quantum-espresso/PHonon/PH/rigid.f90

534 lines
17 KiB
Fortran

!
! Copyright (C) 2001-2012 Quantum ESPRESSO group
! This file is distributed under the terms of the
! GNU General Public License. See the file `License'
! in the root directory of the present distribution,
! or http://www.gnu.org/copyleft/gpl.txt .
!
MODULE rigid
PUBLIC :: rgd_blk, dyndiag, nonanal, nonanal_ifc, cdiagh2
PRIVATE
CONTAINS
!
!-----------------------------------------------------------------------
SUBROUTINE rgd_blk(nr1, nr2, nr3, nat, dyn, q, tau, epsil, zeu, alph, &
bg, omega, alat, loto_2d, sign)
!-----------------------------------------------------------------------
!! Compute the rigid-ion (long-range) term for q.
!! The long-range term used here, to be added to or subtracted from the
!! dynamical matrices, is exactly the same of the formula introduced in:
!! X. Gonze et al, PRB 50. 13035 (1994).
!! Only the G-space term is implemented: the Ewald parameter alpha must
!! be large enough to have negligible r-space contribution.
!
USE kinds, ONLY : DP
USE constants, ONLY : pi, tpi, fpi, e2
!
IMPLICIT NONE
!
LOGICAL :: loto_2d
!! 2D LOTO correction
INTEGER, INTENT(in) :: nr1, nr2, nr3
!! FFT grid
INTEGER, INTENT(in) :: nat
!! Number of atoms
REAL(KIND = DP), INTENT(in) :: q(3)
!! q-vector
REAL(KIND = DP), INTENT(in) :: epsil(3, 3)
!! dielectric constant tensor
REAL(KIND = DP), INTENT(IN) :: alph
!! Ewald parameter
REAL(KIND = DP), INTENT(in) :: zeu(3, 3, nat)
!! effective charges tensor
REAL(KIND = DP), INTENT(in) :: sign
!! sign =+/-1.0 ==> add/subtract rigid-ion term
REAL(KIND = DP), INTENT(in) :: tau(3, nat)
!! Atomic positions
REAL(KIND = DP), INTENT(in) :: bg(3, 3)
!! Reciprocal lattice basis vectors
REAL(KIND = DP), INTENT(in) :: omega
!! Unit cell volume
REAL(KIND = DP), INTENT(in) :: alat
!! Cell dimension units
COMPLEX(KIND = DP), INTENT(inout) :: dyn(3, 3, nat, nat)
!! Dynamical matrix
!
! Local variables
INTEGER :: nr1x, nr2x, nr3x
!! Max nr in direction 1, 2, 3
INTEGER :: na
!! Atom index 1
INTEGER :: nb
!! Atom index 2
INTEGER :: i
!! Cartesian direction 1
INTEGER :: j
!! Cartesian direction 1
INTEGER :: m1, m2, m3
!! Loop over q-points
REAL(KIND = DP):: geg
!! <q+G| epsil | q+G>
REAL(KIND = DP) :: fac
!! Prefactor
REAL(KIND = DP) :: g1, g2, g3
!! G-vectors
REAL(KIND = DP) :: facgd
!! fac * EXP(-geg / (alph * 4.0d0)) / geg
REAL(KIND = DP) :: arg
!! Argument of the function
REAL(KIND = DP) :: gmax
!! Maximum G
REAL(KIND = DP) :: zag(3)
!! Z * G
REAL(KIND = DP) :: zbg(3)
!! Z * G
REAL(KIND = DP) :: zcg(3)
!! Z * G
REAL(KIND = DP) :: fnat(3)
!! Z * G * cos(arg)
REAL(KIND = DP) :: fmtx(3, 3)
!! Z * Z * G * cos(arg)
REAL(KIND = DP) :: reff(2, 2)
!! Effective screening length for 2D materials
REAL(KIND = DP) :: grg
!! G-vector * reff * G-vector for 2D loto
COMPLEX(KIND = DP) :: facg
!! Factor
!
! geg is an estimate of G^2 such that the G-space sum is convergent
! given the value of alph
! very rough estimate: geg/4/alph > gmax = 14
! (exp (-14) = 10^-6)
!
gmax = 14.d0
geg = gmax * alph * 4.0d0
!
! Estimate of nr1x,nr2x,nr3x generating all vectors up to G^2 < geg
! Only for dimensions where periodicity is present, e.g. if nr1=1
! and nr2=1, then the G-vectors run along nr3 only.
! (useful if system is in vacuum, e.g. 1D or 2D)
!
IF (nr1 == 1) THEN
nr1x = 0
ELSE
nr1x = INT(SQRT(geg) / SQRT(bg(1, 1)**2 + bg(2, 1)**2 + bg(3, 1)**2)) + 1
ENDIF
IF (nr2 == 1) THEN
nr2x = 0
ELSE
nr2x = INT(SQRT(geg) / SQRT(bg(1, 2)**2 + bg(2, 2)**2 + bg(3, 2)**2)) + 1
ENDIF
IF (nr3 == 1) THEN
nr3x=0
ELSE
nr3x = INT(SQRT(geg) / SQRT(bg(1, 3)**2 + bg(2, 3)**2 + bg(3, 3)**2)) + 1
ENDIF
!
IF (ABS(sign) /= 1.0_DP) CALL errore('rgd_blk',' wrong value for sign ',1)
!
IF (loto_2d) THEN
! (e^2 * 2\pi) / Area
fac = (sign * e2 * tpi) / (omega * bg(3, 3) / alat)
! Effective screening length
! reff = (epsil - 1) * c/2
reff(:, :) = 0.0d0
reff(:, :) = epsil(1:2, 1:2) * 0.5d0 * tpi / bg(3, 3) ! (eps)*c/2 in 2pi/a units
reff(1, 1) = reff(1, 1) - 0.5d0 * tpi / bg(3, 3) ! (-1)*c/2 in 2pi/a units
reff(2, 2) = reff(2, 2) - 0.5d0 * tpi / bg(3, 3) ! (-1)*c/2 in 2pi/a units
ELSE
! (e^2 * 4\pi) / Volume
fac = (sign * e2 * fpi) / omega
ENDIF
DO m1 = -nr1x, nr1x
DO m2 = -nr2x, nr2x
DO m3 = -nr3x, nr3x
!
g1 = m1 * bg(1, 1) + m2 * bg(1, 2) + m3 * bg(1, 3)
g2 = m1 * bg(2, 1) + m2 * bg(2, 2) + m3 * bg(2, 3)
g3 = m1 * bg(3, 1) + m2 * bg(3, 2) + m3 * bg(3, 3)
!
IF (loto_2d) THEN
geg = g1**2 + g2**2 + g3**2
grg = 0.0d0
IF (g1**2 + g2**2 > 1.0d-8) THEN
grg = g1 * reff(1, 1) * g1 + g1 * reff(1, 2) * g2 + g2 * reff(2, 1) * g1 + g2 * reff(2, 2) * g2
grg = grg / (g1**2 + g2**2)
ENDIF
ELSE
geg = (g1 * (epsil(1, 1) * g1 + epsil(1, 2) * g2 + epsil(1, 3) * g3) + &
g2 * (epsil(2, 1) * g1 + epsil(2, 2) * g2 + epsil(2, 3) * g3) + &
g3 * (epsil(3, 1) * g1 + epsil(3, 2) * g2 + epsil(3, 3) * g3))
ENDIF
!
IF (geg > 0.0d0 .AND. geg / (alph * 4) < gmax) THEN
!
IF (loto_2d) THEN
facgd = fac * (tpi / alat) * EXP(-geg / (alph * 4.0d0)) / (SQRT(geg) * (1.0 + grg * SQRT(geg)))
ELSE
facgd = fac * EXP(-geg / (alph * 4)) / geg
ENDIF
!
!$OMP PARALLELDO DEFAULT(shared) PRIVATE(zcg,zag,arg,nb,na,i,j,fnat)
DO na = 1, nat
zag(:) = g1 * zeu(1, :, na) + g2 * zeu(2, :, na) + g3 * zeu(3, :, na)
fnat(:) = 0.d0
DO nb = 1, nat
arg = 2.d0 * pi * (g1 * (tau(1, na) - tau(1, nb)) + &
g2 * (tau(2, na) - tau(2, nb)) + &
g3 * (tau(3, na) - tau(3, nb)))
zcg(:) = g1 * zeu(1, :, nb) + g2 * zeu(2, :, nb) + g3 * zeu(3, :, nb)
fnat(:) = fnat(:) + zcg(:) * COS(arg)
ENDDO
! Impose Hermiticity on long-range part of dynamical matrix
! Symmetrize long-range part of the on-site dynamical matrix by its conjugate transpose
fmtx = MATMUL(RESHAPE(zag, (/3,1/)), RESHAPE(fnat, (/1,3/)))
fmtx = (fmtx + TRANSPOSE(fmtx)) / 2.d0
DO j = 1, 3
DO i = 1, 3
dyn(i, j, na, na) = dyn(i, j, na, na) - facgd * fmtx(i,j)
ENDDO ! i
ENDDO ! j
ENDDO ! nat
!$OMP END PARALLELDO
ENDIF ! geg
!
g1 = g1 + q(1)
g2 = g2 + q(2)
g3 = g3 + q(3)
!
IF (loto_2d) THEN
geg = g1**2 + g2**2 + g3**2
grg = 0.0d0
IF (g1**2 + g2**2 > 1d-8) THEN
grg = g1 * reff(1, 1) * g1 + g1 * reff(1, 2) * g2 + g2 * reff(2, 1) * g1 + g2 * reff(2, 2) * g2
grg = grg / (g1**2 + g2**2)
ENDIF
ELSE
geg = (g1 * (epsil(1, 1) * g1 + epsil(1, 2) * g2 + epsil(1, 3) * g3) + &
g2 * (epsil(2, 1) * g1 + epsil(2, 2) * g2 + epsil(2, 3) * g3) + &
g3 * (epsil(3, 1) * g1 + epsil(3, 2) * g2 + epsil(3, 3) * g3))
ENDIF
!
IF (geg > 0.0d0 .AND. geg / (alph * 4.0d0) < gmax) THEN
!
IF (loto_2d) THEN
facgd = fac * (tpi / alat) * EXP(-geg / (alph * 4.0d0)) / (SQRT(geg) * (1.0 + grg * SQRT(geg)))
ELSE
facgd = fac * EXP(-geg / (alph * 4.0d0)) / geg
ENDIF
!
!$OMP PARALLELDO DEFAULT(shared) PRIVATE(zbg,zag,arg,nb,na,i,j,facg)
DO nb = 1, nat
zbg(:) = g1 * zeu(1, :, nb) + g2 * zeu(2, :, nb) + g3 * zeu(3, :, nb)
DO na = 1, nat
zag(:) = g1 * zeu(1, :, na) + g2 * zeu(2, :, na) + g3 * zeu(3, :, na)
arg = 2.d0 * pi * (g1 * (tau(1, na) - tau(1 ,nb)) + &
g2 * (tau(2, na) - tau(2, nb)) + &
g3 * (tau(3, na) - tau(3, nb)) )
facg = facgd * CMPLX(COS(arg), SIN(arg), KIND=DP)
!
DO j = 1, 3
DO i = 1, 3
dyn(i, j, na, nb) = dyn(i, j, na, nb) + facg * zag(i) * zbg(j)
ENDDO ! i
ENDDO ! j
ENDDO ! na
ENDDO ! nb
!$OMP END PARALLELDO
ENDIF
ENDDO ! m3
ENDDO ! m2
ENDDO ! m1
!
RETURN
!-----------------------------------------------------------------------
END SUBROUTINE rgd_blk
!-----------------------------------------------------------------------
!
!-----------------------------------------------------------------------
subroutine nonanal(nat, nat_blk, itau_blk, epsil, q, zeu, omega, dyn )
!-----------------------------------------------------------------------
! add the nonanalytical term with macroscopic electric fields
!
use kinds, only: dp
use constants, only: pi, fpi, e2
implicit none
integer, intent(in) :: nat, nat_blk, itau_blk(nat)
! nat: number of atoms in the cell (in the supercell in the case
! of a dyn.mat. constructed in the mass approximation)
! nat_blk: number of atoms in the original cell (the same as nat if
! we are not using the mass approximation to build a supercell)
! itau_blk(na): atom in the original cell corresponding to
! atom na in the supercell
!
complex(DP), intent(inout) :: dyn(3,3,nat,nat) ! dynamical matrix
real(DP), intent(in) :: q(3), &! polarization vector
& epsil(3,3), &! dielectric constant tensor
& zeu(3,3,nat_blk), &! effective charges tensor
& omega ! unit cell volume
!
! local variables
!
real(DP) zag(3),zbg(3), &! eff. charges times g-vector
& qeq ! <q| epsil | q>
integer na,nb, &! counters on atoms
& na_blk,nb_blk, &! as above for the original cell
& i,j ! counters on cartesian coordinates
!
qeq = (q(1)*(epsil(1,1)*q(1)+epsil(1,2)*q(2)+epsil(1,3)*q(3))+ &
q(2)*(epsil(2,1)*q(1)+epsil(2,2)*q(2)+epsil(2,3)*q(3))+ &
q(3)*(epsil(3,1)*q(1)+epsil(3,2)*q(2)+epsil(3,3)*q(3)))
!
!print*, q(1), q(2), q(3)
if (qeq < 1.d-8) then
write(6,'(5x,"A direction for q was not specified:", &
& "TO-LO splitting will be absent")')
return
end if
!
do na = 1,nat
na_blk = itau_blk(na)
do nb = 1,nat
nb_blk = itau_blk(nb)
!
do i=1,3
!
zag(i) = q(1)*zeu(1,i,na_blk) + q(2)*zeu(2,i,na_blk) + &
q(3)*zeu(3,i,na_blk)
zbg(i) = q(1)*zeu(1,i,nb_blk) + q(2)*zeu(2,i,nb_blk) + &
q(3)*zeu(3,i,nb_blk)
end do
!
do i = 1,3
do j = 1,3
dyn(i,j,na,nb) = dyn(i,j,na,nb)+ fpi*e2*zag(i)*zbg(j)/qeq/omega
! print*, zag(i),zbg(j),qeq, fpi*e2*zag(i)*zbg(j)/qeq/omega
end do
end do
end do
end do
!
return
end subroutine nonanal
!-----------------------------------------------------------------------
subroutine nonanal_ifc(nat, nat_blk, itau_blk, epsil, q, zeu, omega, dyn, nr1,nr2,nr3,f_of_q )
!-----------------------------------------------------------------------
! add the nonanalytical term with macroscopic electric fields
!
use kinds, only: dp
use constants, only: pi, fpi, e2
implicit none
integer, intent(in) :: nat, nat_blk, itau_blk(nat), nr1,nr2,nr3
! nat: number of atoms in the cell (in the supercell in the case
! of a dyn.mat. constructed in the mass approximation)
! nat_blk: number of atoms in the original cell (the same as nat if
! we are not using the mass approximation to build a supercell)
! itau_blk(na): atom in the original cell corresponding to
! atom na in the supercell
!
complex(DP), intent(inout) :: dyn(3,3,nat,nat),f_of_q(3,3,nat,nat) ! dynamical matrix
real(DP), intent(in) :: q(3), &! polarization vector
& epsil(3,3), &! dielectric constant tensor
& zeu(3,3,nat_blk), &! effective charges tensor
& omega ! unit cell volume
!
! local variables
!
real(DP) zag(3),zbg(3), &! eff. charges times g-vector
& qeq ! <q| epsil | q>
integer na,nb, &! counters on atoms
& na_blk,nb_blk, &! as above for the original cell
& i,j ! counters on cartesian coordinates
!
IF ( q(1)==0.d0 .AND. &
q(2)==0.d0 .AND. &
q(3)==0.d0 ) return
!
qeq = (q(1)*(epsil(1,1)*q(1)+epsil(1,2)*q(2)+epsil(1,3)*q(3))+ &
q(2)*(epsil(2,1)*q(1)+epsil(2,2)*q(2)+epsil(2,3)*q(3))+ &
q(3)*(epsil(3,1)*q(1)+epsil(3,2)*q(2)+epsil(3,3)*q(3)))
!
!print*, q(1), q(2), q(3)
if (qeq < 1.d-8) then
write(6,'(5x,"A direction for q was not specified:", &
& "TO-LO splitting will be absent")')
return
end if
do na = 1,nat
na_blk = itau_blk(na)
do nb = 1,nat
nb_blk = itau_blk(nb)
!
do i=1,3
!
zag(i) = q(1)*zeu(1,i,na_blk) + q(2)*zeu(2,i,na_blk) + &
q(3)*zeu(3,i,na_blk)
zbg(i) = q(1)*zeu(1,i,nb_blk) + q(2)*zeu(2,i,nb_blk) + &
q(3)*zeu(3,i,nb_blk)
end do
!
do i = 1,3
do j = 1,3
! dyn(i,j,na,nb) = dyn(i,j,na,nb)+ fpi*e2*zag(i)*f_of_q*zbg(j)/qeq/omega/(nr1*nr2*nr3)
f_of_q(i,j,na,nb)=fpi*e2*zag(i)*zbg(j)/qeq/omega/(nr1*nr2*nr3)
! print*, i,j,na,nb, dyn(i,j,na,nb)
end do
end do
end do
end do
!
return
end subroutine nonanal_ifc
!
!-----------------------------------------------------------------------
subroutine dyndiag (nat,ntyp,amass,ityp,dyn,w2,z)
!-----------------------------------------------------------------------
!
! diagonalise the dynamical matrix
! On input: amass = masses, in amu
! On output: w2 = energies, z = displacements
!
use kinds, only: dp
use constants, only: amu_ry
implicit none
! input
integer nat, ntyp, ityp(nat)
complex(DP) dyn(3,3,nat,nat)
real(DP) amass(ntyp)
! output
real(DP) w2(3*nat)
complex(DP) z(3*nat,3*nat)
! local
real(DP) diff, dif1, difrel
integer nat3, na, nta, ntb, nb, ipol, jpol, i, j
complex(DP), allocatable :: dyn2(:,:)
!
! fill the two-indices dynamical matrix
!
nat3 = 3*nat
allocate(dyn2 (nat3, nat3))
!
do na = 1,nat
do nb = 1,nat
do ipol = 1,3
do jpol = 1,3
dyn2((na-1)*3+ipol, (nb-1)*3+jpol) = dyn(ipol,jpol,na,nb)
end do
end do
end do
end do
!
! impose hermiticity
!
diff = 0.d0
difrel=0.d0
do i = 1,nat3
dyn2(i,i) = CMPLX( DBLE(dyn2(i,i)),0.d0,kind=DP)
do j = 1,i - 1
dif1 = abs(dyn2(i,j)-CONJG(dyn2(j,i)))
if ( dif1 > diff .and. &
max ( abs(dyn2(i,j)), abs(dyn2(j,i))) > 1.0d-6) then
diff = dif1
difrel=diff / min ( abs(dyn2(i,j)), abs(dyn2(j,i)))
end if
dyn2(i,j) = 0.5d0* (dyn2(i,j)+CONJG(dyn2(j,i)))
dyn2(j,i) = CONJG(dyn2(i,j))
end do
end do
if ( diff > 1.d-6 ) write (6,'(5x,"Max |d(i,j)-d*(j,i)| = ",f9.6,/,5x, &
& "Max |d(i,j)-d*(j,i)|/|d(i,j)|: ",f8.4,"%")') diff, difrel*100
!
! divide by the square root of masses
!
do na = 1,nat
nta = ityp(na)
do nb = 1,nat
ntb = ityp(nb)
do ipol = 1,3
do jpol = 1,3
dyn2((na-1)*3+ipol, (nb-1)*3+jpol) = &
dyn2((na-1)*3+ipol, (nb-1)*3+jpol) / &
(amu_ry*sqrt(amass(nta)*amass(ntb)))
end do
end do
end do
end do
!
! diagonalisation
!
call cdiagh2(nat3,dyn2,nat3,w2,z)
!
deallocate(dyn2)
!
! displacements are eigenvectors divided by sqrt(amass)
!
do i = 1,nat3
do na = 1,nat
nta = ityp(na)
do ipol = 1,3
z((na-1)*3+ipol,i) = z((na-1)*3+ipol,i)/ sqrt(amu_ry*amass(nta))
end do
end do
end do
!
return
end subroutine dyndiag
!
!-----------------------------------------------------------------------
subroutine cdiagh2 (n,h,ldh,e,v)
!-----------------------------------------------------------------------
!
! calculates all the eigenvalues and eigenvectors of a complex
! hermitean matrix H . On output, the matrix is unchanged
!
use kinds, only: dp
implicit none
!
! on INPUT
integer n, &! dimension of the matrix to be diagonalized
& ldh ! leading dimension of h, as declared
! in the calling pgm unit
complex(DP) h(ldh,n) ! matrix to be diagonalized
!
! on OUTPUT
real(DP) e(n) ! eigenvalues
complex(DP) v(ldh,n) ! eigenvectors (column-wise)
!
! LOCAL variables (LAPACK version)
!
integer lwork, &! aux. var.
& ILAENV, &! function which gives block size
& nb, &! block size
& info ! flag saying if the exec. of libr. routines was ok
!
real(DP), allocatable:: rwork(:)
complex(DP), allocatable:: work(:)
!
! check for the block size
!
nb = ILAENV( 1, 'ZHETRD', 'U', n, -1, -1, -1 )
if (nb.lt.1) nb=max(1,n)
if (nb.eq.1.or.nb.ge.n) then
lwork=2*n-1
else
lwork = (nb+1)*n
endif
!
! allocate workspace
!
call zcopy(n*ldh,h,1,v,1)
allocate(work (lwork))
allocate(rwork (3*n-2))
call ZHEEV('V','U',n,v,ldh,e,work,lwork,rwork,info)
call errore ('cdiagh2','info =/= 0',abs(info))
! deallocate workspace
deallocate(rwork)
deallocate(work)
!
return
end subroutine cdiagh2
END MODULE rigid