adding codes
This commit is contained in:
arjanberger10
parent
60551f3275
commit
6529dd050f
47
1D_eta1_linear.f90
Normal file
47
1D_eta1_linear.f90
Normal file
@ -0,0 +1,47 @@
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program linear
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implicit none
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integer :: nelec
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integer :: i,k
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real*8 :: factor
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real*8 :: zpe
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real*8,allocatable :: cmat(:)
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real*8,allocatable :: omega2(:)
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write(6,*) "number of electrons"
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read(5,*) nelec
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allocate (cmat(nelec))
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allocate (omega2(nelec))
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factor=acos(-1d0)/nelec
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cmat = 0d0
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do i = 1, nelec
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cmat(1) = cmat(1) + (1d0 + cos(factor*i))**2/sin(factor*i)**3
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enddo
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do i = 1, nelec-1
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cmat(i+1) = -(1d0 + cos(factor*i))**2/sin(factor*i)**3
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enddo
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cmat = cmat*factor**3/8d0
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factor = 2*acos(-1d0)/nelec
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omega2 = 0d0
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do k = 0, nelec-1
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do i = 0, nelec-1
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omega2(k+1) = omega2(k+1) + cmat(i+1)*cos(factor*k*i)
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enddo
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enddo
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zpe=0d0
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do k = 1, nelec
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if (omega2(k)<0d0) cycle
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zpe = zpe + sqrt(omega2(k))
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enddo
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zpe=zpe/nelec
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print*,'zero-point energy (in Ry and Ha) =',zpe,zpe/2
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deallocate(cmat,omega2)
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end program linear
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56
2D_eta0_square.f90
Normal file
56
2D_eta0_square.f90
Normal file
@ -0,0 +1,56 @@
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program square
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implicit none
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integer :: nside,nsite,nelec
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integer :: ix,iy,iz,i
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real*16 :: factor,bbfac
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real*16 :: uee,ubb,eta0,aux
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real*16 :: start,finish
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real*16,allocatable :: sin2(:)
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open(unit=10,file='input')
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read(10,*) nside
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close(10)
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call cpu_time(start)
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nsite = nside
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nelec = nside**2
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bbfac = 1.139479116668307748953273191122493968q0
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write(6,*) "total number of electrons",nelec
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allocate(sin2(nsite))
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factor=acos(-1q0)/nsite
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do i = 0, nsite-1
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sin2(i+1) = (sin(factor*i))**2
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enddo
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uee = 0q0
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do ix = 0, nsite-1
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do iy = 0, nsite-1
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if (ix+iy==0) cycle
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aux = sqrt(sin2(ix+1)+sin2(iy+1))
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uee = uee + 1q0/aux
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enddo
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enddo
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factor=sqrt(acos(-1q0))/(nsite*2q0)
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uee=uee*factor
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ubb = nelec*bbfac/nside
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eta0 = uee - ubb
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print*,'eta0 (in Ry and Ha) =', 2q0*eta0, eta0
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print*, uee,ubb
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deallocate(sin2)
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call cpu_time(finish)
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print '("Time = ",f12.3," seconds.")',finish-start
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end program square
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57
2D_eta0_triangle.f90
Normal file
57
2D_eta0_triangle.f90
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@ -0,0 +1,57 @@
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program triangle
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implicit none
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integer :: nside,nsite,nelec
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integer :: ix,iy,iz,i
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real*16 :: factor,bbfac
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real*16 :: uee,ubb,eta0,aux
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real*16 :: start,finish
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real*16,allocatable :: sin2(:)
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open(unit=10,file='input')
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read(10,*) nside
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close(10)
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call cpu_time(start)
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nsite = 2*nside
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nelec = nside**2*2
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!bbfac = 0.7839363355057699q0
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bbfac = 0.78393636789823211548q0
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write(6,*) "total number of electrons",nelec
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allocate(sin2(nsite))
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factor=acos(-1q0)/nsite
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do i = 0, nsite-1
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sin2(i+1) = (sin(factor*i))**2
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enddo
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uee = 0q0
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do ix = 0, nsite-1
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do iy = 0, nsite-1
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if (ix+iy==0) cycle
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if (mod(ix+iy,2)==1) cycle
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aux = sqrt(sin2(ix+1)+3q0*sin2(iy+1))
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uee = uee + 1q0/aux
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enddo
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enddo
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factor=sqrt(acos(-1q0)/2q0)*3q0**(0.25q0)/nsite
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uee=uee*factor
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ubb = nelec*bbfac/nside
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eta0 = uee - ubb
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print*,'eta0 (in Ry and Ha) =', 2q0*eta0, eta0
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deallocate(sin2)
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call cpu_time(finish)
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print '("Time = ",f12.3," seconds.")',finish-start
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end program triangle
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188
2D_eta1_triangle.f90
Normal file
188
2D_eta1_triangle.f90
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@ -0,0 +1,188 @@
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program triangle
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implicit none
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integer :: nside,nsite,nelec
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integer :: ix,iy,kx,ky
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integer :: i,k, ielec,kelec,info
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real*8 :: start,finish
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real*8 :: factor,height,factor2
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real*8 :: zpe
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real*8 :: denom1,denom2,numxy,fx,fy
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real*8 :: work(8)
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real*8,allocatable :: sin2(:),cos2(:)
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real*8,allocatable :: cmat(:,:,:,:),cmatk(:,:,:,:)
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real*8,allocatable :: caux1(:,:,:,:),caux2(:,:,:,:)
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real*8,allocatable :: caux3(:,:,:,:),caux4(:,:,:,:)
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real*8,allocatable :: omega2(:,:)
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open(unit=10,file='input')
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read(10,*) nside
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close(10)
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call cpu_time(start)
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nsite = 2*nside
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nelec = nside**2*2
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write(6,*) "total number of electrons",nelec
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allocate (cmat(2,2,nsite,nsite))
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allocate (cmatk(2,2,nsite,nsite))
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allocate (caux1(2,2,nsite,nsite))
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allocate (caux2(2,2,nsite,nsite))
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allocate (caux3(2,2,nsite,nsite))
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allocate (caux4(2,2,nsite,nsite))
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allocate (sin2(nsite))
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allocate (cos2(nsite))
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allocate (omega2(2,nelec))
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factor=acos(-1d0)/nsite
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height=2d0*sqrt(3d0)
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do i = 0, nsite-1
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sin2(i+1) = (sin(factor*i))**2
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cos2(i+1) = (cos(factor*i))**2
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enddo
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!
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! calculate C(0)
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!
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cmat = 0d0
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do ix = 0, nsite-1
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do iy = 0, nsite-1
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if (ix+iy==0) cycle
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if (mod(ix+iy,2)==1) cycle
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denom1 = (sin2(ix+1)+0.25d0*height**2*sin2(iy+1))**1.5d0
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denom2 = (sin2(ix+1)+0.25d0*height**2*sin2(iy+1))**2.5d0
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numxy = 1.5d0*height*sin(factor*ix)*cos(factor*ix)*sin(factor*iy)*cos(factor*iy)
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cmat(1,1,1,1) = cmat(1,1,1,1) + 3d0*sin2(ix+1)*cos2(ix+1)/denom2 + &
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(sin2(ix+1) - cos2(ix+1))/denom1
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cmat(2,2,1,1) = cmat(2,2,1,1) + 0.75d0*height**2*sin2(iy+1)*cos2(iy+1)/denom2 + &
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(sin2(iy+1) - cos2(iy+1))/denom1
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cmat(1,2,1,1) = cmat(1,2,1,1) + numxy/denom2
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enddo
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enddo
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!
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! calculate C(i) for i not equal to 0
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!
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do ix = 0, nsite-1
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do iy = 0, nsite-1
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if (ix+iy==0) cycle
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if (mod(ix+iy,2)==1) cycle
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denom1 = (sin2(ix+1)+0.25d0*height**2*sin2(iy+1))**1.5d0
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denom2 = (sin2(ix+1)+0.25d0*height**2*sin2(iy+1))**2.5d0
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numxy = -1.5d0*height*sin(factor*ix)*cos(factor*ix)*sin(factor*iy)*cos(factor*iy)
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cmat(1,1,ix+1,iy+1) = -3d0*sin2(ix+1)*cos2(ix+1)/denom2 + &
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(cos2(ix+1) - sin2(ix+1))/denom1
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cmat(2,2,ix+1,iy+1) = -0.75d0*height**2*sin2(iy+1)*cos2(iy+1)/denom2 + &
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(cos2(iy+1) - sin2(iy+1))/denom1
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cmat(1,2,ix+1,iy+1) = numxy/denom2
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enddo
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enddo
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cmat(2,1,:,:) = cmat(1,2,:,:)
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cmat=cmat*(acos(-1d0)*height/nsite**2)**1.5d0
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print*,'testje',cmat(1,1,1,1),cmat(2,2,1,1)
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!
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! calculate sum_{i} C_ab(i) cos(2pi k.i/2n) using index decoupling,
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! i.e., cos (x + y) = cos(x)cos(y)-sin(x)sin(y)
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!
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factor = 2*acos(-1d0)/nsite
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factor2 = 2*acos(-1d0)/(nside*sqrt(3d0))
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caux1=0d0
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caux2=0d0
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do ix = 0, nsite-1
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fx=factor*ix
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do iy = 0, nsite-1
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if (mod(ix+iy,2)==1) cycle
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do kx = 0, nsite-1
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caux1(:,:,kx+1,iy+1) = caux1(:,:,kx+1,iy+1) + cmat(:,:,ix+1,iy+1)*cos(kx*fx)
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caux2(:,:,kx+1,iy+1) = caux2(:,:,kx+1,iy+1) + cmat(:,:,ix+1,iy+1)*sin(kx*fx)
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enddo
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enddo
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enddo
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caux3=0d0
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caux4=0d0
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do iy = 0, nsite-1
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fy=factor*iy
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do kx = 0, nsite-1
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do ky = 0, nsite-1
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if (mod(kx+ky,2)==1) cycle
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caux3(:,:,kx+1,ky+1) = caux3(:,:,kx+1,ky+1) + caux1(:,:,kx+1,iy+1)*cos(ky*fy)
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caux4(:,:,kx+1,ky+1) = caux4(:,:,kx+1,ky+1) + caux2(:,:,kx+1,iy+1)*sin(ky*fy)
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enddo
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enddo
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enddo
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cmatk = caux3-caux4
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!!
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!!debug : implementation without index decoupling
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!!
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!cmatk=0d0
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!do ix = 0, nsite-1
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! do iy = 0, nsite-1
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! if (mod(ix+iy,2)==1) cycle
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! do kx = 0, nsite-1
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! do ky = 0, nsite-1
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! if (mod(kx+ky,2)==1) cycle
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!! print*,'testje2',kx,ky,cmat(1,1,ix+1,iy+1),cos(factor*(ix*kx+iy*ky))
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! cmatk(:,:,kx+1,ky+1) = cmatk(:,:,kx+1,ky+1) + cmat(:,:,ix+1,iy+1)*cos(factor*(ix*kx+iy*ky))
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!! cmatk(:,:,kx+1,ky+1) = cmatk(:,:,kx+1,ky+1) + cmat(:,:,ix+1,iy+1)*cos(factor*ix*kx+factor2*iy*(ky-kx))
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!! cmatk(1,1,kx+1,ky+1) = cmatk(1,1,kx+1,ky+1) + cmat(1,1,ix+1,iy+1)*cos(factor*(ix*kx+iy*ky))
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!! print*,'testje3',kx,ky,cmatk(1,1,kx+1,ky+1)
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! enddo
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! enddo
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! enddo
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!enddo
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!do kx = 0, nsite-1
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! do ky = 0, nsite-1
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! if (mod(kx+ky,2)==1) cycle
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! print*,'testje',kx,ky,cmatk(1,1,kx+1,ky+1),cmatk(2,2,kx+1,ky+1),cmatk(1,2,kx+1,ky+1),cmatk(2,1,kx+1,ky+1)
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! enddo
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!enddo
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!
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! diagonalize 2x2 matrices
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!
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omega2 = 0d0
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kelec=1
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do kx = 0, nsite-1
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do ky = 0, nsite-1
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if (mod(kx+ky,2)==1) cycle
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call dsyev ("v","u", 2, cmatk(:,:,kx+1,ky+1), 2, omega2(:,kelec), work, 8, info)
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kelec = kelec + 1
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enddo
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enddo
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zpe=0d0
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do kelec = 1, nelec
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do i = 1, 2
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! if (omega2(i,kelec)<0d0) print*,'warning',kelec,i,omega2(i,kelec)
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! print*,omega2(i,kelec)
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if (omega2(i,kelec)<0d0) cycle
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zpe = zpe + sqrt(omega2(i,kelec))
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enddo
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enddo
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zpe=zpe/nelec
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print*,'zero-point energy (in Ry and Ha) =',zpe,zpe/2
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deallocate(sin2,cos2,cmat,cmatk,omega2)
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deallocate(caux1,caux2,caux3,caux4)
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call cpu_time(finish)
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print '("Time = ",f6.3," seconds.")',finish-start
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end program triangle
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60
3D_eta0_bcc.f90
Normal file
60
3D_eta0_bcc.f90
Normal file
@ -0,0 +1,60 @@
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program bcc
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implicit none
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integer(kind=8) :: nside,nsite,nelec
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integer(kind=8) :: ix,iy,iz,i
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real*16 :: factor,bbfac
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real*16 :: uee,ubb,eta0,aux
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real*16 :: start,finish
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real*16,allocatable :: sin2(:)
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open(unit=10,file='input')
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read(10,*) nside
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close(10)
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call cpu_time(start)
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nsite = 2*nside
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nelec = nside**3*2
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bbfac = 1.4305055275019529822q0
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write(6,*) "total number of electrons",nelec
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allocate(sin2(nsite))
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factor=acos(-1q0)/nsite
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do i = 0, nsite-1
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sin2(i+1) = (sin(factor*i))**2
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enddo
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uee = 0q0
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do ix = 0, nsite-1
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do iy = 0, nsite-1
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do iz = 0, nsite-1
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if (ix+iy+iz==0) cycle
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if (mod(ix+iy,2)==1.or.mod(ix+iz,2)==1.or.mod(iy+iz,2)==1) cycle
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aux = sqrt(sin2(ix+1)+sin2(iy+1)+sin2(iz+1))
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uee = uee + 1q0/aux
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enddo
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enddo
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enddo
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uee=uee*acos(-1q0)/(2q0*nsite)
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ubb = nelec*bbfac/nsite
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eta0 = uee - ubb
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factor=(acos(-1q0)/3q0)**(1q0/3q0)
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eta0=eta0/factor
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print*,'eta0 (in Ry and Ha) =', 2q0*eta0, eta0
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deallocate(sin2)
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call cpu_time(finish)
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print '("Time = ",f12.3," seconds.")',finish-start
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end program bcc
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60
3D_eta0_fcc.f90
Normal file
60
3D_eta0_fcc.f90
Normal file
@ -0,0 +1,60 @@
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program bcc
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implicit none
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integer(kind=8) :: nside,nsite,nelec
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integer(kind=8) :: ix,iy,iz,i
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real*16 :: factor,bbfac
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real*16 :: uee,ubb,eta0,aux
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real*16 :: start,finish
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real*16,allocatable :: sin2(:)
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open(unit=10,file='input')
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read(10,*) nside
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close(10)
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call cpu_time(start)
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nsite = 2*nside
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nelec = nside**3*4
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|
||||
bbfac = 1.4305055275019529822q0
|
||||
|
||||
write(6,*) "total number of electrons",nelec
|
||||
|
||||
allocate(sin2(nsite))
|
||||
|
||||
factor=acos(-1q0)/nsite
|
||||
do i = 0, nsite-1
|
||||
sin2(i+1) = (sin(factor*i))**2
|
||||
enddo
|
||||
|
||||
uee = 0q0
|
||||
do ix = 0, nsite-1
|
||||
do iy = 0, nsite-1
|
||||
do iz = 0, nsite-1
|
||||
if (ix+iy+iz==0) cycle
|
||||
if (mod(ix+iy+iz,2)==1) cycle
|
||||
aux = sqrt(sin2(ix+1)+sin2(iy+1)+sin2(iz+1))
|
||||
uee = uee + 1q0/aux
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
uee=uee*acos(-1q0)/(2q0*nsite)
|
||||
|
||||
ubb = nelec*bbfac/nsite
|
||||
|
||||
eta0 = uee - ubb
|
||||
|
||||
factor=(acos(-1q0)/1.5q0)**(1q0/3q0)
|
||||
eta0=eta0/factor
|
||||
|
||||
print*,'eta0 (in Ry and Ha) =', 2q0*eta0, eta0
|
||||
|
||||
deallocate(sin2)
|
||||
|
||||
call cpu_time(finish)
|
||||
print '("Time = ",f12.3," seconds.")',finish-start
|
||||
|
||||
end program bcc
|
||||
79
3D_eta0_hcp.f90
Normal file
79
3D_eta0_hcp.f90
Normal file
@ -0,0 +1,79 @@
|
||||
program hcp
|
||||
|
||||
implicit none
|
||||
|
||||
integer(kind=8) :: nside,nsitexz,nsitey,nelec
|
||||
integer(kind=8) :: ix,iy,iz,i
|
||||
real*16 :: factorxz,factory,factor,bbfac,pi
|
||||
real*16 :: uee,ubb,eta0,aux
|
||||
real*16 :: start,finish
|
||||
real*16,allocatable :: sin2xz(:),sin2y(:)
|
||||
|
||||
open(unit=10,file='input')
|
||||
read(10,*) nside
|
||||
close(10)
|
||||
|
||||
call cpu_time(start)
|
||||
|
||||
nsitexz = 2*nside
|
||||
nsitey = 6*nside
|
||||
nelec = nside**3*4
|
||||
|
||||
bbfac = 0.54063377545280790285q0
|
||||
pi = acos(-1q0)
|
||||
|
||||
write(6,*) "total number of electrons",nelec
|
||||
|
||||
allocate(sin2xz(nsitexz))
|
||||
allocate(sin2y(nsitey))
|
||||
|
||||
factorxz=acos(-1q0)/nsitexz
|
||||
factory=acos(-1q0)/nsitey
|
||||
do i = 0, nsitexz-1
|
||||
sin2xz(i+1) = (sin(factorxz*i))**2
|
||||
enddo
|
||||
do i = 0, nsitey-1
|
||||
sin2y(i+1) = (sin(factory*i))**2
|
||||
enddo
|
||||
|
||||
uee = 0q0
|
||||
do ix = 0, nsitexz-1
|
||||
do iy = 0, nsitey-1
|
||||
do iz = 0, nsitexz-1
|
||||
if (ix+iy+iz==0) cycle
|
||||
aux = sqrt(sin2xz(ix+1)+3q0*sin2y(iy+1)+8q0/3q0*sin2xz(iz+1))
|
||||
if (mod(ix,2)==0.and.mod(iz,2)==0.and.mod(iy,6)==0) then
|
||||
uee = uee + 1q0/aux
|
||||
! print*,'testje1',ix,iy,iz,aux
|
||||
endif
|
||||
if (mod(ix,2)==1.and.mod(iz,2)==0.and.mod(iy+3,6)==0) then
|
||||
uee = uee + 1q0/aux
|
||||
! print*,'testje2',ix,iy,iz,aux
|
||||
endif
|
||||
if (mod(ix,2)==0.and.mod(iz,2)==1.and.mod(iy+4,6)==0) then
|
||||
uee = uee + 1q0/aux
|
||||
! print*,'testje3',ix,iy,iz,aux
|
||||
endif
|
||||
if (mod(ix,2)==1.and.mod(iz,2)==1.and.mod(iy+1,6)==0) then
|
||||
uee = uee + 1q0/aux
|
||||
! print*,'testje4',ix,iy,iz,aux
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
factor=(3q0*pi**(2q0)*sqrt(2q0))**(1q0/3q0)/(2q0*nsitexz)
|
||||
uee=uee*factor
|
||||
|
||||
ubb = nelec*bbfac/nside
|
||||
|
||||
eta0 = uee - ubb
|
||||
|
||||
print*,'eta0 (in Ry and Ha) =', 2q0*eta0, eta0
|
||||
|
||||
deallocate(sin2xz,sin2y)
|
||||
|
||||
call cpu_time(finish)
|
||||
print '("Time = ",f12.3," seconds.")',finish-start
|
||||
|
||||
end program hcp
|
||||
59
3D_eta0_sc.f90
Normal file
59
3D_eta0_sc.f90
Normal file
@ -0,0 +1,59 @@
|
||||
program sc
|
||||
|
||||
implicit none
|
||||
|
||||
integer(kind=8) :: nside,nsite,nelec
|
||||
integer(kind=8) :: ix,iy,iz,i
|
||||
real*16 :: factor,bbfac
|
||||
real*16 :: uee,ubb,eta0,aux
|
||||
real*16 :: start,finish
|
||||
real*16,allocatable :: sin2(:)
|
||||
|
||||
open(unit=10,file='input')
|
||||
read(10,*) nside
|
||||
close(10)
|
||||
|
||||
call cpu_time(start)
|
||||
|
||||
nsite = nside
|
||||
nelec = nside**3
|
||||
|
||||
bbfac = 1.4305055275019529822q0
|
||||
|
||||
write(6,*) "total number of electrons",nelec
|
||||
|
||||
allocate(sin2(nsite))
|
||||
|
||||
factor=acos(-1q0)/nsite
|
||||
do i = 0, nsite-1
|
||||
sin2(i+1) = (sin(factor*i))**2
|
||||
enddo
|
||||
|
||||
uee = 0q0
|
||||
do ix = 0, nsite-1
|
||||
do iy = 0, nsite-1
|
||||
do iz = 0, nsite-1
|
||||
if (ix+iy+iz==0) cycle
|
||||
aux = sqrt(sin2(ix+1)+sin2(iy+1)+sin2(iz+1))
|
||||
uee = uee + 1q0/aux
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
uee=uee*acos(-1q0)/(2q0*nsite)
|
||||
|
||||
ubb = nelec*bbfac/nsite
|
||||
|
||||
eta0 = uee - ubb
|
||||
|
||||
factor=(4q0*acos(-1q0)/3q0)**(1q0/3q0)
|
||||
eta0=eta0/factor
|
||||
|
||||
print*,'eta0 (in Ry and Ha) =', 2q0*eta0, eta0
|
||||
|
||||
deallocate(sin2)
|
||||
|
||||
call cpu_time(finish)
|
||||
print '("Time = ",f12.3," seconds.")',finish-start
|
||||
|
||||
end program sc
|
||||
331
3D_eta1_bcc.f90
Normal file
331
3D_eta1_bcc.f90
Normal file
@ -0,0 +1,331 @@
|
||||
program bcc
|
||||
|
||||
implicit none
|
||||
|
||||
integer :: nside,nsite,nelec
|
||||
integer :: ix,iy,iz,kx,ky,kz
|
||||
integer :: i,k, ielec,kelec,info
|
||||
real*8 :: start,finish
|
||||
real*8 :: factor
|
||||
real*8 :: zpe
|
||||
real*8 :: denom1,denom2,numxy,numxz,numyz,fx,fy,fz
|
||||
real*8 :: work(8)
|
||||
real*8,allocatable :: sin2(:),cos2(:)
|
||||
real*8,allocatable :: cmat(:,:,:,:,:)
|
||||
real*8,allocatable :: caux(:,:,:,:,:)
|
||||
real*8,allocatable :: cmatk(:,:,:,:,:)
|
||||
real*8,allocatable :: omega2(:,:)
|
||||
|
||||
open(unit=10,file='input')
|
||||
read(10,*) nside
|
||||
close(10)
|
||||
|
||||
call cpu_time(start)
|
||||
|
||||
nsite = 2*nside
|
||||
nelec = nside**3*2
|
||||
|
||||
write(6,*) "total number of electrons",nelec
|
||||
|
||||
allocate (cmat(3,3,nsite,nsite,nsite))
|
||||
allocate (caux(3,3,nsite,nsite,nsite))
|
||||
allocate (cmatk(3,3,nsite,nsite,nsite))
|
||||
allocate (sin2(nsite))
|
||||
allocate (cos2(nsite))
|
||||
allocate (omega2(3,nelec))
|
||||
|
||||
factor=acos(-1d0)/nsite
|
||||
do i = 0, nsite-1
|
||||
sin2(i+1) = (sin(factor*i))**2
|
||||
cos2(i+1) = (cos(factor*i))**2
|
||||
enddo
|
||||
|
||||
!
|
||||
! calculate C(0)
|
||||
!
|
||||
|
||||
cmat = 0d0
|
||||
do ix = 0, nsite-1
|
||||
do iy = 0, nsite-1
|
||||
do iz = 0, nsite-1
|
||||
if (ix+iy+iz==0) cycle
|
||||
if (mod(ix+iy,2)==1.or.mod(ix+iz,2)==1.or.mod(iy+iz,2)==1) cycle
|
||||
denom1 = (sin2(ix+1)+sin2(iy+1)+sin2(iz+1))**(1.5d0)
|
||||
denom2 = (sin2(ix+1)+sin2(iy+1)+sin2(iz+1))**(2.5d0)
|
||||
cmat(1,1,1,1,1) = cmat(1,1,1,1,1) + 3d0*sin2(ix+1)*cos2(ix+1)/denom2 + (sin2(ix+1) - cos2(ix+1))/denom1
|
||||
cmat(2,2,1,1,1) = cmat(2,2,1,1,1) + 3d0*sin2(iy+1)*cos2(iy+1)/denom2 + (sin2(iy+1) - cos2(iy+1))/denom1
|
||||
cmat(3,3,1,1,1) = cmat(3,3,1,1,1) + 3d0*sin2(iz+1)*cos2(iz+1)/denom2 + (sin2(iz+1) - cos2(iz+1))/denom1
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!
|
||||
! calculate C(i) for i not equal to 0
|
||||
!
|
||||
|
||||
do ix = 0, nsite-1
|
||||
do iy = 0, nsite-1
|
||||
do iz = 0, nsite-1
|
||||
if (ix+iy+iz==0) cycle
|
||||
if (mod(ix+iy,2)==1.or.mod(ix+iz,2)==1.or.mod(iy+iz,2)==1) cycle
|
||||
denom1 = (sin2(ix+1)+sin2(iy+1)+sin2(iz+1))**1.5d0
|
||||
denom2 = (sin2(ix+1)+sin2(iy+1)+sin2(iz+1))**2.5d0
|
||||
numxy = -3d0*sin(factor*ix)*cos(factor*ix)*sin(factor*iy)*cos(factor*iy)
|
||||
numxz = -3d0*sin(factor*ix)*cos(factor*ix)*sin(factor*iz)*cos(factor*iz)
|
||||
numyz = -3d0*sin(factor*iy)*cos(factor*iy)*sin(factor*iz)*cos(factor*iz)
|
||||
cmat(1,1,ix+1,iy+1,iz+1) = -3d0*sin2(ix+1)*cos2(ix+1)/denom2 + (cos2(ix+1) - sin2(ix+1))/denom1
|
||||
cmat(2,2,ix+1,iy+1,iz+1) = -3d0*sin2(iy+1)*cos2(iy+1)/denom2 + (cos2(iy+1) - sin2(iy+1))/denom1
|
||||
cmat(3,3,ix+1,iy+1,iz+1) = -3d0*sin2(iz+1)*cos2(iz+1)/denom2 + (cos2(iz+1) - sin2(iz+1))/denom1
|
||||
cmat(1,2,ix+1,iy+1,iz+1) = numxy/denom2
|
||||
cmat(1,3,ix+1,iy+1,iz+1) = numxz/denom2
|
||||
cmat(2,3,ix+1,iy+1,iz+1) = numyz/denom2
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
cmat(2,1,:,:,:) = cmat(1,2,:,:,:)
|
||||
cmat(3,1,:,:,:) = cmat(1,3,:,:,:)
|
||||
cmat(3,2,:,:,:) = cmat(2,3,:,:,:)
|
||||
|
||||
factor = 3d0*(acos(-1d0))**2/nsite**3
|
||||
do ix = 0, nsite-1
|
||||
do iy = 0, nsite-1
|
||||
do iz = 0, nsite-1
|
||||
if (mod(ix+iy,2)==1.or.mod(ix+iz,2)==1.or.mod(iy+iz,2)==1) cycle
|
||||
cmat(:,:,ix+1,iy+1,iz+1) = cmat(:,:,ix+1,iy+1,iz+1)*factor
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!
|
||||
! calculate sum_{i} C_ab(i) cos(2pi k.i/2n) using index decoupling,
|
||||
! i.e., cos (x + y) = cos(x)cos(y)-sin(x)sin(y)
|
||||
!
|
||||
|
||||
factor = 2*acos(-1d0)/nsite
|
||||
|
||||
caux=0d0
|
||||
do ix = 0, nsite-1
|
||||
fx=factor*ix
|
||||
do iy = 0, nsite-1
|
||||
do iz = 0, nsite-1
|
||||
if (mod(ix+iy,2)==1.or.mod(ix+iz,2)==1.or.mod(iy+iz,2)==1) cycle
|
||||
do kx = 0, nsite-1
|
||||
caux(:,:,kx+1,iy+1,iz+1) = caux(:,:,kx+1,iy+1,iz+1) + cmat(:,:,ix+1,iy+1,iz+1)*cos(kx*fx)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
cmat=0d0
|
||||
do iy = 0, nsite-1
|
||||
fy=factor*iy
|
||||
do iz = 0, nsite-1
|
||||
do kx = 0, nsite-1
|
||||
do ky = 0, nsite-1
|
||||
if (mod(iy+iz,2)==1.or.mod(kx+ky,2)==1) cycle
|
||||
cmat(:,:,kx+1,ky+1,iz+1) = cmat(:,:,kx+1,ky+1,iz+1) + caux(:,:,kx+1,iy+1,iz+1)*cos(ky*fy)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
cmatk=0d0
|
||||
do iz = 0, nsite-1
|
||||
fz=factor*iz
|
||||
do kx = 0, nsite-1
|
||||
do ky = 0, nsite-1
|
||||
do kz = 0, nsite-1
|
||||
if (mod(kx+ky,2)==1.or.mod(kx+kz,2)==1.or.mod(ky+kz,2)==1) cycle
|
||||
cmatk(:,:,kx+1,ky+1,kz+1) = cmatk(:,:,kx+1,ky+1,kz+1) + cmat(:,:,kx+1,ky+1,iz+1)*cos(kz*fz)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
cmat=0d0
|
||||
do iy = 0, nsite-1
|
||||
fy=factor*iy
|
||||
do iz = 0, nsite-1
|
||||
do kx = 0, nsite-1
|
||||
do ky = 0, nsite-1
|
||||
if (mod(iy+iz,2)==1.or.mod(kx+ky,2)==1) cycle
|
||||
cmat(:,:,kx+1,ky+1,iz+1) = cmat(:,:,kx+1,ky+1,iz+1) + caux(:,:,kx+1,iy+1,iz+1)*sin(ky*fy)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
do iz = 0, nsite-1
|
||||
fz=factor*iz
|
||||
do kx = 0, nsite-1
|
||||
do ky = 0, nsite-1
|
||||
do kz = 0, nsite-1
|
||||
if (mod(kx+ky,2)==1.or.mod(kx+kz,2)==1.or.mod(ky+kz,2)==1) cycle
|
||||
cmatk(:,:,kx+1,ky+1,kz+1) = cmatk(:,:,kx+1,ky+1,kz+1) - cmat(:,:,kx+1,ky+1,iz+1)*sin(kz*fz)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
factor=acos(-1d0)/nsite
|
||||
do i = 0, nsite-1
|
||||
sin2(i+1) = (sin(factor*i))**2
|
||||
cos2(i+1) = (cos(factor*i))**2
|
||||
enddo
|
||||
!
|
||||
! calculate C(0)
|
||||
!
|
||||
|
||||
cmat = 0d0
|
||||
do ix = 0, nsite-1
|
||||
do iy = 0, nsite-1
|
||||
do iz = 0, nsite-1
|
||||
if (ix+iy+iz==0) cycle
|
||||
if (mod(ix+iy,2)==1.or.mod(ix+iz,2)==1.or.mod(iy+iz,2)==1) cycle
|
||||
denom1 = (sin2(ix+1)+sin2(iy+1)+sin2(iz+1))**(1.5d0)
|
||||
denom2 = (sin2(ix+1)+sin2(iy+1)+sin2(iz+1))**(2.5d0)
|
||||
cmat(1,1,1,1,1) = cmat(1,1,1,1,1) + 3d0*sin2(ix+1)*cos2(ix+1)/denom2 + (sin2(ix+1) - cos2(ix+1))/denom1
|
||||
cmat(2,2,1,1,1) = cmat(2,2,1,1,1) + 3d0*sin2(iy+1)*cos2(iy+1)/denom2 + (sin2(iy+1) - cos2(iy+1))/denom1
|
||||
cmat(3,3,1,1,1) = cmat(3,3,1,1,1) + 3d0*sin2(iz+1)*cos2(iz+1)/denom2 + (sin2(iz+1) - cos2(iz+1))/denom1
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!
|
||||
! calculate C(i) for i not equal to 0
|
||||
!
|
||||
|
||||
do ix = 0, nsite-1
|
||||
do iy = 0, nsite-1
|
||||
do iz = 0, nsite-1
|
||||
if (ix+iy+iz==0) cycle
|
||||
if (mod(ix+iy,2)==1.or.mod(ix+iz,2)==1.or.mod(iy+iz,2)==1) cycle
|
||||
denom1 = (sin2(ix+1)+sin2(iy+1)+sin2(iz+1))**1.5d0
|
||||
denom2 = (sin2(ix+1)+sin2(iy+1)+sin2(iz+1))**2.5d0
|
||||
numxy = -3d0*sin(factor*ix)*cos(factor*ix)*sin(factor*iy)*cos(factor*iy)
|
||||
numxz = -3d0*sin(factor*ix)*cos(factor*ix)*sin(factor*iz)*cos(factor*iz)
|
||||
numyz = -3d0*sin(factor*iy)*cos(factor*iy)*sin(factor*iz)*cos(factor*iz)
|
||||
cmat(1,1,ix+1,iy+1,iz+1) = -3d0*sin2(ix+1)*cos2(ix+1)/denom2 + (cos2(ix+1) - sin2(ix+1))/denom1
|
||||
cmat(2,2,ix+1,iy+1,iz+1) = -3d0*sin2(iy+1)*cos2(iy+1)/denom2 + (cos2(iy+1) - sin2(iy+1))/denom1
|
||||
cmat(3,3,ix+1,iy+1,iz+1) = -3d0*sin2(iz+1)*cos2(iz+1)/denom2 + (cos2(iz+1) - sin2(iz+1))/denom1
|
||||
cmat(1,2,ix+1,iy+1,iz+1) = numxy/denom2
|
||||
cmat(1,3,ix+1,iy+1,iz+1) = numxz/denom2
|
||||
cmat(2,3,ix+1,iy+1,iz+1) = numyz/denom2
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
cmat(2,1,:,:,:) = cmat(1,2,:,:,:)
|
||||
cmat(3,1,:,:,:) = cmat(1,3,:,:,:)
|
||||
cmat(3,2,:,:,:) = cmat(2,3,:,:,:)
|
||||
|
||||
factor = 3d0*(acos(-1d0))**2/nsite**3
|
||||
do ix = 0, nsite-1
|
||||
do iy = 0, nsite-1
|
||||
do iz = 0, nsite-1
|
||||
if (mod(ix+iy,2)==1.or.mod(ix+iz,2)==1.or.mod(iy+iz,2)==1) cycle
|
||||
cmat(:,:,ix+1,iy+1,iz+1) = cmat(:,:,ix+1,iy+1,iz+1)*factor
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
factor = 2*acos(-1d0)/nsite
|
||||
|
||||
caux=0d0
|
||||
do ix = 0, nsite-1
|
||||
fx=factor*ix
|
||||
do iy = 0, nsite-1
|
||||
do iz = 0, nsite-1
|
||||
if (mod(ix+iy,2)==1.or.mod(ix+iz,2)==1.or.mod(iy+iz,2)==1) cycle
|
||||
do kx = 0, nsite-1
|
||||
caux(:,:,kx+1,iy+1,iz+1) = caux(:,:,kx+1,iy+1,iz+1) + cmat(:,:,ix+1,iy+1,iz+1)*sin(kx*fx)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
cmat=0d0
|
||||
do iy = 0, nsite-1
|
||||
fy=factor*iy
|
||||
do iz = 0, nsite-1
|
||||
do kx = 0, nsite-1
|
||||
do ky = 0, nsite-1
|
||||
if (mod(iy+iz,2)==1.or.mod(kx+ky,2)==1) cycle
|
||||
cmat(:,:,kx+1,ky+1,iz+1) = cmat(:,:,kx+1,ky+1,iz+1) + caux(:,:,kx+1,iy+1,iz+1)*sin(ky*fy)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
do iz = 0, nsite-1
|
||||
fz=factor*iz
|
||||
do kx = 0, nsite-1
|
||||
do ky = 0, nsite-1
|
||||
do kz = 0, nsite-1
|
||||
if (mod(kx+ky,2)==1.or.mod(kx+kz,2)==1.or.mod(ky+kz,2)==1) cycle
|
||||
cmatk(:,:,kx+1,ky+1,kz+1) = cmatk(:,:,kx+1,ky+1,kz+1) - cmat(:,:,kx+1,ky+1,iz+1)*cos(kz*fz)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
cmat=0d0
|
||||
do iy = 0, nsite-1
|
||||
fy=factor*iy
|
||||
do iz = 0, nsite-1
|
||||
do kx = 0, nsite-1
|
||||
do ky = 0, nsite-1
|
||||
if (mod(iy+iz,2)==1.or.mod(kx+ky,2)==1) cycle
|
||||
cmat(:,:,kx+1,ky+1,iz+1) = cmat(:,:,kx+1,ky+1,iz+1) + caux(:,:,kx+1,iy+1,iz+1)*cos(ky*fy)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
do iz = 0, nsite-1
|
||||
fz=factor*iz
|
||||
do kx = 0, nsite-1
|
||||
do ky = 0, nsite-1
|
||||
do kz = 0, nsite-1
|
||||
if (mod(kx+ky,2)==1.or.mod(kx+kz,2)==1.or.mod(ky+kz,2)==1) cycle
|
||||
cmatk(:,:,kx+1,ky+1,kz+1) = cmatk(:,:,kx+1,ky+1,kz+1) - cmat(:,:,kx+1,ky+1,iz+1)*sin(kz*fz)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!
|
||||
! diagonalize 3x3 matrices
|
||||
!
|
||||
|
||||
omega2 = 0d0
|
||||
kelec=1
|
||||
do kx = 0, nsite-1
|
||||
do ky = 0, nsite-1
|
||||
do kz = 0, nsite-1
|
||||
if (mod(kx+ky,2)==1.or.mod(kx+kz,2)==1.or.mod(ky+kz,2)==1) cycle
|
||||
call dsyev ("v","u", 3, cmatk(:,:,kx+1,ky+1,kz+1), 3, omega2(:,kelec), work, 8, info)
|
||||
kelec = kelec + 1
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
zpe=0d0
|
||||
do kelec = 1, nelec
|
||||
do i = 1, 3
|
||||
! if (omega2(i,kelec)<0d0) print*,'warning',kelec,i,omega2(i,kelec)
|
||||
! print*,omega2(i,kelec)
|
||||
if (omega2(i,kelec)<0d0) cycle
|
||||
zpe = zpe + sqrt(omega2(i,kelec))
|
||||
enddo
|
||||
enddo
|
||||
zpe=zpe/nelec
|
||||
|
||||
print*,'zero-point energy (in Ry and Ha) =',zpe,zpe/2
|
||||
|
||||
deallocate(sin2,cos2,omega2)
|
||||
deallocate(cmat,caux,cmatk)
|
||||
|
||||
call cpu_time(finish)
|
||||
print '("Time = ",f6.3," seconds.")',finish-start
|
||||
|
||||
end program bcc
|
||||
Loading…
Reference in New Issue
Block a user