rcnwriteup

一套应用很广的光谱程序

            PROGRAMS  RCN MOD36 / HF MOD8 / RCN2 (Mod 36)
             COMPUTATION OF ATOMIC RADIAL WAVEFUNCTIONS

                          Robert D. Cowan
                  Los Alamos National Laboratory
           August 1993 (revised June 1994, September 1999)

     NOTE: The following page numbers are only approximate, as the
actual pagination will depend on the page setup of the ASCII editor
or word processor used to display or print this document, as well as 
on the font and type size used.  In any case, a mono-width font
such as Courier or Monaco should be used because of the extensive
tabular material.

                            CONTENTS

I.  SUMMARY OF PROGRAMS
      A. Introduction                                             2
      B. Program RCN Mod36                                        3
      C. Program HF Mod8                                          3
      D. Program RCN2                                             4
      E. Computing times                                          4

II. PROGRAM RCN36
      A. Program outline                                          5
      B. Input                                                    8
      C. Calculational procedure                                 13
      D. Convergence problems                                    16
         (a)  SCHEQ eigenvalue iteration for a bound orbital
         (b)  Continuum-function accuracy and normalization
         (c)  SCF-iteration convergence problems
      E. Input/output units                                      19
      F. Output                                                  19
      G. Hartree-Fock calculations for specific LS terms         20
      H. Calculation of continuum functions                      21
      I. Vinti integrals                                         22
      J. Correlation potential                                   23
      K. Frozen-orbital options                                  24
      L. Negative-ion calculations                               24
      M. Dielectronic recombination calculations                 26
      N. Storage requirements                                    26
      O. Conversion to other computers                           27

III. PROGRAM HF8
      A. Outline                                                 28
      B. Input                                                   29
      C. Input/output units                                      30
      D. Storage requirements                                    30
      E. Miscellaneous                                           30

IV. PROGRAM RCN2
      A. Outline                                                 31
      B. Input                                                   32
      C. Calculational procedure                                 35
      D. Input/output units                                      37
      E. Output                                                  37
      F. Plane-wave-Born calculations in RCG                     38
      G. Photoionization and autoionization calculations in RCG  39
      H. Storage requirements                                    40
      I. Conversion to other computers                           40

V. PROGRAM USAGE AND EXAMPLE	
      A. Execution                                               40
      B. Sample input and output                                 41
      C. Command-file methods                                    42
      D. Sample monitor screen output                            45


                      I. SUMMARY OF PROGRAMS


A. Introduction
        This is a set of three FORTRAN 77 programs used on 64-bit-
word CRAY or CDC CYBER 205 computers for the self-consistent-field 
calculation of atomic radial wavefunctions, and of various radial 
integrals involved in the calculation of atomic energy levels and 
spectra.  RCN and RCN2 are easily adaptable to VAX, IBM RISC, SUN, 
Macintosh, and similar 32-bit-word computers because of the 
following coding features:
        (1)  IMPLICIT REAL*8 (A-H,O-Z) statements have been included 
in all program units, so that floating-point variables will be double
precision for 32-bit computers.  (These statements can be commented
out if necessary on 64-bit machines.)
        (2)  Generic names have been used for intrinsic functions, 
with arguments that are never numbers, but rather are variables 
defined by statements, such as HALF=0.5 or TWO=2.0, so that 
conversion to double precision will be automatically performed on 
32-bit machines.
        (3)  Named common blocks of a given name have the same length 
in all subroutines.  In all cases, there are an even number of 
integer storage spaces if followed by a floating-point variable.
        The programs can be run in a chain in any of the following 
four combinations:
                RCN
                RCN/RCN2
                RCN/HF
                RCN/HF/RCN2
        The primary input information is always to RCN, and each 
program automatically provides input information to the succeeding 
program of the chain.  Details of the programs will be described 
later; here we outline only the basic purpose of each program.
        NOTE:  The program RCN Mod36 still contains the possibility 
of feeding information into HF.  However, unlike in pre-1981 
versions, RCN can itself calculate Hartree-Fock wavefunctions.  
Therefore the program HF is no longer used, and is not supplied; 
the pertinent option in RCN has been retained for use by anyone 
desiring wavefunctions on the logarithmic radial mesh used by HF.


B. Program RCN Mod36
        Program RCN calculates single-configuration radial 
wavefunctions Pnl(r) for a spherically symmetrized atom via any 
one of the four following homogeneous-differential-equation 
approximations to the Hartree-Fock method. 
        (1)  Hartree (H);
        (2)  Hartree-Fock-Slater, with any desired value of the 
coefficient for Slater's approximate exchange term, and either 
without (HFS) or with (HFSL) Latter's tail cutoff in the central-
field potential-energy function;
        (3)  Hartree-plus-statistical-exchange (HX);
        (4)  Hartree-Slater (HS).
        (5)  RCN can also be used for true Hartree-Fock (HF) 
calculations, either for the spherically symmetrized atom (center-
of-gravity energy of the configuration), or for the energy of a 
specific LS term of the configuration (LSD-HF) provided there 
exists only one LS term having that value of LS.
        Normally, the center-of-gravity HF method is 
the only one used, except for special solid-state or chemical
investigations.
        In addition to the radial wavefunctions, also calculated for 
each configuration are various radial integrals (<r**m>, Fk, Gk, zeta), 
and the total energy of the atom (Eav) including approximate 
relativistic and correlation energy corrections.  Relativistic 
terms can be included in the potential function of the 
differential equation (HXR or HFR) to give approximate 
relativistic corrections to the radial wavefunctions, as well as 
improved relativistic energy corrections in heavy atoms (important 
for outer orbitals only if Z > 50, and for inner orbitals if Z > 20).  
Similarly, a correlation term can be included in order to make the 
potential function more negative, and thereby help to bind 
negative ions.  Options are available to provide radial 
wavefunctions as input to either program RCN2 or program HF8.


C. Program HF Mod8
        Program HF8 calculates single-configuration Hartree-Fock 
radial wavefunctions corresponding to either the center-of-gravity 
energy of the configuration, or to any specified LS term of the 
configuration (provided the LS value of interest appears only once 
in that configuration).  Radial integrals, Eav, and relativistic 
and correlation corrections are calculated as in RCN.  Except for 
a universal control card, input is entirely from RCN; output 
wavefunctions provide input to RCN2.  Relativistic terms can be 
included in the HF equations if desired (HFR).  Inasmuch as RCN 
can be used to compute HF or HFR wavefunctions, program HF8 is of 
little utility; in contrast to RCN, HF8 does have the advantage 
that off-diagonal Lagrangian parameters are included to ensure 
orthogonality between radial functions of the same l but different 
n (provided the two orbitals have unequal occupation numbers), but 
it cannot handle one-electron configurations nor any single-
subshell configuration nlw, and it cannot be used to compute 
unbound (continuum) functions.


D. Program RCN2
        Program RCN2 accepts radial wavefunctions (for one or more 
different configurations of one or more atoms or ions) from either 
RCN or HF, and for each atom calculates various two-configuration 
radial integrals: overlap integrals <Pnl|Pn'l'>, configuration-
interaction Coulomb integrals Rk and spin-orbit integrals znln'l', 
and radial electric-dipole and electric-quadrupole integrals.  In 
its most commonly used option, it automatically computes all 
quantities required for calculating energy levels and spectra of 
an atom, and writes a file containing this information in exactly 
the form required for input to program RCG, which performs these 
calculations.  For plane-wave-Born calculations in RCG, 
calculation of radial multipole integrals in RCN2 is replaced by 
calculation of radial integrals of spherical Bessel functions.
        For the theory behind all of the above programs, see Robert 
D. Cowan, The Theory of Atomic Structure and Spectra (University 
of California Press, Berkeley, 1981), Chap. 7, and Secs. 8-1, 16-
1, and 18-13 -- hereafter referred to as TASS.


E. Computing Times
        Approximate computing times for RCN and HF on CRAY-1 
computers are as listed below.  Times on a CRAY-YMP would be two 
or three times shorter.  Times on the CYBER 205 would be about the 
same as listed below; times on the CDC 7600 or IBM 360/95 or 
370/195 would be about 3 times longer; times on the CDC 6600 or 
SUN Sparcstation would be about 10 times longer; times on the 
Macintosh Centris 650 (25 MHz 68040 microprocessor) would be about
15 times longer; times on a Macintosh 400 MHz G3 computer would be
about twice as long.

                                   Time (sec)
                 --------------------------------------------                                              
                         RCN                  RCN + HF8    
                 -------------------     ---------------------
    Config.      HX   HXR   HF   HFR     HXa+ HF     HXRb+ HFR
Ar I  3p6        2     2    1     1        1 + 1       1 + 1
Kr I  4p6        3     3    3     3        2 + 2       1 + 3
Xe I  5p6        4     4          5        3 + 4       1 + 5
Dy I  4f10 6s2   6     7         10        4 + 6       2 + 8
Rn I  6p6        6     7         13        4 + 9       2 + 11
U I 5f3 6d 7s2   7     9         17        5 + 18      3 + 30
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aTime for SCF calc (TOLEND = 5