force_a12.f90 10.5 KB
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MODULE m_forcea12
! ************************************************************
! Pulay 1st term  force contribution a la Rici et al., eq. A12
!
! ************************************************************
!
CONTAINS
  SUBROUTINE force_a12(&
       atoms,nobd,sym, DIMENSION, cell,oneD,&
       we,jsp,ne,usdus,acof,bcof,e1cof,e2cof,&
       acoflo,bcoflo, results,f_a12)
    USE m_types
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    USE m_constants
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    IMPLICIT NONE

    TYPE(t_results),INTENT(INOUT)   :: results
    TYPE(t_dimension),INTENT(IN)    :: DIMENSION
    TYPE(t_oneD),INTENT(IN)         :: oneD
    TYPE(t_sym),INTENT(IN)          :: sym
    TYPE(t_cell),INTENT(IN)         :: cell
    TYPE(t_atoms),INTENT(IN)        :: atoms
    TYPE(t_usdus),INTENT(IN)        :: usdus
    !     ..
    !     .. Scalar Arguments ..
    INTEGER, INTENT (IN) :: nobd    
    INTEGER, INTENT (IN) :: ne ,jsp 
    !     ..
    !     .. Array Arguments ..
    REAL,    INTENT (IN) :: we(nobd) 
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    COMPLEX, INTENT (IN) ::  acof(nobd,0:atoms%lmaxd*(atoms%lmaxd+2),atoms%nat )
    COMPLEX, INTENT (IN) ::  bcof(nobd,0:atoms%lmaxd*(atoms%lmaxd+2),atoms%nat )
    COMPLEX, INTENT (IN) :: e1cof(nobd,0:atoms%lmaxd*(atoms%lmaxd+2),atoms%nat )
    COMPLEX, INTENT (IN) :: e2cof(nobd,0:atoms%lmaxd*(atoms%lmaxd+2),atoms%nat )
    COMPLEX, INTENT (IN) :: acoflo(-atoms%llod:atoms%llod,nobd,atoms%nlod,atoms%nat)
    COMPLEX, INTENT (IN) :: bcoflo(-atoms%llod:atoms%llod,nobd,atoms%nlod,atoms%nat)
    COMPLEX, INTENT (INOUT) :: f_a12(3,atoms%ntype)
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    !     ..
    !     .. Local Scalars ..
    COMPLEX a12,cil1,cil2
    REAL,PARAMETER:: zero=0.0
    COMPLEX,PARAMETER:: czero=CMPLX(0.0,0.0)
    COMPLEX,PARAMETER:: ci=CMPLX(0.0,1.0)
    INTEGER i,ie,irinv,is,isinv,it,j,l,l1,l2,lm1,lm2 ,m1,m2,n,natom,natrun,ilo,m
    !     ..
    !     .. Local Arrays ..
    COMPLEX forc_a12(3),gv(3)
    COMPLEX acof_flapw(nobd,0:DIMENSION%lmd),bcof_flapw(nobd,0:DIMENSION%lmd)
    REAL aaa(2),bbb(2),ccc(2),ddd(2),eee(2),fff(2),gvint(3),starsum(3),vec(3),vecsum(3)
    !     ..
    !     .. Statement Functions ..
    REAL   alpha,beta,delta,epslon,gamma,phi 
    INTEGER krondel
    !     ..
    !     .. Statement Function definitions ..
    !  inline functions:
    !
    ! Kronecker delta for arguments >=0 AND <0
    !
    !
    krondel(i,j) = MIN(ABS(i)+1,ABS(j)+1)/MAX(ABS(i)+1,ABS(j)+1)* (1+SIGN(1,i)*SIGN(1,j))/2
    alpha(l,m) = (l+1)*0.5e0*SQRT(REAL((l-m)* (l-m-1))/ REAL((2*l-1)* (2*l+1)))
    beta(l,m) = l*0.5e0*SQRT(REAL((l+m+2)* (l+m+1))/ REAL((2*l+1)* (2*l+3)))
    GAMMA(l,m) = (l+1)*0.5e0*SQRT(REAL((l+m)* (l+m-1))/ REAL((2*l-1)* (2*l+1)))
    delta(l,m) = l*0.5e0*SQRT(REAL((l-m+2)* (l-m+1))/ REAL((2*l+1)* (2*l+3)))
    epslon(l,m) = (l+1)*SQRT(REAL((l-m)* (l+m))/ REAL((2*l-1)* (2*l+1)))
    phi(l,m) = l*SQRT(REAL((l-m+1)* (l+m+1))/REAL((2*l+1)* (2*l+3)))
    !     ..
    !
    !
    natom = 1
    DO  n = 1,atoms%ntype
       IF (atoms%l_geo(n)) THEN
          forc_a12(:) = czero

          !
          DO natrun = natom,natom + atoms%neq(n) - 1

             gv(:) = czero

             !--->       the local orbitals do not contribute to
             !--->       the term a12, because they vanish at the
             !--->       mt-boundary. Therefore, the LO-contribution
             !--->       to the a and b coefficients has to be
             !--->       substracted before calculation a12.
             !
             DO l1 = 0,atoms%lmax(n)
                DO m1 = -l1,l1
                   lm1 = l1* (l1+1) + m1
                   DO ie = 1,ne
                      acof_flapw(ie,lm1) = acof(ie,lm1,natrun)
                      bcof_flapw(ie,lm1) = bcof(ie,lm1,natrun)
                   ENDDO
                ENDDO
             ENDDO
             DO ilo = 1,atoms%nlo(n)
                l1 = atoms%llo(ilo,n)
                DO m1 = -l1,l1
                   lm1 = l1* (l1+1) + m1
                   DO ie = 1,ne
                      acof_flapw(ie,lm1) = acof_flapw(ie,lm1) - acoflo(m1,ie,ilo,natrun)
                      bcof_flapw(ie,lm1) = bcof_flapw(ie,lm1) - bcoflo(m1,ie,ilo,natrun)
                   ENDDO
                ENDDO
             ENDDO
             !
             DO l1 = 0,atoms%lmax(n)
                cil1 = ci**l1
                DO m1 = -l1,l1
                   lm1 = l1* (l1+1) + m1
                   DO l2 = 0,atoms%lmax(n)
                      cil2 = ci**l2
                      DO m2 = -l2,l2
                         lm2 = l2* (l2+1) + m2
                         !
                         a12 = czero
                         DO ie = 1,ne
                            !
                            a12 = a12 + CONJG(cil1*&
                                 ( acof_flapw(ie,lm1)*usdus%us(l1,n,jsp) + bcof_flapw(ie,lm1)*usdus%uds(l1,n,jsp) ))*cil2*&
                                 ( e1cof(ie,lm2,natrun)*usdus%us(l2,n,jsp)+ e2cof(ie,lm2,natrun)*usdus%uds(l2,n,jsp))*we(ie)

                         END DO
                         aaa(1) = alpha(l1,m1)*krondel(l2,l1-1)* krondel(m2,m1+1)
                         aaa(2) = alpha(l2,m2)*krondel(l1,l2-1)* krondel(m1,m2+1)
                         bbb(1) = beta(l1,m1)*krondel(l2,l1+1)* krondel(m2,m1+1)
                         bbb(2) = beta(l2,m2)*krondel(l1,l2+1)* krondel(m1,m2+1)
                         ccc(1) = GAMMA(l1,m1)*krondel(l2,l1-1)* krondel(m2,m1-1)
                         ccc(2) = GAMMA(l2,m2)*krondel(l1,l2-1)* krondel(m1,m2-1)
                         ddd(1) = delta(l1,m1)*krondel(l2,l1+1)* krondel(m2,m1-1)
                         ddd(2) = delta(l2,m2)*krondel(l1,l2+1)* krondel(m1,m2-1)
                         eee(1) = epslon(l1,m1)*krondel(l2,l1-1)* krondel(m2,m1)
                         eee(2) = epslon(l2,m2)*krondel(l1,l2-1)* krondel(m1,m2)
                         fff(1) = phi(l1,m1)*krondel(l2,l1+1)* krondel(m2,m1)
                         fff(2) = phi(l2,m2)*krondel(l1,l2+1)* krondel(m1,m2)
                         !
                         gv(1) = gv(1) + (aaa(1)+bbb(1)-ccc(1)-ddd(1)+&
                              aaa(2)+bbb(2)-ccc(2)-ddd(2))*0.5* atoms%rmt(n)**2*a12
                         !
                         gv(2) = gv(2) + ci* (aaa(1)+bbb(1)+ccc(1)+&
                              ddd(1)-aaa(2)-bbb(2)-ccc(2)-ddd(2))*0.5* atoms%rmt(n)**2*a12
                         !
                         gv(3) = gv(3) + (eee(1)+eee(2)-fff(1)-fff(2))* 0.5*atoms%rmt(n)**2*a12
                         !
                         !  m1,m2 loops end
                      END DO
                   END DO
                   !  l1,l2 loops end
                END DO
             END DO
             !
             !  to complete summation over stars of k now sum
             !  over all operations which leave (k+G)*R(natrun)*taual(natrun)
             !  invariant. We sum over ALL these operations and not only
             !  the ones needed for the actual star of k. Should be
             !  ok if we divide properly by the number of operations
             !  First, we find operation S where RS=T. T -like R- leaves
             !  the above scalar product invariant (if S=1 then R=T).
             !  R is the operation which generates position of equivalent atom
             !  out of position of representative
             !  S=R^(-1) T
             !  number of ops which leave (k+G)*op*taual invariant: invarind
             !  index of inverse operation of R: irinv
             !  index of operation T: invarop
             !  now, we calculate index of operation S: is
             !
             !  transform vector gv into internal coordinates

             vec(:) = REAL(gv(:)) /atoms%neq(n)

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             gvint=MATMUL(cell%bmat,vec)/tpi_const
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             !

             vecsum(:) = zero

             !-gb2002
             !            irinv = invtab(ngopr(natrun))
             !            DO it = 1,invarind(natrun)
             !               is = multab(irinv,invarop(natrun,it))
             !c  note, actually we need the inverse of S but -in principle
             !c  because {S} is agroup and we sum over all S- S should also
             !c  work; to be lucid we take the inverse:
             !                isinv = invtab(is)
             !!               isinv = is
             ! Rotation is alreadt done in to_pulay, here we work only in the
             ! coordinate system of the representative atom (natom):
             !!        
             DO it = 1,sym%invarind(natom)
                is =sym%invarop(natom,it)
                isinv = sym%invtab(is)
                IF (oneD%odi%d1) isinv = oneD%ods%ngopr(natom)
                !-gb 2002
                !  now we have the wanted index of operation with which we have
                !  to rotate gv. Note gv is given in cart. coordinates but
                !  mrot acts on internal ones
                DO i = 1,3
                   vec(i) = zero
                   DO j = 1,3
                      IF (.NOT.oneD%odi%d1) THEN
                         vec(i) = vec(i) + sym%mrot(i,j,isinv)*gvint(j)
                      ELSE
                         vec(i) = vec(i) + oneD%ods%mrot(i,j,isinv)*gvint(j)
                      END IF
                   END DO
                END DO
                DO i = 1,3
                   vecsum(i) = vecsum(i) + vec(i)
                END DO
                !   end operator loop
             END DO
             !
             !   transform from internal to cart. coordinates
             starsum=MATMUL(cell%amat,vecsum)
             DO i = 1,3
                forc_a12(i) = forc_a12(i) + starsum(i)/sym%invarind(natrun)
             END DO
             !
             !  natrun loop end
          END DO
          !
          !
          !
          !     sum to existing forces
          !
          !  NOTE: force() is real and therefore takes only the
          !  real part of forc_a12(). in general, force must be
          !  real after k-star summation. Now, we put the proper
          !  operations into real space. Problem: what happens
          !  if in real space there is no inversion any more?
          !  But we have inversion in k-space due to time reversal
          !  symmetry, E(k)=E(-k)
          !  We argue that k-space inversion is automatically taken
          !  into account if force = (1/2)(forc_a12+conjg(forc_a12))
          !  because time reversal symmetry means that conjg(PSI)
          !  is also a solution of Schr. equ. if psi is one.
          DO i = 1,3
             results%force(i,n,jsp) = results%force(i,n,jsp) + REAL(forc_a12(i))
             f_a12(i,n)     = f_a12(i,n)     + forc_a12(i)
          END DO
          !
          !     write result moved to force_a8
          !
       ENDIF
       natom = natom + atoms%neq(n)
    ENDDO
    !
  END SUBROUTINE force_a12
END MODULE m_forcea12