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Silkowski M, Lesiuk M, Moszynski R. Calculation of the molecular integrals with the range-separated correlation factor. J Chem Phys 2015; 142:124102. [DOI: 10.1063/1.4915272] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Affiliation(s)
- Michał Silkowski
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Michał Lesiuk
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Robert Moszynski
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
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Hättig C, Klopper W, Köhn A, Tew DP. Explicitly Correlated Electrons in Molecules. Chem Rev 2011; 112:4-74. [DOI: 10.1021/cr200168z] [Citation(s) in RCA: 401] [Impact Index Per Article: 30.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Christof Hättig
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany
| | - Wim Klopper
- Abteilung für Theoretische Chemie, Institut für Physikalische Chemie, Karlsruher Institut für Technologie, KIT-Campus Süd, Postfach 6980, D-76049 Karlsruhe, Germany
| | - Andreas Köhn
- Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany
| | - David P. Tew
- School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
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Noga J, Kedzuch S, Simunek J. Second order explicitly correlated R12 theory revisited: A second quantization framework for treatment of the operators’ partitionings. J Chem Phys 2007; 127:034106. [PMID: 17655430 DOI: 10.1063/1.2751163] [Citation(s) in RCA: 67] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Second order R12 theory is presented and derived alternatively using the second quantized hole-particle formalism. We have shown that in order to ensure the strong orthogonality between the R12 and the conventional part of the wave function, the explicit use of projection operators can be easily avoided by an appropriate partitioning of the involved operators to parts which are fully describable within the computational orbital basis and complementary parts that involve imaginary orbitals from the complete orbital basis. Various Hamiltonian splittings are discussed and computationally investigated for a set of nine molecules and their atomization energies. If no generalized Brillouin condition is assumed, with all relevant partitionings the one-particle contribution arising in the explicitly correlated part of the first order wave function has to be considered and has a significant role when smaller atomic orbital basis sets are used. The most appropriate Hamiltonian splitting results if one follows the conventional perturbation theory for a general non-Hartree-Fock reference. Then, no couplings between the R12 part and the conventional part arise within the first order wave function. The computationally most favorable splitting when the whole complementary part of the Hamiltonian is treated as a perturbation fails badly. These conclusions also apply to MP2-F12 approaches with different correlation factors.
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Affiliation(s)
- Jozef Noga
- Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University, Mlynská dolina CHI, SK-84215 Bratislava, Slovakia.
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Patkowski K, Cencek W, Jeziorska M, Jeziorski B, Szalewicz K. Accurate Pair Interaction Energies for Helium from Supermolecular Gaussian Geminal Calculations. J Phys Chem A 2007; 111:7611-23. [PMID: 17550239 DOI: 10.1021/jp071437x] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Nonrelativistic clamped-nuclei pair interaction energy for ground-state helium atoms has been computed for 12 interatomic separations ranging from 3.0 to 9.0 bohr. The calculations applied the supermolecular approach. The major part of the interaction energy was obtained using the Gaussian geminal implementation of the coupled-cluster theory with double excitations (CCD). Relatively small contributions from single, triple, and quadruple excitations were subsequently included employing the conventional orbital coupled-cluster method with single, double, and noniterative triple excitations [CCSD(T)] and the full configuration interaction (FCI) method. For three distances, the single-excitation contribution was taken from literature Gaussian-geminal calculations at the CCSD level. The orbital CCSD(T) and FCI calculations used very large basis sets, up to doubly augmented septuple- and sextuple-zeta size, respectively, and were followed by extrapolations to the complete basis set limits. The accuracy of the total interaction energies has been estimated to be about 3 mK or 0.03% at the minimum of the potential well. For the attractive part of the well, the relative errors remain consistently smaller than 0.03%. In the repulsive part, the accuracy is even better, except, of course, for the region where the potential goes through zero. For interatomic separations smaller than 4.0 bohr, the relative errors do not exceed 0.01%. Such uncertainties are significantly smaller than the expected values of the relativistic and diagonal Born-Oppenheimer contributions to the potential.
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Affiliation(s)
- Konrad Patkowski
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
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Polly R, Werner HJ, Dahle P, Taylor PR. Application of Gaussian-type geminals in local second-order Møller-Plesset perturbation theory. J Chem Phys 2006; 124:234107. [PMID: 16821907 DOI: 10.1063/1.2202102] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work Gaussian-type Geminals (GTGs) are applied in local second-order Moller-Plesset perturbation theory to improve the basis set convergence. Our implementation is based on the weak orthogonality functional of Szalewicz et al., [Chem. Phys. Lett. 91, 169 (1982); J. Chem. Phys. 78, 1420 (1983)] and a newly developed program for calculating the necessary many-electron integrals. The local approximations together with GTGs in the treatment of the correlation energy are introduced and tested. First results for correlation energies of H(2)O, CH(4), CO, C(2)H(2), C(2)H(4), H(2)CO, and N(2)H(4) as well as some reaction and activation energies are presented. More than 97% of the valence-shell correlation energy is recovered using aug-cc-pVDZ basis sets and six GTGs per electron pair. The results are compared with conventional calculations using correlation-consistent basis sets as well as with MP2-R12 results.
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Affiliation(s)
- Robert Polly
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
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Cencek W, Jeziorska M, Bukowski R, Jaszuński M, Jeziorski B, Szalewicz K. Helium Dimer Interaction Energies from Gaussian Geminal and Orbital Calculations. J Phys Chem A 2004. [DOI: 10.1021/jp037544i] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Wojciech Cencek
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, Department of Chemistry, University of Warsaw, Pasteura 1, 02093 Warsaw, Poland, Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44, 01224 Warsaw, Poland, and Department of Chemistry, Princeton University, Princeton, New Jersey 08544
| | - Małgorzata Jeziorska
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, Department of Chemistry, University of Warsaw, Pasteura 1, 02093 Warsaw, Poland, Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44, 01224 Warsaw, Poland, and Department of Chemistry, Princeton University, Princeton, New Jersey 08544
| | - Robert Bukowski
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, Department of Chemistry, University of Warsaw, Pasteura 1, 02093 Warsaw, Poland, Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44, 01224 Warsaw, Poland, and Department of Chemistry, Princeton University, Princeton, New Jersey 08544
| | - Michał Jaszuński
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, Department of Chemistry, University of Warsaw, Pasteura 1, 02093 Warsaw, Poland, Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44, 01224 Warsaw, Poland, and Department of Chemistry, Princeton University, Princeton, New Jersey 08544
| | - Bogumił Jeziorski
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, Department of Chemistry, University of Warsaw, Pasteura 1, 02093 Warsaw, Poland, Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44, 01224 Warsaw, Poland, and Department of Chemistry, Princeton University, Princeton, New Jersey 08544
| | - Krzysztof Szalewicz
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, Department of Chemistry, University of Warsaw, Pasteura 1, 02093 Warsaw, Poland, Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44, 01224 Warsaw, Poland, and Department of Chemistry, Princeton University, Princeton, New Jersey 08544
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