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Direct solution of H +2 Schrödinger equation using the hyperspherical coordinate

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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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Authors and Affiliations

  1. Laboratory of Theoretical Chemistry, Shandong University, 250100, Jinan, P.R. China

    Wensheng Bian & Conghao Deng

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  1. Wensheng Bian
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  2. Conghao Deng
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Bian, W., Deng, C. Direct solution of H +2 Schrödinger equation using the hyperspherical coordinate. Theoret. Chim. Acta 92, 135–147 (1995). https://doi.org/10.1007/BF01114921

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  • DOI: https://doi.org/10.1007/BF01114921

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