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SUBROUTINE Extrapol_baker(s,dist,x0,y0,z0,xgeom,Coef,XgeomF)
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  ! This subroutine constructs the path, andabscissa if dist<>Infinity, it samples
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  ! the path to obtain geometries.
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  ! Basically, you call it twice: i) dist=infinity, it will calculate the length of the path
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  ! ii) dist finite, it will give you the images you want along the path.
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  !
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  ! For now, it gives equidistant geometries.
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  !
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  ! A reference geometry for the alignment: X0(Nat),Y0(Nat),Z0(Nat)
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  use Path_module, only : IntCoordI, NMaxPtPath, XyzGeomF, IntCoordF, &
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       IntTangent, Renum, Nom, Order, MassAt, SGeom, Nat, NGeomI, &
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       NGeomF, Atome, NCoord, OrderInv, XyzGeomI,BTransInvF, &
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       XPrimitive,XPrimitiveF, NPrim,                                      &
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       BTransInv_local,UMatF,UMat_local,FirstTimePathCreate,Pi
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  ! IntCoordI(NGeomI,3*Nat-6), Coef(NGeomI,NCoord), NMaxPtPath=1000 (default value)
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  ! More appropriate: IntCoordI(NGeomI,NCoord)
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  use Io_module
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  IMPLICIT NONE
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  REAL(KREAL), INTENT(OUT) :: s
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  ! A reference geometry for the alignment:
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  REAL(KREAL), INTENT(IN) :: dist,X0(Nat),Y0(Nat),Z0(Nat)
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  ! Xgeom(NGeomI): abscissa of all initial geometries.
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  ! Coef(NGeomI,NCoord): spline coefficients.
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  REAL(KREAL), INTENT(IN) :: Xgeom(NGeomI),Coef(NGeomI,NCoord)
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  ! Number of the cycles for the optimization:
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  ! XGeomF(NGeomF): Final geometries.
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  REAL(KREAL), INTENT(OUT) :: XGeomF(NGeomF)
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  INTEGER(KINT) :: IdxGeom, I, J, K, Idx, IdxAtom
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  REAL(KREAL) :: Rmsd,MRot(3,3), ds, u, v
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  REAL(KREAL) :: a_val, d
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  REAL(KREAL), ALLOCATABLE :: XyzTmp(:,:), XyzTmp2(:,:), DerInt(:) ! (Nat,3)
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  REAL(KREAL), ALLOCATABLE :: Xyz_k(:,:) ! (Nat,3)
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  REAL(KREAL), ALLOCATABLE :: IntCoord_interpol(:) ! (3*Nat-6)
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  REAL(KREAL), ALLOCATABLE :: IntCoord_k(:) ! (3*Nat-6)
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  REAL(KREAL), ALLOCATABLE :: XPrimRef(:),XPrim(:) ! NPrim
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  LOGICAL ::  debug, print,printspline
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  LOGICAL, EXTERNAL :: valid
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  INTEGER(KINT) :: NSpline
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  CHARACTER(LCHARS) :: FileSpline,TmpChar
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  ! We will calculate the length of the path, in MW coordinates...
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  ! this is done in a stupid way: we interpolate the Baker coordinates values,
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  ! convert them into cartesian, weight the cartesian
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  ! and calculate the evolution of the distance !
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  ! We have to follow the same procedure for every geometry,
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  ! so even for the first one, we have to convert it from internal Baker
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  ! coordinates to cartesian !
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  debug=valid("Extrapol_baker")
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  print=valid("printgeom")
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  printspline=(valid("printspline").AND.(dist<=1e30))
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  if (debug) WRITE(*,*) "================= Entering Extrapol_baker ===================="
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  if (debug) WRITE(*,*) "DBG Extrapol_baker dist=",Dist
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  NSpline=int(NMaxPtPath/100)
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  !IF (printspline) THEN
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  !  WRITE(TmpChar,'(I5)') Iopt
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  ! FileSpline=Trim(adjustL(PathName)) // '_spline.' // AdjustL(TRIM(TmpChar))
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  !OPEN(IOTMP,FILE=FileSpline)
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  ! END IF
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  ALLOCATE(XyzTmp(Nat,3),XyzTmp2(Nat,3),IntCoord_interpol(NCoord),DerInt(NCoord))
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  ALLOCATE(IntCoord_k(NCoord),Xyz_k(Nat,3))
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  ALLOCATE(XPrimRef(NPrim),XPrim(NPrim))
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  ! XyzGeomI(:,:,:) ! (NGeomI,3,Nat)
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  ! IntCoordI(:,:) ! (NGeomI,3*Nat-6)
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  !XyzGeomF(1,:,:)=Reshape(XyzTmp2(:,:),(/3,Nat/),ORDER=(/2,1/))
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  XyzGeomF(1,:,:)=XyzGeomI(1,:,:) ! 1st index is geometry-index.
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  IntCoordF(1,:)=IntCoordI(1,:)
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  ! We calculate the first derivatives
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  u=0.d0
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  DO I=1,NCoord
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     ! Given the arrays xgeom(1:NGeomI) and IntCoordI(1:NGeomI,Idx) of length
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     ! NGeomI, which tabulate a function
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     ! (with the xgeom's in order), and given the array Coef(1:NGeomI,Idx),
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     ! which is the output from spline, and given a value of u,
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     ! this routine returns a cubic-spline interpolated value v.
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     ! and the derivative DerInt(Idx).
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     call splintder(u,v,DerInt(I),NGeomI,xgeom(1),IntCoordI(1,I),Coef(1,I))
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  END DO
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  IntTangent(1,:)=DerInt
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  IF (print.AND.(Dist.LE.1e20)) THEN
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     WRITE(IOOUT,'(1X,I5)') Nat
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     WRITE(IOOUT,*) "# Cartesian Coordinates for geom",1
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     DO I=1,Nat
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        If (Renum) THEN
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           WRITE(IOOUT,'(1X,A2,3(1X,F15.6))') Nom(Atome(I)), &
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                (XyzTmp2(Order(I),J),J=1,3)
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        ELSE
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           WRITE(IOOUT,'(1X,A2,3(1X,F15.6))') Nom(Atome(OrderInv(I))), &
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                (XyzTmp2(I,J),J=1,3)
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        END IF
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     END DO
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  END IF ! matches IF (print.AND.(Dist.LE.1e20)) THEN
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  XyzTmp(:,1) = XyzGeomI(1,1,:) ! 1st index is geometry-index.
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  XyzTmp(:,2) = XyzGeomI(1,2,:)
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  XyzTmp(:,3) = XyzGeomI(1,3,:)
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  s=0.d0
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  IntCoord_k=IntCoordF(1,:)
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  Xyz_k(:,1) = XyzGeomI(1,1,:) ! 1st index is geometry-index.
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  Xyz_k(:,2) = XyzGeomI(1,2,:)
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  Xyz_k(:,3) = XyzGeomI(1,3,:)
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  IdxGeom=1
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  XPrimRef=XPrimitive(1,:)
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  XPrimitiveF(1,:)=XPrimitive(1,:)
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  DO K=1,NMaxPtPath
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     u=real(K)/NMaxPtPath*(NGeomI-1.)
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     ! We generate the interpolated internal coordinates in v.
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     ! Given the arrays Xgeom(1:NGeomI) (Xgeom(NGeomI): abscissa of all initial geometries)
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     ! and IntCoordI(1:NGeomI,I) of length NGeomI, which tabulate a function (with the
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     ! Xgeom's in order), and given the array Coef(1:NGeomI,Idx), which is the output from
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     ! spline, and given a value of u, this routine returns a cubic-spline interpolated
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     ! value v and the derivative DerInt(I).
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     ! this loop is to be confirmed:
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     ! IntCoordI(NGeomI,3*Nat-6)
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     DO I=1,NCoord
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        call splintder(u,v,DerInt(I),NGeomI,Xgeom(1),IntCoordI(1,I),Coef(1,I))
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        IntCoord_interpol(I)=v
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     END DO
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     IF(.NOT.FirstTimePathCreate) Then
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       WRITE(*,*) "DBG Extrapol_baker Umat_local=UMatF"
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        DO I=1,NCoord ! these variables are used in ConvertBakerInternal_cart()
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           BTransInv_local(I,:) = BTransInvF(IdxGeom,I,:)
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           UMat_local(:,I) = UMatF(IdxGeom,:,I)
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        END DO
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     END IF
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     ! We convert it into Cartesian coordinates:
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     if (debug) WRITE(*,*) "DBG Extrapol_baker, call ConvertBakerInt_car for k=",k
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     Call ConvertBakerInternal_cart(IntCoord_k,IntCoord_interpol,Xyz_k(1,1), &
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          Xyz_k(1,2),Xyz_k(1,3),XyzTMP2(1,1),XyzTMP2(1,2),XyzTMP2(1,3),XPrim,XPrimRef)
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     XPrimRef=Xprim
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     IF(.NOT.FirstTimePathCreate) Then
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        DO I=1,NCoord ! these variables are used in ConvertBakerInternal_cart()
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           BTransInvF(IdxGeom,I,:) = BTransInv_local(I,:)
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        END DO
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     END IF
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     if (debug) THEN
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        WRITE(*,*) "DBG Extrapol_baker, XyzTmp2 before RMSD"
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           DO I=1,Nat
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              IF (Renum) THEN
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                 WRITE(IOOUT,'(1X,A2,3(1X,F15.6))') Nom(Atome(I)), &
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                      (XyzTmp2(Order(I),J),J=1,3)
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              ELSE
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                 WRITE(IOOUT,'(1X,A2,3(1X,F15.6))') Nom(Atome(OrderInv(I))), &
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                      (XyzTmp2(I,J),J=1,3)
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              END IF
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           END DO
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        END IF
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     call CalcRmsd(Nat,XyzTmp(1:Nat,1),XyzTmp(1:Nat,2),XyzTmp(1:Nat,3), &
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	  XyzTmp2(1:Nat,1),XyzTmp2(1:Nat,2),XyzTmp2(1:Nat,3),           &
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          MRot,rmsd,.TRUE.,.TRUE.)
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     if (debug) THEN
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        WRITE(*,*) "DBG Extrapol_baker, XyzTmp2 after RMSD"
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           DO I=1,Nat
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              IF (Renum) THEN
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                 WRITE(IOOUT,'(1X,A2,3(1X,F15.6))') Nom(Atome(I)), &
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                      (XyzTmp2(Order(I),J),J=1,3)
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              ELSE
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                 WRITE(IOOUT,'(1X,A2,3(1X,F15.6))') Nom(Atome(OrderInv(I))), &
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                      (XyzTmp2(I,J),J=1,3)
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              END IF
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           END DO
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        END IF
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     IntCoord_k=IntCoord_interpol
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     Xyz_k(:,1)=XyzTMP2(:,1)
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     Xyz_k(:,2)=XyzTMP2(:,2)
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     Xyz_k(:,3)=XyzTMP2(:,3)
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     ds=0.
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     DO I=1,Nat
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        DO J=1,3
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           ds=ds+MassAt(I)*(XYZTMp2(I,J)-XYZTmp(I,J))**2
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           XYZTmp(I,J)=XyzTMP2(I,J)
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        END DO
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     END DO
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     s=s+sqrt(ds)
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     IF (s>=dist) THEN
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        if (debug) THEN
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           WRITE(*,*) "DBG Extrapol_baker s,IdxGeom,dist",s,IdxGeom,dist
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           WRITE(*,'(50(1X,F12.8))') IntCoord_interpol
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           WRITE(*,*) "DBG Extrapol_baker Angles in deg ?"
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           WRITE(*,'(50(1X,F12.8))') IntCoord_interpol*180./pi
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        END IF
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        s=s-dist
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        IdxGeom=IdxGeom+1
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        XprimitiveF(IdxGeom,:)=Xprim(:)
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        UMatF(IdxGeom,:,:)=UMat_local(:,:)
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        SGeom(IdxGeom)=s+IdxGeom*dist !SGeom(NGeomF)
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        XgeomF(IdxGeom)=u
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        XyzGeomF(IdxGeom,:,:)=Reshape(XyzTmp2(:,:),(/3,Nat/),ORDER=(/2,1/))
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        ! IntCoordF(NGeomF,NCoord): Final Internal coordinates for number of final
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        ! geometries. NCoord is the number of coordinates (NCoord) of each geometry.
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        IntCoordF(IdxGeom,:)=IntCoord_interpol(:)
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        IntTangent(IdxGeom,:)=DerInt
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        IF (print) THEN
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           WRITE(IOOUT,'(1X,I5)') Nat
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           WRITE(IOOUT,*) "# Cartesian coord for Geometry ",IdxGeom,K
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           ! PFL 17/July/2006: only if we have more than 4 atoms.
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           IF (Nat.GE.4) THEN
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              Call  CalcRmsd(Nat,x0,y0,z0, &
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                   xyzTmp2(1,1),xyzTmp2(1,2),xyzTMP2(1,3), &
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                   MRot,rmsd,.TRUE.,.TRUE.)
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           END IF
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           DO I=1,Nat
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              IF (Renum) THEN
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                 WRITE(IOOUT,'(1X,A2,3(1X,F15.6))') Nom(Atome(I)), &
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                      (XyzTmp2(Order(I),J),J=1,3)
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              ELSE
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                 WRITE(IOOUT,'(1X,A2,3(1X,F15.6))') Nom(Atome(OrderInv(I))), &
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                      (XyzTmp2(I,J),J=1,3)
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              END IF
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           END DO
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        END IF !matches IF (print) THEN
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     END IF ! matches IF (s>=dist) THEN
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  END DO ! matches DO K=1,NMaxPtPath
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  if (s>=0.9*dist) THEN
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     s=s-dist
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     IdxGeom=IdxGeom+1
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     SGeom(IdxGeom)=s+IdxGeom*dist
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     XgeomF(IdxGeom)=min(u,NGeomI-1.d0)
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     XyzGeomF(IdxGeom,:,:)=Reshape(XyzTmp2(:,:),(/3,Nat/),ORDER=(/2,1/))
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     !  XyzGeomF(IdxGeom,:,:)=XyzTmp2(:,:)
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     IntCoordF(IdxGeom,:)=IntCoord_interpol(:)
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     XprimitiveF(IdxGeom,:)=Xprim(:)
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     UMatF(IdxGeom,:,:)=UMat_local(:,:)
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     IntTangent(IdxGeom,:)=DerInt
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     if (print) THEN
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        WRITE(IOOUT,'(1X,I5)') Nat
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        WRITE(IOOUT,*) "# Cartesian coord for Geometry ",IdxGeom,K
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        ! PFL 17/July/2006: only if we have more than 4 atoms.
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        IF (Nat.GE.4) THEN
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           Call  CalcRmsd(Nat,x0,y0,z0, &
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                xyzTmp2(1,1),xyzTmp2(1,2),xyzTMP2(1,3), &
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                MRot,rmsd,.TRUE.,.TRUE.)
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        END IF
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        DO I=1,Nat
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           IF (Renum) THEN
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              WRITE(IOOUT,'(1X,A2,3(1X,F15.6))') Nom(Atome(I)), &
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                   (XyzTmp2(Order(I),J),J=1,3)
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           ELSE
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              WRITE(IOOUT,'(1X,A2,3(1X,F15.6))') Nom(Atome(OrderInv(I))), &
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                   (XyzTmp2(I,J),J=1,3)
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           END IF
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        END DO
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     END IF ! matches if (print) THEN
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  END IF ! matches if (s>=0.9*dist) THEN
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  if (debug) WRITE(*,*) 's final =',s
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   if (debug) THEN
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      WRITE(*,*) "XPrimitiveF"
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      DO I=1,NGeomF
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        WRITE(*,'(1X,I5," : ",50(1X,F10.6))') I,XPrimitiveF(I,:)
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     END DO
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     END IF
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  DEALLOCATE(XyzTmp,XyzTmp2,IntCoord_interpol,IntCoord_k,Xyz_k)
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  if (printspline) CLOSE(IOTMP)
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  if (debug) WRITE(*,*) "================= Extrapol_baker Over ====================="
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END SUBROUTINE EXTRAPOL_BAKER