| 1 |
!! This Module Calculates forces due to SSD potential and VDW interactions |
| 2 |
!! [Chandra and Ichiye, J. Chem. Phys. 111, 2701 (1999)]. |
| 3 |
|
| 4 |
!! This module contains the Public procedures: |
| 5 |
|
| 6 |
|
| 7 |
!! Corresponds to the force field defined in ssd_FF.cpp |
| 8 |
!! @author Charles F. Vardeman II |
| 9 |
!! @author Matthew Meineke |
| 10 |
!! @author Christopher Fennel |
| 11 |
!! @author J. Daniel Gezelter |
| 12 |
!! @version $Id: calc_sticky_pair.F90,v 1.20 2004-05-27 00:48:12 tim Exp $, $Date: 2004-05-27 00:48:12 $, $Name: not supported by cvs2svn $, $Revision: 1.20 $ |
| 13 |
|
| 14 |
module sticky_pair |
| 15 |
|
| 16 |
use force_globals |
| 17 |
use definitions |
| 18 |
use simulation |
| 19 |
#ifdef IS_MPI |
| 20 |
use mpiSimulation |
| 21 |
#endif |
| 22 |
|
| 23 |
implicit none |
| 24 |
|
| 25 |
PRIVATE |
| 26 |
|
| 27 |
logical, save :: sticky_initialized = .false. |
| 28 |
real( kind = dp ), save :: SSD_w0 = 0.0_dp |
| 29 |
real( kind = dp ), save :: SSD_v0 = 0.0_dp |
| 30 |
real( kind = dp ), save :: SSD_v0p = 0.0_dp |
| 31 |
real( kind = dp ), save :: SSD_rl = 0.0_dp |
| 32 |
real( kind = dp ), save :: SSD_ru = 0.0_dp |
| 33 |
real( kind = dp ), save :: SSD_rlp = 0.0_dp |
| 34 |
real( kind = dp ), save :: SSD_rup = 0.0_dp |
| 35 |
real( kind = dp ), save :: SSD_rbig = 0.0_dp |
| 36 |
|
| 37 |
public :: check_sticky_FF |
| 38 |
public :: set_sticky_params |
| 39 |
public :: do_sticky_pair |
| 40 |
|
| 41 |
contains |
| 42 |
|
| 43 |
subroutine check_sticky_FF(status) |
| 44 |
integer :: status |
| 45 |
status = -1 |
| 46 |
if (sticky_initialized) status = 0 |
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return |
| 48 |
end subroutine check_sticky_FF |
| 49 |
|
| 50 |
subroutine set_sticky_params(sticky_w0, sticky_v0, sticky_v0p, & |
| 51 |
sticky_rl, sticky_ru, sticky_rlp, sticky_rup) |
| 52 |
|
| 53 |
real( kind = dp ), intent(in) :: sticky_w0, sticky_v0, sticky_v0p |
| 54 |
real( kind = dp ), intent(in) :: sticky_rl, sticky_ru |
| 55 |
real( kind = dp ), intent(in) :: sticky_rlp, sticky_rup |
| 56 |
|
| 57 |
! we could pass all 5 parameters if we felt like it... |
| 58 |
|
| 59 |
SSD_w0 = sticky_w0 |
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SSD_v0 = sticky_v0 |
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SSD_v0p = sticky_v0p |
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SSD_rl = sticky_rl |
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SSD_ru = sticky_ru |
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SSD_rlp = sticky_rlp |
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SSD_rup = sticky_rup |
| 66 |
|
| 67 |
if (SSD_ru .gt. SSD_rup) then |
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SSD_rbig = SSD_ru |
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else |
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SSD_rbig = SSD_rup |
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endif |
| 72 |
|
| 73 |
sticky_initialized = .true. |
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return |
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end subroutine set_sticky_params |
| 76 |
|
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subroutine do_sticky_pair(atom1, atom2, d, rij, r2, sw, vpair, fpair, & |
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pot, A, f, t, do_pot) |
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|
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!! This routine does only the sticky portion of the SSD potential |
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!! [Chandra and Ichiye, J. Chem. Phys. 111, 2701 (1999)]. |
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!! The Lennard-Jones and dipolar interaction must be handled separately. |
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|
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!! We assume that the rotation matrices have already been calculated |
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!! and placed in the A array. |
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|
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!! i and j are pointers to the two SSD atoms |
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|
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integer, intent(in) :: atom1, atom2 |
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real (kind=dp), intent(inout) :: rij, r2 |
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real (kind=dp), dimension(3), intent(in) :: d |
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real (kind=dp), dimension(3), intent(inout) :: fpair |
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real (kind=dp) :: pot, vpair, sw |
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real (kind=dp), dimension(9,nLocal) :: A |
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real (kind=dp), dimension(3,nLocal) :: f |
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real (kind=dp), dimension(3,nLocal) :: t |
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logical, intent(in) :: do_pot |
| 98 |
|
| 99 |
real (kind=dp) :: xi, yi, zi, xj, yj, zj, xi2, yi2, zi2, xj2, yj2, zj2 |
| 100 |
real (kind=dp) :: r3, r5, r6, s, sp, dsdr, dspdr |
| 101 |
real (kind=dp) :: wi, wj, w, wip, wjp, wp |
| 102 |
real (kind=dp) :: dwidx, dwidy, dwidz, dwjdx, dwjdy, dwjdz |
| 103 |
real (kind=dp) :: dwipdx, dwipdy, dwipdz, dwjpdx, dwjpdy, dwjpdz |
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real (kind=dp) :: dwidux, dwiduy, dwiduz, dwjdux, dwjduy, dwjduz |
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real (kind=dp) :: dwipdux, dwipduy, dwipduz, dwjpdux, dwjpduy, dwjpduz |
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real (kind=dp) :: zif, zis, zjf, zjs, uglyi, uglyj |
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real (kind=dp) :: drdx, drdy, drdz |
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real (kind=dp) :: txi, tyi, tzi, txj, tyj, tzj |
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real (kind=dp) :: fxii, fyii, fzii, fxjj, fyjj, fzjj |
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real (kind=dp) :: fxij, fyij, fzij, fxji, fyji, fzji |
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real (kind=dp) :: fxradial, fyradial, fzradial |
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real (kind=dp) :: rijtest, rjitest |
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real (kind=dp) :: radcomxi, radcomyi, radcomzi |
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real (kind=dp) :: radcomxj, radcomyj, radcomzj |
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integer :: id1, id2 |
| 116 |
|
| 117 |
if (.not.sticky_initialized) then |
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write(*,*) 'Sticky forces not initialized!' |
| 119 |
return |
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endif |
| 121 |
|
| 122 |
|
| 123 |
if ( rij .LE. SSD_rbig ) then |
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|
| 125 |
r3 = r2*rij |
| 126 |
r5 = r3*r2 |
| 127 |
|
| 128 |
drdx = d(1) / rij |
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drdy = d(2) / rij |
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drdz = d(3) / rij |
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|
| 132 |
#ifdef IS_MPI |
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! rotate the inter-particle separation into the two different |
| 134 |
! body-fixed coordinate systems: |
| 135 |
|
| 136 |
xi = A_row(1,atom1)*d(1) + A_row(2,atom1)*d(2) + A_row(3,atom1)*d(3) |
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yi = A_row(4,atom1)*d(1) + A_row(5,atom1)*d(2) + A_row(6,atom1)*d(3) |
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zi = A_row(7,atom1)*d(1) + A_row(8,atom1)*d(2) + A_row(9,atom1)*d(3) |
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|
| 140 |
! negative sign because this is the vector from j to i: |
| 141 |
|
| 142 |
xj = -(A_Col(1,atom2)*d(1) + A_Col(2,atom2)*d(2) + A_Col(3,atom2)*d(3)) |
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yj = -(A_Col(4,atom2)*d(1) + A_Col(5,atom2)*d(2) + A_Col(6,atom2)*d(3)) |
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zj = -(A_Col(7,atom2)*d(1) + A_Col(8,atom2)*d(2) + A_Col(9,atom2)*d(3)) |
| 145 |
#else |
| 146 |
! rotate the inter-particle separation into the two different |
| 147 |
! body-fixed coordinate systems: |
| 148 |
|
| 149 |
xi = a(1,atom1)*d(1) + a(2,atom1)*d(2) + a(3,atom1)*d(3) |
| 150 |
yi = a(4,atom1)*d(1) + a(5,atom1)*d(2) + a(6,atom1)*d(3) |
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zi = a(7,atom1)*d(1) + a(8,atom1)*d(2) + a(9,atom1)*d(3) |
| 152 |
|
| 153 |
! negative sign because this is the vector from j to i: |
| 154 |
|
| 155 |
xj = -(a(1,atom2)*d(1) + a(2,atom2)*d(2) + a(3,atom2)*d(3)) |
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yj = -(a(4,atom2)*d(1) + a(5,atom2)*d(2) + a(6,atom2)*d(3)) |
| 157 |
zj = -(a(7,atom2)*d(1) + a(8,atom2)*d(2) + a(9,atom2)*d(3)) |
| 158 |
#endif |
| 159 |
|
| 160 |
xi2 = xi*xi |
| 161 |
yi2 = yi*yi |
| 162 |
zi2 = zi*zi |
| 163 |
|
| 164 |
xj2 = xj*xj |
| 165 |
yj2 = yj*yj |
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zj2 = zj*zj |
| 167 |
|
| 168 |
call calc_sw_fnc(rij, s, sp, dsdr, dspdr) |
| 169 |
|
| 170 |
wi = 2.0d0*(xi2-yi2)*zi / r3 |
| 171 |
wj = 2.0d0*(xj2-yj2)*zj / r3 |
| 172 |
w = wi+wj |
| 173 |
|
| 174 |
zif = zi/rij - 0.6d0 |
| 175 |
zis = zi/rij + 0.8d0 |
| 176 |
|
| 177 |
zjf = zj/rij - 0.6d0 |
| 178 |
zjs = zj/rij + 0.8d0 |
| 179 |
|
| 180 |
wip = zif*zif*zis*zis - SSD_w0 |
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wjp = zjf*zjf*zjs*zjs - SSD_w0 |
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wp = wip + wjp |
| 183 |
|
| 184 |
vpair = vpair + 0.5d0*(SSD_v0*s*w + SSD_v0p*sp*wp) |
| 185 |
if (do_pot) then |
| 186 |
#ifdef IS_MPI |
| 187 |
pot_row(atom1) = pot_row(atom1) + 0.25d0*(SSD_v0*s*w + SSD_v0p*sp*wp)*sw |
| 188 |
pot_col(atom2) = pot_col(atom2) + 0.25d0*(SSD_v0*s*w + SSD_v0p*sp*wp)*sw |
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#else |
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pot = pot + 0.5d0*(SSD_v0*s*w + SSD_v0p*sp*wp)*sw |
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#endif |
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endif |
| 193 |
|
| 194 |
dwidx = 4.0d0*xi*zi/r3 - 6.0d0*xi*zi*(xi2-yi2)/r5 |
| 195 |
dwidy = - 4.0d0*yi*zi/r3 - 6.0d0*yi*zi*(xi2-yi2)/r5 |
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dwidz = 2.0d0*(xi2-yi2)/r3 - 6.0d0*zi2*(xi2-yi2)/r5 |
| 197 |
|
| 198 |
dwjdx = 4.0d0*xj*zj/r3 - 6.0d0*xj*zj*(xj2-yj2)/r5 |
| 199 |
dwjdy = - 4.0d0*yj*zj/r3 - 6.0d0*yj*zj*(xj2-yj2)/r5 |
| 200 |
dwjdz = 2.0d0*(xj2-yj2)/r3 - 6.0d0*zj2*(xj2-yj2)/r5 |
| 201 |
|
| 202 |
uglyi = zif*zif*zis + zif*zis*zis |
| 203 |
uglyj = zjf*zjf*zjs + zjf*zjs*zjs |
| 204 |
|
| 205 |
dwipdx = -2.0d0*xi*zi*uglyi/r3 |
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dwipdy = -2.0d0*yi*zi*uglyi/r3 |
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dwipdz = 2.0d0*(1.0d0/rij - zi2/r3)*uglyi |
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|
| 209 |
dwjpdx = -2.0d0*xj*zj*uglyj/r3 |
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dwjpdy = -2.0d0*yj*zj*uglyj/r3 |
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dwjpdz = 2.0d0*(1.0d0/rij - zj2/r3)*uglyj |
| 212 |
|
| 213 |
dwidux = 4.0d0*(yi*zi2 + 0.5d0*yi*(xi2-yi2))/r3 |
| 214 |
dwiduy = 4.0d0*(xi*zi2 - 0.5d0*xi*(xi2-yi2))/r3 |
| 215 |
dwiduz = - 8.0d0*xi*yi*zi/r3 |
| 216 |
|
| 217 |
dwjdux = 4.0d0*(yj*zj2 + 0.5d0*yj*(xj2-yj2))/r3 |
| 218 |
dwjduy = 4.0d0*(xj*zj2 - 0.5d0*xj*(xj2-yj2))/r3 |
| 219 |
dwjduz = - 8.0d0*xj*yj*zj/r3 |
| 220 |
|
| 221 |
dwipdux = 2.0d0*yi*uglyi/rij |
| 222 |
dwipduy = -2.0d0*xi*uglyi/rij |
| 223 |
dwipduz = 0.0d0 |
| 224 |
|
| 225 |
dwjpdux = 2.0d0*yj*uglyj/rij |
| 226 |
dwjpduy = -2.0d0*xj*uglyj/rij |
| 227 |
dwjpduz = 0.0d0 |
| 228 |
|
| 229 |
! do the torques first since they are easy: |
| 230 |
! remember that these are still in the body fixed axes |
| 231 |
|
| 232 |
txi = 0.5d0*(SSD_v0*s*dwidux + SSD_v0p*sp*dwipdux)*sw |
| 233 |
tyi = 0.5d0*(SSD_v0*s*dwiduy + SSD_v0p*sp*dwipduy)*sw |
| 234 |
tzi = 0.5d0*(SSD_v0*s*dwiduz + SSD_v0p*sp*dwipduz)*sw |
| 235 |
|
| 236 |
txj = 0.5d0*(SSD_v0*s*dwjdux + SSD_v0p*sp*dwjpdux)*sw |
| 237 |
tyj = 0.5d0*(SSD_v0*s*dwjduy + SSD_v0p*sp*dwjpduy)*sw |
| 238 |
tzj = 0.5d0*(SSD_v0*s*dwjduz + SSD_v0p*sp*dwjpduz)*sw |
| 239 |
|
| 240 |
! go back to lab frame using transpose of rotation matrix: |
| 241 |
|
| 242 |
#ifdef IS_MPI |
| 243 |
t_Row(1,atom1) = t_Row(1,atom1) + a_Row(1,atom1)*txi + & |
| 244 |
a_Row(4,atom1)*tyi + a_Row(7,atom1)*tzi |
| 245 |
t_Row(2,atom1) = t_Row(2,atom1) + a_Row(2,atom1)*txi + & |
| 246 |
a_Row(5,atom1)*tyi + a_Row(8,atom1)*tzi |
| 247 |
t_Row(3,atom1) = t_Row(3,atom1) + a_Row(3,atom1)*txi + & |
| 248 |
a_Row(6,atom1)*tyi + a_Row(9,atom1)*tzi |
| 249 |
|
| 250 |
t_Col(1,atom2) = t_Col(1,atom2) + a_Col(1,atom2)*txj + & |
| 251 |
a_Col(4,atom2)*tyj + a_Col(7,atom2)*tzj |
| 252 |
t_Col(2,atom2) = t_Col(2,atom2) + a_Col(2,atom2)*txj + & |
| 253 |
a_Col(5,atom2)*tyj + a_Col(8,atom2)*tzj |
| 254 |
t_Col(3,atom2) = t_Col(3,atom2) + a_Col(3,atom2)*txj + & |
| 255 |
a_Col(6,atom2)*tyj + a_Col(9,atom2)*tzj |
| 256 |
#else |
| 257 |
t(1,atom1) = t(1,atom1) + a(1,atom1)*txi + a(4,atom1)*tyi + a(7,atom1)*tzi |
| 258 |
t(2,atom1) = t(2,atom1) + a(2,atom1)*txi + a(5,atom1)*tyi + a(8,atom1)*tzi |
| 259 |
t(3,atom1) = t(3,atom1) + a(3,atom1)*txi + a(6,atom1)*tyi + a(9,atom1)*tzi |
| 260 |
|
| 261 |
t(1,atom2) = t(1,atom2) + a(1,atom2)*txj + a(4,atom2)*tyj + a(7,atom2)*tzj |
| 262 |
t(2,atom2) = t(2,atom2) + a(2,atom2)*txj + a(5,atom2)*tyj + a(8,atom2)*tzj |
| 263 |
t(3,atom2) = t(3,atom2) + a(3,atom2)*txj + a(6,atom2)*tyj + a(9,atom2)*tzj |
| 264 |
#endif |
| 265 |
! Now, on to the forces: |
| 266 |
|
| 267 |
! first rotate the i terms back into the lab frame: |
| 268 |
|
| 269 |
radcomxi = (SSD_v0*s*dwidx+SSD_v0p*sp*dwipdx)*sw |
| 270 |
radcomyi = (SSD_v0*s*dwidy+SSD_v0p*sp*dwipdy)*sw |
| 271 |
radcomzi = (SSD_v0*s*dwidz+SSD_v0p*sp*dwipdz)*sw |
| 272 |
|
| 273 |
radcomxj = (SSD_v0*s*dwjdx+SSD_v0p*sp*dwjpdx)*sw |
| 274 |
radcomyj = (SSD_v0*s*dwjdy+SSD_v0p*sp*dwjpdy)*sw |
| 275 |
radcomzj = (SSD_v0*s*dwjdz+SSD_v0p*sp*dwjpdz)*sw |
| 276 |
|
| 277 |
#ifdef IS_MPI |
| 278 |
fxii = a_Row(1,atom1)*(radcomxi) + & |
| 279 |
a_Row(4,atom1)*(radcomyi) + & |
| 280 |
a_Row(7,atom1)*(radcomzi) |
| 281 |
fyii = a_Row(2,atom1)*(radcomxi) + & |
| 282 |
a_Row(5,atom1)*(radcomyi) + & |
| 283 |
a_Row(8,atom1)*(radcomzi) |
| 284 |
fzii = a_Row(3,atom1)*(radcomxi) + & |
| 285 |
a_Row(6,atom1)*(radcomyi) + & |
| 286 |
a_Row(9,atom1)*(radcomzi) |
| 287 |
|
| 288 |
fxjj = a_Col(1,atom2)*(radcomxj) + & |
| 289 |
a_Col(4,atom2)*(radcomyj) + & |
| 290 |
a_Col(7,atom2)*(radcomzj) |
| 291 |
fyjj = a_Col(2,atom2)*(radcomxj) + & |
| 292 |
a_Col(5,atom2)*(radcomyj) + & |
| 293 |
a_Col(8,atom2)*(radcomzj) |
| 294 |
fzjj = a_Col(3,atom2)*(radcomxj)+ & |
| 295 |
a_Col(6,atom2)*(radcomyj) + & |
| 296 |
a_Col(9,atom2)*(radcomzj) |
| 297 |
#else |
| 298 |
fxii = a(1,atom1)*(radcomxi) + & |
| 299 |
a(4,atom1)*(radcomyi) + & |
| 300 |
a(7,atom1)*(radcomzi) |
| 301 |
fyii = a(2,atom1)*(radcomxi) + & |
| 302 |
a(5,atom1)*(radcomyi) + & |
| 303 |
a(8,atom1)*(radcomzi) |
| 304 |
fzii = a(3,atom1)*(radcomxi) + & |
| 305 |
a(6,atom1)*(radcomyi) + & |
| 306 |
a(9,atom1)*(radcomzi) |
| 307 |
|
| 308 |
fxjj = a(1,atom2)*(radcomxj) + & |
| 309 |
a(4,atom2)*(radcomyj) + & |
| 310 |
a(7,atom2)*(radcomzj) |
| 311 |
fyjj = a(2,atom2)*(radcomxj) + & |
| 312 |
a(5,atom2)*(radcomyj) + & |
| 313 |
a(8,atom2)*(radcomzj) |
| 314 |
fzjj = a(3,atom2)*(radcomxj)+ & |
| 315 |
a(6,atom2)*(radcomyj) + & |
| 316 |
a(9,atom2)*(radcomzj) |
| 317 |
#endif |
| 318 |
|
| 319 |
fxij = -fxii |
| 320 |
fyij = -fyii |
| 321 |
fzij = -fzii |
| 322 |
|
| 323 |
fxji = -fxjj |
| 324 |
fyji = -fyjj |
| 325 |
fzji = -fzjj |
| 326 |
|
| 327 |
! now assemble these with the radial-only terms: |
| 328 |
|
| 329 |
fxradial = 0.5d0*(SSD_v0*dsdr*drdx*w + SSD_v0p*dspdr*drdx*wp + fxii + fxji) |
| 330 |
fyradial = 0.5d0*(SSD_v0*dsdr*drdy*w + SSD_v0p*dspdr*drdy*wp + fyii + fyji) |
| 331 |
fzradial = 0.5d0*(SSD_v0*dsdr*drdz*w + SSD_v0p*dspdr*drdz*wp + fzii + fzji) |
| 332 |
|
| 333 |
#ifdef IS_MPI |
| 334 |
f_Row(1,atom1) = f_Row(1,atom1) + fxradial |
| 335 |
f_Row(2,atom1) = f_Row(2,atom1) + fyradial |
| 336 |
f_Row(3,atom1) = f_Row(3,atom1) + fzradial |
| 337 |
|
| 338 |
f_Col(1,atom2) = f_Col(1,atom2) - fxradial |
| 339 |
f_Col(2,atom2) = f_Col(2,atom2) - fyradial |
| 340 |
f_Col(3,atom2) = f_Col(3,atom2) - fzradial |
| 341 |
#else |
| 342 |
f(1,atom1) = f(1,atom1) + fxradial |
| 343 |
f(2,atom1) = f(2,atom1) + fyradial |
| 344 |
f(3,atom1) = f(3,atom1) + fzradial |
| 345 |
|
| 346 |
f(1,atom2) = f(1,atom2) - fxradial |
| 347 |
f(2,atom2) = f(2,atom2) - fyradial |
| 348 |
f(3,atom2) = f(3,atom2) - fzradial |
| 349 |
#endif |
| 350 |
|
| 351 |
#ifdef IS_MPI |
| 352 |
id1 = AtomRowToGlobal(atom1) |
| 353 |
id2 = AtomColToGlobal(atom2) |
| 354 |
#else |
| 355 |
id1 = atom1 |
| 356 |
id2 = atom2 |
| 357 |
#endif |
| 358 |
|
| 359 |
if (molMembershipList(id1) .ne. molMembershipList(id2)) then |
| 360 |
|
| 361 |
fpair(1) = fpair(1) + fxradial |
| 362 |
fpair(2) = fpair(2) + fyradial |
| 363 |
fpair(3) = fpair(3) + fzradial |
| 364 |
|
| 365 |
endif |
| 366 |
endif |
| 367 |
end subroutine do_sticky_pair |
| 368 |
|
| 369 |
!! calculates the switching functions and their derivatives for a given |
| 370 |
subroutine calc_sw_fnc(r, s, sp, dsdr, dspdr) |
| 371 |
|
| 372 |
real (kind=dp), intent(in) :: r |
| 373 |
real (kind=dp), intent(inout) :: s, sp, dsdr, dspdr |
| 374 |
|
| 375 |
! distances must be in angstroms |
| 376 |
|
| 377 |
if (r.lt.SSD_rl) then |
| 378 |
s = 1.0d0 |
| 379 |
dsdr = 0.0d0 |
| 380 |
elseif (r.gt.SSD_ru) then |
| 381 |
s = 0.0d0 |
| 382 |
dsdr = 0.0d0 |
| 383 |
else |
| 384 |
s = ((SSD_ru + 2.0d0*r - 3.0d0*SSD_rl) * (SSD_ru-r)**2) / & |
| 385 |
((SSD_ru - SSD_rl)**3) |
| 386 |
dsdr = 6.0d0*(r-SSD_ru)*(r-SSD_rl)/((SSD_ru - SSD_rl)**3) |
| 387 |
endif |
| 388 |
|
| 389 |
if (r.lt.SSD_rlp) then |
| 390 |
sp = 1.0d0 |
| 391 |
dspdr = 0.0d0 |
| 392 |
elseif (r.gt.SSD_rup) then |
| 393 |
sp = 0.0d0 |
| 394 |
dspdr = 0.0d0 |
| 395 |
else |
| 396 |
sp = ((SSD_rup + 2.0d0*r - 3.0d0*SSD_rlp) * (SSD_rup-r)**2) / & |
| 397 |
((SSD_rup - SSD_rlp)**3) |
| 398 |
dspdr = 6.0d0*(r-SSD_rup)*(r-SSD_rlp)/((SSD_rup - SSD_rlp)**3) |
| 399 |
endif |
| 400 |
|
| 401 |
return |
| 402 |
end subroutine calc_sw_fnc |
| 403 |
end module sticky_pair |
