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Augmented Plane Wave (APW) ??? ????? ??? ?????????? . . . ?????? ?? ??? 1937 ??? APW ?? ??????? ???.?? ??? ??? ?? ???? ?? ?? ????? ????? ?? ???:????? ??? ???????????? ???? ??? ?????? ?? ????? ??????? ? ???? ???? ??????? ?? ??? ????? ?? ???.. . 2. 2. 1. ????? ??? ???????. ??????? ????? ??? ????? ? ????? ???? ?? ???? ??? ??? ?? ???????? ?? ????: F(Kn,r) = 1/O eikn.rO = ??? ?????Kn = ?????? ?? ?? ???? ?????.

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    1. ?????? ?? ??????? ??? - ?? ?????? ???? ????? ???? ??? ???? ??? : ????? ??? ???? ?????????? ???? ??? ????? ??? ???? ?????????? ??? ??? ?????????? ???? ????? ?????? ?? ?????????? ?????? ???? ??? ?? ?? ?? ??? ???? ????? ????.

    3. ?????? ?? ??? 1937 ??? APW ?? ??????? ???. ?? ??? ??? ?? ???? ?? ?? ????? ????? ?? ???: ????? ??? ??????? ????? ???? ??? ?? ???? ?? ????? ??????? ? ???? ???? ??????? ?? ??? ????? ?? ???.

    4. ????? ??? ??????? ??????? ????? ??? ????? ? ????? ???? ?? ???? ??? ??? ?? ???????? ?? ????: F(Kn,r) = 1/O eikn.r O = ??? ????? Kn = ?????? ?? ?? ???? ?????

    5. ???? ????? ??? ???? ??? ?? ??????? ????? ? ????? ???? ?? ???? ??? ????? ?? ???: F(Kn,r) = S S Alm(Kn) ul(r,E) Ylm(r) ul(r,E) ???? ?????? ???????? ????? ?? ???? ????? E ?? ??????? ????? ???? ???? ????? ??? ???. ????? Alm ???? ?????? ?? ???? ?? ????? ????F(Kn,r) ?? ??? ??? ??? ????? ??? ?????? ?????.

    6. ???? ????? ??? ??????? ????? ??? ??? ?? ????? ??????????? ???? ??? ?? ???? ??? ?? ???? ??? ?? ?? ??? ??? ??? ????? ??? ???? ? ???? ?? ???? : 4p S il jl(KnR) ?*(Kn) ?(R) = S Alm(Kn) ul(R,E) ?lm(R) Alm(Kn) = 4p il jl(KnR) ?*(Kn) ul(R,E)

    7. ?? ??? ??? ?? ?? ?? ????? ???? ?????? ?????? ????? ?????? ?? ???? ?? ?? ?? ????? ??? ???? ?? ??? ??? ??? ???? ???? ????? ???????? |Hij – Oij E| ?? ???? ?????? ????? ????? E ?????? ??? ? ??????? ?? ????? ?? ?? ???? ???? ???????? ??? ?? ??? ????? ????. ??? ??????? ?? ???? ?? K ???? ? ?? ?? ?? ?? ?????? ????? ?? ????. ???????? ??? ??????? ?? ??? APW ???? ???.

    8. ?? ??? APW ?? ???? ??????? ?? ????? ?? ?? ???? ?? ????? ul(R,E) ?? ??? ??? ??? ????? ??? ??? ?? ???? ???? ?????? ???? ????. ???? ??? ??????? ??? ??????? ?? ????? ???? Alm ??????? ?? ???. ???? ?? ??? ???? ??? ???? ??? ??????? ?? ????? ??? ? ?? ????? ?? ??? ???? ?? ?????? ????? ?? ???? ? ??? ?? ??????? ???. ?????? ?? ???? ??????? ???? Alm ?? ????? ???? ????? ??????? ???????? ?? ???? ???? ? ????? ??????? ???? ???.

    9. Linearized Augmented Plane Wave (LAPW)

    10. ???? ?? ?????? ??? APW ? ??? ??? ???? ??????? ? ?????? ??????? ??. ????? ???? ?? ????? ??? ??????? ?? ??? ??? ???? ????? ??? ?????. ???? ??? ??? ????? ??? ????? ???? ?? ???? ??? ?????? ?? ????: F(Kn,r) = S S [ Alm(Kn) ul(r,El) _ Blm(Kn) u0l(r,El) ] ?lm(r) u0l(r,El) = ?u0l(r,El) ?E¦E=E1 ?? ???? ?? ??? LAPW ????? ???? ????? ????? El ???? ????? ???? ????? ??? ?? ???? ???? ????? ????? ??? ?? ??? ???? ?????? ??? ?? ????? ????? ???? ????? ??.

    11. ????? Alm ? Blm ?? ?? ?? ?? Kn ????? ????? ?? ????? ???? ???? ????? ???? ? ??? ???? ?? ??? ??? ????? ??? ???? ?? ????. ?? ??? LAPW ????? ?? ????? ????? ???? ???? ???? ?? r ??? ?? ???? r = RMT ?????? ?????. ??????? ?? ?? ??? ??? ???? Alm ? Blm ?? ??? ?? ???? ?? ???? ?? ??? ?? ???? ???? ?????? ???? ??? ???. ??? ???? El ???? ????? ????? ??? ?? ???? ?? ?? ????? ???? ?????? ??? ????? ????? ? ???? ???? ?? ?? ????? ???? ???? ?? ??? ?? ???.

    12. ?????? El ?? ??? ????? ????? ul(r,E) ?? ???? ???? ??? ? ?? ????? ????? ??? ????? ?? ???.

    13. El ?? ???? ?????? ?? ???? ?? ul(R,El) = 0 ? E2 ?? ?????? ?????? ?? ???? ?? ?? ???? ?? u?l(R,E2) = ? ul(r,E) / ?R ¦R=0 ????. ?? ??? ????? ????? ????? El ?? ??????? E1? E2 ?? ??? ?? ?????. ?????? ????? ???? ????? ul(R,El) ?? ??? ????? ?? ???? ??? ?? ????.

    14. E1 ????? ?? ???? ??? ? ?? ???? ?????? ????? ?? ??? ?? ?? ????? ???? ??????? ?? ???? ?? ???. E2 ????? ????? ???? ??? ? ?? ???? ???????? ????? ?? ??? ?? ??????? ???? ??????? ?? ???? ?? ???. ul(r,E1) ?? ??? ??? ????? ??? ??? ?? ??? ? ??? ????? ???? ???????? ??? ??? ul(r,E2) ?? ??? ??? ????? ??? ????? ???? ????? ??? ?? ??? ????? ???? ?????? ???. ???????? ?? ??? ?????????? ??????? ?? E ?? ????? ?? ???? ?? ?? ??? ? ???? ul(R,E) ? u?l(R,E) ??? ??? ? ??? ??????? ???? ??? ?? ????? ?? ?? ????? El ?? ??? ?? ?????.

    15. ?? ????? ???? ?? ??????? ??????? ?? ????? ?? ???? ???? ?? ?? ??? ? ???? ul(R,E) ? u?l(R,E) ??? ???? : ????? ????? ??????? ????? ?? ?? ?? ?? ?????????? s,p,d,f ?? ?????? ? ??? ?? ???? ? ??? ?? ?? ?? ?? ?????? ?? ????? ?? ??????? ??? ?? ????? ?? ?? ???? ?? ?????? ?? ???? ?? ??? ??? ????? ?? ?? ??? ?? ???? ????? ?? ?? ???? ????? ????.

    16. Full Potential Linearized Augmented Plane Wave (FP-LAPW)

    17. ?? ??? ??? ??????? ???? ?? ??????? ?? ?? ??????? ???? ?? ??? ?? ?????. ??????? ?? ????? ??? ??????? ??? ????? ???? ?? ??? ? ?? ???? ??? ??? ????? ??? ?? ??? ??????????? ????? (YLM) ??? ???? ?? ???. (???? ????? ??????????? ????? ??????????? ???? (Ylm) ?????? ???? ?? ???? ?? ?????? ????? ??? ???.) S V(G) exp (i G.r) ???? ??????? V(r) = S VLM (r) YLM (r) ???? ???? ????? ??? ?? ??? ???? YLM ?? ??? Ylm ???? ?? ??? ?? ???? ????? ???? ????? ???? ???? ?? ???? ????? ????? ? ?? ????? ???? ??????? ???? ?? ???.

    18. ??????? ?? ??? FP-LAPW ?? ????? ????? ????? ???? ? ????? ???? ???? ????? ????? ??? ??? ?? ????? ????? ??? LAPW ???. ?? ?? ???? ?k = S Ckn Fkn ????? ?? ???? ?????? ????? ? ?????? ??? ???? ???? ????? Ckn ??????? ???? ?? ???? ?? ???? ?? ??????? ????? ??? ?? ? ??? ??? ???? <E>/d Ckn d ?? ????? ?? ????.

    19. Augmented Plane Wave with Local Orbitals (APW+lo)

    20. ????? ???? ? ?????? ???? ???? ??? ?? LAPW ?????? ??? ???? ??? ???? APW ??? ???? ???? ?? ??? ????? ?? ???? APW ?? ?? ??? ??? ? ???? ????? ??? ???. ?? ??? lAPW+l0 ????? ???? ???? ??? ????? ??? ?? ???? ??? ?? ??? ????? ?? ????: Fkn = S [ Alm,kn ul(r,El) Ylm(r) ] Fkn ????? ???? ???? ?? ??? APW ??? ?? ??? ????? ?? ?? ????? El ?? ????? ???? ???.

    21. ????? ????? ?? ???? ????? ???? ??? ????? ??? ???? ???? ?? ???? ?????????? ????? ?? ??? ??? ?? ??? ????? ?? ???: Flolm = [ Alm ul(r,El,l) + Blm u0l(r,El,l) ] Ylm(r) (??? ???? ???? ?? ?? ?? ????? ?????? ?? ??? ?? ?? ???? ??? ????? ?????.) ????? Alm ? Blm ?? ??? ??? ???????? ???? Flolm ? ??????? ????? ?? ?? ??? ??? ?? ??? ?? ????. ???? ???? ??? ??? ?? ???? ????? ??????? ?? ??? ????? Rkmax ???????? ?? ??? APW+lo ?? ?????? ?? ???? ?? ????? ???? ?? ??? LAPW ???.

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