mirror of https://gitlab.com/QEF/q-e.git
302 lines
9.1 KiB
Fortran
302 lines
9.1 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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!-----------------------------------------------------------------------
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subroutine d2ionq (nat, ntyp, ityp, zv, tau, alat, omega, q, at, &
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bg, g, gg, ngm, gcutm, nmodes, u, dyn)
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!-----------------------------------------------------------------------
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!
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! This routine computes the contribution of the ions to the
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! dynamical matrix. Both the real and reciprocal space terms
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! are included.
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!
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! The original routine was from C. Bungaro.
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! Revised 16 oct. 1995 by Andrea Dal Corso.
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! April 1997: parallel stuff added (SdG)
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!
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#include "machine.h"
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use parameters, only : DP
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implicit none
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!
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! first the dummy variables
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!
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integer :: nat, ntyp, ngm, ityp (nat), nmodes
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! input: the number of atoms
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! input: the number of types of atoms
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! input: the number of G vectors
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! input: the type of each atom
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! input: the number of modes
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real(kind=DP) :: tau (3, nat), g (3, ngm), gg (ngm), zv (ntyp), &
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at (3, 3), bg (3, 3), omega, alat, gcutm, q (3)
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! input: the positions of the atoms
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! input: the coordinates of g vectors
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! input: the modulus of g vectors
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! input: the charge of each type
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! input: the direct lattice vectors
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! input: the reciprocal lattice vectors
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! input: the volume of the unit cell
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! input: the length scale
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! input: cut-off of g vectors
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! input: the q vector
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complex(kind=DP) :: dyn (3 * nat, nmodes), u (3 * nat, nmodes)
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! output: the ionic part of the dyn. mat
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! input: the pattern of the modes
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!
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! three parameters
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!
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integer :: mxr
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! the maximum number of r shells
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real(kind=DP) :: e2, tpi
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! the electron charge
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! twp times pi
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parameter (mxr = 100, e2 = 2.d0, tpi = 2.d0 * 3.14159265358979d0)
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integer :: nu_i, nu_j, na, nb, nta, ntb, ng, nrm, nr, icart, &
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jcart, na_icart, na_jcart, nb_icart, nb_jcart
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! counter on the modes
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! counter on the modes
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! counter on atoms
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! counter on atoms
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! the type of atom na
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! the type of atom nb
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! counter on G vectors
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! the real number of R shells
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! counter on r shells
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! counter on cartesian coordinates
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! counter on cartesian coordinates
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! counter on the modes
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! counter on the modes
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! counter on the modes
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! counter on the modes
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real(kind=DP) :: arg, fpi, argq, tpiba2, alpha, r (3, mxr), r2 (mxr), &
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dtau (3), erfc, rmax, rr, upperbound, charge, fac, df, d2f, ar, &
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gtq2, gt2, facq, qrg
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! the argument of the phase
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! 4 times pi
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! the argument of the phase
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! two pi / alat
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! the parameter alpha used to converge the summ
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! the R_i-\tau_s-\tau_s' parameter
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! the square of this parameter
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! delta tau
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! the erfc function
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! the maximum r on real space summations
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! the rmax
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! an estimate of the error in the real term
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! the total charge
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! the phase factor
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! auxiliary variable
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! auxiliary variable
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!
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! the modulus of |q+G|
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! the modulus of G
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! a phase factor
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!
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complex(kind=DP) :: dy1 (3 * nat, nmodes), dy2 (3 * nat, nmodes), &
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dy3 (3 * nat, nmodes), facg, fnat, work
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! the first term dynamical matrix
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! the second dynamical matrix
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! the third term of the dynamical matrix
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! a phase with g
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! a phase with the atoms
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! working space
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call start_clock ('d2ionq')
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tpiba2 = (tpi / alat) **2
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fpi = 2.d0 * tpi
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charge = 0.d0
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do na = 1, nat
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charge = charge+zv (ityp (na) )
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enddo
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!
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! choose alpha in order to have convergence in the sum over G
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! upperbound is an upper bound for the error in the sum over G
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! estimated for the energy (empirical trust!)
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!
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alpha = 2.9d0
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11 alpha = alpha - 0.1d0
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if (alpha.eq.0.d0) call errore ('d2ion', 'optimal alpha not found', &
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1)
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upperbound = 2.d0 * charge**2 * sqrt (2.d0 * alpha / tpi) * erfc ( &
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sqrt (tpiba2 * gcutm / 4.d0 / alpha) )
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if (upperbound.gt.1.d-9) goto 11
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write (6, '(/5x,"Alpha used in Ewald sum = ",f8.4)') alpha
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call setv (2 * 3 * nat * nmodes, 0.d0, dy1, 1)
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call setv (2 * 3 * nat * nmodes, 0.d0, dy2, 1)
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call setv (2 * 3 * nat * nmodes, 0.d0, dy3, 1)
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!
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! G-space sums here
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!
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do ng = 1, ngm
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!
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! The reciprocal space term has two contributions. The first one
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!
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gtq2 = ( (g (1, ng) + q (1) ) **2 + (g (2, ng) + q (2) ) **2 + &
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(g (3, ng) + q (3) ) **2) * tpiba2
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if (abs (gtq2) .gt.1.d-8) then
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facq = - e2 * fpi * tpiba2 / omega * exp ( - gtq2 / alpha / &
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4.d0) / gtq2
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else
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facq = 0.d0
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endif
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do na = 1, nat
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nta = ityp (na)
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do nb = 1, nat
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ntb = ityp (nb)
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argq = tpi * ( (g (1, ng) + q (1) ) * (tau (1, na) - tau (1, nb) ) &
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+ (g (2, ng) + q (2) ) * (tau (2, na) - tau (2, nb) ) + (g (3, ng) &
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+ q (3) ) * (tau (3, na) - tau (3, nb) ) )
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facg = facq * zv (nta) * zv (ntb) * DCMPLX (cos (argq), sin (argq) &
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)
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do icart = 1, 3
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nu_i = 3 * (na - 1) + icart
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do jcart = 1, 3
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nu_j = 3 * (nb - 1) + jcart
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dy1 (nu_i, nu_j) = dy1 (nu_i, nu_j) + facg * (q (icart) + g ( &
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icart, ng) ) * (q (jcart) + g (jcart, ng) )
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enddo
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enddo
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enddo
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enddo
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!
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! the second term
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!
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gt2 = gg (ng) * tpiba2
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if (abs (gt2) .gt.1.d-8) then
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fac = - e2 * fpi * tpiba2 / omega * exp ( - gt2 / alpha / 4.d0) &
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/ gt2
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else
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fac = 0.d0
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endif
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do na = 1, nat
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nta = ityp (na)
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fnat = (0.d0, 0.d0)
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do nb = 1, nat
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ntb = ityp (nb)
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arg = tpi * ( (g (1, ng) ) * (tau (1, na) - tau (1, nb) ) + &
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(g (2, ng) ) * (tau (2, na) - tau (2, nb) ) + (g (3, ng) ) &
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* (tau (3, na) - tau (3, nb) ) )
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facg = fac * zv (nta) * zv (ntb) * DCMPLX (cos (arg), 0.d0)
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fnat = fnat + facg
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enddo
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do icart = 1, 3
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nu_i = 3 * (na - 1) + icart
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do jcart = 1, 3
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nu_j = 3 * (na - 1) + jcart
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dy2 (nu_i, nu_j) = dy2 (nu_i, nu_j) + fnat * g (icart, ng) &
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* g (jcart, ng)
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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 nu_i = 1, nmodes
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do nu_j = 1, nmodes
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dy3 (nu_i, nu_j) = dy3 (nu_i, nu_j) + dy1 (nu_i, nu_j) - dy2 ( &
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nu_i, nu_j)
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enddo
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enddo
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!
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! Then there is also a part in real space which is computed here.
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#ifdef __PARA
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! ... only by the node that contains G=0
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!
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if (gg (1) .gt.1.d-8) goto 100
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#endif
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!
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rmax = 5.d0 / sqrt (alpha) / alat
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!
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! with this choice terms up to ZiZj*erfc(5) are counted (erfc(5)=2x10^-1
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!
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do na = 1, nat
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nta = ityp (na)
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do nb = 1, nat
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ntb = ityp (nb)
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do icart = 1, 3
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dtau (icart) = tau (icart, na) - tau (icart, nb)
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enddo
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!
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! generates nearest-neighbors shells r(i)=R(i)-dtau(i)
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!
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call rgen (dtau, rmax, mxr, at, bg, r, r2, nrm)
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do nr = 1, nrm
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rr = sqrt (r2 (nr) ) * alat
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ar = sqrt (alpha) * rr
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qrg = tpi * (q (1) * (r (1, nr) + dtau (1) ) + q (2) * (r (2, nr) &
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+ dtau (2) ) + q (3) * (r (3, nr) + dtau (3) ) )
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d2f = (3.d0 * erfc (ar) + sqrt (8.d0 / tpi) * ar * (3.d0 + 2.d0 * &
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ar**2) * exp ( - ar**2) ) / rr**5
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df = ( - erfc (ar) - sqrt (8.d0 / tpi) * ar * exp ( - ar**2) ) &
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/ rr**3
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do icart = 1, 3
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na_icart = 3 * (na - 1) + icart
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nb_icart = 3 * (nb - 1) + icart
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do jcart = 1, 3
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nb_jcart = 3 * (nb - 1) + jcart
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na_jcart = 3 * (na - 1) + jcart
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dy3 (na_icart, nb_jcart) = dy3 (na_icart, nb_jcart) + e2 * zv ( &
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nta) * zv (ntb) * DCMPLX (cos (qrg), sin (qrg) ) * (d2f * alat * &
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r (icart, nr) * alat * r (jcart, nr) )
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dy3 (na_icart, na_jcart) = dy3 (na_icart, na_jcart) - e2 * zv ( &
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nta) * zv (ntb) * (d2f * alat * r (icart, nr) * alat * r (jcart, &
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nr) )
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enddo
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dy3 (na_icart, nb_icart) = dy3 (na_icart, nb_icart) + e2 * zv ( &
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nta) * zv (ntb) * DCMPLX (cos (qrg), sin (qrg) ) * df
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dy3 (na_icart, na_icart) = dy3 (na_icart, na_icart) - e2 * zv ( &
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nta) * zv (ntb) * df
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enddo
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enddo
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enddo
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enddo
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#ifdef __PARA
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100 continue
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call reduce (18 * nat * nat, dy3)
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#endif
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!
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! The dynamical matrix was computed in cartesian axis and now we put
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! it on the basis of the modes
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!
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do nu_i = 1, nmodes
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do nu_j = 1, nmodes
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work = (0.d0, 0.d0)
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do nb_jcart = 1, 3 * nat
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do na_icart = 1, 3 * nat
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work = work + conjg (u (na_icart, nu_i) ) * dy3 (na_icart, &
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nb_jcart) * u (nb_jcart, nu_j)
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enddo
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enddo
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dyn (nu_i, nu_j) = dyn (nu_i, nu_j) - work
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enddo
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enddo
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call stop_clock ('d2ionq')
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return
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end subroutine d2ionq
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