TABLE OF CONTENTS
ABINIT/symatm [ Functions ]
NAME
symatm
FUNCTION
This routine has been improved using ideas of p. 649 of notes, implementing suggestion of Andrew Horsfield: replace search for equivalent atoms using direct primitive cell translations by use of dot product relation which must produce an integer. Relation: $[inv(S(i))*(x(a)-tnons(i)) - x(inv(S)(i,a))] = integer$ where $S(i) =$ symmetry matrix in real space, tnons=nonsymmorphic translation (may be 0 0 0), and $x(inv(S)(i,a))$ is sought atom into which $x(a)$ gets rotated by $inv(S)$. Integer gives primitive translation coordinates to get back to original unit cell. Equivalent to $S*t(b)+tnons-x(a)=another$ $integer$ for $x(b)=x(inv(S))$. For each symmetry operation, find the number of the position to which each atom is sent in the unit cell by the INVERSE of the symmetry operation inv(symrel); i.e. this is the atom which, when acted upon by the given symmetry element isym, gets transformed into atom iatom. This routine uses the fact that inv(symrel)=trans(symrec), the inverse of the symmetry operation expressed in the basis of real space primitive translations equals the transpose of the same symmetry operation expressed in the basis of reciprocal space primitive transl. $xred(nu,indsym(4,isym,ia))=symrec(mu,nu,isym)*(xred(mu,ia)-tnons(mu,isym)) - transl(mu)$ where $transl$ is also a set of integers and where translation transl places coordinates within unit cell (note sign). Note that symrec is the set of arrays which are actually input here. These arrays have integer elements. tnons is the nonsymmorphic translation or else is zero. If nsym=1 (i.e. only the identity symmetry is present) then indsym merely takes each atom into itself. The array of integer translations "transl" gets included within array "indsym" as seen below.
COPYRIGHT
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. nsym=number of space group symmetries. symrec(3,3,nsym)=symmetries expressed in terms of their action on reciprocal space primitive translations (integer). tnons(3,nsym)=nonsymmorphic translations for each symmetry (would be 0 0 0 each for a symmorphic space group) typat(natom)=integer identifying type of atom. xred(3,natom)=reduced coordinates of atoms in terms of real space primitive translations tolsym=tolerance for the symmetries
OUTPUT
indsym(4,nsym,natom)=indirect indexing array described above: 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.
PARENTS
get_npert_rbz,ingeo,initberry,initorbmag,m_ab7_symmetry,m_crystal,m_ddb m_polynomial_coeff,m_tdep_sym,setsym,thmeig
CHILDREN
symchk,wrtout
SOURCE
72 #if defined HAVE_CONFIG_H 73 #include "config.h" 74 #endif 75 76 #include "abi_common.h" 77 78 subroutine symatm(indsym,natom,nsym,symrec,tnons,tolsym,typat,xred) 79 80 use defs_basis 81 use m_errors 82 use m_profiling_abi 83 84 !This section has been created automatically by the script Abilint (TD). 85 !Do not modify the following lines by hand. 86 #undef ABI_FUNC 87 #define ABI_FUNC 'symatm' 88 use interfaces_14_hidewrite 89 use interfaces_41_geometry, except_this_one => symatm 90 !End of the abilint section 91 92 implicit none 93 94 !Arguments ------------------------------------ 95 !scalars 96 integer,intent(in) :: natom,nsym 97 real(dp), intent(in) :: tolsym 98 !arrays 99 integer,intent(in) :: symrec(3,3,nsym),typat(natom) 100 integer,intent(out) :: indsym(4,nsym,natom) 101 real(dp),intent(in) :: tnons(3,nsym),xred(3,natom) 102 103 !Local variables------------------------------- 104 !scalars 105 integer :: eatom,errout,iatom,ii,isym,mu 106 real(dp) :: difmax,err 107 character(len=500) :: message 108 !arrays 109 integer :: transl(3) 110 real(dp) :: difmin(3),tratom(3) 111 112 ! ************************************************************************* 113 114 err=zero 115 errout=0 116 117 do isym=1,nsym 118 do iatom=1,natom 119 120 do mu=1,3 ! Apply inverse transformation to original coordinates. Note transpose of symrec. 121 tratom(mu) = dble(symrec(1,mu,isym))*(xred(1,iatom)-tnons(1,isym))& 122 & +dble(symrec(2,mu,isym))*(xred(2,iatom)-tnons(2,isym))& 123 & +dble(symrec(3,mu,isym))*(xred(3,iatom)-tnons(3,isym)) 124 end do 125 ! 126 ! Find symmetrically equivalent atom 127 call symchk(difmin,eatom,natom,tratom,transl,typat(iatom),typat,xred) 128 ! 129 ! Put information into array indsym: translations and label 130 indsym(1,isym,iatom)=transl(1) 131 indsym(2,isym,iatom)=transl(2) 132 indsym(3,isym,iatom)=transl(3) 133 indsym(4,isym,iatom)=eatom 134 ! 135 ! Keep track of maximum difference between transformed coordinates and 136 ! nearest "target" coordinate 137 difmax=max(abs(difmin(1)),abs(difmin(2)),abs(difmin(3))) 138 err=max(err,difmax) 139 140 if (difmax>tolsym) then ! Print warnings if differences exceed tolerance 141 write(message, '(3a,i3,a,i6,a,i3,a,a,3es12.4,3a)' )& 142 & 'Trouble finding symmetrically equivalent atoms',ch10,& 143 & 'Applying inv of symm number',isym,' to atom number',iatom,' of typat',typat(iatom),ch10,& 144 & 'gives tratom=',tratom(1:3),'.',ch10,& 145 & 'This is further away from every atom in crystal than the allowed tolerance.' 146 MSG_WARNING(message) 147 148 write(message, '(a,3i3,a,a,3i3,a,a,3i3)' ) & 149 & ' The inverse symmetry matrix is',symrec(1,1:3,isym),ch10,& 150 & ' ',symrec(2,1:3,isym),ch10,& 151 & ' ',symrec(3,1:3,isym) 152 call wrtout(std_out,message,'COLL') 153 write(message, '(a,3f13.7)' )' and the nonsymmorphic transl. tnons =',(tnons(mu,isym),mu=1,3) 154 155 call wrtout(std_out,message,'COLL') 156 write(message, '(a,1p,3e11.3,a,a,i5)' ) & 157 & ' The nearest coordinate differs by',difmin(1:3),ch10,& 158 & ' for indsym(nearest atom)=',indsym(4,isym,iatom) 159 call wrtout(std_out,message,'COLL') 160 ! 161 ! Use errout to reduce volume of error diagnostic output 162 if (errout==0) then 163 write(message,'(6a)') ch10,& 164 & ' This indicates that when symatm attempts to find atoms symmetrically',ch10, & 165 & ' related to a given atom, the nearest candidate is further away than some',ch10,& 166 & ' tolerance. Should check atomic coordinates and symmetry group input data.' 167 call wrtout(std_out,message,'COLL') 168 errout=1 169 end if 170 171 end if !difmax>tol 172 end do !iatom 173 end do !isym 174 175 if (.FALSE.) then 176 do iatom=1,natom 177 write(message, '(a,i0,a)' )' symatm: atom number ',iatom,' is reached starting at atom' 178 call wrtout(std_out,message,'COLL') 179 do ii=1,(nsym-1)/24+1 180 if(natom<100)then 181 write(message, '(1x,24i3)' ) (indsym(4,isym,iatom),isym=1+(ii-1)*24,min(nsym,ii*24)) 182 else 183 write(message, '(1x,24i6)' ) (indsym(4,isym,iatom),isym=1+(ii-1)*24,min(nsym,ii*24)) 184 end if 185 call wrtout(std_out,message,'COLL') 186 end do 187 end do 188 end if 189 190 if (err>tolsym) then 191 write(message, '(1x,a,1p,e14.5,a,e12.4)' )'symatm: maximum (delta t)=',err,' is larger than tol=',tolsym 192 call wrtout(std_out,message,'COLL') 193 end if 194 195 !Stop execution if error is really big 196 if (err>0.01d0) then 197 write(message,'(5a)')& 198 & 'Largest error (above) is so large (0.01) that either input atomic coordinates (xred)',ch10,& 199 & 'are wrong or space group symmetry data is wrong.',ch10,& 200 & 'Action : correct your input file.' 201 MSG_ERROR(message) 202 end if 203 204 end subroutine symatm