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  • 1
    ISSN: 1432-2234
    Keywords: Three-body problem ; Hyperspherical coordinate ; Schrödinger equation ; H 2 + ; Generalized-Laguerre function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary By introducing a Gaussian factor to describe the fact that the nuclei in H 2 + vibrate around a fixed point, we have modified the method of hyperspherical harmonics recently proposed by us. The modified method has been applied to solve the three-body Schrödinger equation for H 2 + directly without recourse to the Born-Oppenheimer approximation and the calculations yield well-converged ground-state energies. These are the first-reported results obtained for H 2 + by the method of hyperspherical harmonics. With 25 hyperspherical harmonics and 40 generalized-Laguerre functions, we obtain a ground-state energy of −0.5945 au, which is close to the exact value of −0.5971 au. A detailed presentation of the method of modified hyperspherical harmonics is presented.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-2234
    Keywords: Key words: Three-body problem ; Schroedinger equation ; Potential harmonics ; Hyperspherical coordinate ; Generalized Laguerre function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. A potential harmonic method that is suitable for the three-body coulomb systems is presented. This method is applied to solve the three-body Schroedinger equations for He and e + e − e + directly, and the calculations yield very good results for the energy. For example, we obtain a ground-state energy of −0.26181 hartrees for e + e − e +, and −2.90300 hartrees for He with finite nuclear mass, in good agreement with the exact values of −0.26200 hartrees and −2.90330 hartrees. Compared with the full-set calculations, the errors in the total energy for ground and excited states of e + e − e + are very small, around −0.0001 hartrees. We conclude that the present method is one of the best PH methods for the three-body coulomb problem.
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  • 3
    ISSN: 0040-5744
    Keywords: Key words: Three-body problem ; Hyperspherical coordinate ; Schrödinger equation ; H+2 ; Generalized-Laguerre function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary.  By introducing a Gaussian factor to describe the fact that the nuclei in H+ 2 vibrate around a fixed point, we have modified the method of hyperspherical harmonics recently proposed by us. The modified method has been applied to solve the three-body Schrödinger equation for H+ 2 directly without recourse to the Born–Oppenheimer approximation and the calculations yield well-converged ground-state energies. These are the first-reported results obtained for H+ 2 by the method of hyperspherical harmonics. With 25 hyperspherical harmonics and 40 generalized-Laguerre functions, we obtain a ground-state energy of −0.5945 au, which is close to the exact value of −0.5971 au. A detailed presentation of the method of modified hyperspherical harmonics is presented.
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 23 (1983), S. 1979-1987 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A one-electron correlation operator is introduced into the Hartree-Fock self-consistent field equation. The correlation operator is derived from the second-order perturbation theory. Energies of atomic and molecular systems calculated from this modified Hartree-Fock equation are equal to that from second-order perturbation of Hartree-Fock equation. The modified equation can also be solved self-consistently by the LCAO approximation. We also presented the modified expressions for other operators.
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  • 5
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We apply the HH-GLF method, a new simple hyperspherical harmonic method proposed recently by one of us, to directly solve the three-body Schrödinger equation for e+e-e+. Uniformally convergent energy eigenvalues are obtained with only several GLF and the obtained ground-state energy with 200 HH and 6 GLF is -0.26124 au, which is very near the exact value of -0.26200 au. Energy results for maximum global momentum Km ≤ 20 are compared with those from some other hyperspherical techniques carefully, and we find that, in the example of e+e-e+, the HH-GLF method can yield results as accurate as the best available other HH method, but is conceptually simpler and more convenient for practical calculations with a large number of hyperspherical harmonics. © 1994 John Wiley & Sons, Inc.
    Additional Material: 3 Tab.
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  • 6
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: To accelerate the convergence of the HH expansion, we modified the HH-GLF method, a new simple hyperspherical harmonic method proposed recently by us, into the CFHH-GLF method. Applications of the CFHH-GLF method to the three-body systems He and e- e- e+ exhibit very fast convergence with number of HH basis sets. With only 36 HH and five GLF, we obtain the ground-state energy of -2.90371 au for He, compared with the exact value of -2.90372 au, and with only 36 HH and 10 GLF, we obtained the ground-state energy of -0.26188 au for e- e- e+, compared with the exact value of -0.26200 au. We formulate the CFHH-GLF method in this article. © 1994 John Wiley & Sons, Inc.
    Additional Material: 1 Tab.
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  • 7
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We presented a calculation of the total and partial decay widths of vibrational predissociation (VP) of the HeI2 molecule for low initial vibrational excitations from the lowest van der Waals (vdW) state with total angular momentum J = 0. A time-dependent golden rule wave-packet method was employed in our numerical calculations for the decay widths. The computed total decay widths, lifetimes, and rates of VP are in fairly good agreement with those extrapolated from the experimental data available. Predicted total decay widths as a function of initial vibrational levels exhibit a highly nonlinear behavior. These results demonstrate that a quantum mechanical decay mode for low vibrational excitation remains as well. The total propagation time needed in the time-dependent golden rule wave-packet calculations is much shorter than is the lifetime of the predissociation of HeI2. It is shown that the final-state interaction between the fragments is important for determining the final rotational-state distribution (partial decay width). We find that the major peak position in the final rotational-state distribution shifts to lower rotational energy levels with increase of the initial vibrational quantum number, which is evidently different from that for higher vibrational levels. This fact can be clearly explained by the dependence of the amount of kinetic energy released to the product degrees of freedom on the initial vibrational state. © 1997 John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
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  • 8
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Schrödinger equation for an atom or molecule is expressed in terms of hyperspherical coordinates. The eigenfunction is expanded in a series of orthonormal complete sets: Yλ,μ(Ω), eigenfunctions of generalized angular momentum scalar operator, and Lvn, generalized Laguerre polynomials. The recurrence relation of the expansion coefficients are derived and the eigenvalues can be obtained from the secular equation. © 1993 John Wiley & Sons, Inc.
    Additional Material: 1 Tab.
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  • 9
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We apply the CFHH-GLF method, a modified version of our HH-GLF method, to directly solve the three-body Schrödinger equation for a set of He-like systems, including H-, He, Li+, Be2+, and B3+. Correlation functions with no adjustable parameters are determined from the cusp condition of the wave function. Our calculational results exhibit very fast and good convergence with hyperspherical harmonics (HH) and a generalized Laguerre function (GLF) and substantial improvement over the HH-GLF method. With only 36 HH and 6 GLF, we obtained the ground-state energy of -2.90371, -7.27988, -13.6555, and -22.0308 au for He, Li+, Be2+, and B3+, respectively. This compares with -2.89361, -7.26131, -13.6253, and -21.9859 au, respectively, by the HH-GLF method and Pekeris' results of -2.90372, -7.27991, -13.6556, and -22.0310 au, respectively. So, the inclusion of 36 HH and 6 GLF has yielded the precision of a few parts in 106 for He, Li+, Be2+, and B3+. However, our calculational results for H- are not so good. We analyzed the cause of this kind of exception and improved our calculations in this respect by using a slightly different correlation function. We finally obtained the ground-state energy of -0.527754 au for H- with 36 HH and 15 GLF, which is very near Pekeris' result of -0.527751 au and of the same order of precision as those achieved for other He-like ions. © 1995 John Wiley & Sons, Inc.
    Additional Material: 5 Tab.
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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