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Barca GM, Loos PF. Recurrence Relations for Four-Electron Integrals Over Gaussian Basis Functions. ADVANCES IN QUANTUM CHEMISTRY 2018. [DOI: 10.1016/bs.aiq.2017.03.004] [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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Turbiner AV, Lopez Vieyra JC. Ground state of the H3(+) molecular ion: physics behind. J Phys Chem A 2013; 117:10119-28. [PMID: 23581885 DOI: 10.1021/jp401439c] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Five physics mechanisms of interaction leading to the binding of the H3(+) molecular ion are identified. They are realized in a form of variational trial functions, and their respective total energies are calculated. Each of them provides subsequently the most accurate approximation for the Born–Oppenheimer (BO) ground state energy among (two–three–seven)-parametric trial functions being, correspondingly, H2-molecule plus proton (two variational parameters), H2(+)-ion plus H-atom (three variational parameters), and generalized Guillemin–Zener (seven variational parameters). These trial functions are chosen following a criterion of physical adequacy. They include the electronic correlation in the exponential form, exp(γr12), where γ is a variational parameter. Superpositions of two different mechanisms of binding are investigated, and a particular one, which is a generalized Guillemin–Zener plus H2-molecule plus proton (ten variational parameters), provides the total energy at the equilibrium of E = −1.3432 au. The superposition of three mechanisms, generalized Guillemin–Zener plus (H2-molecule plus proton) plus (H2(+)-ion plus H) (14 parameters) leads to the total energy, which deviates from the best known BO energy to 0.0004 au, it reproduces two–three significant digits in exact, non-BO total energy. In general, our variational energy agrees in two–three–four significant digits with the most accurate results available at present as well as major expectation values.
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Affiliation(s)
- A V Turbiner
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México , Apartado Postal 70-543, 04510 México, D.F., Mexico
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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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Szalay PG, Müller T, Gidofalvi G, Lischka H, Shepard R. Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications. Chem Rev 2011; 112:108-81. [DOI: 10.1021/cr200137a] [Citation(s) in RCA: 470] [Impact Index Per Article: 36.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Péter G. Szalay
- Laboratory for Theoretical Chemistry, Institute of Chemistry, Eötvös Loránd University, P. O. Box 32, H-1518 Budapest, Hungary
| | - Thomas Müller
- Jülich Supercomputer Centre, Institute of Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Gergely Gidofalvi
- Department of Chemistry and Biochemistry, Gonzaga University, 502 East Boone Avenue, Spokane, Washington 99258-0102, United States
| | - Hans Lischka
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, United States
- Institute for Theoretical Chemistry, University of Vienna, Waehringerstrasse 17, A-1090 Vienna, Austria
| | - Ron Shepard
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
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Kong L, Bischoff FA, Valeev EF. Explicitly Correlated R12/F12 Methods for Electronic Structure. Chem Rev 2011; 112:75-107. [DOI: 10.1021/cr200204r] [Citation(s) in RCA: 353] [Impact Index Per Article: 27.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Liguo Kong
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Florian A. Bischoff
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
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MULLER BHENDRIK, KUTZELNIGG WERNER. A CCSD(T)-R12 study of the ten-electron systems Ne, F-, HF, H2O, NH3, NH4+ and CH4. Mol Phys 2010. [DOI: 10.1080/002689797170284] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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Quack M, Kutzelnigg W. Molecular Spectroscopy and Molecular Dynamics: Theory and Experiment. ACTA ACUST UNITED AC 2010. [DOI: 10.1002/bbpc.19950990302] [Citation(s) in RCA: 78] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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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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Jaquet R, Röhse R. Rovibrational energy levels and transitions for H3 + computed from a new highly accurate potential energy surface. Mol Phys 2006. [DOI: 10.1080/00268979500100211] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Ralph Jaquet
- a Theoretische Chemie , Universität Siegen , D-57068 , Siegen , Germany
| | - Robert Röhse
- b Lehrstuhl für Theoretische Chemie , Ruhr-Universität Bochum , D-44780 , Bochum , Germany
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Nakatsuji H. Deepening and Extending the Quantum Principles in Chemistry. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 2005. [DOI: 10.1246/bcsj.78.1705] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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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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Lee JS, Park SY. Basis set convergence of correlated calculations on He, H2, and He2. J Chem Phys 2000. [DOI: 10.1063/1.481718] [Citation(s) in RCA: 74] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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POLYANSKY OLEGL, PROSMITI RITA, KLOPPER WIM, TENNYSON JONATHAN. An accurate, global,ab initiopotential energy surface for the H+3molecule. Mol Phys 2000. [DOI: 10.1080/00268970009483290] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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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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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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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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Ottschofski E, Kutzelnigg W. Direct perturbation theory of relativistic effects for explicitly correlated wave functions: The He isoelectronic series. J Chem Phys 1997. [DOI: 10.1063/1.473663] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kleinekathöfer U, Patil SH, Tang KT, Toennies JP. Boundary-condition-determined wave function for the ground state of helium and isoelectronic ions. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1996; 54:2840-2849. [PMID: 9913798 DOI: 10.1103/physreva.54.2840] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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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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Ichihara A, Yokoyama K. Ab initiopotential energy surfaces for the two lowest1A′ states of H+3. J Chem Phys 1995. [DOI: 10.1063/1.469686] [Citation(s) in RCA: 51] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
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Gianturco FA, Kumar S. Dynamics of vibrationally inelastic collisions in H+−H2: comparing quantum calculations with experiments. Chem Phys 1995. [DOI: 10.1016/0301-0104(95)00118-8] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Bressanini D, Mella M, Morosi G. Many-electron correlated exponential wavefunctions. A quantum Monte Carlo application to H2 and He2+. Chem Phys Lett 1995. [DOI: 10.1016/0009-2614(95)00561-h] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Noga J, Tunega D, Klopper W, Kutzelnigg W. The performance of the explicitly correlated coupled cluster method. I. The four‐electron systems Be, Li−, and LiH. J Chem Phys 1995. [DOI: 10.1063/1.469643] [Citation(s) in RCA: 65] [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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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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Ramón Álvarez‐Collado J, Aguado A, Paniagua M. The vibrational structure of H+4 and D+4. J Chem Phys 1995. [DOI: 10.1063/1.469303] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Bukowski R, Jeziorski B, Rybak S, Szalewicz K. Second‐order correlation energy for H2O using explicitly correlated Gaussian geminals. J Chem Phys 1995. [DOI: 10.1063/1.469155] [Citation(s) in RCA: 43] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Rychlewski J, Cencek W, Komasa J. The equivalence of explicitly correlated Slater and Gaussian functions in variational quantum chemistry computations. Chem Phys Lett 1994. [DOI: 10.1016/0009-2614(94)01108-7] [Citation(s) in RCA: 55] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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Ackermann J, Erdmann B, Roitzsch R. A self‐adaptive multilevel finite element method for the stationary Schrödinger equation in three space dimensions. J Chem Phys 1994. [DOI: 10.1063/1.468257] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Röhse R, Kutzelnigg W, Jaquet R, Klopper W. Potential energy surface of the H+3 ground state in the neighborhood of the minimum with microhartree accuracy and vibrational frequencies derived from it. J Chem Phys 1994. [DOI: 10.1063/1.467663] [Citation(s) in RCA: 112] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
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Tennyson J, Polyansky OL. Non-Born-Oppenheimer correction to the H3+ potential from experimental data. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1994; 50:314-316. [PMID: 9910895 DOI: 10.1103/physreva.50.314] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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