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CACYAMCHF77. A GENERAL MULTI-CONFIGURATION HARTREE-FOCK PROGRAM.
C1 C.F. FISCHER.
CREF. IN COMP. PHYS. COMMUN. 14 (1978) 145
C ------------------------------------------------------------------
C M C H F 7 7
C ------------------------------------------------------------------
C
C A MULTI-CONFIGURATION HARTREE FOCK PROGRAM FOR ATOMS FOR THE
C IBM SYSTEM 360/370 (DOUBLE PRECISION) BY
C
C CHARLOTTE FROESE FISCHER
C DEPARTMENT OF COMPUTER SCIENCE
C PENN STATE UNIVERSITY
C UNIVERSITY PARK, PA 16801
C
C
C REVISION OF : MCHF72
C COMPUTER PHYSICS COMMUNICATIONS 4 (1972) 107
C DEVELOPED AT: THE UNIVERSITY OF WATERLOO
C WATERLOO, ONTARIO
C SUPPORTED BY: THE NATIONAL RESEARCH COUNCIL OF CANADA
C
C
C REVISION OF : MULTI-CONFIGURATION HARTREE-FOCK
C COMPUTER PHYSICS COMMUNICATIONS 1 (1969) 151
C DEVELOPED AT: THE UNIVERSITY OF BRITISH COLUMBIA
C VANCOUVER, BC
C SUPPORTED BY: THE NATIONAL RESEARCH COUNCIL OF CANADA
C
C
C
C
C
C
C THE PRESENT PROGRAM WAS DEVELOPED IN PART WHILE AT THE UNIVERSITY
C OF WATERLOO AND SUPPORTED BY A NATIONAL RESEARCH COUNCIL OF
C CANADA GRANT, AND IN PART AT PENN STATE SUPPORTED BY A US ERDA
C GRANT.
C
C ------------------------------------------------------------------
C 1 I N T R O D U C T I O N
C ------------------------------------------------------------------
C
C A MULTI-CONFIGURATION HARTREE-FOCK APPROXIMATION IS A WAVEFUNCTION
C OF THE FORM
C
C W(CLS) = SUM ON I $ WT(I) * ! CONFIG(I) > $
C (I .LE. NCFG)
C
C WHERE CLS SPECIFIES THE STATE AND ! > DESIGNATES A
C A CONFIGURATION STATE FUNCTION DEFINED IN TERMS OF SPIN-ORBITALS
C OF THE FORM
C
C PHI = (1/R)P(NL;R)<SPHERICAL HARMONIC><SPIN FUNCTION>
C
C BOTH THE COEFFICIENTS WT(I) IN THE EXPANSION AND THE RADIAL
C FUNCTIONS P(NL;R) ARE DETERMINED VARIATIONALLY SO AS TO LEAVE
C THE TOTAL ENERGY OF THE SYSTEM STATIONARY WITH RESPECT TO ALL
C PERTURBATIONS SATISFYING CERTAIN ORTHOGONALITY CONSTRAINTS. ALL
C ORBITALS WITHIN A CONFIGURATION STATE FUNCTION ARE ASSUMED TO BE
C ORTHOGONAL BUT SOME FLEXIBILITY IS ALLOWED IN THE ORTHOGONALITY
C CONSTRAINT OF ORBITALS IN DIFFERENT CONFIGURATIONS. THE
C CONSTRAINTS MUST BE SUCH THAT THE MOST GENERAL FORM OF THE ENERGY
C EXPRESSION IS
C
C E(ALS) = SUM ON I $ WT(I)**2 * EAV(I) $
C (I .LE. NCFG)
C
C + SUM ON M $A(M)*WT(J1(M))*WT(J2(M))*FK(M)(I1(M),I2(M))$
C (M .LE. NF)
C
C + SUM ON M $B(M)*WT(J1(M))*WT(J2(M))*GK(M)(I1(M),I2(M))$
C (M .LE. NG)
C
C + SUM ON M $D(M)*WT(J1(M))*WT(J2(M))
C (M .LE. NR)
C *RK(M)(I1(M),I2(M),I3(M),I4(M))
C
C *<IO(M)!JO(M)>**P(M)
C
C + SUM ON M $C(M)*WT(J1(M))*WT(J2(M))
C (M .LE. NL)
C *L(I1(M),I2(M))*<IO(M)!JO(M)>**P(M)
C
C WHERE EAV(I) IS THE AVERAGE ENERGY FOR THE I'TH CONFIGURATION,
C FK(I,J), GK(I,J) AND RK(I1, I2, I3, I4) ARE SLATER INTEGRALS AND
C THE CONTRIBUTION FROM THE ONE-ELECTRON PART OF THE HAMILTONIAN IS
C
C I(NL,N'L) = -(1/2)L(NL,N'L)
C
C
C NOTE THAT CONTRIBUTIONS FROM INTERACTIONS BETWEEN CONFIGURATIONS
C CONTRIBUTE TWICE TO THE ENERGY EXPRESSION AND SO HAVE A FACTOR OF
C TWO INCLUDED IN THE COEFFICIENT. ALSO, BY THE SYMMETRY PROPERTIES
C OF THE RK INTEGRALS, CERTAIN INTERACTION INTEGRALS MAY BE EXPRES-
C SED AS FK OR GK INTEGRALS. THE LATTER ARE TREATED MORE EFFIC-
C IENTLY BY THE PROGRAM AND ARE THE PREFERRED FORM.
C
C THE ABOVE EXPRESSION FOR THE ENERGY ASSUMES THE CONFIGURATION
C STATE FUNCTIONS AND THE RADIAL FUNCTIONS HAVE EACH BEEN ORDERED
C SO THAT THEY CAN BE REFERENCED BY THEIR INDEX IN THE LIST. THE
C INDICES FOR WT ALWAYS REFER TO CONFIGURATIONS WHEREAS THE
C INDICES FOR THE SLATER INTEGRALS, L AND OVERLAP INTEGRALS ARE
C ALWAYS RADIAL FUNCTIONS.
C
C THE STATIONARY CONDITIONS FOR THE RADIAL FUNCTIONS LEAD TO A
C SYSTEM OF COUPLED INTEGRODIFFERENTIAL EQUATIONS THAT DEPEND ON THE
C MIXING COEFFICIENTS WT(I). THESE ARE THE MCHF EQUATIONS FOR THE
C RADIAL FUNCTIONS. AS IN A CONFIGURATION INTERACTION CALCULATION,
C THE STATIONARY CONDITIONS FOR THE MIXING COEFFICIENTS ARE SOLU-
C TIONS OF A SECULAR PROBLEM, (H - E)WT = 0, WHERE H IS THE INTER-
C ACTION MATRIX, AND E THE TOTAL ENERGY. CLEARLY THE ENTRIES IN
C THE MATRIX DEPEND ON THE RADIAL FUNCTIONS. CONSEQUENTLY THE
C MCHF EQUATIONS AND THE SECULAR PROBLEM ARE COUPLED . TOGETHER
C THEY DEFINE THE MCHF PROBLEM. A MORE DETAILED DISCUSSION OF THE
C DERIVATION OF HF EQUATIONS, THEIR PROPERTIES, AND THEIR NUMERICAL
C SOLUTION IS CONTAINED IN THE BOOK, "THE HARTREE-FOCK METHOD FOR
C ATOMS - A NUMERICAL APPROACH", PUBLISHED BY WILEY INTERSCIENCE,
C NEW YORK, 1977. SECTION AND EQUATION REFERENCES IN THE DOCUMENT-
C ATION OF THIS PROGRAM REFER TO THIS BOOK.
C
C THIS PROGRAM DETERMINES THE RADIAL FUNCTIONS AS WELL AS THE
C MIXING COEFFICIENTS FOR A MULTICONFIGURATION APPROXIMATION TO THE
C TOTAL WAVEFUNCTION.
C
C ------------------------------------------------------------------
C 2 I N P U T D A T A
C ------------------------------------------------------------------
C
C THE PROGRAM ALLOWS DATA TO BE READ FROM, AND OUTPUT ROUTED TO,
C A VARIETY OF UNITS. UNLESS INDICATED OTHERWISE, THE INPUT DATA
C HERE WILL BE DESCRIBED ASSUMING ALL DATA IS READ FROM THE SAME
C UNIT, NAMELY INPUT UNIT 5. IF SECTIONS ARE TO BE READ FROM OTHER
C UNITS, THE DATA ON A GIVEN UNIT SHOULD APPEAR IN THE SAME ORDER.
C
CARD 0. IUC, IUD, IUF, IUH, OUC, OUD, OUF, OUH IN FORMAT(4I3)
C
C IUC - INPUT UNIT FOR THE CONFIGURATION CARDS (CARD 2.)
C IUD - INPUT UNIT FOR THE DATA CARDS DEFINING THE ENERGY EXPRESSION
C (CARDS 4., 5., 6., AND 7.) IF ANY.
C IUF - INPUT UNIT FOR THE FUNCTION CARDS (CARD 8.) IF ANY.
C IUH - INPUT UNIT FOR THE HAMILTONIAN MATRIX (CARD 10.) IF ANY.
C THIS UNIT NUMBER SHOULD BE ZERO IF NO MATRIX IS TO BE READ.
C OUC - OUTPUT UNIT FOR A HEADER AND CONFIGURATION CARDS.
C OUD - OUTPUT UNIT FOR VALUES OF THE SLATER INTEGRALS ENTERING INTO
C THE ENERGY EXPRESSION. IF OUD > 0, THE FULL ENERGY EXP-
C RESSION WILL ALSO BE PRINTED; OTHERWISE THIS PRINTING IS
C OMITTED.
C OUF - OUTPUT UNIT FOR THE FUNCTION VALUES
C OUH - OUTPUT UNIT FOR THE HAMILTONIAN MATRIX
C
C IN EACH CASE, THE OUTPUT WILL BE OMITTED IF THE UNIT NUMBER IS SET
C TO ZERO.
C
CARD 1. ATOM, TERM, Z, NO, NWF, NIT, NCFG, NF, NG, NR, NL, ORTHO, OMIT,
C NEW IN THE FORMAT(2A6,F6.0,I6,7I3,2L3,I3)
C
C ATOM - IDENTIFYING LABEL
C TERM - IDENTIFYING LABEL
C Z - ATOMIC NUMBER
C NO - MAXIMUM NUMBER OF POINTS IN THE RANGE OF THE FUNCTION
C VARYING FROM 160 FOR A SMALL ATOM TO 220 FOR A LARGE
C ATOM
C NWF - NUMBER OF FUNCTIONS
C NIT - NUMBER OF FUNCTIONS TO BE MADE SELF-CONSISTENT WITH THE
C REMAINING INNER CORE TO BE KEPT "FROZEN"
C NCFG - NUMBER OF CONFIGURATIONS
C NF - NUMBER OF FK INTEGRALS IN THE EXPRESSION FOR THE ENERGY
C NG - NUMBER OF GK INTEGRALS IN THE EXPRESSION FOR THE ENERGY
C NR - NUMBER OF RK INTEGRALS IN THE EXPRESSION FOR THE ENERGY
C NL - NUMBER OF L INTEGRALS IN THE EXPRESSION FOR THE ENERGY
C ORTHO- LOGICAL VARIABLE: IF .FALSE. ONLY THE ORBITALS WITHIN A
C CONFIGURATION WILL BE MADE ORTHOGONAL, OTHERWISE ALL
C ORBITALS WITH DIFFERENT NL VALUES WILL BE MADE ORTHOGONAL.
C WHEN NON-ORTHOGONAL ORBITALS ARE PRESENT, ORTHO MUST BE
C .TRUE. IF A CORE ORBITAL IS TO BE DETERMINED WHICH SIMULT-
C ANEOUSLY MUST BE ORTHOGONAL TO TWO NON-ORTHOGONAL ORBITALS
C WITH THE SAME NL VALUES. ORTHO MAY BE .FALSE. IF THE
C COMMON CORE IS FIXED. THE PROGRAM CANNOT DEAL WITH CASES
WHERE AN ORBITAL TO BE DETERMINED MUST BE ORTHOGONAL TO
C MORE THAN A SINGLE PAIR OF NON-ORTHOGONAL ORBITALS.
C OMIT - LOGICAL VARIABLE: IF .FALSE. ORTHOGONALIZATION WILL OCCUR
C ONLY AT THE END OF AN SCF CYCLE (WEAK ORTHOGONALITY),
C THOUGH STRICT (STRONG) ORTHOGONALITY WILL BE MAINTAINED
C WITH A FIXED CORE. OTHERWISE, FUNCTIONS WILL BE KEPT
C ORTHOGONAL AT ALL STAGES (STRONG ORTHOGONALITY).
C NEW - THE NUMBER OF NEW CONFIGURATIONS. IF NEW = 0, ALL
C CONFIGURATIONS WILL BE TREATED AS NEW, BUT WHEN NEW > 0,
C AN MXM HAMILTONIAN MATRIX, WHERE M = (NCFG - NEW), WILL BE
C LEFT UNCHANGED OR READ IN AS DATA IF IUH > 0. IT IS
C ASSUMED THE NEW CONFIGURATIONS HAVE BEEN ADDED AT THE END
C OF THE LIST OF CONFIGURATIONS. THIS OPTION ALLOWS A CALC-
C ULATION TO TREAT THE FIRST M CONFIGURATIONS AS PART OF A
C FIXED OR FROZEN CORE. THE RADIAL FUNCTIONS DEFINING THE
C ASSOCIATED ENTRIES IN THE HAMILTONIAN MATRIX SHOULD THEN
C ALSO BE KEPT FIXED.
C
C THE MAXIMUM ALLOWED VALUE OF MANY OF THE ABOVE VARIABLES DEPENDS
C ON THE DIMENSIONS OF ARRAYS. THE MAXIMUM VALUES FOR THE PRESENT
C PROGRAM ARE GIVEN BELOW:
C
C VARIABLE MAXIMUM VALUE
C -------- -------------
C
C NO 220
C NWF 20
C NCFG 40
C NF + NG 200
C NR 300
C NL 20
C
CARD 2. FOR EACH I, I = 1,NCFG A CONFIGURATION CARD WITH
C
C CONFIG1,CONFIG2,CONFIG3, WT, WTL IN FORMAT( 3A8, F10.8, L1)
C
C CONFIG - IDENTIFYING LABEL FOR THE CONFIGURATION
C WT - THE COEFFICIENT OR WEIGHT FOR THE CONFIGURATION:
C IF OMITTED, ALL CONFIGURATIONS HAVE EQUAL WEIGHT.
C THE WEIGHTS ARE NORMALIZED TO UNITY BY THE PROGRAM.
C IN AN MCHF CALCULATION IT IS IMPORTANT THAT THE INITIAL
C EXPECTED OCCUPATION NUMBER OF ALL FUNCTIONS TO BE
C DETERMINED BE DIFFERENT FROM ZERO, AND THAT FUNCTIONS
C CONSTRAINED BY ORTHOGONALITY HAVE DIFFERING OCCUPATION
C NUMBERS INITIALLY IF THEY WILL DIFFER IN THE FINAL
C ANSWER.
C WTL - LOGICAL VARIABLE: IF .TRUE. THE THE WEIGHT IS TO BE
C LEFT UNCHANGED FROM THE PREVIOUS CASE, OTHERWISE THE
C VALUE OF WT IS TO BE USED.
C
CARD 3. FOR EACH I, I = 1,NWF A CARD WITH
C EL(I),N(I),L(I),S(I),METH(I),ACC(I),IND(I),(QC(I,J),J=1,NCFG)
C IN THE FORMAT(A3, 2I3, F6.2, I3, F3.1, I3, 15F3.0/(24X,15F3.0))
C
C EL - IDENTIFYING LABEL FOR THE ELECTRON
C N - PRINCIPAL QUANTUM NUMBER
C L - ANGULAR QUANTUM NUMBER
C S - SCREENING PARAMETER
C METH- METHOD TO BE USED FOR SOLVING THE DIFFERENTIAL EQUATION
C 1 - METHOD 1 SOLVES A SINGLE BOUNDARY VALUE PROBLEM FOR AN
C ACCEPTABLE SOLUTION WHICH NEED NOT BE NORMALIZED.
C 2 - METHOD 2 SOLVES A SINGLE BOUNDARY VALUE PROBLEM FOR AN
C ACCEPTABLE SOLUTION WHICH IS NORMALIZED TO FIRST ORDER.
C IF THE EXCHANGE FUNCTION IS IDENTICALLY ZERO, THE PROG-
C RAM WILL AUTOMATICALLY SELECT METHOD 2.
C 3 - METHOD 3 IS SIMILAR TO METHOD 1 BUT OMITS ALL CHECKS
C FOR ACCEPTABILITY. IT IS THE PREFERRED METHOD FOR
C VIRTUAL ORBITALS WHOSE OCCUPATION NUMBER IS SMALL.
C ACC - INITIAL ACCELERATING FACTOR, 0 .LE. ACC .LT. 1
C IND - INDICATOR SPECIFYING THE TYPE OF INITIAL ESTIMATES
C -1 - INPUT DATA TO BE READ FROM UNIT IUF
C 0 - SCREENED HYDROGENIC FUNCTIONS
C 1 - SAME AS RESULTS ALREADY IN MEMORY
C QC - NUMBER OF ELECTRONS I IN CONFIGURATION J. A VALUE
C OF -1 INDICATES THAT I'TH ORBITAL IS TO BE TREATED
C AS OCCUPIED IN THE J'TH CONFIGURATION FOR ORTHO-
C GONALITY PURPOSES WHEN ORTHO = .FALSE.
C
CARD 4. FOR EACH M, M = 1,NF (IF NF > 0) A CARD WITH
C A, W, K, I1, J1, I2, J2 IN THE FORMAT(F12.8,A1,I1,1X,2I2,1X,2I2)
C
C A - COEFFICIENT OF THE FK INTEGRAL
C W - THE CHARACTER 'F'
C K - THE VALUE OF K
C I1, J1 - THE I'TH RADIAL FUNCTION IN THE J'TH CONFIGURATION
C I2, J2
C
CARD 5. FOR EACH M, M = 1,NG (IF NG > 0) A CARD WITH
C B, W, K, I1, J1, I2, J2 IN THE FORMAT(F12.8,A1,I1,1X,2I2,1X,2I2)
C
C B - COEFFICIENT OF THE GK INTEGRAL
C W - THE CHARACTER 'G'
C K - THE VALUE OF K
C I1, J1 - THE I'TH RADIAL FUNCTION IN THE J'TH CONFIGURATION
C I2, J2
C
CARD 6. FOR EACH M, M = 1,NR (IF NR > 0) A CARD WITH
C D, W, K, I1, I2, J1, I3, I4, J2, IO, JO, P
C IN THE FORMAT(F12.8, 1X, I1, 1X, 3I2, 1X, 3I2, 1X,3(1X,I2))
C
C D - COEFFICIENT OF THE RK INTEGRAL
C W - THE CHARACTER 'R'
C K - THE VALUE OF K
C I1,I2,J1 - THE I'TH RADIAL FUNCTION IN THE J'TH CONFIGURATION
C I3,I4,J2
C IO,JO - RADIAL FUNCTIONS IN THE OVERLAP FACTOR <IO!JO>**P
C P - EXPONENT FOR THE OVERLAP FACTOR
C
CARD 7. FOR EACH M, M = 1,NL (IF NL > 0) A CARD WITH
C C, W, K, I1, J1, I2, J2, IO, JO, P
C IN THE FORMAT(F12.8, 2X, 2I2, 1X. 2I2, 1X, 3(1X,I2))
C
C C - COEFFICIENT OF THE L INTEGRAL
C W - THE CHARACTER 'L'
C I1, J1 - THE I'TH RADIAL FUNCTION IN THE J'TH CONFIGURATION
C I2, J2
C IO,JO - RADIAL FUNCTIONS IN THE OVERLAP FACTOR <IO!JO>**P
C P - EXPONENT FOR THE OVERLAP FACTOR.
C
CARD 8. FOR EACH I, I=1,NWF FOR WHICH IND(I) = -1, A RADIAL FUNCTION
C WHICH WAS OUTPUT DURING A PREVIOUS RUN MUST BE READ FROM
C UNIT IUF. IF THIS UNIT IS THE SAME AS THE SYSTEM INPUT UNIT
C FOR THE REST OF THE DATA, THE CARDS MUST BE INSERTED AT THIS
C POINT IN THE ORDER IN WHICH THEY WILL BE READ.
C
CARD 9. PRINT, NSCF, IC, ACFG, ID, CFGTOL, SCFTOL, LD
C IN THE FORMAT(L3, 2I3, F3.1, I3, 2D6.1, L3)
C
C PRINT - A LOGICAL VARIABLE: IF .TRUE. THE RADIAL FUNCTIONS WILL
C BE PRINTED ON UNIT 6, SEVEN FUNCTIONS PER PAGE. THE
C LOGICAL RECORD LENGTH FOR THIS UNIT MUST BE AT LEAST 130.
C NSCF - THE MAXIMUM NUMBER OF CYCLES FOR THE SCF PROCESS. IF
C LEFT BLANK OR ZERO, A DEFAULT OF 12 IS ASSUMED.
C IC - THE NUMBER OF ADDITIONAL IMPROVEMENTS OF RADIAL FUNCTIONS
C SELECTED ON THE BASIS OF GREATEST CHANGE, FOLLOWING A
C SWEEP THROUGH THE SYSTEM OF EQUATIONS BUT PRIOR TO
C REORTHOGONALIZATION, RECOMPUTATION OF OFF-DIAGONAL
C ENERGY PARAMETERS, AND REDIAGONALIZATION OF THE ENERGY
C MATRIX IN A MULTI-CONFIGURATION APPROXIMATION. IF = 0,
C THE DEFAULT VALUE OF 3 + NIT/4 IS ASSUMED IN A SINGLE
C CONFIGURATION APPROXIMATION. THEN A CYCLE CONSISTING ONLY
C OF SWEEPS THROUGH THE SYSTEM OF EQUATIONS REQUIRES THAT IC
C BE SET TO -1. WHEN NCFG > 1, THE ACTUAL VALUE IS USED.
C ACFG - ACCELERATING PARAMETER TO BE APPLIED TO THE WEIGHTS
C WT(I) AFTER AN ENERGY DIAGONALIZATION, 0 .LE. ACFG .LT. 1
C ID - IF NOT = 0, THE ENERGY MATRIX WILL BE COMPUTED BUT NOT
C DIAGONALIZED AND THE WEIGHTS LEFT UNCHANGED.
C CFGTOL- THE ENERGY CONVERGENCE TOLERANCE FOR A MULTI-CONFIGURATION
C CALCULATION. IF = 0, A DEFAULT OF 1.D-10 IS ASSUMED.
C SCFTOL- THE PARAMETER DEFINING THE SELF-CONSISTENCY TOLERANCE
C FOR RADIAL FUNCTIONS. IF = 0, A DEFAULT VALUE OF
C 1.D-7 IS ASSUMED.
C LD - A LOGICAL VARIABLE: IF .TRUE. THE ENERGY MATRIX IS DIAG-
C ONALIZED BEFORE THE SCF ITERATIONS BEGIN. THIS IS RECOM-
C MENDED ONLY WHEN THE RADIAL FUNCTIONS ARE KNOWN TO GOOD
C ACCURACY.
CARD 10. AT THIS POINT, IF IUH > 0, AN MXM HAMILTONIAN MATRIX AS OUTPUT
C FROM SOME PREVIOUS CALCULATION SHOULD BE INSERTED, WHERE
C M = (NCFG - NEW). DURING THE CALCULATION THIS PORTION
C OF THE INTERACTION MATRIX WILL BE LEFT UNCHANGED UNLESS
C DATA CARDS ARE INCLUDED FOR THIS PORTION OF THE MATRIX.
C THE TERMS REPRESENTED BY SUCH DATA CARDS WILL BE ADDED
C TO THE INITIAL MATRIX. WHEN IUH = 0, IT IS ASSUMED THAT
C THIS PORTION OF THE MATRIX IS ALREADY IN MEMORY.
C
CARD 10. END, NEXT, ATOM, ZZ, (ACC(I), I=1,NWF)
C IN THE FORMAT(A1, I2, A6, F6.0, 20F3.1)
C
C END - SPECIAL SYMBOL '*' DENOTING THE END OF A CASE. THE PROGRAM
C ASSUMES THAT THE NEXT CARD, IF ANY, IS A CARD OF TYPE 1.
C (THE ASTERISK IS IMPORTANT ONLY IN THE CASE OF A FAILURE
C TO CONVERGE WHEN THE PROGRAM ATTEMPTS TO FIND THE BEGINNING
C OF THE NEXT CASE.)
C NEXT - A VARIABLE DETERMINING SUBSEQUENT ACTION. IF NEXT = 0, THE
C CASE HAS COMPLETED SUCCESSFULLY AND THE FOLLOWING CARD, IF
C ANY, IS ASSUMED TO BE A CARD OF TYPE 1. IF NEXT = 1, THE
C PROGRAM WILL SCALE PRESENT RESULTS FOR ATOMIC NUMBER Z TO
C THOSE FOR ATOMIC NUMBER ZZ, USING A SCREENED HYDROGENIC
C SCALING LAW, AND REPEAT THE CALCULATION FOR THE NEW CASE.
C THE NEXT CARD WILL BE ASSUMED TO BE OF TYPE 9.
C ZZ - THE NEW ATOMIC NUMBER FOR THE NEXT CASE.
C ACC - THE NEW ACCELERATING PARAMETERS FOR THE NEXT CASE
C
C ALL CALCULATIONS FOR AN ISOELECTRONIC SEQUENCE ARE ASSUMED TO BE
C ONE CASE. SEVERAL EXAMPLES OF INPUT DATA NOW FOLLOW BUT NOTE
C THAT THE DATA CARDS MUST BE REMOVED BEFORE THE PROGRAM CAN BE
C COMPILED.
C
C
C ------------------------------------------------------------------
C 3 P R O G R A M L I S T I N G
C ------------------------------------------------------------------
C
C
C ALL COMMENTS IN THE PROGRAM LISTING ASSUME THE RADIAL FUNCTION P
C IS THE SOLUTION OF AN EQUATION OF THE FORM
C
C P" + ( 2Z/R - Y - L(L+1)/R**2 - E)P = X + T
C
C WHERE Y IS CALLED A POTENTIAL FUNCTION
C X IS CALLED AN EXCHANGE FUNCTION, AND
C T INCLUDES CONTRIBUTIONS FROM OFF-DIAGONAL ENERGY PARAMETER,
C INTERACTIONS BETWEEN CONFIGURATIONS, ETC.
C
C THE PROGRAM USES LOG(Z*R) AS INDEPENDENT VARIABLE AND
C P/SQRT(R) AS DEPENDENT VARIABLE.
C AS A RESULT ALL EQUATIONS MUST BE TRANSFORMED AS DESCRIBED IN
C SEC. 6-2 AND 6-4.
C
C THIS PROGRAM IS WRITTEN AS A SYSTEM 360/370 DOUBLE PRECISION
C PROGRAM. HOWEVER, ON COMPUTERS WITH A WORD LENGTH OF 48 BITS OR
C MORE IT SHOULD BE RUN AS A SINGLE PRECISION PROGRAM. SUCH CON-
C VERSION IS FACILITATED THROUGH THE USE OF IMPLICIT TYPE DECLAR-
C ATIONS AND THE INITIALIZATION OF VIRTUALLY ALL DOUBLE PRECISION
C CONSTANTS IN THE INIT PROGRAM. CONVERSION TO A SINGLE PRECISION
C PROGRAM REQUIRES THAT:
C 1. ALL IMPLICIT REAL*8 CARDS BE REMOVED
C 2. TYPE DECLARATIONS REAL*8 AND REAL*4 BE REPLACED BY REAL
C INTEGER*2 BE REPLACED BY INTEGER
C LOGICAL*1 BE REPLACED BY LOGICAL
C 3. DOUBLE PRECISION BE REMOVED FROM FUNCTION DEFINITION CARDS
C 4. DOUBLE PRECISION CONSTANTS BE CHANGED
C 5. FUNCTION NAMES SUCH AS DABS, DSQRT, ETC. BE CHANGED TO ABS,
C SQRT, ETC.
C
C ON THE S360/370, END-OF-DATA IS TREATED AS AN ERROR EXIT AND SO
C IN MAIN THE END=5 OPTION IS USED TO TRANSFER CONTROL TO STATE-
C MENT 5 WHEN END OF DATA IS DETECTED. THE END=5 OPTION COULD
C BE REMOVED.
C
C THE ARRAYS CV AND CN ARE INITIALIZED IN SUMMRY BY STATEMENTS
C WHICH INITIALIZE THE WHOLE TRIPLY DIMENSIONED ARRAY IN THE ORDER
C THEY ARE STORED IN MEMORY. FOR EXAMPLE, IF THE DIMENSIONS OF
C ARRAY ARE N1, N2, N3, THEN
C DATA ARRAY/.........
C IS EQUIVALENT TO
C DATA (((ARRAY(I,J,K),I=1,N1),J=1,N2),K=1,N3)/.......
C
C
C ------------------------------------------------------------------
C 3-1 M A I N P R O G R A M
C ------------------------------------------------------------------
C
C THE MAIN PROGRAM CONTROLS THE OVERALL CALCULATION AND ALLOWS
C A SERIES OF CASES TO BE PROCESSED AS ONE RUN. EACH CASE ITSELF
C MAY CONSIST OF A SERIES OF ATOMS OR IONS IN AN ISO-ELECTRONIC
C SEQUENCE. IN EACH CASE, ALL BUT THE INITIAL ESTIMATES FOR THE
C FIRST ARE OBTAINED BY SCALING THE PREVIOUS RESULTS USING THE
C SCALING OF SEC. (7-2). MIXING COEFFICIENTS ARE LEFT UNCHANGED.
C
▶EOF◀