mirror of https://gitlab.com/QEF/q-e.git
194 lines
5.9 KiB
Fortran
194 lines
5.9 KiB
Fortran
!
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! Copyright (C) 2001 PWSCF group
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! This file is distributed under the terms of the
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! GNU General Public License. See the file `License'
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! in the root directory of the present distribution,
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! or http://www.gnu.org/copyleft/gpl.txt .
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!
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!-----------------------------------------------------------------------
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subroutine dqvan2 (ngy, ih, jh, np, qmod, dqg, ylmk0, dylmk0, ipol)
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!-----------------------------------------------------------------------
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!
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! This routine computes the derivatives of the fourier transform of
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! the Q function needed in stress assuming that the radial fourier
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! trasform is already computed and stored in table qrad.
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!
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! The formula implemented here is
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!
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! dq(g,l,k) = sum_lm (-i)^l ap(lm,l,k) *
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! ( yr_lm(g^) dqrad(g,l,l,k) + dyr_lm(g^) qrad(g,l,l,k))
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!
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! here the dummy variables
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!
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#include "f_defs.h"
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USE kinds, ONLY: DP
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USE gvect, ONLY: g
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USE us, ONLY: dq, qrad
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USE uspp_param, ONLY: lmaxq, nbetam
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USE uspp, ONLY: nlx, lpl, lpx, ap, indv, nhtol, nhtolm
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implicit none
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integer :: ngy, ih, jh, np, ipol
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! input: the number of G vectors to compute
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! input: the first index of Q
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! input: the second index of Q
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! input: the number of the pseudopotential
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! input: the polarization of the derivative
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real(DP) :: ylmk0 (ngy, lmaxq * lmaxq), dylmk0 (ngy, lmaxq * lmaxq), &
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qmod (ngy)
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! the spherical harmonics
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! the spherical harmonics derivetives
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! input: moduli of the q+g vectors
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complex(DP) :: dqg (ngy)
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! output: the fourier transform of interest
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!
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! here the local variables
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!
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complex(DP) :: sig
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! (-i)^L
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integer :: nb, mb, ijv, ivl, jvl, ig, lp, l, lm, i0, i1, i2, i3
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! the atomic index corresponding to ih
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! the atomic index corresponding to jh
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! combined index (nb,mb)
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! the lm corresponding to ih
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! the lm corresponding to jh
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! counter on g vectors
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! the actual LM
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! the angular momentum L
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! the possible LM's compatible with ih,j
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! counters for interpolation table
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real(DP) :: sixth, dqi, qm, px, ux, vx, wx, uvx, pwx, work, work1
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! 1 divided by six
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! 1 divided dq
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! qmod/dq
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! measures for interpolation table
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! auxiliary variables for intepolation
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! auxiliary variable
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! auxiliary variable
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!
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! compute the indices which correspond to ih,jh
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!
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sixth = 1.d0 / 6.d0
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dqi = 1 / dq
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nb = indv (ih, np)
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mb = indv (jh, np)
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if (nb.ge.mb) then
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ijv = nb * (nb - 1) / 2 + mb
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else
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ijv = mb * (mb - 1) / 2 + nb
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endif
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ivl = nhtolm (ih, np)
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jvl = nhtolm (jh, np)
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if (nb > nbetam .OR. mb > nbetam) &
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call errore (' dqvan2 ', ' wrong dimensions (1)', MAX(nb,mb))
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if (ivl > nlx .OR. jvl > nlx) &
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call errore (' dqvan2 ', ' wrong dimensions (2)', MAX(ivl,jvl))
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dqg(:) = (0.d0,0.d0)
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!
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! and make the sum over the non zero LM
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!
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do lm = 1, lpx (ivl, jvl)
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lp = lpl (ivl, jvl, lm)
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!
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! extraction of angular momentum l from lp:
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!
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if (lp.eq.1) then
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l = 1
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elseif ( (lp.ge.2) .and. (lp.le.4) ) then
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l = 2
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elseif ( (lp.ge.5) .and. (lp.le.9) ) then
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l = 3
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elseif ( (lp.ge.10) .and. (lp.le.16) ) then
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l = 4
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elseif ( (lp.ge.17) .and. (lp.le.25) ) then
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l = 5
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elseif ( (lp.ge.26) .and. (lp.le.36) ) then
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l = 6
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elseif ( (lp.ge.37) .and. (lp.le.49) ) then
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l = 7
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else
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call errore (' qvan ', ' lp.gt.49 ', lp)
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endif
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sig = (0.d0, -1.d0) ** (l - 1)
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sig = sig * ap (lp, ivl, jvl)
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!
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! need to explicitly do qmod(1) outside of the loop to avoid
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! out of bounds array access
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!
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qm = qmod (1) * dqi
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px = qm - int (qm)
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ux = 1.d0 - px
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vx = 2.d0 - px
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wx = 3.d0 - px
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i0 = qm + 1
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i1 = i0 + 1
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i2 = i0 + 2
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i3 = i0 + 3
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uvx = ux * vx * sixth
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pwx = px * wx * 0.5d0
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work = qrad (i0, ijv, l, np) * uvx * wx + &
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qrad (i1, ijv, l, np) * pwx * vx - &
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qrad (i2, ijv, l, np) * pwx * ux + &
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qrad (i3, ijv, l, np) * px * uvx
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work1 = - qrad(i0, ijv, l, np) * (ux*vx + vx*wx + ux*wx) * sixth &
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+ qrad(i1, ijv, l, np) * (wx*vx - px*wx - px*vx) * 0.5d0 &
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- qrad(i2, ijv, l, np) * (wx*ux - px*wx - px*ux) * 0.5d0 &
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+ qrad(i3, ijv, l, np) * (ux*vx - px*ux - px*vx) * sixth
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work1 = work1 * dqi
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dqg (1) = dqg (1) + sig * dylmk0 (1, lp) * work
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if (qmod (1) .gt.1.d-9) dqg (1) = dqg (1) + &
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sig * ylmk0 (1, lp) * work1 * g (ipol, 1) / qmod (1)
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!
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! and now the rest starting at ig=2
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!
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do ig = 2, ngy
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!
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! calculate quantites depending on the module of G only when needed
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!
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if (abs (qmod (ig) - qmod (ig - 1) ) .gt.1.0d-6) then
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qm = qmod (ig) * dqi
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px = qm - int (qm)
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ux = 1.d0 - px
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vx = 2.d0 - px
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wx = 3.d0 - px
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i0 = qm + 1
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i1 = i0 + 1
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i2 = i0 + 2
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i3 = i0 + 3
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uvx = ux * vx * sixth
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pwx = px * wx * 0.5d0
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work = qrad (i0, ijv, l, np) * uvx * wx + &
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qrad (i1, ijv, l, np) * pwx * vx - &
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qrad (i2, ijv, l, np) * pwx * ux + &
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qrad (i3, ijv, l, np) * px * uvx
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work1 = - qrad(i0, ijv, l, np) * (ux*vx + vx*wx + ux*wx) * sixth &
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+ qrad(i1, ijv, l, np) * (wx*vx - px*wx - px*vx) * 0.5d0 &
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- qrad(i2, ijv, l, np) * (wx*ux - px*wx - px*ux) * 0.5d0 &
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+ qrad(i3, ijv, l, np) * (ux*vx - px*ux - px*vx) * sixth
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work1 = work1 * dqi
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end if
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dqg (ig) = dqg (ig) + sig * dylmk0 (ig, lp) * work
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if (qmod (ig) .gt.1.d-9) dqg (ig) = dqg (ig) + &
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sig * ylmk0 (ig, lp) * work1 * g (ipol, ig) / qmod (ig)
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enddo
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enddo
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return
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end subroutine dqvan2
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