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MODULE m_cored
CONTAINS
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   SUBROUTINE cored(input, jspin, atoms, rho, DIMENSION, sphhar, vr, qint, rhc, tec, seig, EnergyDen)
      !     *******************************************************
      !     *****   set up the core densities for compounds.  *****
      !     *****                      d.d.koelling           *****
      !     *******************************************************
      USE m_juDFT
      USE m_intgr, ONLY : intgr3,intgr0,intgr1
      USE m_constants, ONLY : c_light,sfp_const
      USE m_setcor
      USE m_differ
      USE m_types
      USE m_xmlOutput
      IMPLICIT NONE
      TYPE(t_dimension),INTENT(IN)   :: DIMENSION
      TYPE(t_input),INTENT(IN)       :: input
      TYPE(t_sphhar),INTENT(IN)      :: sphhar
      TYPE(t_atoms),INTENT(IN)       :: atoms
      !
      !     .. Scalar Arguments ..
      INTEGER, INTENT (IN) :: jspin
      REAL,    INTENT (OUT) :: seig
      !     ..
      !     .. Array Arguments ..
      REAL, INTENT(IN)              :: vr(atoms%jmtd,atoms%ntype)
      REAL, INTENT(INOUT)           :: rho(atoms%jmtd,0:sphhar%nlhd,atoms%ntype,input%jspins)
      REAL, INTENT(INOUT)           :: rhc(DIMENSION%msh,atoms%ntype,input%jspins)
      REAL, INTENT(INOUT)           :: qint(atoms%ntype,input%jspins)
      REAL, INTENT(INOUT)           :: tec(atoms%ntype,input%jspins)
      REAL, INTENT(INOUT), OPTIONAL :: EnergyDen(atoms%jmtd,0:sphhar%nlhd,atoms%ntype,input%jspins)
      !     ..
      !     .. Local Scalars ..
      REAL eig,fj,fl,fn,q,rad,rhos,rhs,sea,sume,t2
      REAL d,dxx,rn,rnot,z,t1,rr,r,lambd,c,bmu,weight, aux_weight
      INTEGER i,j,jatom,korb,n,ncmsh,nm,nm1,nst ,l,ierr
      !     ..
      !     .. Local Arrays ..

      REAL rhcs(DIMENSION%msh),rhoc(DIMENSION%msh),rhoss(DIMENSION%msh),vrd(DIMENSION%msh),f(0:3)
      REAL rhcs_aux(DIMENSION%msh), rhoss_aux(DIMENSION%msh) !> quantities for energy density calculations
      REAL occ(DIMENSION%nstd),a(DIMENSION%msh),b(DIMENSION%msh),ain(DIMENSION%msh),ahelp(DIMENSION%msh)
      REAL occ_h(DIMENSION%nstd,2)
      INTEGER kappa(DIMENSION%nstd),nprnc(DIMENSION%nstd)
      CHARACTER(LEN=20) :: attributes(6)
      REAL stateEnergies(29)
      !     ..
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      c = c_light(1.0)
      seig = 0.
      !
      IF (input%frcor) THEN
         DO  n = 1,atoms%ntype
            rnot = atoms%rmsh(1,n) ; dxx = atoms%dx(n)
            ncmsh = NINT( LOG( (atoms%rmt(n)+10.0)/rnot ) / dxx + 1 )
            ncmsh = MIN( ncmsh, DIMENSION%msh )
            !     --->    update spherical charge density
            DO  i = 1,atoms%jri(n)
               rhoc(i) = rhc(i,n,jspin)
               rho(i,0,n,jspin) = rho(i,0,n,jspin) + rhoc(i)/sfp_const
            ENDDO
            !     ---> for total energy calculations, determine the sum of the
            !     ---> eigenvalues by requiring that the core kinetic energy
            !     ---> remains constant.
            DO  i = 1,atoms%jri(n)
               rhoc(i) = rhoc(i)*vr(i,n)/atoms%rmsh(i,n)
            ENDDO
            nm = atoms%jri(n)
            CALL intgr3(rhoc,atoms%rmsh(1,n),atoms%dx(n),nm,rhos)
            sea = tec(n,jspin) + rhos
            WRITE (6,FMT=8030) n,jspin,tec(n,jspin),sea
            seig = seig + atoms%neq(n)*sea
         ENDDO
         RETURN
      END IF

      !     ---> set up densities
      DO  jatom = 1,atoms%ntype
         sume = 0.
         z = atoms%zatom(jatom)
         !         rn = rmt(jatom)
         dxx = atoms%dx(jatom)
         bmu = 0.0
         CALL setcor(jatom,input%jspins,atoms,input,bmu,nst,kappa,nprnc,occ_h)
         IF ((bmu > 99.)) THEN
            occ(1:nst) = input%jspins *  occ_h(1:nst,jspin)
         ELSE
            occ(1:nst) = occ_h(1:nst,1)
         ENDIF
         rnot = atoms%rmsh(1,jatom)
         d = EXP(atoms%dx(jatom))
         ncmsh = NINT( LOG( (atoms%rmt(jatom)+10.0)/rnot ) / dxx + 1 )
         ncmsh = MIN( ncmsh, DIMENSION%msh )
         rn = rnot* (d** (ncmsh-1))
         WRITE (6,FMT=8000) z,rnot,dxx,atoms%jri(jatom)
         DO  j = 1,atoms%jri(jatom)
            rhoss(j)     = 0.0
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            if(present(EnergyDen)) rhoss_aux(j) = 0.0
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            vrd(j) = vr(j,jatom)
         ENDDO
         !
         IF (input%l_core_confpot) THEN
            !--->    linear extension of the potential with slope t1 / a.u.
            t1=0.125
            t1 = MAX( (vrd(atoms%jri(jatom)) - vrd(atoms%jri(jatom)-1)*d)*&
                     d / (atoms%rmt(jatom)**2 * (d-1) ) , t1)
            t2=vrd(atoms%jri(jatom))/atoms%rmt(jatom)-atoms%rmt(jatom)*t1
            rr = atoms%rmt(jatom)
         ELSE
            t2 = vrd(atoms%jri(jatom)) / ( atoms%jri(jatom) - ncmsh )
         ENDIF
         IF ( atoms%jri(jatom) < ncmsh) THEN
            DO  i = atoms%jri(jatom) + 1,ncmsh
               rhoss(i) = 0.
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               if(present(EnergyDen)) rhoss_aux(i) = 0.0
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               IF (input%l_core_confpot) THEN
                  rr = d*rr
                  vrd(i) = rr*( t2 + rr*t1 )
                  !               vrd(i) = 2*vrd(jri(jatom)) - rr*( t2 + rr*t1 )
               ELSE
                  vrd(i) = vrd(atoms%jri(jatom)) + t2* (i-atoms%jri(jatom))
               ENDIF
               !
            ENDDO
         END IF

         nst = atoms%ncst(jatom)        ! for lda+U

         IF (input%gw==1 .OR. input%gw==3)&
              &                      WRITE(15) nst,atoms%rmsh(1:atoms%jri(jatom),jatom)

         stateEnergies = 0.0
         DO  korb = 1,nst
            IF (occ(korb) /= 0.0) THEN
               fn = nprnc(korb)
               fj = iabs(kappa(korb)) - .5e0

               weight = 2*fj + 1.e0
               IF (bmu > 99.) weight = occ(korb)

               fl = fj + (.5e0)*isign(1,kappa(korb))
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               eig        = -2* (z/ (fn+fl))**2

               CALL differ(fn,fl,fj,c,z,dxx,rnot,rn,d,ncmsh,vrd, eig, a,b,ierr)
               stateEnergies(korb) = eig
               WRITE (6,FMT=8010) fn,fl,fj,eig,weight
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               IF (ierr/=0)  CALL juDFT_error("error in core-level routine" ,calledby ="cored")
               IF (input%gw==1 .OR. input%gw==3) WRITE (15) NINT(fl),weight,eig,&
                  a(1:atoms%jri(jatom)),b(1:atoms%jri(jatom))

               sume = sume + weight*eig/input%jspins
               DO j = 1,ncmsh
                  rhcs(j)  = weight* (a(j)**2+b(j)**2)
                  rhoss(j) = rhoss(j) + rhcs(j)
               ENDDO

               IF(present(EnergyDen)) THEN
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                  !rhoss_aux = rhoss
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                  DO j = 1,ncmsh
                     ! for energy density we want to multiply the weights
                     ! with the eigenenergies
                     rhoss_aux(j) = rhoss_aux(j) + (rhcs(j) * eig)
                  ENDDO
               ENDIF
            ENDIF
         ENDDO
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         !     ---->update spherical charge density rho with the core density.
         !     ---->for spin-polarized (jspins=2), take only half the density
         nm = atoms%jri(jatom)
         DO  j = 1,nm
            rhoc(j) = rhoss(j)/input%jspins
            rho(j,0,jatom,jspin) = rho(j,0,jatom,jspin) + rhoc(j)/sfp_const
         ENDDO

         IF(present(EnergyDen)) then
            DO  j = 1,nm
               EnergyDen(j,0,jatom,jspin) = EnergyDen(j,0,jatom,jspin) &
                                            + rhoss_aux(j) /(input%jspins * sfp_const)
            ENDDO
         ENDIF

         rhc(1:ncmsh,jatom,jspin)   = rhoss(1:ncmsh) / input%jspins
         rhc(ncmsh+1:DIMENSION%msh,jatom,jspin) = 0.0

         seig = seig + atoms%neq(jatom)*sume
         DO  i = 1,nm
            rhoc(i) = rhoc(i)*vr(i,jatom)/atoms%rmsh(i,jatom)
         ENDDO
         CALL intgr3(rhoc,atoms%rmsh(1,jatom),atoms%dx(jatom),nm,rhs)
         tec(jatom,jspin) = sume - rhs
         WRITE (6,FMT=8030) jatom,jspin,tec(jatom,jspin),sume
195
         
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         !     ---> simpson integration
         rad = atoms%rmt(jatom)
         q = rad*rhoss(nm)/2.
         DO  nm1 = nm + 1,ncmsh - 1,2
            rad = d*rad
            q = q + 2*rad*rhoss(nm1)
            rad = d*rad
            q = q + rad*rhoss(nm1+1)
         ENDDO
         q = 2*q*dxx/3
         !+sb
         WRITE (6,FMT=8020) q/input%jspins
         !-sb
         qint(jatom,jspin) = q*atoms%neq(jatom)
         attributes = ''
         WRITE(attributes(1),'(i0)') jatom
         WRITE(attributes(2),'(i0)') NINT(z)
         WRITE(attributes(3),'(i0)') jspin
         WRITE(attributes(4),'(f18.10)') tec(jatom,jspin)
         WRITE(attributes(5),'(f18.10)') sume
         WRITE(attributes(6),'(f9.6)') q/input%jspins
         CALL openXMLElementForm('coreStates',(/'atomType     ','atomicNumber ','spin         ','kinEnergy    ',&
                                                'eigValSum    ','lostElectrons'/),&
                                 attributes,RESHAPE((/8,12,4,9,9,13,6,3,1,18,18,9/),(/6,2/)))
         DO korb = 1, atoms%ncst(jatom)
            fj = iabs(kappa(korb)) - .5e0
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            weight = 2*fj + 1.e0
            IF (bmu > 99.) weight = occ(korb)
            fl = fj + (.5e0)*isign(1,kappa(korb))
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            attributes = ''
            WRITE(attributes(1),'(i0)') nprnc(korb)
            WRITE(attributes(2),'(i0)') NINT(fl)
            WRITE(attributes(3),'(f4.1)') fj
            WRITE(attributes(4),'(f20.10)') stateEnergies(korb)
            WRITE(attributes(5),'(f15.10)') weight
            CALL writeXMLElementForm('state',(/'n     ','l     ','j     ','energy','weight'/),&
                                     attributes(1:5),RESHAPE((/1,1,1,6,6,2,2,4,20,15/),(/5,2/)))
         END DO
         CALL closeXMLElement('coreStates')
      ENDDO

      RETURN

8000  FORMAT (/,/,10x,'z=',f4.0,5x,'r(1)=',e14.6,5x,'dx=',f9.6,5x,&
          &       'm.t.index=',i4,/,15x,'n',4x,'l',5x,'j',4x,'energy',7x,&
          &       'weight')
8010  FORMAT (12x,2f5.0,f6.1,f10.4,f12.4)
8020  FORMAT (f20.8,'  electrons lost from core.')
8030  FORMAT (10x,'atom type',i3,'  (spin',i2,') ',/,10x,&
          &       'kinetic energy=',e20.12,5x,'sum of the eigenvalues=',&
          &       e20.12)
   END SUBROUTINE cored
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END MODULE m_cored