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Molecular Physics
An International Journal at the Interface Between Chemistry and Physics
Volume 49, 1983 - Issue 1
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Original Articles

Hyperspherical coordinates in four particle systems

Yngve Öhrn Departments of Chemistry and Physics, University of Florida, Gainsville, Florida, 32611, U.S.A.
&
Jan Linderberg Department of Chemistry, Aarhus University, DK-8000, Aarhus C, Denmark
Pages 53-64 | Received 20 Oct 1982, Accepted 21 Dec 1982, Published online: 23 Aug 2006

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VINCENZO AQUILANTI, ANDREA BEDDONI, SIMONETTA CAVALLI, ANDREA LOMBARDI & ROBERT LITTLEJOHN. (2000) Collective hyperspherical coordinates for polyatomic molecules and clusters. Molecular Physics 98:21, pages 1763-1770.
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L.S. COSTA & J.J.SOARES NETO. (1999) A wave function expansion for the study of tetra-atomic molecules in hyperspherical coordinate systems. Molecular Physics 97:6, pages 725-730.
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VINCENZO AQUILANTI, LAURENT BONNET & SIMONETTA CAVALLI. (1996) Kinematic rotations for four-centre reactions: mapping tetra-atomic potential energy surfaces on the kinetic sphere. Molecular Physics 89:1, pages 1-12.
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Articles from other publishers (41)

Kristoffer H. Hellton. (2022) Penalized angular regression for personalized predictions. Scandinavian Journal of Statistics 50:1, pages 184-212.
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Frank E. Harris & Victor V. Albert. 2013. Proceedings of MEST 2012: Exponential Type Orbitals for Molecular Electronic Structure Theory. Proceedings of MEST 2012: Exponential Type Orbitals for Molecular Electronic Structure Theory 3 18 .
M. N. Guimarães & F. V. Prudente. (2011) A variational adiabatic hyperspherical finite element R matrix methodology: general formalism and application to H + H2 reaction. The European Physical Journal D 64:2-3, pages 287-296.
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Aron Kuppermann. (2011) Reactive scattering with row-orthonormal hyperspherical coordinates. 4. Four-dimensional-space Wigner rotation function for pentaatomic systems. Physical Chemistry Chemical Physics 13:18, pages 8259.
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Aron Kuppermann. (2009) Reactive Scattering with Row-Orthonormal Hyperspherical Coordinates. 3. Hamiltonian and Transformation Properties for Pentaatomic Systems. The Journal of Physical Chemistry A 113:16, pages 4518-4533.
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Aron Kuppermann. (2006) Incorporating the Geometric Phase Effect in Triatomic and Tetraatomic Hyperspherical Harmonics. The Journal of Physical Chemistry A 110:2, pages 809-816.
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Frank E. Harris. 2005. Response Theory and Molecular Properties (A Tribute to Jan Linderberg and Poul Jørgensen). Response Theory and Molecular Properties (A Tribute to Jan Linderberg and Poul Jørgensen) 61 75 .
Vincenzo Aquilanti, Andrea Lombardi & Mikhail B. Sevryuk. (2004) Phase-space invariants for aggregates of particles: Hyperangular momenta and partitions of the classical kinetic energy. The Journal of Chemical Physics 121:12, pages 5579-5589.
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Frank E. Harris. 2004. Fundamental World of Quantum Chemistry. Fundamental World of Quantum Chemistry 115 127 .
Aron Kuppermann. (2010) Quantum reaction dynamics and hyperspherical harmonics. Israel Journal of Chemistry 43:3-4, pages 229-241.
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Xiao-Yan Gu, Bin Duan & Zhong-Qi Ma. (2001) Generalized radial equations in a quantum N-body system with non-orthogonal coordinates. Physics Letters A 289:1-2, pages 82-88.
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Xiao-Yan Gu, Bin Duan & Zhong-Qi Ma. (2001) Independent eigenstates of angular momentum in a quantum N -body system . Physical Review A 64:4.
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Xiao-Yan Gu, Bin Duan & Zhong-Qi Ma. (2001) Conservation of angular momentum and separation of global rotation in a quantum N-body system. Physics Letters A 281:2-3, pages 168-175.
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Ralph Jaquet. 2001. Methods in Reaction Dynamics. Methods in Reaction Dynamics 83 126 .
Gunnar Nyman & Hua-Gen Yu. (2000) Quantum theory of bimolecular chemical reactions. Reports on Progress in Physics 63:7, pages 1001-1059.
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L. S. Costa, Frederico V. Prudente & Paulo H. Acioli. (1999) Generalized rotating wave function for quantum Monte Carlo calculations of rovibrational levels of n -body systems . Physical Review A 61:1.
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M. W. Cadilhe & J. J. Soares Neto. (1999) Classical four-body problem in hyperspherical coordinates. International Journal of Quantum Chemistry 71:1, pages 15-24.
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Robert G. Littlejohn, Kevin A. Mitchell, Vincenzo Aquilanti & Simonetta Cavalli. (1998) Body frames and frame singularities for three-atom systems. Physical Review A 58:5, pages 3705-3717.
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Sergei K. Pogrebnya, Julian Echave & David C. Clary. (1997) Quantum theory of four-atom reactions using arrangement channel hyperspherical coordinates: Formulation and application to OH+H2↔H2O+H. The Journal of Chemical Physics 107:21, pages 8975-8984.
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Aron Kuppermann. (1997) Reactive Scattering with Row-Orthonormal Hyperspherical Coordinates. 2. Transformation Properties and Hamiltonian for Tetraatomic Systems. The Journal of Physical Chemistry A 101:36, pages 6368-6383.
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Aron Kuppermann. (1996) Reactive Scattering with Row-Orthonormal Hyperspherical Coordinates. 1. Transformation Properties and Hamiltonian for Triatomic Systems. The Journal of Physical Chemistry 100:7, pages 2621-2636.
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Jan Linderberg. 1996. New Methods in Quantum Theory. New Methods in Quantum Theory 203 223 .
L. Lathouwers. 1995. Frontiers of Chemical Dynamics. Frontiers of Chemical Dynamics 349 356 .
J. Broeckhove & L. Lathouwers. 1993. Numerical Grid Methods and Their Application to Schrödinger’s Equation. Numerical Grid Methods and Their Application to Schrödinger’s Equation 49 56 .
Jan Linderberg. (1991) Propagation in hyperspherical coordinates. Theoretica Chimica Acta 79:3-4, pages 271-281.
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Qiyan Sun & Joel M. Bowman. (1990) Reduced dimensionality quantum reactive scattering: H2+CN→H+HCN. The Journal of Chemical Physics 92:9, pages 5201-5210.
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A. N. Brooks & D. C. Clary. (1990) Application of hyperspherical coordinates to four-atom reactive scattering: H2+CN→H+HCN. The Journal of Chemical Physics 92:7, pages 4178-4190.
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Qiyan Sun & Joel M. Bowman. (1990) Reduced dimensionality diatom–diatom reactive scattering: Application to a model H2+A2→H+HA2 reaction. The Journal of Chemical Physics 92:2, pages 1021-1029.
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John Avery & Frank Antonsen. (2009) A new approach to the quantum mechanics of atoms and small molecules. International Journal of Quantum Chemistry 36:S23, pages 159-168.
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Qiyan Sun & Joel M. Bowman. (2009) Diatom-diatom reactive scattering in hypercylindrical coordinates. International Journal of Quantum Chemistry 36:S23, pages 115-126.
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John Avery & Peter Sommer-Larsen. (1988) Iteration of the many-particle schr�dinger equation in momentum space. International Journal of Quantum Chemistry 34:S22, pages 437-444.
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James O. Jensen & Ajit Banerjee. (1987) Cartesian internal coordinates: translational and rotational invariance. Chemical Physics 116:3, pages 369-379.
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John Avery. (1987) Correlation in iterated solutions of the momentum-space schrödinger equation. Chemical Physics Letters 138:6, pages 520-524.
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J.P. Leroy & R. Wallace. (1987) Procedures leading to a variety of orthonormal Jacobi-type coordinates of relevance to large-amplitude vibration and scattering problems. Chemical Physics 111:1, pages 11-16.
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Vincenzo Aquilanti & Simonetta Cavalli. (1986) Coordinates for molecular dynamics: Orthogonal local systems. The Journal of Chemical Physics 85:3, pages 1355-1361.
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Osvaldo Goscinski & Vladimiro Mujica. (2004) Adiabatic coordinate separation and large N ‐dimensional limit in two‐electron ions . International Journal of Quantum Chemistry 29:4, pages 897-908.
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John Avery. (1986) Many-dimensional hydrogenlike wave functions and the quantum mechanical many-body problem. International Journal of Quantum Chemistry 30:S20, pages 57-63.
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V. Aquilanti & A. Laganà. 1986. Nonequilibrium Vibrational Kinetics. Nonequilibrium Vibrational Kinetics 159 190 .
John Avery, Peter Sommer Larsen & Shen Hengyi. (2004) The quantum mechanical many‐body problem in hyperspherical coordinates. Analysis of systems with coulomb interactions in terms of many‐dimensional hydrogen‐like wave functions. International Journal of Quantum Chemistry 29:1, pages 129-147.
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Jan Linderberg. (2009) Basis for coupled channel approach to reactive scattering. International Journal of Quantum Chemistry 28:S19, pages 467-476.
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Paul G. Mezey. (1984) Hyperspherical coordinate representation of potential surfaces of large molecules. International Journal of Quantum Chemistry 26:S11, pages 267-272.
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