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Volumn 44, Issue 16, 1991, Pages 8503-8513

Analysis of separable potentials

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EID: 33646656867     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevB.44.8503     Document Type: Article
Times cited : (470)

References (36)
  • 15
    • 84927864594 scopus 로고    scopus 로고
    • P. Blöchl, Phys. Rev. B 41, 5415 1990).
  • 24
    • 84927864591 scopus 로고    scopus 로고
    • A. Messiah, Quantum Mechanics, Volume 1 (North-Holland, Amsterdam, 1974), pp. 98–111.
  • 26
    • 84927864590 scopus 로고    scopus 로고
    • Independently of us, D. Vanderbilt also used this algorithm to get the results of Ref. 9 (private communication).
  • 27
    • 84927864589 scopus 로고    scopus 로고
    • The reference wave functions ulup10 ps, eigenstates of the one-dimensional local Hamiltonian, can be shown to be real. Nevertheless, for the sake of generality, we have written Eq. (24) as if they were complex, and have kept this option in the whole paper.
  • 28
    • 84927864588 scopus 로고    scopus 로고
    • Using the concepts developed in Ref. 12 and the present paper, the modification of the large KB energy to a more reasonable value (<300 eV) is easy, in addition to restoring a good convergence rate for the Car-Parrinello algorithm.
  • 30
    • 84927864587 scopus 로고    scopus 로고
    • In Ref. 14, ``ccd'' for Se is equal to 2.0. In order to explain the apparent discrepancy between the KB energies in Fig. 4 of Ref. 12 and the values quoted in Table I, the following facts should be pointed out. Bachelet, Hamann, and Schlüter (Ref. 14) state to determine rmax as the mean value of the spin-up and spin-down wave-functions maxima. We found, however, that they used the smaller value of both, i.e., the spin-up result. In order to construct Fig. 4 of Ref. 12, the procedure described in Ref. 12 was used, with a different rmax for spin-up and spin-down components. This is one difference between the results from Ref. 14 (used in Table I) and in Fig. 4 of Ref. 12. The other significant difference is that in Ref. 12 quadruple precision arithmetic was used in order to become numerically stable in the inversion of the Schrödinger equation.


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