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  • 1
    Electronic Resource
    Electronic Resource
    Global ab initio potential energy surfaces for the ClH2 reactive system (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 220-229 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Two new global ab initio potential energy surfaces (called BW1 and BW2) for the ClH2 reactive system are presented. These are based on internally contracted multireference configuration interaction calculations using a very large basis set, performed at 1200 geometries. Accurate analytical fits have been generated using the functional form proposed by Aguado and Paniagua. The BW1 surface is based on the original ab initio points. This surface slightly underestimates the dissociation energies of the diatomic fragments and overestimates the barrier height. Therefore, a second surface (BW2) has been computed by scaling the correlation energies at all geometries with a constant factor, which was chosen such that the dissociation energies of HCl and H2 are reproduced more accurately. The barrier heights for the collinear transition state of the Cl+H2→HCl+H reaction are computed to be 8.14 kcal/mol and 7.61 kcal/mol for the BW1 and BW2 surfaces, respectively. To these values the spin–orbit correction of 0.84 kcal/mol has to be added, yielding a best estimate for the true barrier height of 8.45 kcal/mol. In the entrance channel of the Cl+H2→HCl+H reaction a T-shaped van der Waals well with a depth of 0.51 kcal/mol is found, while in the exit channel a van der Waals well with a collinear geometry and a depth of 0.45 kcal/mol is predicted. For the H+ClH exchange reaction, which also has a collinear transition state, the barrier heights are computed to be 18.5 kcal/mol and 17.9 kcal/mol for BW1 and BW2, respectively. It is shown that the topology of the new surfaces differs qualitatively from previous semiempirical surfaces, and the implications on the dynamics of the H2+Cl reaction are discussed. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.480574
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  • 2
    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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  • 3
    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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  • 4
    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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  • 5
    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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  • 6
    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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  • 7
    Electronic Resource
    Electronic Resource
    Direct solution of the many-body Schrödinger equation in the hyperspherical formalism: Formulation of the CFHH-GLF method (1994)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 51 (1994), S. 285-291 
    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: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560510504
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  • 8
    Electronic Resource
    Electronic Resource
    Fourier transform approach to potential harmonics (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 5-14 
    Details
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Because of the high degeneracy of hyperspherical harmonics, a method is needed for selecting the most important ones for inclusion in hyperangular basis sets. Such a method was developed by M. Fabre de la Ripelle, who showed that the most important harmonics are λ-projections of the product of the potential and a zeroth-order wave function; and he gave these the name, “potential harmonics.” In the present study we develop Fourier-transform-based methods for generating potential harmonics and for evaluating matrix elements between them. These methods are illustrated by a small calculation on three-body Coulomb systems with a variety of mass ratios. © 1997 John Wiley & Sons, Inc.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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