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  • 1
    Electronic Resource
    Electronic Resource
    A potential harmonic method for the three-body coulomb problem (1997)
    Springer
    Theoretical chemistry accounts 98 (1997), S. 110-116 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002140050284
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  • 2
    Electronic Resource
    Electronic Resource
    Direct solution of H 2 + Schrödinger equation using the hyperspherical coordinate (1995)
    Springer
    Theoretical chemistry accounts 92 (1995), S. 135-147 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF01114921
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  • 3
    Electronic Resource
    Electronic Resource
    Direct solution of H+2 Schrödinger equation using the hyperspherical coordinate (1995)
    Springer
    Theoretica chimica acta 92 (1995), S. 135-147 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01114921
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  • 4
    Electronic Resource
    Electronic Resource
    CFPHGLF calculation of 3S excited states for heliumlike three-body systems (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 61 (1997), S. 101-105 
    Details
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The correlation-function potential-harmonic and generalized Laguerre function method (CFPHGLF) proposed recently by us is used to directly solve the Schrödinger equations of low-lying triplet states n3S (n = 2-5) for a set of heliumlike systems, including He, Li+, and Be2+. The eigenenergies converge fast and steadily with potential harmonics (PH) and generalized Laguerre functions (GLF). With 10 PH, the percentage errors in the convergent ionization energies for 23S, 33S, 43S, and 53S states of the helium atom are 0.548, 0.291, 0.247, and 0.265% relative to the Hylleraas CI variational values. Somewhat better precision is achieved for Li+ and Be2+ systems. © 1997 John Wiley & Sons, Inc.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Total and partial decay widths in vibrational predissociation of the HeI2 van der Waals complex for lower initial vibrational excitations (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 89-96 
    Details
    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.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 6
    Electronic Resource
    Electronic Resource
    The modified hartree-fock self-consistent field equation (1985)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 233-234 
    Details
    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
    URL: http://dx.doi.org/10.1002/qua.560270214
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  • 7
    Electronic Resource
    Electronic Resource
    The properties of n-electron wave functions built up with two kinds of geminals (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 42 (1992), S. 339-347 
    Details
    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 properties of the n-electron wave functions with symplectic symmetries have been discussed. These functions are built up with two kinds of geminals. The well-known antisymmetrized geminal power (AGP) function is only a special case of them. The first- and second-order reduced density matrices and the natural expansions of these functions have been given, and the uniform expressions for system energies in the states corresponding to these functions have been deduced. It has been shown that the special case is probably another consistent ground state for the particle-hole propegator or random-phase approximation (RPA) besides the AGP function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560420207
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  • 8
    Electronic Resource
    Electronic Resource
    Applications of n-electron wave functions built up with two kinds of geminals (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 43 (1992), S. 301-309 
    Details
    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 ground states of atoms and molecules Li-, Be, LiH, LiH2-, and Li2 have been calculated using the n-electron wave functions built up with two kinds of geminals. As a comparison, the above systems have been calculated with the Hartree-Fock self-consistent field and the multi-configuration self-consistent field method as well. The results show that the wave functions in this work are capable of describing the electron correlations, and both kinds of geminals can be taken as a starting point in building up n-electron ground states.
    Additional Material: 8 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560430211
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  • 9
    Electronic Resource
    Electronic Resource
    Direct solution of the many-body schröudinger equation in the hyperspherical formalism: Application of the HH-GLF method to the positronium ion e+e-e+ (1994)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 50 (1994), S. 395-400 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560500603
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  • 10
    Electronic Resource
    Electronic Resource
    Direct solution of the many-body Schrödinger equation in the hyperspherical formalism: Application of the CFHH-GLF method to a set of He-like systems (1995)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 54 (1995), S. 273-279 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560540502
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