 2021. [DOI: 10.1007/s00214-021-02819-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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2
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Pedroza-Montero JN, Morales JL, Geudtner G, Álvarez-Ibarra A, Calaminici P, Köster AM. Variational Density Fitting with a Krylov Subspace Method. J Chem Theory Comput 2020; 16:2965-2974. [PMID: 32223134 DOI: 10.1021/acs.jctc.9b01212] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In this work, we present the implementation of a variational density fitting methodology that uses iterative linear algebra for solving the associated system of linear equations. It is well known that most difficulties with this system arise from the fact that the coefficient matrix is in general ill-conditioned and, due to finite precision round-off errors, it may not be positive definite. The dimensionality, given by the number of auxiliary functions, also poses a challenge in terms of memory and time demand since the coefficient matrix is dense. The methodology presented is based on a preconditioned Krylov subspace method able to deal with indefinite ill-conditioned equation systems. To assess its potential, it has been combined with double asymptotic electron repulsion integral expansions as implemented in the deMon2k package. A numerical study on a set of problems with up to 130,000 auxiliary functions shows its effectiveness to alleviate the abovementioned problematic. A comparison with the default methodology used in deMon2k based on a truncated eigenvalue decomposition of the coefficient matrix indicates that the proposed method exhibits excellent robustness and scalability when implemented in a parallel setting.
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Affiliation(s)
- Jesús N Pedroza-Montero
- Programa de Doctorado de Nanociencias y Nanotecnologı́as, CINVESTAV, Av. Instituto Politécnico Nacional 2508, Ciudad de México 07360, Mexico
| | - José Luis Morales
- Departamento de Quı́mica, CINVESTAV, Av. Instituto Politécnico Nacional 2508, Ciudad de México 07360, Mexico
| | - Gerald Geudtner
- Departamento de Quı́mica, CINVESTAV, Av. Instituto Politécnico Nacional 2508, Ciudad de México 07360, Mexico
| | - Aurelio Álvarez-Ibarra
- Laboratoire de Chimie Physique, Université Paris Sud, CNRS, Université Paris Saclay. 15 avenue Jean Perrin, F91405 Orsay, France
| | - Patrizia Calaminici
- Programa de Doctorado de Nanociencias y Nanotecnologı́as, CINVESTAV, Av. Instituto Politécnico Nacional 2508, Ciudad de México 07360, Mexico.,Departamento de Quı́mica, CINVESTAV, Av. Instituto Politécnico Nacional 2508, Ciudad de México 07360, Mexico
| | - Andreas M Köster
- Programa de Doctorado de Nanociencias y Nanotecnologı́as, CINVESTAV, Av. Instituto Politécnico Nacional 2508, Ciudad de México 07360, Mexico.,Departamento de Quı́mica, CINVESTAV, Av. Instituto Politécnico Nacional 2508, Ciudad de México 07360, Mexico
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3
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Local density fitting applied to second order propagator equations for core electron binding energies. COMPUT THEOR CHEM 2018. [DOI: 10.1016/j.comptc.2018.05.014] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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4
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Wirz LN, Reine SS, Pedersen TB. On Resolution-of-the-Identity Electron Repulsion Integral Approximations and Variational Stability. J Chem Theory Comput 2017; 13:4897-4906. [DOI: 10.1021/acs.jctc.7b00801] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Lukas N. Wirz
- Hylleraas Centre for Quantum
Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033
Blindern, N-0315 Oslo, Norway
| | - Simen S. Reine
- Hylleraas Centre for Quantum
Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033
Blindern, N-0315 Oslo, Norway
| | - Thomas Bondo Pedersen
- Hylleraas Centre for Quantum
Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033
Blindern, N-0315 Oslo, Norway
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5
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Mata RA, Suhm MA. Benchmarking Quantum Chemical Methods: Are We Heading in the Right Direction? Angew Chem Int Ed Engl 2017; 56:11011-11018. [PMID: 28452424 PMCID: PMC5582598 DOI: 10.1002/anie.201611308] [Citation(s) in RCA: 100] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2016] [Revised: 12/20/2016] [Indexed: 11/15/2022]
Abstract
Theoreticians and experimentalists should work together more closely to establish reliable rankings and benchmarks for quantum chemical methods. Comparison to carefully designed experimental benchmark data should be a priority. Guidelines to improve the situation for experiments and calculations are proposed.
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Affiliation(s)
- Ricardo A. Mata
- Institut für Physikalische ChemieUniversität GöttingenTammannstrasse 637077GöttingenGermany
| | - Martin A. Suhm
- Institut für Physikalische ChemieUniversität GöttingenTammannstrasse 637077GöttingenGermany
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6
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Wu X, Teuler JM, Cailliez F, Clavaguéra C, Salahub DR, de la Lande A. Simulating Electron Dynamics in Polarizable Environments. J Chem Theory Comput 2017; 13:3985-4002. [DOI: 10.1021/acs.jctc.7b00251] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Xiaojing Wu
- Laboratoire
de Chimie Physique, CNRS - Université Paris Sud, Université Paris-Saclay, 15 avenue Jean Perrin, 91405 Orsay CEDEX, France
| | - Jean-Marie Teuler
- Laboratoire
de Chimie Physique, CNRS - Université Paris Sud, Université Paris-Saclay, 15 avenue Jean Perrin, 91405 Orsay CEDEX, France
| | - Fabien Cailliez
- Laboratoire
de Chimie Physique, CNRS - Université Paris Sud, Université Paris-Saclay, 15 avenue Jean Perrin, 91405 Orsay CEDEX, France
| | - Carine Clavaguéra
- Laboratoire
de Chimie Physique, CNRS - Université Paris Sud, Université Paris-Saclay, 15 avenue Jean Perrin, 91405 Orsay CEDEX, France
| | - Dennis R. Salahub
- Department
of Chemistry, Centre for Molecular Simulation, Institute for Quantum
Science and Technology and Quantum Alberta, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4
- College
of Chemistry and Chemical Engineering, Henan University of Technology, No. 100, Lian Hua Street, High-Tech Development Zone, Zhengzhou 450001, P. R. China
| | - Aurélien de la Lande
- Laboratoire
de Chimie Physique, CNRS - Université Paris Sud, Université Paris-Saclay, 15 avenue Jean Perrin, 91405 Orsay CEDEX, France
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7
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Mata RA, Suhm MA. Quantenchemische Methoden im Leistungsvergleich: Stimmt die Richtung noch? Angew Chem Int Ed Engl 2017. [DOI: 10.1002/ange.201611308] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Ricardo A. Mata
- Institut für Physikalische Chemie; Universität Göttingen; Tammannstraße 6 37077 Göttingen Deutschland
| | - Martin A. Suhm
- Institut für Physikalische Chemie; Universität Göttingen; Tammannstraße 6 37077 Göttingen Deutschland
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8
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Duchemin I, Li J, Blase X. Hybrid and Constrained Resolution-of-Identity Techniques for Coulomb Integrals. J Chem Theory Comput 2017; 13:1199-1208. [DOI: 10.1021/acs.jctc.6b01215] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ivan Duchemin
- INAC, SP2M/L_Sim,
CEA/UJF Cedex 09, Université Grenoble Alpes, 38054 Grenoble, France
| | - Jing Li
- Université Grenoble Alpes, CNRS, Inst NEEL, F-38042 Grenoble, France
| | - Xavier Blase
- Université Grenoble Alpes, CNRS, Inst NEEL, F-38042 Grenoble, France
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9
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Delgado-Venegas RI, Mejía-Rodríguez D, Flores-Moreno R, Calaminici P, Köster AM. Analytic second derivatives from auxiliary density perturbation theory. J Chem Phys 2016; 145:224103. [PMID: 27984884 DOI: 10.1063/1.4971292] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Rogelio Isaac Delgado-Venegas
- Departamento de Química, CINVESTAV, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, México D.F. 07000, Mexico
| | - Daniel Mejía-Rodríguez
- Departamento de Química, CINVESTAV, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, México D.F. 07000, Mexico
| | - Roberto Flores-Moreno
- Departamento de Química, Universidad de Guadalajara, Boulevard Marcelino García Barragán 1421, Guadalajara, Jalisco 44430, Mexico
| | - Patrizia Calaminici
- Departamento de Química, CINVESTAV, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, México D.F. 07000, Mexico
| | - Andreas M. Köster
- Departamento de Química, CINVESTAV, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, México D.F. 07000, Mexico
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10
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11
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Vuckovic S, Irons TJP, Savin A, Teale AM, Gori-Giorgi P. Exchange-Correlation Functionals via Local Interpolation along the Adiabatic Connection. J Chem Theory Comput 2016; 12:2598-610. [PMID: 27116427 PMCID: PMC4910137 DOI: 10.1021/acs.jctc.6b00177] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
The construction
of density-functional approximations is explored
by modeling the adiabatic connection locally, using
energy densities defined in terms of the electrostatic potential of
the exchange–correlation hole. These local models are more
amenable to the construction of size-consistent approximations than
their global counterparts. In this work we use accurate input local
ingredients to assess the accuracy of a range of local interpolation
models against accurate exchange–correlation energy densities.
The importance of the strictly correlated electrons (SCE) functional
describing the strong coupling limit is emphasized, enabling the corresponding
interpolated functionals to treat strong correlation effects. In addition
to exploring the performance of such models numerically for the helium
and beryllium isoelectronic series and the dissociation of the hydrogen
molecule, an approximate analytic model is presented for the initial
slope of the local adiabatic connection. Comparisons are made with
approaches based on global models, and prospects for future approximations
based on the local adiabatic connection are discussed.
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Affiliation(s)
- Stefan Vuckovic
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit , De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Tom J P Irons
- School of Chemistry, University of Nottingham , University Park, Nottingham NG7 2RD, United Kingdom
| | - Andreas Savin
- Laboratoire de Chimie Théorique, UPMC, Paris 06, UMR 7616, Sorbonne Universités , F-75005 Paris, France.,Laboratoire de Chimie Théorique, UMR 7616, CNRS F-75005, Paris, France
| | - Andrew M Teale
- School of Chemistry, University of Nottingham , University Park, Nottingham NG7 2RD, United Kingdom
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit , De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
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12
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13
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Grajciar L. Low-memory iterative density fitting. J Comput Chem 2015; 36:1521-35. [PMID: 26058451 DOI: 10.1002/jcc.23961] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2015] [Revised: 05/11/2015] [Accepted: 05/15/2015] [Indexed: 12/14/2022]
Abstract
A new low-memory modification of the density fitting approximation based on a combination of a continuous fast multipole method (CFMM) and a preconditioned conjugate gradient solver is presented. Iterative conjugate gradient solver uses preconditioners formed from blocks of the Coulomb metric matrix that decrease the number of iterations needed for convergence by up to one order of magnitude. The matrix-vector products needed within the iterative algorithm are calculated using CFMM, which evaluates them with the linear scaling memory requirements only. Compared with the standard density fitting implementation, up to 15-fold reduction of the memory requirements is achieved for the most efficient preconditioner at a cost of only 25% increase in computational time. The potential of the method is demonstrated by performing density functional theory calculations for zeolite fragment with 2592 atoms and 121,248 auxiliary basis functions on a single 12-core CPU workstation.
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Affiliation(s)
- Lukáš Grajciar
- Otto-Schott-Institut für Materialforschung, Friedrich-Schiller-Universität Jena, Löbdergraben 32, 07743, Jena, Germany
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14
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Mejía-Rodríguez D, Venegas RID, Calaminici P, Köster AM. Robust and Efficient Auxiliary Density Perturbation Theory Calculations. J Chem Theory Comput 2015; 11:1493-500. [PMID: 26574360 DOI: 10.1021/ct501065g] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A new iterative solver for the recently developed time-dependent auxiliary density perturbation theory is presented. It is based on the Eirola-Nevanlinna algorithm for large nonsymmetric linear equation systems. The new methodology is validated by static and dynamic polarizability calculations of small molecules. Comparison between the analytic and iterative solutions of the response equation system shows excellent agreement for the calculated static and dynamic polarizabilities. The new iterative solver reduces the formal scaling from [Symbol: see text](N(4)) to [Symbol: see text](N(3)). Furthermore, the observed computational scaling for linear alkane chains is N(1.6). This subquadratic behavior is possible in systems with a few hundred atoms because of the very small prefactors of the [Symbol: see text](N(3)) and [Symbol: see text](N(2)) steps remaining in the iterative solver. To demonstrate the potential of this new methodology, static polarizabilities of giant fullerenes up to C960, with more than 14,000 basis functions, are calculated.
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Affiliation(s)
- Daniel Mejía-Rodríguez
- Departamento de Quı́mica, Cinvestav , Avenida Instituto Politénico Nacional 2508, A.P. 14-740 México D.F. 07000, México
| | - Rogelio Isaac Delgado Venegas
- Departamento de Quı́mica, Cinvestav , Avenida Instituto Politénico Nacional 2508, A.P. 14-740 México D.F. 07000, México
| | - Patrizia Calaminici
- Departamento de Quı́mica, Cinvestav , Avenida Instituto Politénico Nacional 2508, A.P. 14-740 México D.F. 07000, México
| | - Andreas M Köster
- Departamento de Quı́mica, Cinvestav , Avenida Instituto Politénico Nacional 2508, A.P. 14-740 México D.F. 07000, México
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15
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Hybrid Functionals with Variationally Fitted Exact Exchange. ADVANCES IN QUANTUM CHEMISTRY 2015. [DOI: 10.1016/bs.aiq.2015.03.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register]
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16
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Mejía-Rodríguez D, Köster AM. Robust and efficient variational fitting of Fock exchange. J Chem Phys 2014; 141:124114. [DOI: 10.1063/1.4896199] [Citation(s) in RCA: 53] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Daniel Mejía-Rodríguez
- Departamento de Química, CINVESTAV. Avenida Instituto Politénico Nacional 2508, A.P. 14-740, México D.F. 07000, Mexico
| | - Andreas M. Köster
- Departamento de Química, CINVESTAV. Avenida Instituto Politénico Nacional 2508, A.P. 14-740, México D.F. 07000, Mexico
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17
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Alvarez-Ibarra A, Köster AM. Double asymptotic expansion of three-center electronic repulsion integrals. J Chem Phys 2013; 139:024102. [PMID: 23862924 DOI: 10.1063/1.4812183] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A double asymptotic expansion for the evaluation of three-center electron repulsion integrals (ERIs) in the long-range limit is presented. For the definition of this limit, a natural division of space based on the atomic coordinates and basis function exponents in utilized. The resulting analytical expression for the calculation of three-center ERIs in the long-range limit are implemented in the density functional theory program deMon2k. Validation and benchmark calculations of n-alkanes, hydrogen saturated graphene sheets and hydrogen saturated diamond blocks are discussed. It is shown that for a sufficient large number of long-range ERIs, the linear scaling regime is reached.
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Affiliation(s)
- A Alvarez-Ibarra
- Departamento de Química, CINVESTAV, Avenida Instituto Politécnico Nacional 2508 A.P. 14-740 México D.F. 07000, Mexico.
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18
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Merlot P, Kjaergaard T, Helgaker T, Lindh R, Aquilante F, Reine S, Pedersen TB. Attractive electron-electron interactions within robust local fitting approximations. J Comput Chem 2013; 34:1486-96. [DOI: 10.1002/jcc.23284] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2012] [Revised: 03/01/2013] [Accepted: 03/05/2013] [Indexed: 11/07/2022]
Affiliation(s)
- Patrick Merlot
- Centre for Theoretical and Computational Chemistry; Department of Chemistry; University of Oslo; P.O. Box 1033; Blindern; N-0315; Oslo; Norway
| | - Thomas Kjaergaard
- Centre for Theoretical and Computational Chemistry; Department of Chemistry; University of Oslo; P.O. Box 1033; Blindern; N-0315; Oslo; Norway
| | - Trygve Helgaker
- Centre for Theoretical and Computational Chemistry; Department of Chemistry; University of Oslo; P.O. Box 1033; Blindern; N-0315; Oslo; Norway
| | - Roland Lindh
- Department of Chemistry-Ångström; Theoretical Chemistry Programme; Uppsala University; P.O. Box 518; S-75120; Uppsala; Sweden
| | | | - Simen Reine
- Centre for Theoretical and Computational Chemistry; Department of Chemistry; University of Oslo; P.O. Box 1033; Blindern; N-0315; Oslo; Norway
| | - Thomas Bondo Pedersen
- Centre for Theoretical and Computational Chemistry; Department of Chemistry; University of Oslo; P.O. Box 1033; Blindern; N-0315; Oslo; Norway
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19
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Cuevas-Saavedra R, Ayers PW. Addressing the Coulomb potential singularity in exchange-correlation energy integrals with one-electron and two-electron basis sets. Chem Phys Lett 2012. [DOI: 10.1016/j.cplett.2012.04.037] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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20
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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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21
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Geudtner G, Calaminici P, Carmona-Espíndola J, del Campo JM, Domínguez-Soria VD, Moreno RF, Gamboa GU, Goursot A, Köster AM, Reveles JU, Mineva T, Vásquez-Pérez JM, Vela A, Zúñinga-Gutierrez B, Salahub DR. deMon2k. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2011. [DOI: 10.1002/wcms.98] [Citation(s) in RCA: 154] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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22
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Cholesky Decomposition Techniques in Electronic Structure Theory. CHALLENGES AND ADVANCES IN COMPUTATIONAL CHEMISTRY AND PHYSICS 2011. [DOI: 10.1007/978-90-481-2853-2_13] [Citation(s) in RCA: 61] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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23
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Reine S, Krapp A, Iozzi MF, Bakken V, Helgaker T, Pawłowski F, Sałek P. An efficient density-functional-theory force evaluation for large molecular systems. J Chem Phys 2010; 133:044102. [DOI: 10.1063/1.3459061] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
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