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rkr.f
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rkr.f
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c=======================================================================
c|..optional...Register...optional...Register...optional...Register...|c
c|--------------------------------------------------------------------|c
c| You have choosen to download the attached source code for my |c
c| Fortran program RKR1. I would appreciate it if you would please go |c
c| to the www address http://scienide2.uwaterloo.ca/~rleroy/RKR16/ |c
c| fill in the registration form there if you wish to be accessible |c
c| so that I can send you possible future updates and/or corrections |c
c| for this code. This address list will be held securely by me and |c
c| used for no other purpose................. Robert J. Le Roy .......|c
c|..Register...optional....Register...optional...Register...optional..|c
c=======================================================================
c**********************************************************************
c** R.J. Le Roy's program 'RKR1' for calculating RKR turning points in
c either simple first order or first-order Kaiser approximation.
c** 'G(v)' and 'B(v)' may be generated using conventional (Dunham)
c polynomials in (v+1/2), using Near-Dissociation expansions (NDE's),
c or using Tellinguisen's MXS 'mixed' Dunha,-at-low-v and NDE-at-high-v
c functional representations.
c** If desired (see manual), this program will also extrapolate up the
c inner wall past a chosen point with an exponential fitted to the 3
c preceeding points, & adjust 'RT(outer)' accordingly.
c******************** Version of 8 January 2016 **********************
c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
c COPYRIGHT 2003-2016 by Robert J. Le Roy +
c Dept. of Chemistry, Univ. of Waterloo, Waterloo, Ontario, Canada +
c This software may not be sold or any other commercial use made +
c of it without the explicit written permission of the author. +
c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
INTEGER MXTP,MXLEV,MXDUN
PARAMETER (MXLEV=500,MXTP=1001,MXDUN=25)
c!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
c** NOTE: Current dimensioning allows calculation of pairs of turning
c points for up to MXLEV 500 vibrational levels with a total of
c MXTP=2*MXLEV+1 turning points, and for Dunham and NDE
c polynomial expansions of defined by up to MXDUN= 25 parameters.
c These limits may may be changed by the user.
c!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
CHARACTER*78 TITLE
CHARACTER*6 PTYPE(6)
CHARACTER*2 NAME1,NAME2,CCDC(0:1)
INTEGER IAN1,IAN2,IMN1,IMN2,GEL1,GEL2,GNS1,GNS2,CHARGE,
1 KORDR,MORSE,NGP,Kaiser,IBIS,NBIS,IDIV,NDIV,NSV,NTP,
2 IVIB,NVIB,IVB,I634,I638,I,J,K,L,NN,I1,I2,I1P1,I1P2,I640,I644,
3 IR1,IDR
c
REAL*8 CU,SQCU,MASS1,MASS2,ZMASE,ABUND1,ABUND2,TOLER,ZMU,Req,Be,
1 AE,De,WE,WEXE,BETA,V00,DV0,Sw,SwLR,VEXT,F,FF,FB,G,GG,GB,VST,VFN,
2 RANGE,TSTF,TSTG,TSTFB,TSTGB,VUP,GUP,BUP,DGUP,RMIN,RMAX,RMIN2,
3 RMIN3,VRAT,CEXT,DCEXT,ADCEXT,BDCEXT,EXP1,EXP2,EXP3,FUN,
4 DFUN,AEXT,BEXT,REXT,DR1,DEI,DEIB,DRI,DRIB,D1,D2,TT,HEL,
5 V1(9),V2(9),DV(9),V(MXLEV),RT(-4:MXTP),
4 ET(-4:MXTP),VX(MXDUN),BV(MXDUN),GV(MXDUN),DGDV(MXDUN),WW(16)
c** Common block for Dunham & MXS function parameters
INTEGER LMAXGv,LMAXBv,NDEGv,NDEBv
REAL*8 VS,DVS,Y00,YL0(0:MXDUN),YL1(0:MXDUN)
COMMON /DUNPRM/Y00,VS,DVS,YL0,YL1,LMAXGv,LMAXBv,NDEGv,NDEBv
c** Common block for NDE function parameters
INTEGER NLR,ITYPE,ITYPB,IZP0,IZQ0,IZP1,IZQ1,NP0,NQ0,NP1,NQ1
REAL*8 VD,DLIM,XCN0,XCN1,P0(MXDUN),Q0(MXDUN),P1(MXDUN),Q1(MXDUN)
COMMON /NDEPRM/VD,DLIM,XCN0,XCN1,P0,Q0,P1,Q1,NLR,ITYPE,ITYPB,
1 IZP0,IZQ0,IZP1,IZQ1,NP0,NQ0,NP1,NQ1
c** Common block for quadrature weights & points
REAL*8 XG(32),WG(32),X2(16),W2(16)
COMMON /GWGHT/XG,WG,X2,W2
c
DATA CCDC/'Gv','Bv'/
DATA PTYPE/' OUTER',' INNER','Expone',' Pade ',' Pade ','ntial '/
DATA ZMASE /5.4857990946D-04/ !! 2010 physical constants d:mohr12
c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
c** Quadratures performed using NGP point Gaussian integrations.
NGP= 16
CALL WGHT(NGP)
c** Quadrature convergence criterion is TOLER
TOLER= 1.d-10
c** Use up to NBIS interval bisections in the NGP-point gaussian
c integration for the "f" and "g" integrals (typically set NBIS=3-5).
NBIS= 5
c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
c** Begin by reading in the (integer) atomic numbers and mass numbers
c defining the effective reduced mass of the system considered.
c** IAN1 & IAM2, and IMN1 & IMN2 are, respectively, the atomic numbers
c and the mass numbers identifying the atoms forming the molecule.
c Their masses are extracted from data subroutine MASSES and used
c to generate the the reduced mass ZMU.
c** If IMN1 or IMN2 lie outside the range of mass numbers for normal
c stable isotopes of that species, subroutine MASSES returns the
c average atomic mass based on the natural isotope abundance.
c** If the read-in value of IAN1 and/or IAN2 is .LE.0, then instead of
c using the MASS table, read an actual particle mass for it/them.
c** CHARGE (integer) is the charge on the molecule (=0 for neutral). If
c (CHARGE.ne.0) generate & use Watson's charge-adjusted reduced mass.
c** NDEGv(s) & NDEBv(s) specify whether Gv & Bv are represented by:
c (a) pure Dunham expansions when NDEXv(s) = 0
c (b) pure NDE expressions when NDEXv(s) = 1
c (c) MXS mixed NDE/Dunham expressions when NDEXv(s) > 1
c!! SPECIAL CASE: if have NO v-dependent rotational data and wish to
c define inner potential wall by Morse function, set: NDEBv =-1 !!
c!! NOTE: Program does NOT allow cases with NDEBv > NDEGv
c----------------------------------------------------------------------
2 READ(5,*,END=99) IAN1, IMN1, IAN2, IMN2, CHARGE, NDEGv, NDEBv
c----------------------------------------------------------------------
Y00= 0.d0
V00= -0.5d0
MORSE= 0
IF(NDEBv.GT.NDEGv) THEN
WRITE(6,598) NDEGv, NDEBv
STOP
ENDIF
I640= 0
I644= 0
c** Subroutine MASSES returns the names of the atoms NAMEi,ground
c electronic state degeneracy GELi, nuclear spin degeneracy GNSi,
c mass MASSi, and isotopic abundance ABUNDi for a given atomic isotope.
IF((IAN1.GT.0).AND.(IAN1.LE.109)) THEN
CALL MASSES(IAN1,IMN1,NAME1,GEL1,GNS1,MASS1,ABUND1)
ELSE
c** If particle-i is not a normal atomic isotope, read a 2-character
c NAME (enclosed between ', as in 'mu') and its actual mass.
c----------------------------------------------------------------------
READ(5,*) NAME1, MASS1
c----------------------------------------------------------------------
ENDIF
IF((IAN2.GT.0).AND.(IAN2.LE.109)) THEN
CALL MASSES(IAN2,IMN2,NAME2,GEL2,GNS2,MASS2,ABUND2)
ELSE
c----------------------------------------------------------------------
READ(5,*) NAME2, MASS2
c----------------------------------------------------------------------
ENDIF
ZMU= (MASS1*MASS2)/(MASS1+MASS2 - DBLE(CHARGE)*ZMASE)
c** Numerical factor 16.857629206 (+/- 0.000,000,013) based on Compton
c wavelength of proton & proton mass (u) from 2011 physical constants.
CU= 16.857629206d0/ZMU
SQCU= DSQRT(CU)
c=======================================================================
c TITLE is a title or output header of up to 78 characters, read on a
c single line enclosed between single quotes: e.g. 'title of problem'
c=======================================================================
READ(5,*) TITLE
c-----------------------------------------------------------------------
WRITE(6,600) TITLE,NAME1,IMN1,NAME2,IMN2,CHARGE,ZMU,CU,MASS1,
1 MASS2
WRITE(6,602) TOLER,NBIS,NGP
c=======================================================================
IF((NDEGv.LE.0).OR.(NDEGv.GE.2)) THEN
c** For Dunham or MXS vibrational energy function, read in order LMAXGv
c and values YL0(i) (i=1,LMAXGv) of Dunham vibrational coefficients
c-----------------------------------------------------------------------
READ(5,*) LMAXGv
READ(5,*) (YL0(L),L= 1,LMAXGv)
c-----------------------------------------------------------------------
WE= YL0(1)
WEXE= -YL0(2)
c=======================================================================
c** If using Tellinghuisen-style Mixed Representations ... read
c VS the v value (floating point) where Dunham switches to NDE,
c DVS the width parameter on the switching function, and
c DLIM the well depth, or energy at the asymptote assuming an energy
c zero at v= -1/2
c=======================================================================
IF(NDEGv.GE.2) READ(5,*) VS, DVS, DLIM
c-----------------------------------------------------------------------
IF(NDEGv.GE.2) WRITE(6,604) CCDC(0),LMAXGv,VS,DVS,DLIM
WRITE(6,606) LMAXGv,CCDC(0),(YL0(I),I= 1,LMAXGv)
ENDIF
IF(NDEGv.GE.1) THEN
c
c** If use NDE or MXS expression for vibrational energies, read NDE
c control parameters and expansion constants here.
c* For an "outer" Pade expansion, ITYPE=1 ; for an "inner" Pade,
c ITYPE=2 ; if ITYPE=3, use an exponential polynomial NDE .
c* Expansion variable is (vD-v), and the leading non-zero contribution
c to the NP-term numerator polynomial is the power IZP0 of (vD-v),
c while the corresponding leading term in the NQ0-term denominator
c polynomial is (vD-v)**IZQ0
c-----------------------------------------------------------------------
READ(5,*) NLR, ITYPE, IZP0, IZQ0, NP0, NQ0, VD, XCN0
IF(NP0.GT.0) READ(5,*) (P0(I),I= 1,NP0)
IF(NQ0.GT.0) READ(5,*) (Q0(I),I= 1,NQ0)
c-----------------------------------------------------------------------
IF(NDEGv.EQ.1) DLIM= 0.d0
IZP0= IZP0- 1
IZQ0= IZQ0- 1
KORDR= 0
FF= V00 - 1.d-5
DO I= 1,3
CALL NDEDKM(FF,KORDR,GV(I),DGDV(I),NLR,XCN0,DLIM,VD,
1 IZP0,IZQ0,ITYPE,NP0,NQ0,P0,Q0)
FF= FF+ 1.d-5
ENDDO
IF(NDEGv.EQ.1) DLIM= -GV(2)
WRITE(6,608) CCDC(0),NP0,NQ0,(PTYPE(I),I= ITYPE,6,3),0,NLR,
1 XCN0,IZP0+1,IZQ0+1,VD,DLIM
IF(NP0.GT.0) WRITE(6,610) (P0(I),I= 1,NP0)
IF(NQ0.GT.0) WRITE(6,612) (Q0(I),I= 1,NQ0)
WE= DGDV(2)
WEXE= (DGDV(1)-DGDV(3))/4.D-5
IF(NDEGv.GE.2) THEN
SwLR= DEXP(-(VS+ 0.5d0)/DVS)
Sw= 1.d0/(1.d0+ SwLR)
SwLR= SwLR/(1.d0 + SwLR)
WE= SwLR*WE + Sw*YL0(1)
WEXE= SwLR*WEXE - Sw*YL0(2)
ENDIF
ENDIF
c
IF(NDEBv.LT.0) THEN
c** If have NO v-dependent rotational data and wish to define inner
c potential wall by Morse function, read Req value to define position
c of potential minimum.
c-----------------------------------------------------------------------
READ(5,*) Req
c-----------------------------------------------------------------------
c** Use vibrational constants to determine Morse parameters at minimum.
BE= CU/Req**2
AE= (SQRT(WEXE/BE) - 1.d0)*6.d0*BE**2/WE
De= 0.25d0*WE**2/WEXE
BETA= DSQRT(DABS(WEXE)/CU)
WRITE(6,614) Req,WE,WEXE,De,BETA
MORSE= 1
ENDIF
IF((NDEBv.EQ.0).OR.(NDEBv.GE.2)) THEN
c** For Dunham or MXS Bv function, read in order LMAXBv of Dunham
c expansion in (v+1/2) and coefficients YL1(i) (i=0,LMAXBv)
c-----------------------------------------------------------------------
READ(5,*) LMAXBv
IF(LMAXBv.GE.0) READ(5,*) (YL1(L),L= 0,LMAXBv)
c-----------------------------------------------------------------------
c** Use vibrational constants to determine Morse parameters at minimum.
BE= YL1(0)
AE= -YL1(1)
IF(NDEBv.GE.2) WRITE(6,604) CCDC(1),LMAXBv,VS
WRITE(6,606) LMAXBv+1,CCDC(1),(YL1(I),I= 0,LMAXBv)
ENDIF
IF(NDEBv.GE.1) THEN
c** If use NDE or MXS expression for Bv values, read NDE control
c parameters and expansion constants which are defined in exactly the
c same way as those for the vibrational NDE.
c-----------------------------------------------------------------------
READ(5,*) ITYPB, IZP1, IZQ1, NP1, NQ1, XCN1
IF(NP1.GT.0) READ(5,*) (P1(I),I= 1,NP1)
IF(NQ1.GT.0) READ(5,*) (Q1(I),I= 1,NQ1)
c-----------------------------------------------------------------------
WRITE(6,608) CCDC(1),NP1,NQ1,(PTYPE(I),I= ITYPB,6,3),1,NLR,
1 XCN1,IZP1,IZQ1
IF(NP1.GT.0) WRITE(6,610) (P1(I),I= 1,NP1)
IF(NQ1.GT.0) WRITE(6,612) (Q1(I),I= 1,NQ1)
IZP1= IZP1- 1
IZQ1= IZQ1- 1
KORDR= 1
FF= V00
CALL NDEDKM(FF,KORDR,BE,AE,NLR,XCN1,DLIM,VD,
1 IZP1,IZQ1,ITYPB,NP1,NQ1,P1,Q1)
AE= -AE
IF(NDEBv.GE.2) THEN
IF(MAX(DABS(BE/YL1(0)),DABS(AE/YL1(1))).GT.0.01d0/SwLR)
1 WRITE(6,609) FF,SwLR,YL1(0),BE,-YL1(1),AE
BE= SwLR*BE + Sw*YL1(0)
AE= SwLR*AE - Sw*YL1(1)
ENDIF
ENDIF
c** Kaiser (integer) controls sophistication of RKR calculation.
c If(Kaiser.le.0) do simple first order with Y00=0
c If(Kaiser > 0) apply "Kaiser" correction by setting lower bound of
c integration as v(min)= -1/2 - Y00/Y10 where Dunham Y00 & Y10
c calculated from energy derivatives evaluated at v=-1/2.
c** NSV is the number of different v-increments to be used in defining
c the set of v-values for which turning points are to be calculated.
c** If(VEXT.le.0) perform RKR calculation with no inner wall smoothing
c but calculate & print exponent coefficients cEXT Cext of exponential
c functions approximately fitted to the 3 preceeding inner turning pts.
c** If(VEXT.gt.0) extrapolate inner wall above v=VEXT with an
c exponential exactly fitted to last 3 inner T.P. with v.le.VEXT
c-----------------------------------------------------------------------
READ(5,*) Kaiser, NSV, VEXT
c-----------------------------------------------------------------------
IF(MORSE.EQ.1) THEN
VEXT= -1.d0
Kaiser= 0
ENDIF
IF(Kaiser.GT.0) then
c** For (Kaiser > 0) calculate Y00 and vib quantum no. at minimum V00 and
c in NDE case, adjust D value to actual well depth De= G(v=-1/2)+Y00
Y00= AE*WE/(BE*12.d0)
Y00= (BE- WEXE)/4.d0 + Y00 + Y00**2/BE
IF(NDEGv.GE.1) DLIM= DLIM + Y00
DV0= -Y00/WE
V00= V00+ DV0
c* Iterate to correct for linear Y00/WE approximation
I= 1
VX(1)= V00
CALL GVBV(I,VX,GV,DGDV,BV)
DV0= -GV(1)/WE
V00= V00+ DV0
DV0= DV0- Y00/WE
WRITE(6,618) Y00,DV0,V00,WE,WEXE,BE,AE
IF(NDEGv.GE.1) WRITE(6,620) DLIM
ENDIF
I=1
VX(I)= V00
CALL GVBV(I,VX,GV,DGDV,BV)
IF(MORSE.NE.1) BE= BV(1)
REQ= DSQRT(CU/BE)
WRITE(6,622) V00,GV(1),DGDV(1),-WEXE,BE,REQ,AE
IF(VEXT.GT.0.d0) WRITE(6,624) VEXT
DO I= 1, NSV
c** Read and generate v-s at which turning points desired
c** For each of the NSV cases, generate v values ranging from V1(j)
c to V2(j) with (positive) increment DV(j) (for j= 1 to NSV).
c* The resulting values should increase monotonically.
c-----------------------------------------------------------------------
READ(5,*,end=99) V1(I), DV(I), V2(I)
c-----------------------------------------------------------------------
ENDDO
IF((NDEGv.GE.1).AND.(V2(NSV).GT.VD)) V2(NSV)= DINT(VD)
I= 0
DO J= 1,NSV
NN= (V2(J)- V1(J)+ 1.d-4)/DV(J)
IF(J.LT.NSV) NN= (V1(J+1)-V1(J))/DV(J)- 1
I= I+1
V(I)= V1(J)
DO K= 1,NN
I= I+1
V(I)= V(I-1) + DV(J)
ENDDO
IF(DABS(V(I)).LT.1.D-12) V(I)= 0.d0
ENDDO
NVIB= I
NTP= 2*NVIB+1
WRITE(6,626) NVIB,(V(I),I= 1,NVIB)
c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
c++ Commence actual turning point calculation here +++++++++++++++++++++
WRITE(6,630)
I638= 0
DEI= 0.d0
DRI= 0.d0
c** Commence loop over the NVIB values of vib quantum no. v ********
DO IVB= 1,NVIB
I634= 0
VUP= V(IVB)
VX(1)= VUP
I= 1
CALL GVBV(I,VX,GV,DGDV,BV)
GUP= GV(1)
BUP= BV(1)
DGUP= DGDV(1)
IF(DGUP.LE.0.d0) THEN
WRITE(6,632) VUP,GUP,DGUP
IVIB= IVB-1
NTP= 2*IVIB+ 1
I1= NVIB- IVIB+ 1
GO TO 72
ENDIF
F= 0.d0
G= 0.d0
NDIV= 1
TSTF= 9.d99
TSTG= 9.d99
c** In attempting to achieve integral convergence, consider up to NBIS
c bisections of the interval.
DO 50 IBIS= 0,NBIS
TSTFB= TSTF
TSTGB= TSTG
VFN= V00
FF= 0.d0
GG= 0.d0
RANGE= (VUP-V00)/DBLE(NDIV)
c** Sum over contributions from the NDIV segments of the interval
DO IDIV= 1,NDIV
VST= VFN
VFN= VST+RANGE
IF(IDIV.NE.NDIV) THEN
c** Quadrature weights and points for range with no singularity
D1= 0.5d0*(VFN+ VST)
D2= 0.5d0*(VFN- VST)
DO I= 1,NGP
WW(I)= WG(I)
VX(I)= D1+D2*XG(I)
ENDDO
ELSE
VFN= VUP
FF= FF/2.d0
GG= GG/2.d0
c** Weights and points for range with 1/sqrt(E-V) singularity
D2= RANGE
DO I= 1,NGP
WW(I)= W2(I)
VX(I)= VST+X2(I)*D2
ENDDO
ENDIF
CALL GVBV(NGP,VX,GV,DGDV,BV)
c** Actual quadrature loop starts here
DO I= 1,NGP
TT= WW(I)/DSQRT(GUP-GV(I))
FF= FF+TT
GG= GG+TT*BV(I)
ENDDO
ENDDO
c** End of quadrature - now test for convergence
FB= F
GB= G
F= FF*RANGE*SQCU
G= GG*RANGE/SQCU
TSTF= DABS(1.d0- FB/F)
TSTG= 0.d0
IF(((NDEGv.NE.0).OR.(LMAXBv.GE.1)).AND.(VUP.le.VEXT))
1 TSTG= DABS(1.d0- GB/G)
IF(MORSE.EQ.1) TSTG= 0.d0
IF(DMAX1(TSTF,TSTG).LT.TOLER) GO TO 54
IF((TSTF.GT.TSTFB).OR.(TSTG.GT.TSTGB)) THEN
I634= I634+ 1
IF((I634.GE.1).AND.(NDIV.GT.4)) THEN
WRITE(6,634) NDIV, TSTF,TSTFB, TSTG,TSTGB
GOTO 54
ENDIF
ENDIF
NDIV= 2*NDIV
50 CONTINUE
NDIV= NDIV/2
WRITE(6,636) NDIV,TSTF,TSTG,TOLER
54 IF(MORSE.EQ.1) THEN
c** Use Morse inner turning point when no rotational data input
RMIN= Req - DLOG(1.d0 + DSQRT(GUP/De))/BETA
RMAX= RMIN + F + F
BUP= BE
ELSE
HEL= DSQRT(F/G+F*F)
RMIN= HEL-F
RMAX= HEL+F
ENDIF
I1= NVIB+1-IVB
I2= NVIB+1+IVB
IF(IVB.LE.1) GO TO 60
DEIB= DEI
DRIB= DRI
I1P1= I1+1
RMIN2= RT(I1P1)
DEI= GUP- ET(I1P1)
DRI= RMIN- RMIN2
IF(IVB.LE.2) GO TO 60
IF((VEXT.GT.0.d0).AND.(VUP.GT.VEXT)) GO TO 56
IF(RMIN.GE.RT(I1P1)) THEN
c** If inner wall turns over, print warning
IF(I638.LE.0) THEN
I638= I1P1
WRITE(6,638) VUP
ENDIF
GOTO 60
ENDIF
IF((MORSE.GT.0).OR.(I638.GT.0)) GO TO 60
c** Use differences to get rough estimate of exponent coefficient CEXT
c for local exponential fit to inner wall.
I1P2= I1+2
RMIN3= RT(I1P2)
VRAT= DEI/DEIB
CEXT= 2.d0*(DRI-VRAT*DRIB)/(DRI**2 + VRAT*DRIB**2)
c** Iteratively converge on exact (to machine precision) value of CEXT
IF((DABS(CEXT*RMIN3).GT.70.D0).AND.(VUP.GT.0.d0)) THEN
IF(I640.LE.0) WRITE(6,640)
I640= 1
GO TO 55
ENDIF
VRAT= (GUP-ET(I1P1))/(GUP-ET(I1P2))
ADCEXT= 1.d99
DO I= 1,15
BDCEXT= ADCEXT
EXP1= 1.d0
EXP2= DEXP(-CEXT*(RT(I1P1)-RMIN))
EXP3= DEXP(-CEXT*(RT(I1P2)-RMIN))
FUN= (EXP1-EXP2)/(EXP1-EXP3)-VRAT
DFUN= ((RMIN*EXP1-RT(I1P1)*EXP2) - (RMIN*EXP1-
1 RT(I1P2)*EXP3)*(EXP1-EXP2)/(EXP1-EXP3))/(EXP1-EXP3)
DCEXT= FUN/DFUN
ADCEXT= DABS(DCEXT)
IF((ADCEXT.GE.BDCEXT).AND.(ADCEXT.LT.1.d-10)) GO TO 230
IF(ADCEXT.LE.0.d0) GO TO 230
CEXT= CEXT+DCEXT
ENDDO
WRITE(6,642) DCEXT
230 CONTINUE
IF(CEXT.LE.0.d0) THEN
I644= I644+ 1
IF(I644.EQ.1) WRITE(6,644) VUP
ENDIF
EXP1= DEXP(-CEXT*RMIN)
EXP2= EXP2*EXP1
BEXT= (GUP-ET(I1P1))/(EXP1-EXP2)
AEXT= GUP-BEXT*EXP1
c** Parameters for possible inner wall extrapolation now determined.
c
55 WRITE(6,646) VUP,GUP,DGUP,BUP,RMIN,RMAX,NDIV,TSTF,TSTG,CEXT
GO TO 64
c** Apply option to smoothly extrapolate inner wall above v=VEXT
c using a simple exponential
56 REXT= DLOG(BEXT/(GUP-AEXT))/CEXT
DR1= REXT-RMIN
RMIN= REXT
RMAX= RMAX+DR1
WRITE(6,646)VUP,GUP,DGUP,BUP,RMIN,RMAX,NDIV,TSTF,TSTG,CEXT,DR1
GO TO 64
60 WRITE(6,646) VUP,GUP,DGUP,BUP,RMIN,RMAX,NDIV,TSTF,TSTG
64 RT(I1)= RMIN
RT(I2)= RMAX
ET(I1)= GUP
ET(I2)= GUP
ENDDO
I1= 1
I2= NTP
72 IF(VEXT.GT.0.d0) WRITE(6,648) VEXT,AEXT,BEXT,CEXT
c** Write ordered turning points compactly on channel 7
c** To facilitate use of resulting potential array, add 5 extrapolated
c inner-wall points in the output file
IF((CEXT.GT.0.d0).AND.(CEXT.LT.20.d0)) THEN
IDR= -INT(1.0d3*ET(I1)*(RT(I1+1)-RT(I1))/(ET(I1+1)-ET(I1)))
IR1= INT(1.d4*RT(I1))
DO I= 1,5
RT(I1-I)= 1.D-4*(IR1- I*IDR)
ET(I1-I)= AEXT + BEXT*DEXP(-CEXT*RT(I1-I))
ENDDO
I1= I1 - 5
I2= NTP + I1 + 4
ENDIF
RT(NVIB+1)= REQ
ET(NVIB+1)= 0.d0
IF(I1.LT.0) WRITE(7,700) TITLE,NTP+5,ZMU
IF(I1.GT.0) WRITE(7,700) TITLE,NTP,ZMU
WRITE(7,702) (RT(I),ET(I),I= I1,I2)
WRITE(6,650)
GO TO 2
99 STOP
598 FORMAT(/' *** Input ERROR *** NDEBv=',i3,' .GT. NDEGv=',i3,
1 ' is NOT allowed!')
600 FORMAT(1x,A78/1x,35('**')/' RKR potential for ',A2,'(',I3,')-',
1 A2,'(',I3,') with Charge=',I2/' Reduced mass ZMU=',
2 F15.11,' and constant C_u/ZMU =',F16.12/5x,'from atomic masse
3s:',f15.10,' & ',F15.10,'(u)')
602 FORMAT(/' Seek relative quadrature convergence',1PD8.1,
1 '. Bisect interval up to',i3,' times.'/5x,'performing',i3,
2 '-point Gaussian quadrature in each segment')
604 FORMAT(/' Represent ',A2,"'s by Tellinghuisen-type MXS mixed rep
1resentation:"/ 1x,16('==')/I5,"'th order Dunham for v .le. VS &
2 NDE for v > VS, with VS=",F8.4:/4x,'with switching functio
3n F_s = 1/[1 + exp{(v-VS)/DVS}] with DVS=',f7.4/5x,'and a
4sympotote energy (dissociation limit) DLIM=',F11.4,' [cm-1]')
606 FORMAT(/' The',i3,' Dunham ',A2,' expansion coefficients are'/
1 (6X,1P4D18.10:))
608 FORMAT(/' NDE for ',A2,' is an (NP=',I2,'/NQ=',I2,') ',2A6,
1 ' expansion in (vD-v) with'/8x,'X',I1,'(n=',I1,')=',1PD14.7:
2 ' and leading num. and denom. powers',I3,' & ',I3:/8X,'vD=',
3 0PF12.6:' D-G(v=-1/2)=',F14.6)
609 FORMAT(/' *** CAUTION *** DVS may be too large. At v=',f7.3,
1 ' where Sw(LR)=',1PD9.2/6x,'Be(Dun)=',d8.1,' Be(NDE)=',
2 d8.1,' ae(Dun)=',d8.1,' ae(NDE)=',d8.1)
610 FORMAT(5X,'Numerator coefficients are:',2(1PD20.12:)/
1 (12X,3D20.12:))
612 FORMAT(5X,'Denominator coefficients : ',2(1PD20.12:)/
1 (12X,3D20.12:))
614 FORMAT(/' NO rotational constants input, so inner wall of potentia
1l is Morse function.'/' Input Req=',f9.6,'(Angst) plus we=
2',f9.3,' & wexe=',f9.5,' [cm-1]'/' yields Morse with De=',
3 f10.3,' [cm-1] and beta=',f9.6,' [1/Angst.]')
618 FORMAT(/' Calculate Y00=',F13.9,4X,'v(cor)=',F14.10,4x,'v(min)='
1 ,F14.10/5x,'using we=',f9.4,' wexe=',f9.6,' Be=',f10.6,
2 ' ae=',f11.8)
620 FORMAT(5x,'and corrected effective De=',F13.6,' (after adding Y0
10)')
622 FORMAT(/' At v00=',F9.5,' Gv=',F12.8,' dG/dv=',F9.4,
1 ' (1/2)d2G/dv2=',F10.6/21x,'Bv=',F12.8,' { ==> Req=',F12.9,
2 '(A) }'/21x,'alpha_e =',F12.9)
624 FORMAT(/' Above v =',f8.3,' extrapolate inner wall with expone
1ntial'/9x,'fitted to last 3 points ( & shift RMAX accordingly)')
626 FORMAT(/' Calculate turning points at the',i4,' v-values'/
1 (1X,11F7.2:))
630 FORMAT(/' Resulting Turning Points:'/
1 5X,'v',8X,'E(v)',4X,'dE(v)/dv',7X,'B(v)',10X,'Rmin(v)',8X,
2 'Rmax(v)',3X,'NDIV tst(f) tst(g)',4X,'C(exp)',7X,'d(RMIN)'/
3 1X,61('**'))
632 format(/' STOP calculation at v=',f6.2,' where E(v)=',f8.2,
1 ' & dE(v)/dv =',G14.7)
634 FORMAT(' *** STOP ITERATION: At NDIV=',i3,
1 ' tst(f)/(previous)=',1Pd8.1,'/',d7.1,' tst(g)/(previous)=',
2 d8.1,'/',d7.1)
636 FORMAT(' *** CAUTION:',i3,' interval incomplete convergence: tst(
1f) & tst(g)=',1P2d8.1,' while TOLER=',d8.1)
638 FORMAT(' *** WARNING *** inner wall becomes unstable at v =',
1 F6.2,' where RMIN turns outward!')
640 FORMAT(' *** CAUTION *** inner wall exponent parameter becomes ver
1y large so skip converging it.')
642 FORMAT(' *** CAUTION *** FAIL to converge C(exp) after 15 tries.',
1 ' Last step =',1PD10.2)
644 FORMAT(' *** CAUTION *** Inner potential wall has negative curvat
1ure and requires smoothing for VEXT .ge.',f7.2)
646 FORMAT(F7.3,F12.4,F11.4,F15.10,2F15.10,I4,1P2D9.1,0PF11.6,F15.10)
648 FORMAT(1X,61('**')//' For v .GE.',f6.2,' inner wall extrapolate
1d as: V(R) =',F13.4,' +',D15.8,'*exp(-',f12.8,'*R)')
650 FORMAT(1x,61('**')/////)
700 FORMAT(/1x,A78/' NTP=',I5,' RKR turning points for mu=',f14.10)
702 FORMAT((F20.14,F19.11))
END
c23456789 123456789 123456789 123456789 123456789 123456789 123456789 12
c***********************************************************************
SUBROUTINE GVBV(NL,VX,GV,DG,BV)
c** At the NL values of the vibrational quantum number VX, generate
c values of Bv, Gv and their first derivatives w.r.t. v from
c (i) pure Dunham (NDEXv= 0), (ii) pure NDE (NDEXv= 1) or
c (iii) Tellinghuisen 'mixed' MXS function NDEXv .ge. 2 where
c require NDEBv .le. NDEGv
c
INTEGER MXDUN !! max polynomial order for vib expansions
PARAMETER (MXDUN=25)
c*** define types for local variables
INTEGER I,L,KORDR,NL
REAL*8 VX(NL),GV(NL),DG(NL),BV(NL),KM,DKM,Sw,SwLR,VPH,YY,DY
c** Common block for Dunham & MXS function parameters
INTEGER LMAXGv,LMAXBv,NDEGv,NDEBv
REAL*8 VS,DVS,Y00,YL0(0:MXDUN),YL1(0:MXDUN)
COMMON /DUNPRM/Y00,VS,DVS,YL0,YL1,LMAXGv,LMAXBv,NDEGv,NDEBv
c** Common block for NDE function parameters
INTEGER NLR,ITYPE,ITYPB,IZP0,IZQ0,IZP1,IZQ1,NP0,NQ0,NP1,NQ1
REAL*8 VD,DLIM,XCN0,XCN1,P0(MXDUN),Q0(MXDUN),P1(MXDUN),Q1(MXDUN)
COMMON /NDEPRM/VD,DLIM,XCN0,XCN1,P0,Q0,P1,Q1,NLR,ITYPE,ITYPB,
1 IZP0,IZQ0,IZP1,IZQ1,NP0,NQ0,NP1,NQ1
c-----------------------------------------------------------------------
DO I= 1, NL
c** Loop over all levels, calculating energies, Bv's and their first
c derivatives w.r.t. v
VPH= VX(I)+ 0.5d0
c** First - for Dunham vib energy (or Dunham part of MXS energy)
IF(NDEGv.NE.1) THEN
YY= YL0(LMAXGv)
DY= LMAXGv*YY
DO L= LMAXGv-1, 1, -1
YY= YY*VPH + YL0(L)
dY= DY*VPH + L*YL0(L)
ENDDO
YY= YY*VPH + Y00
GV(I)= YY
DG(I)= DY
ENDIF
IF(NDEGv.GE.1) THEN
c** For NDE or MXS vibrational energy .....
KORDR= 0
CALL NDEDKM(VX(I),KORDR,KM,DKM,NLR,XCN0,DLIM,VD,
1 IZP0,IZQ0,ITYPE,NP0,NQ0,P0,Q0)
IF(NDEGv.EQ.1) THEN
GV(I)= KM
DG(I)= DKM
ELSE
SwLR= DEXP((VX(i)- VS)/DVS)
Sw= 1.d0/(1.d0+ SwLR)
SwLR= SwLR * Sw
GV(I)= Sw*YY + SwLR*KM
DG(I)= Sw*DY + SwLR*DKM - (YY - KM)*Sw*SwLR/DVS
ENDIF
ENDIF
IF(NDEBv.NE.1) THEN
c
c** First - for Dunham Bv value (or Dunham part of MXS function for Bv)
DY= 1.d0
YY= 0.d0
IF(LMAXBv.GE.0) THEN
YY= YL1(LMAXBv)
DY= LMAXBv*YY
DO L= LMAXBv-1, 0, -1
YY= YY*VPH + YL1(L)
DY= DY*VPH + L*YL1(L)
ENDDO
BV(I)= YY
ENDIF
ENDIF
IF(NDEBv.GE.1) THEN
c** For NDE or MXS function for Bv value ...
KORDR= 1
CALL NDEDKm(VX(I),KORDR,KM,DKM,NLR,XCN1,DLIM,VD,
1 IZP1,IZQ1,ITYPB,NP1,NQ1,P1,Q1)
IF(NDEBv.EQ.1) THEN
BV(I)= KM
ELSE
BV(I)= Sw*YY + SwLR*KM
ENDIF
ENDIF
ENDDO
RETURN
END
c23456789 123456789 123456789 123456789 123456789 123456789 123456789 12
c**********************************************************************
SUBROUTINE NDEDKM(VV,KORDR,KM,DKM,NLR,XCN,DLIM,VD,IZP,IZQ,ITYP,
1 NP,NQ,P,Q)
c** Subroutine which uses Near-Dissociation Expansions to generate
c predicted value KM and vibrational first derivative DKM of band
c constant of rotational order KORDR (KORDR= 0 for Gv, =1 for Bv,
c =2 for -Dv, =3 for Hv, ... etc., for vibrational level (integer) IV
c-----------------------------------------------------------------------
INTEGER KORDR,IZP,IZQ,ITYP,IPW,J,NLR,NP,NQ
REAL*8 KM,DKM,XCN,DLIM,VD,P(NP),Q(NQ), PW,PAB,DV,DVP,SMN,SMD,DSMN,
1 DSMD,VV
IPW= 2*NLR/(NLR-2)
PW= 2.d0*NLR/(DBLE(NLR)- 2.d0)
IF(KORDR.GE.1) THEN
IPW= IPW - 2*KORDR
PW= PW - 2.d0*KORDR
ENDIF
PAB= 1.d0
IF(ITYP.EQ.2) PAB= PW
DV= VD- VV
c** Evaluate the NDE numerator & denominator polynomials
SMN= 1.d0
SMD= 1.d0
DSMN= 0.d0
DSMD= 0.d0
IF(NP.GT.0) THEN
c ... numerator polynomial ...
DVP= 1.d0
IF(IZP.GT.0) DVP= DV**IZP
DO J= 1,NP
DSMN= DSMN+(J+IZP)*P(J)*DVP
DVP= DVP*DV
SMN= SMN+P(J)*DVP
ENDDO
ENDIF
IF(NQ.GT.0) THEN
c ... denominator polynomial ...
DVP= 1.d0
IF(IZQ.GT.0) DVP= DV**IZQ
DO J= 1,NQ
DSMD= DSMD+(J+IZQ)*Q(J)*DVP
DVP= DVP*DV
SMD= SMD+Q(J)*DVP
ENDDO
ENDIF
IF(ITYP.EQ.3) THEN
KM= XCN*DV**PW *DEXP(SMN- 1.d0)
DKM= -KM*(PW/DV + DSMN)
IF(KORDR.EQ.0) THEN
KM= DLIM - KM
DKM= -DKM
ENDIF
ELSE
IF(ITYP.EQ.1) THEN
KM= XCN*SMN/SMD
DKM= DV
ENDIF
IF(ITYP.EQ.2) THEN
KM= XCN
DKM= DV*SMN/SMD
ENDIF
IF(NLR.EQ.5) KM= KM*DABS(DKM)**PW
IF(NLR.NE.5) KM= KM*DKM**IPW
DKM= - KM*(PW/DV + PAB*(DSMN/SMN- DSMD/SMD))
IF(KORDR.EQ.0) THEN
KM= DLIM - KM
DKM= -DKM
ENDIF
ENDIF
RETURN
END
c=======================================================================
c***********************************************************************
SUBROUTINE MASSES(IAN,IMN,NAME,GELGS,DGNS,MASS,ABUND)
c***********************************************************************
c** For isotope with (input) atomic number IAN and mass number IMN,
c return (output): (i) as the right-adjusted 2-character variable NAME
c the alphabetic symbol for that element, (ii) the ground state
c electronic degeneracy GELGS, (iii) the nuclear spin degeneracy DGNS,
c (iv) the atomic mass MASS [amu], and (v) the natural isotopic
c abundance ABUND [in percent]. GELGS values based on atomic states
c in Moore's "Atomic Energy Level" tables, the isotope masses are taken
c from the 2012 mass table [Wang, Audi, Wapstra, Kondev, MacCormick, Xu
c & Pfeiffer, Chin.Phys.C 36, 1603-2014 (2012)] ,the proton, deuteron,
c and triton masses are taken from the 2010 fundamental constants table
c [Mohr, Taylor, & Newell, Rev. Mod. Phys. 84, 1587-1591 (2012)] and other
c quantities from Tables 6.2 and 6.3 of "Quantities, Units and Symbols in
c Physical Chemistry", by Mills et al.(Blackwell,2'nd Edition, Oxford,1993).
c** If the input value of IMN does not equal one of the tabulated values
c for atomic species IAN, return the abundance-averaged standard atomic
c weight of that atom and set DGNS=-1 and ABUND=-1.
c** For Atomic number IAN=0 and isotope mass numbers IMN=1-3, return the
c masses of the proton, deuteron, and triton, p,d & t, respectively
c Masses and properties of selected Halo nuclei an unstable nuclei included
c COPYRIGHT 2005-2015 : last updated 10 January 2016
c** By R.J. Le Roy, with assistance from
c G.T. Kraemer, J.Y. Seto and K.V. Slaughter.
c***********************************************************************
REAL*8 zm(0:123,0:15),mass,ab(0:123,15),abund
INTEGER i,ian,imn,gel(0:123),nmn(0:123),mn(0:123,15),
1 gns(0:123,15),DGNS,gelgs
CHARACTER*2 NAME,AT(0:123)
cc
DATA at(0),gel(0),nmn(0),(mn(0,i),i=1,3)/' p',1,3,1,2,3/
DATA (zm(0,i),i=0,3)/1.008d0,1.007276466812d0,2.013553212712d0,
2 3.0155007134d0/
DATA (gns(0,i),i=1,3)/2,3,2/
DATA (ab(0,i),i=1,3)/0.d0, 0.d0, 0.d0/
c
DATA at(1),gel(1),nmn(1),(mn(1,i),i=1,3)/' H',2,3,1,2,3/
DATA (zm(1,i),i=0,3)/1.00794d0, 1.00782503223d0, 2.01410177812d0,
1 3.0160492779d0/
DATA (gns(1,i),i=1,3)/2,3,2/
DATA (ab(1,i),i=1,3)/99.985d0,0.015d0,0.d0/
c
DATA at(2),gel(2),nmn(2),(mn(2,i),i=1,4)/'He',1,4,3,4,6,8/
DATA (zm(2,i),i=0,4)/4.002602d0, 3.0160293201d0, 4.00260325413d0,
1 6.0188891d0, 8.033922d0/
DATA (gns(2,i),i=1,4)/2,1,1,1/
DATA (ab(2,i),i=1,4)/0.000137d0,99.999863d0, 2*0.d0/
c
DATA at(3),gel(3),nmn(3),(mn(3,i),i=1,6)/'Li',2,6,6,7,8,9,11,12/
DATA (zm(3,i),i=0,6)/6.941d0, 6.0151228874d0, 7.016003437d0,
1 8.02248736d0,9.0267895d0,11.043798d0,12.05378d0/
DATA (gns(3,i),i=1,6)/3,4,5,4,4,1/
DATA (ab(3,i),i=1,6)/7.5d0, 92.5d0, 4*0.d0/
c
DATA at(4),gel(4),nmn(4),(mn(4,i),i=1,8)/'Be',1,8,7,9,10,11,12,
1 14,15,16/
DATA (zm(4,i),i=0,8)/9.012182d0, 7.01692983d0, 9.01218307d0,
1 10.0135338d0, 11.021658d0, 12.026921d0, 14.04289d0, 15.05346d0,
2 16.06192d0/
DATA (gns(4,i),i=1,8)/4,4,3,2,1,1,2,1/
DATA (ab(4,i),i=1,8)/0.d0, 100.d0, 6*0.d0/
c
DATA at(5),gel(5),nmn(5),(mn(5,i),i=1,10)/' B',2,10,8,10,11,12,
1 13,14,15,17,18,19/
DATA (zm(5,i),i=0,10)/10.811d0, 8.0246072d0, 10.0129369d0,
1 11.0093054d0, 12.0143521d0, 13.0177802d0, 14.025404d0,
2 15.031103d0, 17.04699d0, 18.05617d0,19.06373d0/
DATA (gns(5,i),i=1,10)/5,7,4,3,4,5,4,4,1,4/
DATA (ab(5,i),i=1,10)/0.d0, 19.9d0,80.1d0, 7*0.d0/
c
DATA at(6),gel(6),nmn(6),(mn(6,i),i=1,14)/' C',1,14,9,10,11,12,13,
1 14,15,16,17,18,19,20,21,22/
DATA (zm(6,i),i=0,14)/12.011d0, 9.0310367d0, 10.0168532d0,
1 11.0114336d0, 12.d0, 13.00335483507d0, 14.003241989d0,
1 15.0105993d0, 16.014701d0, 17.022586d0, 18.02676d0, 19.03481d0,
2 20.04032d0, 21.04934d0, 22.05720d0/
DATA (gns(6,i),i=1,14)/4,1,4,1,2,1,2,1,4,1,2,1,2,1/
DATA (ab(6,i),i=1,14)/3*0.d0, 98.90d0,1.10d0, 9*0.d0/
c
DATA at(7),gel(7),nmn(7),(mn(7,i),i=1,2)/' N',4,2,14,15/
DATA (zm(7,i),i=0,2)/14.00674d0, 14.00307400443d0,15.0001088989d0/
DATA (gns(7,i),i=1,2)/3,2/
DATA (ab(7,i),i=1,2)/99.634d0,0.366d0/
c
DATA at(8),gel(8),nmn(8),(mn(8,i),i=1,3)/' O',5,3,16,17,18/
DATA (zm(8,i),i=0,3)/15.9994d0, 15.99491461957d0, 16.9991317565d0,
1 17.9991596129d0/
DATA (gns(8,i),i=1,3)/1,6,1/
DATA (ab(8,i),i=1,3)/99.762d0, 0.038d0, 0.200d0/
c
DATA at(9),gel(9),nmn(9),(mn(9,i),i=1,1)/' F',4,1,19/
DATA (zm(9,i),i=0,1)/18.9984032d0, 18.9984031627d0/
DATA (gns(9,i),i=1,1)/2/
DATA (ab(9,i),i=1,1)/100.d0/
c
DATA at(10),gel(10),nmn(10),(mn(10,i),i=1,4)/'Ne',1,4,17,20,21,22/
DATA (zm(10,i),i=0,4)/20.1797d0, 17.017672d0, 19.9924401762d0,
1 20.99384669d0,21.991385115d0/
DATA (gns(10,i),i=1,4)/2,1,4,1/
DATA (ab(10,i),i=1,4)/0.d0, 90.48d0, 0.27d0, 9.25d0/
c
DATA at(11),gel(11),nmn(11),(mn(11,i),i=1,1)/'Na',2,1,23/
DATA (zm(11,i),i=0,1)/22.989768d0, 22.9897692820d0/
DATA (gns(11,i),i=1,1)/4/
DATA (ab(11,i),i=1,1)/100.d0/
c
DATA at(12),gel(12),nmn(12),(mn(12,i),i=1,3)/'Mg',1,3,24,25,26/
DATA (zm(12,i),i=0,3)/24.3050d0, 23.985041698d0, 24.98583698d0,
1 25.98259297d0/
DATA (gns(12,i),i=1,3)/1,6,1/
DATA (ab(12,i),i=1,3)/78.99d0, 10.00d0, 11.01d0/
c
DATA at(13),gel(13),nmn(13),(mn(13,i),i=1,1)/'Al',2,1,27/
DATA (zm(13,i),i=0,1)/26.981539d0, 26.98153853d0/
DATA (gns(13,i),i=1,1)/6/
DATA (ab(13,i),i=1,1)/100.d0/
c
DATA at(14),gel(14),nmn(14),(mn(14,i),i=1,3)/'Si',1,3,28,29,30/
DATA (zm(14,i),i=0,3)/28.0855d0, 27.9769265346d0, 28.9764946649d0,
1 29.973770136d0/
DATA (gns(14,i),i=1,3)/1,2,1/
DATA (ab(14,i),i=1,3)/92.23d0, 4.67d0, 3.10d0/
DATA at(15),gel(15),nmn(15),(mn(15,i),i=1,2)/' P',4,2,26,31/
DATA (zm(15,i),i=0,2)/30.973762d0, 26.01178d0, 30.9737619984d0/
DATA (gns(15,i),i=1,2)/15,2/
DATA (ab(15,i),i=1,2)/0.d0, 100.d0/
c
DATA at(16),gel(16),nmn(16),(mn(16,i),i=1,5)/' S',5,5,27,32,33,
1 34,36/
DATA (zm(16,i),i=0,5)/32.066d0, 27.01883d0, 31.9720711744d0,
1 32.9714589098d0,33.96786700d0, 35.96708071d0/
DATA (gns(16,i),i=1,5)/6,1,4,1,1/
DATA (ab(16,i),i=1,5)/0.d0, 95.02d0, 0.75d0, 4.21d0, 0.02d0/
c
DATA at(17),gel(17),nmn(17),(mn(17,i),i=1,2)/'Cl',4,2,35,37/
DATA (zm(17,i),i=0,2)/35.4527d0, 34.96885268d0, 36.96590260d0/
DATA (gns(17,i),i=1,2)/4,4/
DATA (ab(17,i),i=1,2)/75.77d0, 24.23d0/
c
DATA at(18),gel(18),nmn(18),(mn(18,i),i=1,3)/'Ar',1,3,36,38,40/
DATA (zm(18,i),i=0,3)/39.948d0, 35.967545105d0, 37.96273211d0,
1 39.9623831237d0/
DATA (gns(18,i),i=1,3)/1,1,1/
DATA (ab(18,i),i=1,3)/0.337d0, 0.063d0, 99.600d0/
c
DATA at(19),gel(19),nmn(19),(mn(19,i),i=1,3)/' K',2,3,39,40,41/
DATA (zm(19,i),i=0,3)/39.0983d0, 38.963706486d0, 39.96399817d0,
1 40.961825258d0/
DATA (gns(19,i),i=1,3)/4,9,4/
DATA (ab(19,i),i=1,3)/93.2581d0, 0.0117d0, 6.7302d0/
DATA at(20),gel(20),nmn(20),(mn(20,i),i=1,6)/'Ca',1,6,40,42,43,44,
1 46,48/
DATA (zm(20,i),i=0,6)/40.078d0, 39.962590864d0, 41.95861783d0,
1 42.95876644d0, 43.9554816d0, 45.9536890d0, 47.95252277d0/
DATA (gns(20,i),i=1,6)/1,1,8,1,1,1/
DATA (ab(20,i),i=1,6)/96.941d0, 0.647d0, 0.135d0, 2.086d0,
1 0.004d0, 0.187d0/
c
DATA at(21),gel(21),nmn(21),(mn(21,i),i=1,1)/'Sc',4,1,45/
DATA (zm(21,i),i=0,1)/44.955910d0, 44.9559083d0/
DATA (gns(21,i),i=1,1)/8/
DATA (ab(21,i),i=1,1)/100.d0/
c
DATA at(22),gel(22),nmn(22),(mn(22,i),i=1,5)/'Ti',5,5,46,47,48,49,
1 50/
DATA (zm(22,i),i=0,5)/47.88d0, 45.9526277d0, 46.9517588d0,
1 47.9479420d0, 48.9478657d0, 49.9447869d0/
DATA (gns(22,i),i=1,5)/1,6,1,8,1/
DATA (ab(22,i),i=1,5)/8.0d0, 7.3d0, 73.8d0, 5.5d0, 5.4d0/
c
DATA at(23),gel(23),nmn(23),(mn(23,i),i=1,2)/' V',4,2,50,51/
DATA (zm(23,i),i=0,2)/50.9415d0, 49.9471560d0, 50.9439570d0/
DATA (gns(23,i),i=1,2)/13,8/
DATA (ab(23,i),i=1,2)/0.250d0, 99.750d0/
c
DATA at(24),gel(24),nmn(24),(mn(24,i),i=1,4)/'Cr',7,4,50,52,53,54/
DATA (zm(24,i),i=0,4)/51.9961d0, 49.9460418d0, 51.9405062d0,
1 52.9406481d0, 53.9388792d0/
DATA (gns(24,i),i=1,4)/1,1,4,1/
DATA (ab(24,i),i=1,4)/4.345d0, 83.789d0, 9.501d0, 2.365d0/
c
DATA at(25),gel(25),nmn(25),(mn(25,i),i=1,1)/'Mn',6,1,55/
DATA (zm(25,i),i=0,1)/54.93805d0, 54.938049d0/
DATA (gns(25,i),i=1,1)/6/
DATA (ab(25,i),i=1,1)/100.d0/
c
DATA at(26),gel(26),nmn(26),(mn(26,i),i=1,4)/'Fe',9,4,54,56,57,58/
DATA (zm(26,i),i=0,4)/55.847d0, 53.9396090d0, 55.9349363d0,
1 56.9353928d0, 57.9332744d0/
DATA (gns(26,i),i=1,4)/1,1,2,1/
DATA (ab(26,i),i=1,4)/5.8d0, 91.72d0, 2.2d0, 0.28d0/
c
DATA at(27),gel(27),nmn(27),(mn(27,i),i=1,1)/'Co',10,1,59/
DATA (zm(27,i),i=0,1)/58.93320d0, 58.9331943d0/
DATA (gns(27,i),i=1,1)/8/
DATA (ab(27,i),i=1,1)/100.d0/
c
DATA at(28),gel(28),nmn(28),(mn(28,i),i=1,5)/'Ni',9,5,58,60,61,62,
1 64/
DATA (zm(28,i),i=0,5)/58.69d0, 57.9353424d0, 59.9307859d0,
1 60.9310556d0, 61.9283454d0, 63.9279668d0/
DATA (gns(28,i),i=1,5)/1,1,4,1,1/
DATA (ab(28,i),i=1,5)/68.077d0,26.223d0,1.140d0,3.634d0,0.926d0/
c
DATA at(29),gel(29),nmn(29),(mn(29,i),i=1,2)/'Cu',2,2,63,65/
DATA (zm(29,i),i=0,2)/63.546d0, 62.9295977d0,64.9277897d0/
DATA (gns(29,i),i=1,2)/4,4/
DATA (ab(29,i),i=1,2)/69.17d0, 30.83d0/
c
DATA at(30),gel(30),nmn(30),(mn(30,i),i=1,5)/'Zn',1,5,64,66,67,68,
1 70/
DATA (zm(30,i),i=0,5)/65.40d0, 63.9291420d0, 65.9260338d0,
1 66.9271277d0, 67.9248446d0, 69.9253192d0/
DATA (gns(30,i),i=1,5)/1,1,6,1,1/
DATA (ab(30,i),i=1,5)/48.6d0, 27.9d0, 4.1d0, 18.8d0, 0.6d0/
c
DATA at(31),gel(31),nmn(31),(mn(31,i),i=1,2)/'Ga',2,2,69,71/
DATA (zm(31,i),i=0,2)/69.723d0, 68.9255735d0, 70.9247026d0/
DATA (gns(31,i),i=1,2)/4,4/
DATA (ab(31,i),i=1,2)/60.108d0, 39.892d0/
c
DATA at(32),gel(32),nmn(32),(mn(32,i),i=1,5)/'Ge',1,5,70,72,73,74,
1 76/
DATA (zm(32,i),i=0,5)/72.61d0, 69.9242488d0, 71.92207583d0,
1 72.92345896d0, 73.921177762d0, 75.921402726d0/
DATA (gns(32,i),i=1,5)/1,1,10,1,1/
DATA (ab(32,i),i=1,5)/21.23d0, 27.66d0, 7.73d0, 35.94d0, 7.44d0/
c
DATA at(33),gel(33),nmn(33),(mn(33,i),i=1,1)/'As',4,1,75/
DATA (zm(33,i),i=0,1)/74.92159d0, 74.9215946d0/
DATA (gns(33,i),i=1,1)/4/
DATA (ab(33,i),i=1,1)/100.d0/
c
DATA at(34),gel(34),nmn(34),(mn(34,i),i=1,6)/'Se',5,6,74,76,77,78,
1 80,82/