Chimie Théorique » Opt'n Path

     ! Geom = input parameter vector (Geometry), Grad = input gradient vector, HEAT is Energy(Geom)

      SUBROUTINE Step_GEDIIS_All(NGeomF,IGeom,Step,Geom,Grad,HEAT,Hess,NCoord,allocation_flag,Tangent)

!----------------------------------------------------------------------

! This routine was adapted from the public domain mopac6 diis.f

!  source file (c) 2009, Stewart Computational Chemistry.

!  <http://www.openmopac.net/Downloads/Downloads.html>

!

!----------------------------------------------------------------------

!  Copyright 2003-2014 Ecole Normale Supérieure de Lyon,

!  Centre National de la Recherche Scientifique,

!  Université Claude Bernard Lyon 1. All rights reserved.

!

!  This work is registered with the Agency for the Protection of Programs

!  as IDDN.FR.001.100009.000.S.P.2014.000.30625

!

!  Authors: P. Fleurat-Lessard, P. Dayal

!  Contact: optnpath@gmail.com

!

! This file is part of "Opt'n Path".

!

!  "Opt'n Path" is free software: you can redistribute it and/or modify

!  it under the terms of the GNU Affero General Public License as

!  published by the Free Software Foundation, either version 3 of the License,

!  or (at your option) any later version.

!

!  "Opt'n Path" is distributed in the hope that it will be useful,

!  but WITHOUT ANY WARRANTY; without even the implied warranty of

!

!  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

!  GNU Affero General Public License for more details.

!

!  You should have received a copy of the GNU Affero General Public License

!  along with "Opt'n Path". If not, see <http://www.gnu.org/licenses/>.

!

! Contact The Office of Technology Licensing, valorisation@ens-lyon.fr,

! for commercial licensing opportunities.

!----------------------------------------------------------------------

    use Io_module

    use Path_module, only :  Vfree

      IMPLICIT NONE

      INTEGER(KINT) :: NGeomF,IGeom

      INTEGER(KINT), INTENT(IN) :: NCoord

      REAL(KREAL) :: Geom(NCoord), Grad(NCoord), Hess(NCoord*NCoord), Step(NCoord)

    REAL(KREAL) :: HEAT ! HEAT= Energy

    LOGICAL :: allocation_flag

    REAL(KREAL), INTENT(INOUT) :: Tangent(Ncoord)

      ! MRESET = maximum number of iterations.

      INTEGER(KINT), PARAMETER :: MRESET=15, M2=(MRESET+1)*(MRESET+1) !M2 = 256

      REAL(KREAL), ALLOCATABLE, SAVE :: GeomSet(:,:), GradSet(:,:) ! NGeomF,MRESET*NCoord

      REAL(KREAL), ALLOCATABLE, SAVE :: GSAVE(:,:) !NGeomF,NCoord

    REAL(KREAL), ALLOCATABLE, SAVE :: ESET(:,:)

    REAL(KREAL) :: ESET_tmp(MRESET), B(M2), BS(M2), BST(M2), B_tmp(M2) ! M2=256

      LOGICAL :: DEBUG, PRINT, ci_lt_zero

      INTEGER(KINT), ALLOCATABLE, SAVE :: MSET(:) ! mth Iteration

    LOGICAL, ALLOCATABLE, SAVE :: FRST(:)

    REAL(KREAL) :: ci(MRESET), ci_tmp(MRESET) ! MRESET = maximum number of iterations.

      INTEGER(KINT) :: NGEDIIS, MPLUS, INV, ITERA, MM, cis_zero

      INTEGER(KINT) :: I, J, K, JJ, JNV, II, IONE, IJ, IX, JX, KX

    INTEGER(KINT) :: current_size_B_mat, MyPointer, Isch, NFree, Idx

      REAL(KREAL) :: XMax, XNorm, DET, THRES, tmp, ER_star, ER_star_tmp, Norm

    REAL(KREAL), PARAMETER :: eps=1e-12

      REAL(KREAL), PARAMETER :: crit=1e-8

    REAL(KREAL), ALLOCATABLE :: Tanf(:) ! NCoord

    REAL(KREAL), ALLOCATABLE :: HFree(:) ! NFree*NFree

    REAL(KREAL), ALLOCATABLE :: Htmp(:,:) ! NCoord,NFree

    REAL(KREAL), ALLOCATABLE :: Grad_free(:), Step_free(:) ! NFree

    REAL(KREAL), ALLOCATABLE :: Geom_free(:), Geom_new_free(:) ! NFree

    REAL(KREAL), ALLOCATABLE, SAVE :: GeomSet_free(:,:), GradSet_free(:,:)

      DEBUG=.TRUE.

      PRINT=.FALSE.

      IF (PRINT)  WRITE(*,'(/,''      BEGIN Step_GEDIIS_ALL   '')')

      ! Initialization

      IF (allocation_flag) THEN

      ! allocation_flag will be set to False in SPACE_GEDIIS, so no need to modify it here

         IF (ALLOCATED(GeomSet)) THEN

            IF (PRINT)  WRITE(*,'(/,''    In allocation_flag, GEDIIS_ALL  Dealloc  '')')

            DEALLOCATE(GeomSet,GradSet,GSave,GeomSet_free,GradSet_free)

            RETURN

         ELSE

            IF (PRINT)  WRITE(*,'(/,''     In allocation_flag,  GEDIIS_ALL  Alloc  '')')

            ALLOCATE(GeomSet(NGeomF,MRESET*NCoord),GradSet(NGeomF,MRESET*NCoord),GSAVE(NGeomF,NCoord))

      ALLOCATE(GeomSet_free(NGeomF,MRESET*NCoord),GradSet_free(NGeomF,MRESET*NCoord))

      ALLOCATE(MSET(NGeomF),FRST(NGeomF),ESET(NGeomF,MRESET))

      DO I=1,NGeomF

         FRST(I) = .TRUE.

         GeomSet(I,:) = 0.d0

         GradSet(I,:) = 0.d0

         GSAVE(I,:)=0.d0

         GeomSet_free(I,:) = 0.d0

         GradSet_free(I,:) = 0.d0

      END DO

      MSET(:)=0

         END IF

     allocation_flag = .FALSE.

      END IF ! IF (allocation_flag) THEN

    ! ADDED FROM HERE:

    Call FreeMv(NCoord,Vfree) ! VFree(Ncoord,Ncoord), as of now, an Identity matrix.

      ! we orthogonalize Vfree to the tangent vector of this geom only if Tangent/=0.d0

      Norm=sqrt(dot_product(Tangent,Tangent))

      IF (Norm.GT.eps) THEN

         ALLOCATE(Tanf(NCoord))

         ! We normalize Tangent

         Tangent=Tangent/Norm

         ! We convert Tangent into Vfree only displacements. This is useless for now (2007.Apr.23)

     ! as Vfree=Id matrix but it will be usefull as soon as we introduce constraints.

         DO I=1,NCoord

            Tanf(I)=dot_product(reshape(Vfree(:,I),(/NCoord/)),Tangent)

         END DO

         Tangent=0.d0

         DO I=1,NCoord

            Tangent=Tangent+Tanf(I)*Vfree(:,I)

         END DO

         ! first we subtract Tangent from vfree

         DO I=1,NCoord

            Norm=dot_product(reshape(vfree(:,I),(/NCoord/)),Tangent)

            Vfree(:,I)=Vfree(:,I)-Norm*Tangent

     END DO

         Idx=0

         ! Schmidt orthogonalization of the Vfree vectors

         DO I=1,NCoord

            ! We subtract the first vectors, we do it twice as the Schmidt procedure is not numerically stable.

            DO Isch=1,2

               DO J=1,Idx

                  Norm=dot_product(reshape(Vfree(:,I),(/NCoord/)),reshape(Vfree(:,J),(/NCoord/)))

                  Vfree(:,I)=Vfree(:,I)-Norm*Vfree(:,J)

               END DO

            END DO

            Norm=dot_product(reshape(Vfree(:,I),(/NCoord/)),reshape(Vfree(:,I),(/NCoord/)))

            IF (Norm.GE.crit) THEN

               Idx=Idx+1

               Vfree(:,Idx)=Vfree(:,I)/sqrt(Norm)

            END IF

         END DO

         IF (Idx/= NCoord-1) THEN

            WRITE(*,*) "Pb in orthogonalizing Vfree to tangent for geom",IGeom

            WRITE(IOOut,*) "Pb in orthogonalizing Vfree to tangent for geom",IGeom

            STOP

         END IF

         DEALLOCATE(Tanf)

         NFree=Idx

      ELSE ! Tangent =0, matches IF (Norm.GT.eps) THEN

         if (debug) WRITE(*,*) "Tangent=0, using full displacement"

         NFree=NCoord

      END IF !IF (Norm.GT.eps) THEN

      if (debug) WRITE(*,*) 'DBG Step_GEDIIS_All, IGeom, NFree=', IGeom, NFree

      ! We now calculate the new step

      ! we project the hessian onto the free vectors

      ALLOCATE(HFree(NFree*NFree),Htmp(NCoord,NFree),Grad_free(NFree))

    ALLOCATE(Geom_free(NFree),Step_free(NFree),Geom_new_free(NFree))

      DO J=1,NFree

        DO I=1,NCoord

           Htmp(I,J)=0.d0

           DO K=1,NCoord

              Htmp(I,J)=Htmp(I,J)+Hess(((I-1)*NCoord)+K)*Vfree(K,J)

           END DO

        END DO

      END DO

      DO J=1,NFree

        DO I=1,NFree

       HFree(I+((J-1)*NFree))=0.d0

           DO K=1,NCoord

        HFree(I+((J-1)*NFree))=HFree(I+((J-1)*NFree))+Vfree(K,I)*Htmp(K,J)

           END DO

        END DO

      END DO

      DO I=1,NFree

         Grad_free(I)=dot_product(reshape(Vfree(:,I),(/NCoord/)),Grad)

     Geom_free(I)=dot_product(reshape(Vfree(:,I),(/NCoord/)),Geom)

      END DO

      !ADDED ENDS HERE.***********************************************

      ! SPACE_GEDIIS SIMPLY LOADS THE CURRENT VALUES OF Geom AND Grad INTO THE ARRAYS GeomSet

      ! AND GradSet, MSET is set to zero and then 1 in SPACE_GEDIIS_All at first iteration.

      CALL SPACE_GEDIIS_All(NGeomF,IGeom,MRESET,MSET,Geom,Grad,HEAT,NCoord,GeomSet,GradSet,ESET,FRST)

      IF (PRINT)  WRITE(*,'(/,''       GEDIIS after SPACE_GEDIIS_ALL   '')')

    DO J=1,MSet(IGeom)

         DO K=1,NFree

            GradSet_free(IGeom,((J-1)*NFree)+K)=dot_product(reshape(Vfree(:,K),(/NCoord/)),&

               GradSet(IGeom,((J-1)*NCoord)+1:((J-1)*NCoord)+NCoord))

        GeomSet_free(IGeom,((J-1)*NFree)+K)=dot_product(reshape(Vfree(:,K),(/NCoord/)),&

                GeomSet(IGeom,((J-1)*NCoord)+1:((J-1)*NCoord)+NCoord))

         END DO

    END DO

      ! INITIALIZE SOME VARIABLES AND CONSTANTS:

      NGEDIIS = MSET(IGeom) !MSET=mth iteration

      MPLUS = MSET(IGeom) + 1

      MM = MPLUS * MPLUS

      ! CONSTRUCT THE GEDIIS MATRIX:

      ! B_ij calculations from <B_ij=(g_i-g_j)(R_i-R_j)>

      JJ=0

      INV=-NFree

      DO I=1,MSET(IGeom)

         INV=INV+NFree

         JNV=-NFree

         DO J=1,MSET(IGeom)

            JNV=JNV+NFree

            JJ = JJ + 1

            B(JJ)=0.D0

      DO K=1, NFree

         B(JJ) = B(JJ) + (((GradSet_free(IGeom,INV+K)-GradSet_free(IGeom,JNV+K))* &

                 (GeomSet_free(IGeom,INV+K)-GeomSet_free(IGeom,JNV+K)))/2.D0)

      END DO

         END DO

      END DO

     ! The following shifting is required to correct indices of B_ij elements in the GEDIIS matrix.

   ! The correction is needed because the last coloumn of the matrix contains all 1 and one zero.

      DO I=MSET(IGeom)-1,1,-1

         DO J=MSET(IGeom),1,-1

            B(I*MSET(IGeom)+J+I) = B(I*MSET(IGeom)+J)

         END DO

    END DO

      ! For the last row and last column of GEDIIS matrix:

      DO I=1,MPLUS

         B(MPLUS*I) = 1.D0

         B(MPLUS*MSET(IGeom)+I) = 1.D0

      END DO

      B(MM) = 0.D0

    DO I=1, MPLUS

       !WRITE(*,'(10(1X,F20.4))') B((I-1)*MPLUS+1:I*(MPLUS))

    END DO

      ! ELIMINATE ERROR VECTORS WITH THE LARGEST NORM:

   80 CONTINUE

      DO I=1,MM !MM = (MSET(IGeom)+1) * (MSET(IGeom)+1)

         BS(I) = B(I) !just a copy of the original B (GEDIIS) matrix

      END DO

      IF (NGEDIIS .NE. MSET(IGeom)) THEN

        DO II=1,MSET(IGeom)-NGEDIIS

           XMAX = -1.D10

           ITERA = 0

           DO I=1,MSET(IGeom)

              XNORM = 0.D0

              INV = (I-1) * MPLUS

              DO J=1,MSET(IGeom)

                 XNORM = XNORM + ABS(B(INV + J))

              END DO

              IF (XMAX.LT.XNORM .AND. XNORM.NE.1.0D0) THEN

                 XMAX = XNORM

                 ITERA = I

                 IONE = INV + I

              ENDIF

           END DO

           DO I=1,MPLUS

              INV = (I-1) * MPLUS

              DO J=1,MPLUS

                 JNV = (J-1) * MPLUS

                 IF (J.EQ.ITERA) B(INV + J) = 0.D0

                 B(JNV + I) = B(INV + J)

              END DO

       END DO

           B(IONE) = 1.0D0

        END DO

    END IF ! matches IF (NGEDIIS .NE. MSET(IGeom)) THEN

      ! SCALE GEDIIS MATRIX BEFORE INVERSION:

      DO I=1,MPLUS

         II = MPLUS * (I-1) + I ! B(II)=diagonal elements of B matrix

         GSAVE(IGeom,I) = 1.D0 / DSQRT(1.D-20+DABS(B(II)))

     !Print *, 'GSAVE(',IGeom,',',I,')=', GSAVE(IGeom,I)

      END DO

      GSAVE(IGeom,MPLUS) = 1.D0

      DO I=1,MPLUS

         DO J=1,MPLUS

            IJ = MPLUS * (I-1) + J

            B(IJ) = B(IJ) * GSAVE(IGeom,I) * GSAVE(IGeom,J)

         END DO

      END DO

     ! INVERT THE GEDIIS MATRIX B:

    DO I=1, MPLUS

       !WRITE(*,'(10(1X,F20.4))') B((I-1)*MPLUS+1:I*(MPLUS))

    END DO

      CALL MINV(B,MPLUS,DET) ! matrix inversion.

    DO I=1, MPLUS

       !WRITE(*,'(10(1X,F20.16))') B((I-1)*MPLUS+1:I*(MPLUS))

    END DO

      DO I=1,MPLUS

         DO J=1,MPLUS

            IJ = MPLUS * (I-1) + J

            B(IJ) = B(IJ) * GSAVE(IGeom,I) * GSAVE(IGeom,J)

         END DO

      END DO

      ! COMPUTE THE NEW INTERPOLATED PARAMETER VECTOR (Geometry):

    ci=0.d0

    ci_tmp=0.d0

    ci_lt_zero= .FALSE.

    DO I=1, MSET(IGeom)

     DO J=1, MSET(IGeom) ! B matrix is read column-wise

        ci(I)=ci(I)+B((J-1)*(MPLUS)+I)*ESET(IGeom,J) !ESET is energy set.

     END DO

     ci(I)=ci(I)+B((MPLUS-1)*(MPLUS)+I)

     !Print *, 'NO ci < 0 yet, c(',I,')=', ci(I)

     IF((ci(I) .LT. 0.0D0) .OR. (ci(I) .GT. 1.0D0)) THEN

       ci_lt_zero=.TRUE.

       EXIT

     END IF

      END DO !matches DO I=1, MSET(IGeom)

    IF (ci_lt_zero) Then

       cis_zero = 0

         ER_star = 0.D0

     ER_star_tmp = 1e32

     ! B_ij calculations from <B_ij=(g_i-g_j)(R_i-R_j)>, Full B matrix created first and then rows and columns are removed.

         JJ=0

         INV=-NFree

         DO IX=1,MSET(IGeom)

            INV=INV+NFree

            JNV=-NFree

            DO JX=1,MSET(IGeom)

               JNV=JNV+NFree

               JJ = JJ + 1

               BST(JJ)=0.D0

           DO KX=1, NFree

              BST(JJ) = BST(JJ) + (((GradSet_free(IGeom,INV+KX)-GradSet_free(IGeom,JNV+KX))* &

                    (GeomSet_free(IGeom,INV+KX)-GeomSet_free(IGeom,JNV+KX)))/2.D0)

           END DO

            END DO

       END DO

     DO I=1, (2**MSET(IGeom))-2 ! all (2**MSET(IGeom))-2 combinations of cis, except the one where all cis are .GT. 0 and .LT. 1

         !Print *, 'Entering into DO I=1, (2**MSET(IGeom))-2  loop, MSET(IGeom)=', MSET(IGeom), ', I=', I

         ci(:)=1.D0

         ! find out which cis are zero in I:

       DO IX=1, MSET(IGeom)

          JJ=IAND(I, 2**(IX-1))

        IF(JJ .EQ. 0) Then

          ci(IX)=0.D0

          END IF

       END DO

       ci_lt_zero = .FALSE.

       ! B_ij calculations from <B_ij=(g_i-g_j)(R_i-R_j)>, Full B matrix created first and then rows and columns are removed.

       DO IX=1, MSET(IGeom)*MSET(IGeom)

                B(IX) = BST(IX) !just a copy of the original B (GEDIIS) matrix

             END DO

             ! Removal of KXth row and KXth column in order to accomodate cI to be zero:

       current_size_B_mat=MSET(IGeom)

       cis_zero = 0

       ! The bits of I (index of the upper loop 'DO I=1, (2**MSET(IGeom))-2'), gives which cis are zero.

       DO KX=1, MSET(IGeom) ! searching for each bit of I (index of the upper loop 'DO I=1, (2**MSET(IGeom))-2')

          IF (ci(KX) .EQ. 0.D0) Then !remove KXth row and KXth column

           cis_zero = cis_zero + 1

             ! First row removal: (B matrix is read column-wise)

             JJ=0

                   DO IX=1,current_size_B_mat ! columns reading

                      DO JX=1,current_size_B_mat ! rows reading

                 IF (JX .NE. KX) Then

                     JJ = JJ + 1

                     B_tmp(JJ) = B((IX-1)*current_size_B_mat+JX)

                 END IF

              END DO

             END DO

             DO IX=1,current_size_B_mat*(current_size_B_mat-1)

                B(IX) = B_tmp(IX)

             END DO

             ! Now column removal:

             JJ=0

                   DO IX=1,KX-1 ! columns reading

                      DO JX=1,current_size_B_mat-1 ! rows reading

                 JJ = JJ + 1

                 B_tmp(JJ) = B(JJ)

              END DO

             END DO

                   DO IX=KX+1,current_size_B_mat

                      DO JX=1,current_size_B_mat-1

                 JJ = JJ + 1

                    B_tmp(JJ) = B(JJ+current_size_B_mat-1)

              END DO

             END DO

             DO IX=1,(current_size_B_mat-1)*(current_size_B_mat-1)

                B(IX) = B_tmp(IX)

             END DO

           current_size_B_mat = current_size_B_mat - 1

        END IF ! matches IF (ci(KX) .EQ. 0.D0) Then !remove

           END DO ! matches DO KX=1, MSET(IGeom)

       ! The following shifting is required to correct indices of B_ij elements in the GEDIIS matrix.

       ! The correction is needed because the last coloumn and row of the matrix contains all 1 and one zero.

       DO IX=MSET(IGeom)-cis_zero-1,1,-1

        DO JX=MSET(IGeom)-cis_zero,1,-1

           B(IX*(MSET(IGeom)-cis_zero)+JX+IX) = B(IX*(MSET(IGeom)-cis_zero)+JX)

        END DO

       END DO

       ! for last row and last column of GEDIIS matrix

       DO IX=1,MPLUS-cis_zero

        B((MPLUS-cis_zero)*IX) = 1.D0

        B((MPLUS-cis_zero)*(MSET(IGeom)-cis_zero)+IX) = 1.D0

       END DO

       B((MPLUS-cis_zero) * (MPLUS-cis_zero)) = 0.D0

           DO IX=1, MPLUS

              !WRITE(*,'(10(1X,F20.4))') B((IX-1)*MPLUS+1:IX*(MPLUS))

           END DO

       ! ELIMINATE ERROR VECTORS WITH THE LARGEST NORM:

             IF (NGEDIIS .NE. MSET(IGeom)) THEN

          JX = min(MSET(IGeom)-NGEDIIS,MSET(IGeom)-cis_zero-1)

                DO II=1,JX

                   XMAX = -1.D10

                   ITERA = 0

                   DO IX=1,MSET(IGeom)-cis_zero

                      XNORM = 0.D0

                      INV = (IX-1) * (MPLUS-cis_zero)

                      DO J=1,MSET(IGeom)-cis_zero

                         XNORM = XNORM + ABS(B(INV + J))

                      END DO

                      IF (XMAX.LT.XNORM .AND. XNORM.NE.1.0D0) THEN

                         XMAX = XNORM

                         ITERA = IX

                         IONE = INV + IX

                      ENDIF

           END DO

                   DO IX=1,MPLUS-cis_zero

                      INV = (IX-1) * (MPLUS-cis_zero)

                      DO J=1,MPLUS-cis_zero

                         JNV = (J-1) * (MPLUS-cis_zero)

                         IF (J.EQ.ITERA) B(INV + J) = 0.D0

                         B(JNV + IX) = B(INV + J)

            END DO

               END DO

                   B(IONE) = 1.0D0

          END DO

           END IF ! matches IF (NGEDIIS .NE. MSET(IGeom)) THEN

       ! SCALE GEDIIS MATRIX BEFORE INVERSION:

       DO IX=1,MPLUS-cis_zero

        II = (MPLUS-cis_zero) * (IX-1) + IX ! B(II)=diagonal elements of B matrix

        GSAVE(IGeom,IX) = 1.D0 / DSQRT(1.D-20+DABS(B(II)))

       END DO

       GSAVE(IGeom,MPLUS-cis_zero) = 1.D0

       DO IX=1,MPLUS-cis_zero

        DO JX=1,MPLUS-cis_zero

           IJ = (MPLUS-cis_zero) * (IX-1) + JX

           B(IJ) = B(IJ) * GSAVE(IGeom,IX) * GSAVE(IGeom,JX)

        END DO

       END DO

       ! INVERT THE GEDIIS MATRIX B:

       CALL MINV(B,MPLUS-cis_zero,DET) ! matrix inversion.

       DO IX=1,MPLUS-cis_zero

        DO JX=1,MPLUS-cis_zero

           IJ = (MPLUS-cis_zero) * (IX-1) + JX

           B(IJ) = B(IJ) * GSAVE(IGeom,IX) * GSAVE(IGeom,JX)

        END DO

       END DO

           DO IX=1, MPLUS

              !WRITE(*,'(10(1X,F20.4))') B((IX-1)*MPLUS+1:IX*(MPLUS))

           END DO

             ! ESET is rearranged to handle zero cis and stored in ESET_tmp:

       JJ=0

       DO IX=1, MSET(IGeom)

        IF (ci(IX) .NE. 0) Then

           JJ=JJ+1

           ESET_tmp(JJ) = ESET(IGeom,IX)

        END IF

       END DO

       ! DETERMINATION OF nonzero cis:

       MyPointer=1

            DO IX=1, MSET(IGeom)-cis_zero

          tmp = 0.D0

            DO J=1, MSET(IGeom)-cis_zero ! B matrix is read column-wise

           tmp=tmp+B((J-1)*(MPLUS-cis_zero)+IX)*ESET_tmp(J)

        END DO

            tmp=tmp+B((MPLUS-cis_zero-1)*(MPLUS-cis_zero)+IX)

            IF((tmp .LT. 0.0D0) .OR. (tmp .GT. 1.0D0)) THEN

               ci_lt_zero=.TRUE.

               EXIT

        ELSE

           DO JX=MyPointer,MSET(IGeom)

              IF (ci(JX) .NE. 0) Then

                 ci(JX) = tmp

               MyPointer=JX+1

               EXIT

            END IF

           END DO

            END IF

             END DO !matches DO I=1, MSET(IGeom)-cis_zero

           !Print *, 'Local set of cis, first 10:, MSET(IGeom)=', MSET(IGeom), ', I of (2**MSET(IGeom))-2=', I

       !WRITE(*,'(10(1X,F20.4))') ci(1:MSET(IGeom))

           !Print *, 'Local set of cis ends:****************************************'

             ! new set of cis determined based on the lower energy (ER_star):

       IF (.NOT. ci_lt_zero) Then

                Call Energy_GEDIIS(MRESET,MSET(IGeom),ci,GeomSet_free(IGeom,:),GradSet_free(IGeom,:),ESET(IGeom,:),NFree,ER_star)

        IF (ER_star .LT. ER_star_tmp) Then

           ci_tmp=ci

           ER_star_tmp = ER_star

        END IF

             END IF ! matches IF (.NOT. ci_lt_zero) Then

          END DO !matches DO I=1, (2**K)-2 ! all (2**K)-2 combinations of cis, except the one where all cis are .GT. 0 and .LT. 1

      ci = ci_tmp

    END IF! matches IF (ci_lt_zero) Then

    Print *, 'Final set of cis, first 10:***********************************'

    WRITE(*,'(10(1X,F20.4))') ci(1:MSET(IGeom))

    Print *, 'Final set of cis ends:****************************************'

    Geom_new_free(:) = 0.D0

    DO I=1, MSET(IGeom)

         Geom_new_free(:) = Geom_new_free(:) + (ci(I)*GeomSet_free(IGeom,(I-1)*NFree+1:I*NFree)) !MPLUS=MSET(IGeom)+1

     ! R_(N+1)=R*+DeltaR:

     DO J=1, NFree

      tmp=0.D0

      DO K=1,NFree

         ! this can be commented:

         !tmp=tmp+HFree((J-1)*NFree+K)*GradSet_free(IGeom,(I-1)*NFree+K) ! If Hinv=.False., then we need to invert Hess

      END DO

      Geom_new_free(J) = Geom_new_free(J) - (ci(I)*tmp)

     END DO

    END DO

    Step_free(:) =  Geom_new_free(:) - Geom_free(:)

      XNORM = SQRT(DOT_PRODUCT(Step_free,Step_free))

      IF (PRINT) THEN

         WRITE (6,'(/10X,''DEVIATION IN X '',F10.4,8X,''DETERMINANT '',G9.3)') XNORM, DET

         !WRITE(*,'(10X,''GEDIIS COEFFICIENTS'')')

         !WRITE(*,'(10X,5F12.5)') (B(MPLUS*MSET(IGeom)+I),I=1,MSET(IGeom))

      ENDIF

      ! THE FOLLOWING TOLERENCES FOR XNORM AND DET ARE SOMEWHAT ARBITRARY!

      THRES = MAX(10.D0**(-NFree), 1.D-25)

      IF (XNORM.GT.2.D0 .OR. DABS(DET) .LT. THRES) THEN

         IF (PRINT)THEN

            WRITE(*,*) "THE GEDIIS MATRIX IS ILL CONDITIONED"

            WRITE(*,*) " - PROBABLY, VECTORS ARE LINEARLY DEPENDENT - "

            WRITE(*,*) "THE GEDIIS STEP WILL BE REPEATED WITH A SMALLER SPACE"

         END IF

         DO K=1,MM

      B(K) = BS(K) ! why this is reverted? Because "IF (NGEDIIS .GT. 0) GO TO 80", see below

         END DO

         NGEDIIS = NGEDIIS - 1

         IF (NGEDIIS .GT. 0) GO TO 80

         IF (PRINT) WRITE(*,'(10X,''NEWTON-RAPHSON STEP TAKEN'')')

         Geom_new_free(:) = Geom_free(:) ! Geom_new is set to original Geom, thus Step = Geom(:) - Geom_new(:)=zero, the whole

                           ! new update to Geom_new is discarded, since XNORM.GT.2.D0 .OR. DABS(DET) .LT. THRES

      END IF ! matches IF (XNORM.GT.2.D0 .OR. DABS(DET).LT. THRES) THEN

    !******************************************************************************************************************

    Geom_new_free(:) = 0.D0

    DO I=1, MSET(IGeom)

         Geom_new_free(:) = Geom_new_free(:) + (ci(I)*GeomSet_free(IGeom,(I-1)*NFree+1:I*NFree)) !MPLUS=MSET(IGeom)+1

     ! R_(N+1)=R*+DeltaR:

     DO J=1, NFree

      tmp=0.D0

      DO K=1,NFree

         tmp=tmp+HFree((J-1)*NFree+K)*GradSet_free(IGeom,(I-1)*NFree+K) ! If Hinv=.False., then we need to invert Hess

      END DO

      Geom_new_free(J) = Geom_new_free(J) - (ci(I)*tmp)

     END DO

    END DO

    Step_free(:) =  Geom_new_free(:) - Geom_free(:)

   !******************************************************************************************************************

    Step = 0.d0

      DO I=1,NFree

     Step = Step + Step_free(I)*Vfree(:,I)

      END DO

      DEALLOCATE(Hfree,Htmp,Grad_free,Step_free,Geom_free,Geom_new_free)

      IF (PRINT)  WRITE(*,'(/,''       END Step_GEDIIS_ALL   '',/)')

      END SUBROUTINE Step_GEDIIS_All