./67_common/sygrad.F90

ABINIT/sygrad

ABINIT/sygrad [ Functions ]

NAME

 sygrad

FUNCTION

 Symmetrize derivatives of energy with respect to coordinates.
 Unsymmetrized gradients are input as dedt; symmetrized grads are then
 placed in fred.
 If nsym=1 simply copy dedt into fred (only symmetry is identity).

 Copyright (C) 1998-2018 ABINIT group (DCA, XG, GMR)
 This file is distributed under the terms of the
 GNU General Public License, see ~abinit/COPYING
 or http://www.gnu.org/copyleft/gpl.txt .
 For the initials of contributors, see ~abinit/doc/developers/contributors.txt .

INPUTS

  natom=number of atoms in cell
  dedt(3,natom)=unsymmetrized gradients wrt dimensionless tn (hartree)
  nsym=number of symmetry operators in group
  symrec(3,3,nsym)=symmetries of group in terms of operations on
    reciprocal space primitive translations--see comments below
  indsym(4,nsym,natom)=label given by subroutine symatm, indicating atom
   label which gets rotated into given atom by given symmetry
   (first three elements are related primitive translation--
   see symatm where this is computed)

OUTPUT

 fred(3,3,natom)=symmetrized gradients wrt reduced coordinates (hartree)

NOTES

 symmetrization of gradients with respect to reduced
 coordinates tn is conducted according to the expression
 $[d(e)/d(t(n,a))]_{symmetrized} = (1/Nsym)*Sum(S)*symrec(n,m,S)*
              [d(e)/d(t(m,b))]_{unsymmetrized}$
 where $t(m,b)= (symrel^{-1})(m,n)*(t(n,a)-tnons(n))$ and tnons
 is a possible nonsymmorphic translation.  The label "b" here
 refers to the atom which gets rotated into "a" under symmetry "S".
 symrel is the symmetry matrix in real space, which is the inverse
 transpose of symrec.  symrec is the symmetry matrix in reciprocal
 space.  $sym_{cartesian} = R * symrel * R^{-1} = G * symrec * G^{-1}$
 where the columns of R and G are the dimensional primitive translations
 in real and reciprocal space respectively.
 Note the use of "symrec" in the symmetrization expression above.

PARENTS

      forces

CHILDREN

SOURCE

 56 #if defined HAVE_CONFIG_H
 57 #include "config.h"
 58 #endif
 59 
 60 #include "abi_common.h"
 61 
 62 
 63 subroutine sygrad(fred,natom,dedt,nsym,symrec,indsym)
 64 
 65  use m_profiling_abi
 66 
 67  use defs_basis
 68 
 69 !This section has been created automatically by the script Abilint (TD).
 70 !Do not modify the following lines by hand.
 71 #undef ABI_FUNC
 72 #define ABI_FUNC 'sygrad'
 73 !End of the abilint section
 74 
 75  implicit none
 76 
 77 !Arguments ------------------------------------
 78 !scalars
 79  integer,intent(in) :: natom,nsym
 80 !arrays
 81  integer,intent(in) :: indsym(4,nsym,natom),symrec(3,3,nsym)
 82  real(dp),intent(in) :: dedt(3,natom)
 83  real(dp),intent(out) :: fred(3,natom)
 84 
 85 !Local variables-------------------------------
 86 !scalars
 87  integer :: ia,ind,isym,mu
 88  real(dp),parameter :: tol=1.0d-30
 89  real(dp) :: summ
 90 
 91 ! *************************************************************************
 92 !
 93  if (nsym==1) then
 94 !  only symmetry is identity so simply copy
 95    fred(:,:)=dedt(:,:)
 96  else
 97 !  actually conduct symmetrization
 98    do ia=1,natom
 99      do mu=1,3
100        summ=0._dp
101        do isym=1,nsym
102          ind=indsym(4,isym,ia)
103          summ=summ+dble(symrec(mu,1,isym))*dedt(1,ind)+&
104 &         dble(symrec(mu,2,isym))*dedt(2,ind)+&
105 &         dble(symrec(mu,3,isym))*dedt(3,ind)
106        end do
107        fred(mu,ia)=summ/dble(nsym)
108        if(abs(fred(mu,ia))<tol)fred(mu,ia)=0.0_dp
109      end do
110    end do
111  end if
112 
113 end subroutine sygrad

TABLE OF CONTENTS

ABINIT/sygrad [ Functions ]