TABLE OF CONTENTS
ABINIT/dfpt_sydy [ Functions ]
NAME
dfpt_sydy
FUNCTION
Symmetrize dynamical matrix (eventually diagonal wrt to the atoms) Unsymmetrized dynamical matrix is input as dyfrow; symmetrized dynamical matrix is then placed in sdyfro. If nsym=1 simply copy dyfrow into sdyfro.
COPYRIGHT
Copyright (C) 1999-2018 ABINIT group (XG,MT) 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
cplex=1 if dynamical matrix is real, 2 if it is complex dyfrow(3,3,natom,1+(natom-1)*nondiag)=unsymmetrized dynamical matrix indsym(4,msym*natom)=indirect indexing array: for each isym,iatom, fourth element is label of atom into which iatom is sent by INVERSE of symmetry operation isym; first three elements are the primitive translations which must be subtracted after the transformation to get back to the original unit cell. natom=number of atoms in cell. nondiag=0 if dynamical matrix is diagonal with respect to atoms nsym=number of symmetry operators in group. qphon(3)=wavevector of the phonon symq(4,2,nsym)=1 if symmetry preserves present qpoint. From littlegroup_q symrec(3,3,nsym)=symmetries of group in terms of operations on real space primitive translations (integers).
OUTPUT
sdyfro(3,3,natom,1+(natom-1)*nondiag)=symmetrized dynamical matrix
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
dfpt_dyfro
CHILDREN
SOURCE
62 #if defined HAVE_CONFIG_H 63 #include "config.h" 64 #endif 65 66 #include "abi_common.h" 67 68 69 subroutine dfpt_sydy(cplex,dyfrow,indsym,natom,nondiag,nsym,qphon,sdyfro,symq,symrec) 70 71 use defs_basis 72 use m_profiling_abi 73 74 !This section has been created automatically by the script Abilint (TD). 75 !Do not modify the following lines by hand. 76 #undef ABI_FUNC 77 #define ABI_FUNC 'dfpt_sydy' 78 !End of the abilint section 79 80 implicit none 81 82 !Arguments ------------------------------- 83 !scalars 84 integer,intent(in) :: cplex,natom,nondiag,nsym 85 !arrays 86 integer,intent(in) :: indsym(4,nsym,natom),symq(4,2,nsym),symrec(3,3,nsym) 87 real(dp),intent(in) :: dyfrow(cplex,3,3,natom,1+(natom-1)*nondiag),qphon(3) 88 real(dp),intent(out) :: sdyfro(cplex,3,3,natom,1+(natom-1)*nondiag) 89 90 !Local variables ------------------------- 91 !scalars 92 integer :: ia,indi,indj,isym,ja,kappa,mu,natom_nondiag,nsym_used,nu 93 logical :: qeq0 94 real(dp) :: arg,div,phasei,phaser 95 !arrays 96 real(dp) :: work(cplex,3,3) 97 98 ! ********************************************************************* 99 100 if (nsym==1) then 101 102 ! Only symmetry is identity so simply copy 103 sdyfro(:,:,:,:,:)=dyfrow(:,:,:,:,:) 104 105 else 106 107 ! Actually carry out symmetrization 108 sdyfro(:,:,:,:,:)=zero 109 qeq0=(qphon(1)**2+qphon(2)**2+qphon(3)**2<1.d-14) 110 ! === Diagonal dyn. matrix OR q=0 111 if (nondiag==0.or.qeq0) then 112 natom_nondiag=1;if (nondiag==1) natom_nondiag=natom 113 do ja=1,natom_nondiag 114 do ia=1,natom 115 do isym=1,nsym 116 indi=indsym(4,isym,ia) 117 indj=1;if (nondiag==1) indj=indsym(4,isym,ja) 118 work(:,:,:)=zero 119 do mu=1,3 120 do nu=1,3 121 do kappa=1,3 122 work(:,mu,kappa)=work(:,mu,kappa)+symrec(mu,nu,isym)*dyfrow(:,nu,kappa,indi,indj) 123 end do 124 end do 125 end do 126 do mu=1,3 127 do nu=1,3 128 do kappa=1,3 129 sdyfro(:,kappa,mu,ia,ja)=sdyfro(:,kappa,mu,ia,ja)+symrec(mu,nu,isym)*work(:,kappa,nu) 130 end do 131 end do 132 end do 133 end do 134 end do 135 end do 136 div=one/dble(nsym) 137 sdyfro(:,:,:,:,:)=div*sdyfro(:,:,:,:,:) 138 ! === Non diagonal dyn. matrix AND q<>0 139 else 140 do ja=1,natom 141 do ia=1,natom 142 nsym_used=0 143 do isym=1,nsym 144 if (symq(4,1,isym)==1) then 145 arg=two_pi*(qphon(1)*(indsym(1,isym,ia)-indsym(1,isym,ja)) & 146 & +qphon(2)*(indsym(2,isym,ia)-indsym(2,isym,ja)) & 147 & +qphon(3)*(indsym(3,isym,ia)-indsym(3,isym,ja))) 148 phaser=cos(arg);phasei=sin(arg) 149 nsym_used=nsym_used+1 150 indi=indsym(4,isym,ia) 151 indj=indsym(4,isym,ja) 152 work(:,:,:)=zero 153 do mu=1,3 154 do nu=1,3 155 do kappa=1,3 156 work(:,mu,kappa)=work(:,mu,kappa)+symrec(mu,nu,isym)*dyfrow(:,nu,kappa,indi,indj) 157 end do 158 end do 159 end do 160 do mu=1,3 161 do nu=1,3 162 do kappa=1,3 163 sdyfro(1,kappa,mu,ia,ja)=sdyfro(1,kappa,mu,ia,ja) & 164 & +symrec(mu,nu,isym)*(work(1,kappa,nu)*phaser-work(2,kappa,nu)*phasei) 165 end do 166 end do 167 end do 168 if (cplex==2) then 169 do mu=1,3 170 do nu=1,3 171 do kappa=1,3 172 sdyfro(2,kappa,mu,ia,ja)=sdyfro(2,kappa,mu,ia,ja) & 173 & +symrec(mu,nu,isym)*(work(1,kappa,nu)*phasei+work(2,kappa,nu)*phaser) 174 end do 175 end do 176 end do 177 end if 178 end if 179 end do 180 div=one/dble(nsym_used) 181 sdyfro(:,:,:,ia,ja)=div*sdyfro(:,:,:,ia,ja) 182 end do 183 end do 184 end if 185 186 end if 187 188 end subroutine dfpt_sydy