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calQ.f90
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! Fortran code to calculate Order Parameter Q
! Zhipan Liu Group 2020
! Use YLMB FORTRAN code from internet
subroutine Get_Order_parameter(na,iza,cell,xa,atom,Qglobal, ene, sym)
implicit none
integer:: namx !,lmax
parameter(namx=100)
integer::na,ntol,i,j,i1,i2,i3,k,bond,l,m,super(3),km,atom,totalbond,control,Iiza
integer :: iza(na),maxiza,miniza, sym
double precision,allocatable , save ::xac(:,:),xa0(:,:),r0(:,:)
double precision xa(3,na),r1,cell0(3,3)
double precision Q1,co1,co2
double precision alpha,Pi,Qlocal(4),Qglobal(4)
double precision dist_all,dist,dtmp,r(3),cell(3,3),celli(3,3)
double precision rij(namx*namx),theta(namx*namx),phi(namx*namx),radi(namx*namx),rmax
double precision :: ene
logical, save :: first=.true.
COMPLEX*16 Y(49),Q(49),Qall(49)
logical CONT
integer:: imode=1
save maxiza,miniza
Pi=3.14159265359d0
alpha=1.0d0
rmax=10.0d0
if(first) then
allocate(xac(3,na),xa0(3,na),r0(na,na))
first = .false.
maxiza=0
miniza=100
do i=1,na
do j=1,na
call fastbond(iza(i),iza(j),r0(i,j))
if(r0(i,j) < 0.05d0) then
call species_radius(iza(i),co1)
call species_radius(iza(j),co2)
r0(i,j) = co1 + co2
if(r0(i,j) < 0.5d0) then
r0(i,j)=2d0
endif
end if
enddo
enddo
endif
if(atom==0) then
Iiza=0 !maxiza
else
Iiza=atom
endif
xa0=xa
cell0=cell
if(Imode>=0) then
call cellconstraint(na,cell0,xa0,1)
endif
call reclat_loc(cell0, celli, 0)
do i = 1,na
xac(:,i) = matmul(transpose(celli),xa0(:,i))
xac(:,i)= modulo(xac(:,i)+100.0d0,1.0d0)
enddo
do k = 1,na
do j = 1,3
xa0(j,k) = cell0(j,1) * xac(1,k) + cell0(j,2) * xac(2,k) + cell0(j,3) * xac(3,k)
enddo
enddo
CONT=.false.
Qall=0.0d0
Qlocal=0d0
totalbond=0
super=0
if(Imode>=0) super(:)= 6
do km=1 , na
bond=1
if(iza(km)==Iiza .or. Iiza==0) then !goto 90
j=km
! write(6,'(A,3f12.4)') 'Si ', xa0(1,j),xa0(2,j),xa0(3,j)
Q=0d0
do i=1,na
! if((iza(i)/=iza(j) .or. CONT) ) then !.and. i/=j) then
do i1=-super(1),super(1)
do i2=-super(2),super(2)
do i3=-super(3),super(3)
r(:)=(xac(1,i)+dble(i1))*cell0(:,1)+(xac(2,i)+ &
dble(i2))*cell0(:,2)+(xac(3,i)+dble(i3))*cell0(:,3) - xa0(:,j)
r1=dsqrt(sum(r*r))
if(r1 > 20d0) cycle ! 20 cutoff radius
if(r1>r0(i,j)*0.6d0 .and. r1<r0(i,j)*1.3d0) bond=bond+1
if(r1>r0(i,j)*0.6d0 .and. r1<r0(i,j)*1.3d0 ) then
!
call YLMB(r,6,Y) ! sphe_harm(l,m,theta(i),phi(i))
Q=Q+Y
Qall=Qall+Y
endif
enddo
enddo
enddo
! endif
enddo
if(bond>1) bond=bond-1
do j=0,6,2
Q1=0d0
do i=j*j+1,(j+1)*(j+1)
Q1=Q1+Q(i)*DCONJG(Q(i))
enddo
Q1=sqrt(4.0d0*Pi*Q1/(2.0d0*dble(j)+1.0d0))
Q1=Q1/dble(na)/dble(bond)
Qlocal(j/2+1)=Q1+Qlocal(j/2+1)
enddo
endif ! Iiza
enddo ! km
Qglobal=Qlocal
End subroutine
subroutine fastbond(zi,zj,bondlen)
double precision,dimension(53,53),save :: bondmap
integer :: zi,zj,i,j
double precision :: bondlen
logical ,save :: init=.true.
if(init) then
bondmap=0d0
bondmap(1,1) = 0.80
bondmap(1,5) = 1.084
bondmap(1,6) = 1.084
bondmap(1,7) = 1.001
bondmap(1,8) = 0.947
bondmap(1,9) = 0.92
bondmap(1,14) = 1.48
bondmap(1,15) = 1.415
bondmap(1,16) = 1.326
bondmap(1,17) = 1.28
bondmap(1,35) = 1.41
bondmap(1,53) = 1.60
bondmap(5,8) = 1.512
bondmap(6,6) = 1.512
bondmap(6,7) = 1.439
bondmap(6,8) = 1.393
bondmap(6,9) = 1.353
bondmap(6,14) = 1.86
bondmap(6,15) = 1.84
bondmap(6,16) = 1.812
bondmap(6,17) = 1.781
bondmap(6,35) = 1.94
bondmap(6,53) = 2.16
bondmap(7,7) = 1.283
bondmap(7,8) = 1.333
bondmap(7,9) = 1.36
bondmap(7,14) = 1.74
bondmap(7,15) = 1.65
bondmap(7,16) = 1.674
bondmap(7,17) = 1.75
bondmap(7,35) = 1.90
bondmap(7,53) = 2.10
bondmap(8,8) = 1.45
bondmap(8,9) = 1.42
bondmap(8,14) = 1.63
bondmap(8,15) = 1.66
bondmap(8,16) = 1.470
bondmap(8,17) = 1.70
bondmap(8,22) = 2.1 ! Ti-O
bondmap(8,35) = 1.85
bondmap(8,53) = 2.05
bondmap(9,14) = 1.57
bondmap(9,15) = 1.54
bondmap(9,16) = 1.55
bondmap(14,8) = 2.0
bondmap(14,14) = 2.32
bondmap(14,15) = 2.25
bondmap(14,16) = 2.15
bondmap(14,17) = 2.02
bondmap(14,35) = 2.19
bondmap(14,53) = 2.44
bondmap(15,15) = 2.21
bondmap(15,16) = 2.10
bondmap(15,17) = 2.03
bondmap(15,35) = 2.21
bondmap(15,53) = 2.47
bondmap(16,16) = 2.052
bondmap(16,17) = 2.04
bondmap(16,35) = 2.24
bondmap(16,53) = 2.40
bondmap(17,17) = 1.99
bondmap(35,35) = 2.28
bondmap(53,53) = 2.67
init = .false.
end if
if(zi > 53 .or. zj > 53) then
bondlen = 0.0d0
else
if(zi<zj) then
bondlen = bondmap(zi,zj)
else
bondlen = bondmap(zj,zi)
end if
end if
end subroutine
subroutine species_radius(atom,radius)
integer::atom
double precision::radius
radius=0.0d0
if(atom==1) radius=0.400d0
if(atom==2) radius=0.490d0
if(atom==3) radius=1.400d0
if(atom==4) radius=1.400d0
if(atom==5) radius=1.170d0
if(atom==6) radius=0.650d0
if(atom==7) radius=0.620d0
if(atom==8) radius=0.600d0
if(atom==9) radius=0.570d0
if(atom==10) radius=0.510d0
if(atom==11) radius=2.230d0
if(atom==12) radius=1.720d0
if(atom==13) radius=1.820d0
if(atom==14) radius=1.222d0
if(atom==15) radius=1.230d0
if(atom==16) radius=1.120d0
if(atom==17) radius=1.120d0
if(atom==18) radius=0.880d0
if(atom==19) radius=2.770d0
if(atom==20) radius=2.230d0
if(atom==21) radius=2.090d0
if(atom==22) radius=2.000d0
if(atom==23) radius=1.920d0
if(atom==24) radius=1.850d0
if(atom==25) radius=1.790d0
if(atom==26) radius=1.720d0
if(atom==27) radius=1.670d0
if(atom==28) radius=1.350d0
if(atom==29) radius=1.570d0
if(atom==30) radius=1.530d0
if(atom==31) radius=1.810d0
if(atom==32) radius=1.520d0
if(atom==33) radius=1.330d0
if(atom==34) radius=1.170d0
if(atom==35) radius=1.120d0
if(atom==36) radius=1.030d0
if(atom==37) radius=2.210d0
if(atom==38) radius=1.860d0
if(atom==39) radius=2.270d0
if(atom==40) radius=2.160d0
if(atom==41) radius=2.080d0
if(atom==42) radius=2.010d0
if(atom==43) radius=1.950d0
if(atom==44) radius=1.340d0
if(atom==45) radius=1.340d0
if(atom==46) radius=1.340d0
if(atom==47) radius=1.340d0
if(atom==48) radius=1.340d0
if(atom==49) radius=2.000d0
if(atom==50) radius=1.720d0
if(atom==51) radius=1.530d0
if(atom==52) radius=1.420d0
if(atom==53) radius=1.320d0
if(atom==54) radius=1.240d0
if(atom==55) radius=3.340d0
if(atom==56) radius=2.780d0
if(atom==57) radius=2.740d0
if(atom==58) radius=2.700d0
if(atom==59) radius=2.670d0
if(atom==60) radius=2.640d0
if(atom==61) radius=2.620d0
if(atom==62) radius=2.590d0
if(atom==63) radius=2.560d0
if(atom==64) radius=2.540d0
if(atom==65) radius=2.510d0
if(atom==66) radius=2.490d0
if(atom==67) radius=2.470d0
if(atom==68) radius=2.450d0
if(atom==69) radius=2.420d0
if(atom==70) radius=2.400d0
if(atom==71) radius=2.250d0
if(atom==72) radius=2.160d0
if(atom==73) radius=2.090d0
if(atom==74) radius=2.020d0
if(atom==75) radius=1.370d0
if(atom==76) radius=1.320d0
if(atom==77) radius=1.370d0
if(atom==78) radius=1.350d0
if(atom==79) radius=1.350d0
if(atom==80) radius=1.760d0
if(atom==81) radius=2.080d0
if(atom==82) radius=1.810d0
if(atom==83) radius=1.630d0
if(atom==84) radius=1.530d0
if(atom==85) radius=1.430d0
if(atom==86) radius=1.340d0
end subroutine
subroutine cellconstraint(na,cell,xa,control)
implicit none
double precision :: cell(3,3),xa(3,na),aplusb,zz
integer :: iv, i,ix,ia,j,na,k,i0,j0,k0,m,control
double precision :: cellm(3), ang(3),celang(3),cell2(3,3),celli(3,3),Pi,cell0(3,3)
double precision :: latt_abc(3),latt_ang0(3),latt_ang(3),alplp,betlp,gamlp,alp,blp,latt_abc2(3)
double precision :: clp,xac(3),xxx,ab(3),abl
logical CONT,SSWoutput
logical , save :: first = .true.
integer, save :: change(50,4) ,Lastchange(50,4) !,last_m
! data last_m /0/
SSWoutput=.false.
if(first) then
Lastchange=0
first=.false.
endif
Pi=3.1415926535897932384626d0
cell0=cell
call outcell_output_loc(cell,latt_abc,latt_ang)
! write(6,'(A8,6F15.10)') 'cell0',latt_abc,latt_ang
! change=0
! endif
if(.true.) then
! last_m=m
change=0
m=0
291 continue
m=m+1
do iv = 1,3
cellm(iv) = dot_product(cell(:,iv),cell(:,iv))
cellm(iv) = dabs(cellm(iv))
enddo
i=minloc(cellm,1)
j=maxloc(cellm,1)
if(i==j) then
i=1
j=2
k=3
else
k=6-i-j
endif
zz = dot_product(cell(:,i),cell(:,j))
ab(:)=cell(:,j)-ceiling(dabs(zz)/cellm(i))*sign(1.0d0,zz)*cell(:,i)
if( sqrt(sum(ab**2))<sqrt(cellm(j))-1d-14) then
cell(:,j)=ab
change(m,1)=1
change(m,2)=i
change(m,3)=j
goto 291
endif
ab(:)=cell(:,j)-floor(dabs(zz)/cellm(i))*sign(1.0d0,zz)*cell(:,i)
if( sqrt(sum(ab**2))<sqrt(cellm(j))-1d-14) then
cell(:,j)=ab
change(m,1)=3
change(m,2)=i
change(m,3)=j
goto 291
endif
celang(:) = cell(:,i)+cell(:,k)
aplusb=sum(celang*celang)
aplusb= dabs(aplusb)
zz = dot_product(cell(:,j),celang(:))
ab(:)=cell(:,j)-ceiling(dabs(zz)/aplusb)*sign(1.0d0,zz)*celang(:)
if( sqrt(sum(ab**2))<sqrt(cellm(j))-1d-14) then
cell(:,j)=ab
change(m,1)=2
change(m,2)=i
change(m,3)=k
change(m,4)=j
goto 291
endif
ab(:)=cell(:,j)-floor(dabs(zz)/aplusb)*sign(1.0d0,zz)*celang(:)
if( sqrt(sum(ab**2))<sqrt(cellm(j))-1d-14) then
cell(:,j)=ab
change(m,1)=4
change(m,2)=i
change(m,3)=k
change(m,4)=j
goto 291
endif
celang(:) = cell(:,i)-cell(:,k)
aplusb=sum(celang*celang)
aplusb= dabs(aplusb)
zz = dot_product(cell(:,j),celang(:))
ab(:)=cell(:,j)-ceiling(dabs(zz)/aplusb)*sign(1.0d0,zz)*celang(:)
if( sqrt(sum(ab**2))<sqrt(cellm(j))-1d-14) then
cell(:,j)=ab
change(m,1)=2
change(m,2)=i
change(m,3)=-k
change(m,4)=j
goto 291
endif
ab(:)=cell(:,j)-floor(dabs(zz)/aplusb)*sign(1.0d0,zz)*celang(:)
if( sqrt(sum(ab**2))<sqrt(cellm(j))-1d-14) then
cell(:,j)=ab
change(m,1)=4
change(m,2)=i
change(m,3)=-k
change(m,4)=j
goto 291
endif
celang(:) = cell(:,i)+cell(:,j)
aplusb=sum(celang*celang)
aplusb= dabs(aplusb)
zz = dot_product(cell(:,k),celang(:))
ab(:)=cell(:,k)-ceiling(dabs(zz)/aplusb)*sign(1.0d0,zz)*celang(:)
if( sqrt(sum(ab**2))<sqrt(cellm(k))-1d-14) then
cell(:,k)=ab
change(m,1)=2
change(m,2)=i
change(m,3)=j
change(m,4)=k
goto 291
endif
ab(:)=cell(:,k)-floor(dabs(zz)/aplusb)*sign(1.0d0,zz)*celang(:)
if( sqrt(sum(ab**2))<sqrt(cellm(k))-1d-14) then
cell(:,k)=ab
change(m,1)=4
change(m,2)=i
change(m,3)=j
change(m,4)=k
goto 291
endif
celang(:) = cell(:,i)-cell(:,j)
aplusb=sum(celang*celang)
aplusb= dabs(aplusb)
zz = dot_product(cell(:,k),celang(:))
ab(:)=cell(:,k)-ceiling(dabs(zz)/aplusb)*sign(1.0d0,zz)*celang(:)
if( sqrt(sum(ab**2))<sqrt(cellm(k))-1d-14) then
cell(:,k)=ab
change(m,1)=2
change(m,2)=i
change(m,3)=-j
change(m,4)=k
goto 291
endif
ab(:)=cell(:,k)-floor(dabs(zz)/aplusb)*sign(1.0d0,zz)*celang(:)
if( sqrt(sum(ab**2))<sqrt(cellm(k))-1d-14) then
cell(:,k)=ab
change(m,1)=4
change(m,2)=i
change(m,3)=-j
change(m,4)=k
goto 291
endif
celang(:) = cell(:,k)+cell(:,j)
aplusb=sum(celang*celang)
aplusb= dabs(aplusb)
zz = dot_product(cell(:,i),celang(:))
ab(:)=cell(:,i)-ceiling(dabs(zz)/aplusb)*sign(1.0d0,zz)*celang(:)
if( sqrt(sum(ab**2))<sqrt(cellm(i))-1d-14) then
cell(:,i)=ab
change(m,1)=2
change(m,2)=k
change(m,3)=j
change(m,4)=i
goto 291
endif
ab(:)=cell(:,i)-floor(dabs(zz)/aplusb)*sign(1.0d0,zz)*celang(:)
if( sqrt(sum(ab**2))<sqrt(cellm(i))-1d-14) then
cell(:,i)=ab
change(m,1)=4
change(m,2)=k
change(m,3)=j
change(m,4)=i
goto 291
endif
celang(:) = cell(:,k)-cell(:,j)
aplusb=sum(celang*celang)
aplusb= dabs(aplusb)
zz = dot_product(cell(:,i),celang(:))
ab(:)=cell(:,i)-ceiling(dabs(zz)/aplusb)*sign(1.0d0,zz)*celang(:)
if( sqrt(sum(ab**2))<sqrt(cellm(i))-1d-14) then
cell(:,i)=ab
change(m,1)=2
change(m,2)=k
change(m,3)=-j
change(m,4)=i
goto 291
endif
ab(:)=cell(:,i)-floor(dabs(zz)/aplusb)*sign(1.0d0,zz)*celang(:)
if( sqrt(sum(ab**2))<sqrt(cellm(i))-1d-14) then
cell(:,i)=ab
change(m,1)=4
change(m,2)=k
change(m,3)=-j
change(m,4)=i
goto 291
endif
zz = dot_product(cell(:,i),cell(:,k))
ab(:)=cell(:,k)-ceiling(dabs(zz)/cellm(i))*sign(1.0d0,zz)*cell(:,i)
if( sqrt(sum(ab**2))<sqrt(cellm(k))-1d-14) then
cell(:,k)=ab
change(m,1)=1
change(m,2)=i
change(m,3)=k
goto 291
endif
ab(:)=cell(:,k)-floor(dabs(zz)/cellm(i))*sign(1.0d0,zz)*cell(:,i)
if( sqrt(sum(ab**2))<sqrt(cellm(k))-1d-14) then
cell(:,k)=ab
change(m,1)=3
change(m,2)=i
change(m,3)=k
goto 291
endif
zz = dot_product(cell(:,k),cell(:,j))
ab(:)=cell(:,j)-ceiling(dabs(zz)/cellm(k))*sign(1.0d0,zz)*cell(:,k)
if( sqrt(sum(ab**2))<sqrt(cellm(j))-1d-14) then
cell(:,j)=ab
change(m,1)=1
change(m,2)=k
change(m,3)=j
goto 291
endif
ab(:)=cell(:,j)-floor(dabs(zz)/cellm(k))*sign(1.0d0,zz)*cell(:,k)
if( sqrt(sum(ab**2))<sqrt(cellm(j))-1d-14) then
cell(:,j)=ab
change(m,1)=3
change(m,2)=k
change(m,3)=j
goto 291
endif
if(SSWoutput) then
do i=1,m-1
write(6,*) change(i,1:4)
enddo
! write(6,*) 'lattice change in cellconstraint',m-1
endif
if(m>1.or.Lastchange(1,1)/=0) then
do i=1,50
do j=1,4
if(change(i,j)/=Lastchange(i,j)) then
goto 45
endif
enddo
enddo
endif
45 continue
Lastchange=change
else !if(.not.LallowRot) then
m=1
do while (change(m,1)/=0)
do iv = 1,3
cellm(iv) = dot_product(cell(:,iv),cell(:,iv))
cellm(iv) = dabs(cellm(iv))
enddo
if(change(m,1)==1) then
j=change(m,3)
i=change(m,2)
zz = dot_product(cell(:,i),cell(:,j))
cell(:,j)=cell(:,j)-ceiling(dabs(zz)/cellm(i))*sign(1.0d0,zz)*cell(:,i)
elseif(change(m,1)==2) then
i=change(m,2)
k=change(m,3)
j=change(m,4)
if(k>0) then
celang(:) = cell(:,i)+cell(:,k)
else
celang(:) = cell(:,i)-cell(:,k)
endif
aplusb=sum(celang*celang)
aplusb= dabs(aplusb)
zz = dot_product(cell(:,j),celang(:))
cell(:,j)=cell(:,j)-ceiling(dabs(zz)/aplusb)*sign(1.0d0,zz)*celang(:)
elseif(change(m,1)==3) then
j=change(m,3)
i=change(m,2)
zz = dot_product(cell(:,i),cell(:,j))
cell(:,j)=cell(:,j)-floor(dabs(zz)/cellm(i))*sign(1.0d0,zz)*cell(:,i)
elseif(change(m,1)==4) then
i=change(m,2)
k=change(m,3)
j=change(m,4)
if(k>0) then
celang(:) = cell(:,i)+cell(:,k)
elseif(k<0) then
celang(:) = cell(:,i)-cell(:,k)
endif
aplusb=sum(celang*celang)
aplusb= dabs(aplusb)
zz = dot_product(cell(:,j),celang(:))
cell(:,j)=cell(:,j)-floor(dabs(zz)/aplusb)*sign(1.0d0,zz)*celang(:)
endif
m=m+1
enddo
endif ! LallowRot end
292 continue
cell2=cell
call outcell_output_loc(cell,latt_abc,latt_ang)
! write(6,'(A8,6F15.10)') 'cell1',latt_abc,latt_ang
alplp=latt_ang(3)* pi/180.d0
betlp=latt_ang(2)* pi/180.d0
gamlp=latt_ang(1)* pi/180.d0
alp=latt_abc(1)
blp=latt_abc(2)
clp=latt_abc(3)
cell(3,3) = clp
cell(2,3) = 0.d0
cell(1,3) = 0.d0
cell(3,2) = blp * dcos(alplp)
cell(2,2) = blp * dsin(alplp)
cell(1,2) = 0.d0
cell(3,1) = alp * dcos(betlp)
xxx = (dcos(gamlp) - dcos(betlp)*dcos(alplp))/dsin(alplp)
cell(2,1) = alp * xxx
cell(1,1) = alp * dsqrt(dsin(betlp)*dsin(betlp) - xxx*xxx)
! now find the rotation matrix
call reclat_loc(cell, celli, 0)
call reclat_loc(cell2, celli, 0)
do ia = 1,na
xac(:) = matmul(transpose(celli),xa(:,ia))
if(control==1) xac(:) =modulo(xac(:)+100.0d0,1.0d0)
do ix = 1,3
xa(ix,ia) = cell(ix,1) * xac(1) + cell(ix,2) * xac(2) + cell(ix,3) * xac(3)
enddo
enddo
end subroutine
SUBROUTINE reclat_loc (A,B,IOPT)
integer :: iopt, i
DOUBLE PRECISION A(3,3),B(3,3), pi, c , ci
PI=ACOS(-1.D0)
B(1,1)=A(2,2)*A(3,3)-A(3,2)*A(2,3)
B(2,1)=A(3,2)*A(1,3)-A(1,2)*A(3,3)
B(3,1)=A(1,2)*A(2,3)-A(2,2)*A(1,3)
B(1,2)=A(2,3)*A(3,1)-A(3,3)*A(2,1)
B(2,2)=A(3,3)*A(1,1)-A(1,3)*A(3,1)
B(3,2)=A(1,3)*A(2,1)-A(2,3)*A(1,1)
B(1,3)=A(2,1)*A(3,2)-A(3,1)*A(2,2)
B(2,3)=A(3,1)*A(1,2)-A(1,1)*A(3,2)
B(3,3)=A(1,1)*A(2,2)-A(2,1)*A(1,2)
C=1.D0
IF (IOPT.EQ.1) C=2.D0*PI
DO 20 I=1,3
CI=C/(A(1,I)*B(1,I)+A(2,I)*B(2,I)+A(3,I)*B(3,I))
B(1,I)=B(1,I)*CI
B(2,I)=B(2,I)*CI
B(3,I)=B(3,I)*CI
20 CONTINUE
END
SUBROUTINE YLMB(V,LMAX,Y)
INTEGER LMAX
DOUBLE PRECISION V(3)
COMPLEX*16 Y(*)
!
! ..................................................................
! 1. PROGRAM UNIT 'YLM'
! Calculates spherical harmonics
! FORTRAN 77 SUBROUTINE
!
! 2. PURPOSE
! The spherical harmonics (Condon and Shortley convention)
! Y(0,0),Y(1,-1),Y(1,0),Y(1,1),Y(2,-2) ... Y(LMAX,LMAX)
! for vector V (given in Cartesian coordinates)
! are calculated. In the Condon Shortley convention the
! spherical harmonics are defined as
! +------+
! m | 1 m im(Phi)
! Y(l,m) = (-1) -+ | ----- P (cos(Theta)) e
! \| 2(Pi) l
! m
! where P (cos(Theta)) is the normalized Associated Legendre
! l
! function. Thus,
! m *
! Y(l,-m) = (-1) Y(l,m)
!
!
! 3. USAGE
! DOUBLE PRECISION V(3), Y(5*5)
! V(1) = ...
! V(2) = ...
! V(3) = ...
! CALL YLM(V,4,Y)
!
! ARGUMENT-DESCRIPTION
! V - DOUBLE PRECISION vector, dimension 3 (input)
! Must be given in Cartesian coordinates.
! Conversion of V to polar coordinates gives the
! angles Theta and Phi necessary for the calculation
! of the spherical harmonics.
! LMAX - INTEGER value (input)
! upper bound of L for which spherical harmonics
! will be calculated
! constraint:
! LMAX .GE. 0 (not checked)
! Y - COMPLEX*16 array, dimension (LMAX+1)**2 (output)
! contains the calculated spherical harmonics
! Y(1) for L .EQ. 0 (M = 0)
! Y(2), ..., Y(4) for L .EQ. 1 (M = -1, 0, 1)
! ...
! Y(LMAX*LMAX+1), ..., Y((LMAX+1)*(LMAX+1))
! for L .EQ. LMAX
! (M = -L,...,L)
! constraint:
! Dimension of Y .GE. (LMAX+1)**2 (not checked)
!
! USED SUBROUTINES (DIRECTLY CALLED)
! none
!
! INDIRECTLY CALLED SUBROUTINES
! none
!
! UTILITY-SUBROUTINES (USE BEFOREHAND OR AFTERWARDS)
! none
!
! INPUT/OUTPUT (READ/WRITE)
! none
!
! MACHINENDEPENDENT PROGRAMPARTS
! Type COMPLEX*16 is used which does not conform to the
! FORTRAN 77 standard.
! Also the non-standard type conversion function DCMPLX()
! is used which combines two double precision values into
! one double complex value.
!
! 4. REMARKS
! none
!
! 5. METHOD
! The basic algorithm used to calculate the spherical
! harmonics for vector V is as follows:
!
! Y(0,0)
! Y(1,0)
! Y(1,1)
! Y(1,-1) = -Y(1,1)
! DO L = 2, LMAX
! Y(L,L) = f(Y(L-1,L-1)) ... Formula 1
! Y(L,L-1) = f(Y(L-1,L-1)) ... Formula 2
! DO M = L-2, 0, -1
! Y(L,M) = f(Y(L-1,M),Y(L-2,M)) ... Formula 2
! Y(L,-M)= (-1)**M*Y(L,M)
! ENDDO
! ENDDO
!
! In the following the necessary recursion formulas and
! starting values are given:
!
! Start:
! +------+
! | 1
! Y(0,0) = -+ | -----
! \| 4(Pi)
!
! +------+
! | 3
! Y(1,0) = cos(Theta) -+ | -----
! \| 4(Pi)
!
! +------+
! | 3 i(Phi)
! Y(1,1) = - sin(Theta) -+ | ----- e
! \| 8(Pi)
!
! Formula 1:
!
! Y(l,l) =
! +--------+
! | (2l+1) i(Phi)
! -sin(Theta) -+ | ------ e Y(l-1,l-1)
! \| 2l
!
! Formula 2:
! +---------------+
! | (2l-1)(2l+1)
! Y(l,m) = cos(Theta) -+ | -------------- Y(l-1,m) -
! \| (l-m)(l+m)
!
! +--------------------+
! |(l-1+m)(l-1-m)(2l+1)
! - -+ |-------------------- Y(l-2,m)
! \| (2l-3)(l-m)(l+m)
!
! Formula 3: (not used in the algorithm because of the division
! by sin(Theta) which may be zero)
!
! +--------------+
! cos(Theta) | 4(m+1)(m+1) -i(Phi)
! Y(l,m) = - ---------- -+ | ------------ e Y(l,m+1) -
! sin(Theta) \| (l+m+1)(l-m)
!
! +--------------+
! |(l-m-1)(l+m+2) -2i(Phi)
! - -+ |-------------- e Y(l,m+2)
! \| (l-m)(l+m+1)
!
! 6. DATE
! 26. April 1994 Version 1.2
!
! INSTITUT FUER TECHNISCHE ELEKTROCHEMIE -- TU VIENNA
! ..................................................................
!
!
INTEGER I2L, I4L2, INDEX, INDEX2, L, M, MSIGN
DOUBLE PRECISION A, B, C, AB, ABC, ABMAX, ABCMAX
DOUBLE PRECISION D4LL1C, D2L13, PI
DOUBLE PRECISION COSTH, SINTH, COSPH, SINPH
DOUBLE PRECISION TEMP1, TEMP2, TEMP3
DOUBLE PRECISION YLLR, YLL1R, YL1L1R, YLMR
DOUBLE PRECISION YLLI, YLL1I, YL1L1I, YLMI
!
PI = (4.0D+0)*ATAN(1.0D+0)
!
! Y(0,0)
!
YLLR = 1.0D+0/SQRT(4.0D+0*PI)
YLLI = 0.0D+0
Y(1) = DCMPLX(YLLR,YLLI)
!
! continue only if spherical harmonics for (L .GT. 0) are desired
!
IF (LMAX .LE. 0) GOTO 999
!
! calculate sin(Phi), cos(Phi), sin(Theta), cos(Theta)
! Theta, Phi ... polar angles of vector V
!
ABMAX = MAX(ABS(V(1)),ABS(V(2)))
IF (ABMAX .GT. 0.0D+0) THEN
A = V(1)/ABMAX
B = V(2)/ABMAX
AB = SQRT(A*A+B*B)
COSPH = A/AB
SINPH = B/AB
ELSE
COSPH = 1.0D+0
SINPH = 0.0D+0
ENDIF
ABCMAX = MAX(ABMAX,ABS(V(3)))
IF (ABCMAX .GT. 0.0D+0) THEN
A = V(1)/ABCMAX
B = V(2)/ABCMAX
C = V(3)/ABCMAX
AB = A*A + B*B
ABC = SQRT(AB + C*C)
COSTH = C/ABC
SINTH = SQRT(AB)/ABC
ELSE
COSTH = 1.0D+0
SINTH = 0.0D+0
ENDIF
!
! Y(1,0)
!
Y(3) = DCMPLX(SQRT(3.0D+0)*YLLR*COSTH,0.0D+0)
!
! Y(1,1) ( = -DCONJG(Y(1,-1)))
!
TEMP1 = -SQRT(1.5D+0)*YLLR*SINTH
Y(4) = DCMPLX(TEMP1*COSPH,TEMP1*SINPH)
Y(2) = -DCONJG(Y(4))
!
DO 20 L = 2, LMAX
INDEX = L*L+1
INDEX2 = INDEX + 2*L
MSIGN = 1 - 2*MOD(L,2)
!
! YLL = Y(L,L) = f(Y(L-1,L-1)) ... Formula 1
!
YL1L1R = DBLE(Y(INDEX-1))
YL1L1I = DIMAG(Y(INDEX-1))
TEMP1 = -SQRT(DBLE(2*L+1)/DBLE(2*L))*SINTH
YLLR = TEMP1*(COSPH*YL1L1R - SINPH*YL1L1I)
YLLI = TEMP1*(COSPH*YL1L1I + SINPH*YL1L1R)
Y(INDEX2) = DCMPLX(YLLR,YLLI)
Y(INDEX) = MSIGN*DCONJG(Y(INDEX2))
INDEX2 = INDEX2 - 1
INDEX = INDEX + 1
!
! YLL1 = Y(L,L-1) = f(Y(L-1,L-1)) ... Formula 2
! (the coefficient for Y(L-2,L-1) in Formula 2 is zero)
!
TEMP2 = SQRT(DBLE(2*L+1))*COSTH
YLL1R = TEMP2*YL1L1R
YLL1I = TEMP2*YL1L1I
Y(INDEX2) = DCMPLX(YLL1R,YLL1I)
Y(INDEX) = -MSIGN*DCONJG(Y(INDEX2))
INDEX2 = INDEX2 - 1
INDEX = INDEX + 1
!
I4L2 = INDEX2 - 4*L + 2
I2L = INDEX2 - 2*L
D4LL1C = COSTH*SQRT(DBLE(4*L*L-1))
D2L13 = -SQRT(DBLE(2*L+1)/DBLE(2*L-3))
!
DO 10 M = L - 2, 0, -1
!
! YLM = Y(L,M) = f(Y(L-2,M),Y(L-1,M)) ... Formula 2
!
TEMP1 = 1.0D+0/SQRT(DBLE((L+M)*(L-M)))
TEMP2 = D4LL1C*TEMP1
TEMP3 = D2L13*SQRT(DBLE((L+M-1)*(L-M-1)))*TEMP1
YLMR = TEMP2*DBLE(Y(I2L)) + TEMP3*DBLE(Y(I4L2))
YLMI = TEMP2*DIMAG(Y(I2L)) + TEMP3*DIMAG(Y(I4L2))
Y(INDEX2) = DCMPLX(YLMR,YLMI)
Y(INDEX) = MSIGN*DCONJG(Y(INDEX2))
!
MSIGN = -MSIGN
INDEX2 = INDEX2 - 1
INDEX = INDEX + 1
I4L2 = I4L2 - 1
I2L = I2L - 1
10 CONTINUE
20 CONTINUE
!
999 RETURN
!
! End of 'YLM'
!
END
subroutine outcell_output_loc(cell,cellm,celang)
implicit none
integer,parameter :: dp = selected_real_kind(precision(1.0d0))
real(dp), intent(in) :: cell(3,3)
integer :: iv, ix
real(dp) :: cellm(3), celang(3), volume, volcel
real(dp), save :: Ang = 1.0d0/0.529177d0
real(dp), save :: pi = 3.14159265358d0
external volcel
do iv = 1,3
cellm(iv) = dot_product(cell(:,iv),cell(:,iv))
cellm(iv) = sqrt(cellm(iv))
enddo
celang(1) = dot_product(cell(:,1),cell(:,2))
celang(1) = acos(celang(1)/(cellm(1)*cellm(2)))*180._dp/pi
celang(2) = dot_product(cell(:,1),cell(:,3))
celang(2) = acos(celang(2)/(cellm(1)*cellm(3)))*180._dp/pi