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Rubin TM, Sarrazin M, Zobov NF, Tennyson J, Polyansky OL. Sub-percent accuracy for the intensity of a near-infrared water line at 10,670 cm −1: experiment and analysis. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2063769] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Tom M. Rubin
- PTB (Physikalisch-Technische Bundesanstalt), Berlin, Germany
| | - Marian Sarrazin
- PTB (Physikalisch-Technische Bundesanstalt), Berlin, Germany
| | - Nikolai F. Zobov
- Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia
| | - Jonathan Tennyson
- Department of Physics and Astronomy, University College London, London, UK
| | - Oleg L. Polyansky
- Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia
- Department of Physics and Astronomy, University College London, London, UK
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Siłkowski M, Pachucki K. Born–Oppenheimer potentials for Π, Δ, and Φ states of the hydrogen molecule. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2062471] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Cioslowski J, Strasburger K. Angular-Momentum Extrapolations to the Complete Basis Set Limit: Why and When They Work. J Chem Theory Comput 2021; 17:3403-3413. [PMID: 34003646 DOI: 10.1021/acs.jctc.1c00202] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The leading L-3 dependence of the errors in the energies computed with nuclei-centered basis sets comprising functions with angular momenta not exceeding L is rigorously proven for the 1Σ states of linear molecules and molecular ions with arbitrary even numbers of electrons. This major expansion of the domain of applicability over that offered by the routinely cited Hill asymptotic expression, which is valid only for the helium isoelectronic series, is accomplished with a formalism in which the off-diagonal cusp conditions for the one- and two-electron reduced density matrices play the central role. Despite being provided by these results with theoretical foundations more solid than ever before, the angular-momentum extrapolations to the complete basis set limit appear to work more by happenstance than mathematical rigor due to the poorly predictable variability in the prefactor multiplying the L-3 term and the far from negligible contributions from the terms involving higher powers of L-1.
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Affiliation(s)
- Jerzy Cioslowski
- Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
| | - Krzysztof Strasburger
- Department of Physical and Quantum Chemistry, Faculty of Chemistry, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
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Nakashima H, Nakatsuji H. Solving the Schrödinger equation of hydrogen molecule with the free complement-local Schrödinger equation method: Potential energy curves of the ground and singly excited singlet and triplet states, Σ, Π, Δ, and Φ. J Chem Phys 2019; 149:244116. [PMID: 30599736 DOI: 10.1063/1.5060659] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The free-complement (FC) theory for solving the Schrödinger equation (SE) was applied to calculate the potential energy curves of the ground and excited states of the hydrogen molecule (H2) with the 1Σg +, 1Σu +, 3Σg +, 3Σu +, 1Πg, 1Πu, 3Πg, 3Πu, 1Δg, 1Δu, 3Δg, 3Δu, 1Φg, 1Φu, 3Φg, and 3Φu symmetries (in total, 54 states). The initial functions of the FC theory were formulated based on the atomic states of the hydrogen atom and its positive and negative ions at the dissociation limits. The local Schrödinger equation (LSE) method, which is a simple sampling-type integral-free methodology, was employed instead of the ordinary variational method and highly accurate results were obtained stably and smoothly along the potential energy curves. Thus, with the FC-LSE method, we succeeded to perform the comprehensive studies of the H2 molecule from the ground to excited states belonging up to higher angular momentum symmetries and from equilibriums to dissociation limits with almost satisfying spectroscopic accuracy, i.e., 10-6 hartree order around 1 cm-1, as absolute solutions of the SE by moderately small calculations.
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Affiliation(s)
- Hiroyuki Nakashima
- Quantum Chemistry Research Institute, Kyoto Technoscience Center 16, 14 Yoshida Kawaramachi, Sakyo-ku, Kyoto 606-8305, Japan
| | - Hiroshi Nakatsuji
- Quantum Chemistry Research Institute, Kyoto Technoscience Center 16, 14 Yoshida Kawaramachi, Sakyo-ku, Kyoto 606-8305, Japan
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Harris FE. Atomic Electronic Structure Computations With Hylleraas-CI Wave Functions. ADVANCES IN QUANTUM CHEMISTRY 2018. [DOI: 10.1016/bs.aiq.2017.04.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Harris FE. Integrals arising in atomic Hylleraas methods. Mol Phys 2017. [DOI: 10.1080/00268976.2016.1277593] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Frank E. Harris
- Department of Physics, University of Utah, Salt Lake City, UT, USA
- Quantum Theory Project, University of Florida, Gainesville, FL, USA
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Pachucki K, Komasa J. Schrödinger equation solved for the hydrogen molecule with unprecedented accuracy. J Chem Phys 2016; 144:164306. [DOI: 10.1063/1.4948309] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Krzysztof Pachucki
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Jacek Komasa
- Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland
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Tung WC, Adamowicz L. Accurate potential energy curve of the LiH+ molecule calculated with explicitly correlated Gaussian functions. J Chem Phys 2014; 140:124315. [DOI: 10.1063/1.4869517] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Polyansky OL, Alijah A, Zobov NF, Mizus II, Ovsyannikov RI, Tennyson J, Lodi L, Szidarovszky T, Császár AG. Spectroscopy of H3+ based on a new high-accuracy global potential energy surface. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2012; 370:5014-5027. [PMID: 23028150 DOI: 10.1098/rsta.2012.0014] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The molecular ion H(3)(+) is the simplest polyatomic and poly-electronic molecular system, and its spectrum constitutes an important benchmark for which precise answers can be obtained ab initio from the equations of quantum mechanics. Significant progress in the computation of the ro-vibrational spectrum of H(3)(+) is discussed. A new, global potential energy surface (PES) based on ab initio points computed with an average accuracy of 0.01 cm(-1) relative to the non-relativistic limit has recently been constructed. An analytical representation of these points is provided, exhibiting a standard deviation of 0.097 cm(-1). Problems with earlier fits are discussed. The new PES is used for the computation of transition frequencies. Recently measured lines at visible wavelengths combined with previously determined infrared ro-vibrational data show that an accuracy of the order of 0.1 cm(-1) is achieved by these computations. In order to achieve this degree of accuracy, relativistic, adiabatic and non-adiabatic effects must be properly accounted for. The accuracy of these calculations facilitates the reassignment of some measured lines, further reducing the standard deviation between experiment and theory.
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Affiliation(s)
- Oleg L Polyansky
- Institute of Applied Physics, Russian Academy of Sciences, Ulyanov Street 46, Nizhny Novgorod 603950, Russia.
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Bubin S, Pavanello M, Tung WC, Sharkey KL, Adamowicz L. Born–Oppenheimer and Non-Born–Oppenheimer, Atomic and Molecular Calculations with Explicitly Correlated Gaussians. Chem Rev 2012; 113:36-79. [DOI: 10.1021/cr200419d] [Citation(s) in RCA: 115] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Sergiy Bubin
- Department
of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235,
United States
| | - Michele Pavanello
- Department
of Chemistry, Rutgers University Newark, Newark, New Jersey 07102,
United States
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Jaquet R, Khoma MV. A systematic investigation of the ground state potential energy surface of H3+. J Chem Phys 2012; 136:154307. [PMID: 22519326 DOI: 10.1063/1.4704123] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Based on different ab initio electronic structure calculations (CI-R12 and Gaussian Geminals) of the Born-Oppenheimer electronic energy E(BO) of H(3)(+) from high to highest quality, we build up a potential energy surface which represents a highly reliable form of the topology of the whole potential region, locally and globally. We use the CI-R12 method in order to get within reasonable CPU-time a relatively dense grid of energy points. We demonstrate that CI-R12 is good enough to give an accurate surface, i.e., Gaussian Geminals are not absolutely necessary. For different types of potential energy surface fits, we performed variational calculations of all bound vibrational states, including resonances above the dissociation limit, for total angular momentum J = 0. We clarify the differences between different fits of the energy to various functional forms of the potential surface. Small rms-values (<1 cm(-1)) of the fit do not provide precise information about the interpolatory behaviour of the fit functions.
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Affiliation(s)
- Ralph Jaquet
- Theoretische Chemie, Universität Siegen, D-57068 Siegen, Germany.
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12
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Development of the explicitly correlated Gaussian–nuclear orbital plus molecular orbital theory: Incorporation of electron–electron correlation. Chem Phys Lett 2012. [DOI: 10.1016/j.cplett.2012.02.070] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Komornicki A, King HF. A general formulation for the efficient evaluation of n-electron integrals over products of Gaussian charge distributions with Gaussian geminal functions. J Chem Phys 2011; 134:244115. [DOI: 10.1063/1.3600745] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
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Tung WC, Pavanello M, Adamowicz L. Very accurate potential energy curve of the LiH molecule. J Chem Phys 2011; 134:064117. [DOI: 10.1063/1.3554211] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
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Szalewicz K, Jeziorski B. Explicitly-correlated Gaussian geminals in electronic structure calculations. Mol Phys 2010. [DOI: 10.1080/00268976.2010.522206] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Chakraborty A, Pak MV, Hammes-Schiffer S. Inclusion of explicit electron-proton correlation in the nuclear-electronic orbital approach using Gaussian-type geminal functions. J Chem Phys 2008; 129:014101. [DOI: 10.1063/1.2943144] [Citation(s) in RCA: 67] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kutzelnigg W, Jaquet R. Explicitly correlated potential energy surface of H3+, including relativistic and adiabatic corrections. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2006; 364:2855-74; discussion 2874-6. [PMID: 17015373 DOI: 10.1098/rsta.2006.1871] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
After a short historical account of the theory of the H3+ ion, two ab initio methods are reviewed that allow the computation of the ground-state potential energy surface (PES) of H3+ in the Born-Oppenheimer (BO) approximation, with microhartree or even sub-microhartree accuracy, namely the R12 method and the method of explicitly correlated Gaussians. The BO-PES is improved by the inclusion of relativistic effects and adiabatic corrections. It is discussed how non-adiabatic effects on rotation and vibration can be simulated by corrections to the moving nuclear masses. The importance of the appropriate analytic fit to the computed points of the PES for the subsequent computation of the rovibronic spectrum is addressed. Some recent extensions of the computed PES in the energy region above the barrier to linearity are reviewed. This involves a large set of input geometries and the correct treatment of the dissociation asymptotics, including the coupling with the first excited singlet state. Some comments on this state as well as on the lowest triplet state of H3+ are made. The paper ends with a few remarks on the ion H5+.
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Affiliation(s)
- Werner Kutzelnigg
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany.
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Sims JS, Hagstrom SA. High precision variational calculations for the Born-Oppenheimer energies of the ground state of the hydrogen molecule. J Chem Phys 2006; 124:94101. [PMID: 16526839 DOI: 10.1063/1.2173250] [Citation(s) in RCA: 66] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Born-Oppenheimer approximation Hylleraas variational calculations with up to 7034 expansion terms are reported for the 1sigma(g)+ ground state of neutral hydrogen at various internuclear distances. The nonrelativistic energy is calculated to be -1.174 475 714 220(1) hartree at R = 1.4 bohr, which is four orders of magnitude better than the best previous Hylleraas calculation, that of Wolniewicz [J. Chem. Phys. 103, 1792 (1995)]. This result agrees well with the best previous variational energy, -1.174 475 714 216 hartree, of Cencek (personal communication), obtained using explicitly correlated Gaussians (ECGs) [Cencek and Rychlewski, J. Chem. Phys. 98, 1252 (1993); Cencek et al., ibid. 95, 2572 (1995); Rychlewski, Adv. Quantum Chem. 31, 173 (1998)]. The uncertainty in our result is also discussed. The nonrelativistic energy is calculated to be -1.174 475 931 399(1) hartree at the equilibrium R = 1.4011 bohr distance. This result also agrees well with the best previous variational energy, -1.174 475 931 389 hartree, of Cencek and Rychlewski [Rychlewski, Handbook of Molecular Physics and Quantum Chemistry, edited by S. Wilson (Wiley, New York, 2003), Vol. 2, pp. 199-218; Rychlewski, Explicitly Correlated Wave Functions in Chemistry and Physics Theory and Applications, edited by J. Rychlewski (Kluwer Academic, Dordrecht, 2003), pp. 91-147.], obtained using ECGs.
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Affiliation(s)
- James S Sims
- National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8911, USA.
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Komasa J. In Search for the Negative Polarizability States – the State of Hydrogen Molecule. ADVANCES IN QUANTUM CHEMISTRY 2005. [DOI: 10.1016/s0065-3276(05)48011-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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Jaquet R. First-principles rovibrational analysis of the H3+-molecule. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2002; 58:691-725. [PMID: 11991491 DOI: 10.1016/s1386-1425(01)00665-5] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
The fitting of highly accurate potential energy points and of the diagonal adiabatic coupling for H3+ using different functional forms is presented. A recently derived analytical potential based on 69 points has been extended to give a highly reliable form of the topology of the surface far beyond the barrier to linearity. Rovibrational frequencies have been derived and are compared with experiment. Detailed information about the experimentally observed rovibrational transitions near 1.25 microm will be given. The computed transition frequencies reproduce experimental transitions within a tenth up to a few hundredths of a wavenumber, if a simulation of non-adiabatic effects is taken into account.
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Affiliation(s)
- Ralph Jaquet
- Theoretische Chemie, Universität Siegen, Germany.
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Patkowski K, Jeziorski B, Szalewicz K. Symmetry-adapted perturbation theory with regularized Coulomb potential. ACTA ACUST UNITED AC 2001. [DOI: 10.1016/s0166-1280(01)00478-x] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Kutzelnigg W, von Herigonte P. Electron correlation at the dawn of the 21st century. ADVANCES IN QUANTUM CHEMISTRY 2000. [DOI: 10.1016/s0065-3276(08)60484-0] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
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Strasburger K. Binding energy, structure, and annihilation properties of the positron-LiH molecule complex, studied with explicitly correlated Gaussian functions. J Chem Phys 1999. [DOI: 10.1063/1.480408] [Citation(s) in RCA: 52] [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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Bukowski R, Jeziorski B, Szalewicz K. Gaussian geminals in explicitly correlated coupled cluster theory including single and double excitations. J Chem Phys 1999. [DOI: 10.1063/1.479109] [Citation(s) in RCA: 62] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Strasburger K, Chojnacki H. Quantum chemical study of simple positronic systems using explicitly correlated Gaussian functions – PsH and PsLi+. J Chem Phys 1998. [DOI: 10.1063/1.475717] [Citation(s) in RCA: 86] [Impact Index Per Article: 3.3] [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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Cencek W, Rychlewski J, Jaquet R, Kutzelnigg W. Sub-microhartree accuracy potential energy surface for H3+ including adiabatic and relativistic effects. I. Calculation of the potential points. J Chem Phys 1998. [DOI: 10.1063/1.475702] [Citation(s) in RCA: 165] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Sanders FC. Recent Developments in High-precision Computational Methods for Simple Atomic and Molecular Systems. ADVANCES IN QUANTUM CHEMISTRY 1998. [DOI: 10.1016/s0065-3276(08)60445-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Cencek W, Kutzelnigg W. Accurate adiabatic correction for the hydrogen molecule using the Born-Handy formula. Chem Phys Lett 1997. [DOI: 10.1016/s0009-2614(97)00017-1] [Citation(s) in RCA: 51] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Cencek W, Kutzelnigg W. Accurate relativistic energies of one‐ and two‐electron systems using Gaussian wave functions. J Chem Phys 1996. [DOI: 10.1063/1.472429] [Citation(s) in RCA: 73] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Komasa J, Rychlewski J. Explicitly correlated Gaussian functions in variational calculatiions. Microhartree accuracy of the helium dimer energy. Chem Phys Lett 1996. [DOI: 10.1016/0009-2614(95)01392-x] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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37
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Benchmark calculations for two-electron systems using explicitly correlated Gaussian functions. Chem Phys Lett 1995. [DOI: 10.1016/0009-2614(95)01146-8] [Citation(s) in RCA: 90] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Komasa J, Cencek W, Rychlewski J. Explicitly correlated Gaussian functions in variational calculations: The ground state of the beryllium atom. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 52:4500-4507. [PMID: 9912788 DOI: 10.1103/physreva.52.4500] [Citation(s) in RCA: 56] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Wolniewicz L. Nonadiabatic energies of the ground state of the hydrogen molecule. J Chem Phys 1995. [DOI: 10.1063/1.469753] [Citation(s) in RCA: 217] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Klopper W. Limiting values for Mo/ller–Plesset second‐order correlation energies of polyatomic systems: A benchmark study on Ne, HF, H2O, N2, and He...He. J Chem Phys 1995. [DOI: 10.1063/1.469351] [Citation(s) in RCA: 140] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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