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4
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0003442182
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edited by J. K. Labanowski and J. W. Andzelm Springer-Verlag, New York
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For a recent review, see Density Functional Methods in Chemistry, edited by J. K. Labanowski and J. W. Andzelm (Springer-Verlag, New York, 1991).
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Density Functional Methods in Chemistry
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13
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35949018705
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E. Wimmer, H. Krakauer, M. Weinert, and A. J. Freeman, Phys. Rev. B 24, 864 (1981).
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Phys. Rev. B
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Wimmer, E.1
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Weinert, M.3
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0001470765
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N. Godbout, D. R. Salahub, J. Andzelm, and E. Wimmer, Can. J. Chem. 70, 560 (1992);
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Can. J. Chem.
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Godbout, N.1
Salahub, D.R.2
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22944484208
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K. Eichkom, O. Treutier, H. Öhm, M. Häser, and R. Ahlrichs, Chem. Phys. Lett. 240, 283 (1995).
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Treutier, O.2
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Häser, M.4
Ahlrichs, R.5
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18
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4243580175
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-2 need to be reoptimized. For an example of a study of Gaussian basis set effects in periodic DFT, see J. Z. Wu, S. B. Trickey, J. R. Sabin, and J. C. Boettger, Phys. Rev. B 51, 14576 (1995).
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Phys. Rev. B
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Wu, J.Z.1
Trickey, S.B.2
Sabin, J.R.3
Boettger, J.C.4
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19
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0000382025
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R. Dovesi, C. Roetti, C. Freyria Fava, E. Aprà, V. R. Saunders, and N. M. Harrison, Philos. Trans. R. Soc. 341, 203 (1992), and references therein. These papers deal with the reoptimization of molecular basis sets for periodic calculations in the context of Hartree-Fock theory, but similar considerations will apply in our case as far as the orbital basis is concerned. See Ref. 9 for discussions of density fitting basis sets.
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Philos. Trans. R. Soc.
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, pp. 203
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Dovesi, R.1
Roetti, C.2
Freyria Fava, C.3
Aprà, E.4
Saunders, V.R.5
Harrison, N.M.6
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20
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85033056389
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note
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Another problem with this approach is that localized functions may be a poor basis for conduction band states, except possibly those just above the gap in an insulator or semiconductor.
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21
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84931507903
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These corrections are often called "Pulay forces" after their original derivation in the molecular Hartree-Fock context; see P. Pulay, Mol. Phys. 17, 197 (1969).
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(1969)
Mol. Phys.
, vol.17
, pp. 197
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Pulay, P.1
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25
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0003470014
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Saunders College, Philadelphia, Chaps. 4-8
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For a general discussion of crystal lattices and single-electron states in crystals, see N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College, Philadelphia, 1976), Chaps. 4-8.
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(1976)
Solid State Physics
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Ashcroft, N.W.1
Mermin, N.D.2
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26
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85033063173
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note
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k=1.
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28
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85033062215
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note
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Such a technique is discussed by J. W. Mintmire (Ref. 3, op. cit., p. 125) in the context of one-dimensional periodicity (polymers) where the additional convergence techniques described in our Sec. III are unnecessary.
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31
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0000203611
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V. R. Saunders, C. Freyria-Fava, R. Dovesi, L. Salasco, and C. Roetti, Mol. Phys. 77, 629 (1992).
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Mol. Phys.
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Saunders, V.R.1
Freyria-Fava, C.2
Dovesi, R.3
Salasco, L.4
Roetti, C.5
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34
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85033044525
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note
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Parry derives these expressions from the three-dimensional Ewald function by taking the limit of a periodic stack of slabs becoming infinitely separated. We have also derived them (J. E. Jaffe, unpublished) directly from first principles, but Parry's limiting process has the advantage that it carries over the rigorous justification of the Ewald potential (Refs. 18-20) from three- to two-dimensional periodicity.
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36
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85033041827
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note
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p.
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38
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11944256577
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and references therein
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This simple SCF process was chosen mainly for its ease of programming, since the code GAPSS is still under development. Our general formalism is readily compatible with more sophisticated convergence schemes such as conjugate gradients. See M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, Rev. Mod. Phys. 64, 1045 (1992) and references therein.
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Rev. Mod. Phys.
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Payne, M.C.1
Teter, M.P.2
Allan, D.C.3
Arias, T.A.4
Joannopoulos, J.D.5
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40
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85033058689
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note
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In the test case shown, i and j were 2s contracted orbital basis functions on Mg and O respectively in bulk MgO, R=0 and p was a diffuse s-type fitting function on Mg.
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41
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85033063972
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note
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Recently we have found that including higher-order interactions of this type in Eqs. (45) and 48) can also greatly improve the practical convergence of Eq. (40).
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42
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0001170012
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This paper also contains references to the experimental data
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K. J. Chang and M. L. Cohen, Phys. Rev. B 30, 4774 (1984). This paper also contains references to the experimental data.
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Phys. Rev. B
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Chang, K.J.1
Cohen, M.L.2
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47
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33645815761
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edited by O. Madelung Springer-Verlag, Berlin, and references therein
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Semiconductors: Group IV Elements and III-V Compounds, edited by O. Madelung (Springer-Verlag, Berlin, 1991) pp. 5-7, and references therein.
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Semiconductors: Group IV Elements and III-V Compounds
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50
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0007140114
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and references therein
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R. C. Chaney, C. C. Lin, and E. E. Lafon, Phys. Rev. B 3, 459 (1971), and references therein.
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Phys. Rev. B
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Chaney, R.C.1
Lin, C.C.2
Lafon, E.E.3
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57
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0001020259
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This approach is a periodic generalization of the molecular method of H. Sambe and R. H. Felton, J. Chem. Phys. 62, 1122 (1975).
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(1975)
J. Chem. Phys.
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, pp. 1122
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Sambe, H.1
Felton, R.H.2
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62
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0040554181
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X. Chen, X. Hua, J. Hu, J.-M. Langlois, and W. A. Goddard, Phys. Rev. B 53, 1377 (1996).
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Phys. Rev. B
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Chen, X.1
Hua, X.2
Hu, J.3
Langlois, J.-M.4
Goddard, W.A.5
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