How to make non- or scalar-relativistic pseudo-potential.
 
 Masahiro Yamamoto, IAE, Kyoto Univ.   1994


(I)------- non-relativistic calculation -------
1. atom(or ion) LDA and LSDA calculation for bound electrons.
           program         data
     LDA: atomlda.f       atomlda.dat    
     LSDA:atomlsd.f      atomlsd.dat

   (i)  LSDA calculation should be done to
       include the spin-polarization effect in the total-energy.
   (ii) Some good potential  and eigen values
    are needed for the input data.
    Herman-Skillman table is recommended.
  >>> input >>>
   electron configuration
   eigenvalues
   potential
  >>> output >>>
   eigenvalues  (1)
   SCF potential(2)
   wavefunctions(3)


2. calculation of all electron atom(ion) total energy
       program
    LDA:   atotlda.f
    LSDA:  atotlsd.f
   
   >> The output of the above calculation is used for input data.


3. calculation of unbound states.
     D.R. Hamann, Phys. Rev. B, 40, 2980(1989).
     Calculate the wavefunction of the nonbound state for Kerker
     pseudo-potential generation.(e.g. oxygen d states.)
     Spin-orbit efeect is not considered here. Only L dependent.

     program      data
     nonbound.f   nonbou

   >>> input >>>
       eigenvalue(= highest occupied level of the atomic states.)
       angular momentum
       rcut
       potential(use(2))
   >>> output >>>
       wavefunction of the nonbound state(4)

4. Generalized Kerker pseudo-potential calcuation
   N.Troullier and J.L. Martins, PRB 43, 1993(1991).

  >>> Note that the PP is not unique.

    program:genkerplda.f
    data   :tmkp.dat
clda   Input data (tmkp.dat) calculated by atomlda.f    are required.
c      for nonbound state the cal. by nonbound.f is required.
clda    e.g. Oxygen 2s --> s
clda                2p --> p
clda           nonbound d which has the highest eigen value --->d
c     !!!!!!!!!!!!!  caution  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
c     !     There are a few solutions for the set (c0,c2,---,c12).    !
c     !      by changing the initial c2 value.                        !
            note  >>>>>> c2 can be changable inside the program!!!!!
c     !  Check log. derivative and the other values from the physical !
c     !   point of view.                                              !
c     !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 
c     ---------- input data set format -----------------------
c     in: # of wave functions considered
c     rcut :cut off radius. The same radius is assumed for all l's.
c     w(i):# of occupation of the i state
c     e(i): energy eigenvalue/ nonbound state higest bound e.value  Use (1)
c     pqn(i):principal quantum number of i state
c     elu(i):orbital angular momentum l of i state
c     rv(j):all electron Potential r*v(r) at r(j) pointa            Use (2)
c     f(i,j):wave function of i state at r(j) point                 Use (3) and (4)
c     ---------- output data set ---------------------------
c     'psescreen' v/s,screen(i)-v/f,screen(i)
c     'pseuion'    v/s,ion(r)-v/f,ion(r)
c     'pseuwavef'  f(i,j) of bound states
c     ---the total energy of the pseudo-atom dose not include
c         spin-poralization. Please check the result(2).--------------


5.  Check Programs
    (i) Log. derivative   :logder.f
    (ii) V_PP(Q)/V_coulomb(Q) :grapotq.f



(II)--------------- relativistic calculation -----------------
1. atom(or ion) LDA  calculation for bound electrons.
           program   
     LDA: rscf.f           
      Some good potential  and eigen values
    are needed for the input data.
    Herman-Skillman table is recommended.
  >>> input >>>
   electron configuration
   eigenvalues
   potential
  >>> output >>>
   eigenvalues  (1)
   SCF potential(2)
   wavefunctions major components(3)
                 minor components

2. calculation of all electron atom(ion) total energy
       program
       rscftot.f
   
   >> The output of the above calculation is used for input data.


3. calculation of unbound states.
     D.R. Hamann, Phys. Rev. B, 40, 2980(1989).
     Calculate the wavefunction of the nonbound state for Kerker
     pseudo-potential generation.(e.g. oxygen d states.)
     Spin-orbit efeect is not considered here. Only L dependent.

     program      data
     nonbound.f   nonbou

   >>> input >>>
       eigenvalue(= highest occupied level of the atomic states.)
       angular momentum
       rcut
       potential(use(2))
   >>> output >>>
       wavefunction of the nonbound state(4)

4. Generalized Kerker pseudo-potential calcuation
   N.Troullier and J.L. Martins, PRB 43, 1993(1991).

  >>> Note that the PP is not unique.

    program:genkerprela.f
    data   :TMKP.DAT
c      written by Masahiro Yamamoto (Kyoto Univ.) 1993 Jan.
c                                               at  Ames Lab. ISU
c      nonbound electron can be considered by Hamann's method.
c                                   Phys. Rev. B.  1989, 40 2980.
c      Input data (TMKP.DAT) calculated by RSCF program are required.
c      RSCF cal. see M. Yamamoto et al. J. Phys. Chem. 96, 1992 10784 
c      for nonbound state the cal. by nonbound.f is required.
c       e.g. Oxygen 2s1/2 --> s
c                   2p1/2 and 2p3/2 --> p
c                 nonbound d which has the highest eigen value --->d
c                 the spin-orbit cp. is not included for unbound state.
c                  for d3/2 and d5/2 the same data set is used.
c     !!!!!!!!!!!!!  caution  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
c     !     There are a few solutions for the set (c0,c2,---,c12).    !
c     !      by changing the initial c2 value.                        !
           note  >>>>>> c2 can be changable inside the program!!!!!
c     !  Check log. derivative and the other values from the physical !
c     !   point of view.                                              !
c     !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 
c     ---------- input data set format -----------------------
c     in: # of wave functions considered
         e.g. Sn=5  5s1/2 5p1/2 5p3/2 d3/2 d/5/2
c     rcut :cut off radius. The same radius is assumed for all l's.
                 e.g. Sn 2.5  a.u. judging from wavefunctions
c     w(i):# of occupation of the i state
                 e.g. Sn(s2p2)  2.0 0.67 1.33 0.0  0.0
            for 5s1/2 5p1/2 5p3/2 d3/2 d/5/2
            j=l-1/2  2*l degenarate states:#*l/(2*l+1)
            j=l+1/2  2*l+2 degenarate states:#*(l+1)/(2*l+1)
c     e(i): energy eigenvalue/ nonbound state higest bound e.value 
                from RSCFEN.DAT
c     pqn(i):principal quantum number of i state
c     tam(i):total angular momentum j=l+1/2 or l-1/2
c     elu(i):orbital angular momentum l of i state
c     rv(j):all electron Potential r*v(r) at r(j) point
                from RSCFPO.DAT
c     f(i,j):wave function of i state at r(j) point
                from major wavefunctions
        e.g. Sn FO1.DAT FO2.DAT FO3.DAT NONBWF.DAT NONBWF.DAT
c     ---------- output data set ---------------------------
c     'psescreen' v/s,screen(i)-v/f,screen(i)
c     'pseuion'    v/s,ion(r)-v/f,ion(r)
c     'pseuwavef'  f(i,j) of bound states
c     ---the total energy of the pseudo-atom dose not include
c         spin-poralization. Please check the result(2).--------------
        It is very hard to include relativistic spin-pol. effect.

5.  Check Programs
    (i) Log. derivative   :logder.f
    (ii) V_PP(Q)/V_coulomb(Q) :grapotq.f


----JCPE program explanation-----

プログラム番号 P097
プロクラム名 atom-1da/1sda
著者 山本 雅博
所属と連絡先 京都大学原子エネルギー研究所， masahiro＠cmpl.kuiae.kyoto-u.ac.jp
概　要 球対称なポテンシャル場での原子，イオンの電子構造，全エネルギーを局所密 度近似(LDA)局所スピン密度近似(LSDA)に基づき，セルフコンシステントな数値解をもとめるプログラム．
参考文献 [１]F.Herman, S. Skillman, Atomic structure calculations , Prentice‐Hall, Engelwood Cliffs, 1963.
[２]S. Cohen, Phys. Rev., 1960, 118, 489.
[３]J. Perdew and A. Zunger, Phys. Rev. B, 1981, 23, 5048.
U. von Barth, L. Hedin, J. Phys. C, 1972, 5, 1629.
S. H. Vosko, L. Wilk, M. Nusair, Can. J. Phys., 1980, 58, 　1200.
使用言語 FORTRAN77
プログラムの大きさ  
ハードウェア Cray，HP，IBMのUNIXマシーン，98で動作確認，配列の大き さ，入出力，組み込み関数さえチェックすればどのマシーンでもOK．
プログラム性能上の制限  
改訂版製作責任者 山本 雅博，京都大学原子エネルギー研究所，masahiro＠cmpl.kuiae.kyoto-u.ac.jp
媒　体 3.5インチMac 1.4MB format text file形式
頒布価格 無　料
利用に関する条件
  1. 入力として参考文献[１]に記載されている原子のエネルギー固有値，，screening potentialの数値データが必要．
  2. このプログラムを用いて計算された成果を発表する際は，M. Yamamoto, atom-1da/1sda code(JCPE Program No.)の形で引用して下さい．