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subroutine ssd_forces(natoms, i, j, atom1, atom2, dx, dy, dz, rij, pot, r2, & |
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flx, fly, flz, tlx, tly, tlz, a) |
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|
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implicit none |
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|
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include 'f_ssd.inc' |
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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(9, max_mol) array. |
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! |
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! i and j are pointers to the two SSD molecules, while atom1 and |
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! atom2 are the pointers to the location of the atoms in the force |
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! and position arrays. These are both necessary since the rotation |
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! matrix is a property of the molecule, while the force is acting on |
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! the atom. The indexing of atoms and molecules is not necessarily |
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! the same in simulations of mixtures. |
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|
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|
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integer :: i, j, atom1, atom2, natoms |
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double precision dx, dy, dz, rij, pot, r2 |
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double precision, dimension(natoms) ::flx, fly, flz, tlx, tly, tlz |
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double precision, dimension(9,natoms):: a |
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|
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|
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double precision xi, yi, zi, xj, yj, zj, xi2, yi2, zi2, xj2, yj2, zj2 |
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double precision r3, r5, r6, s, sp, dsdr, dspdr |
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double precision wi, wj, w, wip, wjp, wp |
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double precision dwidx, dwidy, dwidz, dwjdx, dwjdy, dwjdz |
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double precision dwipdx, dwipdy, dwipdz, dwjpdx, dwjpdy, dwjpdz |
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double precision dwidux, dwiduy, dwiduz, dwjdux, dwjduy, dwjduz |
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double precision dwipdux, dwipduy, dwipduz, dwjpdux, dwjpduy, dwjpduz |
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double precision zif, zis, zjf, zjs, uglyi, uglyj |
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double precision drdx, drdy, drdz |
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double precision txi, tyi, tzi, txj, tyj, tzj |
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double precision fxii, fyii, fzii, fxjj, fyjj, fzjj |
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double precision fxij, fyij, fzij, fxji, fyji, fzji |
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|
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|
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! Use molecular positions, since the SSD model has only one atom, and the |
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! rotation matrix is for the molecule itself: |
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|
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r3 = r2*rij |
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r5 = r3*r2 |
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|
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drdx = dx / rij |
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drdy = dy / rij |
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drdz = dz / rij |
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|
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! rotate the inter-particle separation into the two different |
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! body-fixed coordinate systems: |
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|
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xi = a(1,i)*dx + a(2,i)*dy + a(3,i)*dz |
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yi = a(4,i)*dx + a(5,i)*dy + a(6,i)*dz |
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zi = a(7,i)*dx + a(8,i)*dy + a(9,i)*dz |
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|
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! negative sign because this is the vector from j to i: |
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|
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xj = -(a(1,j)*dx + a(2,j)*dy + a(3,j)*dz) |
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yj = -(a(4,j)*dx + a(5,j)*dy + a(6,j)*dz) |
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zj = -(a(7,j)*dx + a(8,j)*dy + a(9,j)*dz) |
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|
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xi2 = xi*xi |
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yi2 = yi*yi |
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zi2 = zi*zi |
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|
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xj2 = xj*xj |
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yj2 = yj*yj |
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zj2 = zj*zj |
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|
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call calc_s(rij, s, sp, dsdr, dspdr) |
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|
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wi = 2.0d0*(xi2-yi2)*zi / r3 |
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wj = 2.0d0*(xj2-yj2)*zj / r3 |
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w = wi+wj |
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|
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zif = zi/rij - 0.6d0 |
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zis = zi/rij + 0.8d0 |
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|
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zjf = zj/rij - 0.6d0 |
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zjs = zj/rij + 0.8d0 |
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|
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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 |
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|
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pot = pot + 0.5d0*SSD_v0*(s*w + sp*wp) |
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|
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dwidx = 4.0d0*xi*zi/r3 - 6.0d0*xi*zi*(xi2-yi2)/r5 |
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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 |
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|
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dwjdx = 4.0d0*xj*zj/r3 - 6.0d0*xj*zj*(xj2-yj2)/r5 |
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dwjdy = - 4.0d0*yj*zj/r3 - 6.0d0*yj*zj*(xj2-yj2)/r5 |
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dwjdz = 2.0d0*(xj2-yj2)/r3 - 6.0d0*zj2*(xj2-yj2)/r5 |
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|
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uglyi = zif*zif*zis + zif*zis*zis |
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uglyj = zjf*zjf*zjs + zjf*zjs*zjs |
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|
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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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|
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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 |
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|
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dwidux = 4.0d0*(yi*zi2 + 0.5d0*yi*(xi2-yi2))/r3 |
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dwiduy = 4.0d0*(xi*zi2 - 0.5d0*xi*(xi2-yi2))/r3 |
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dwiduz = - 8.0d0*xi*yi*zi/r3 |
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|
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dwjdux = 4.0d0*(yj*zj2 + 0.5d0*yj*(xj2-yj2))/r3 |
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dwjduy = 4.0d0*(xj*zj2 - 0.5d0*xj*(xj2-yj2))/r3 |
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dwjduz = - 8.0d0*xj*yj*zj/r3 |
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|
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dwipdux = 2.0d0*yi*uglyi/rij |
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dwipduy = -2.0d0*xi*uglyi/rij |
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dwipduz = 0.0d0 |
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|
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dwjpdux = 2.0d0*yj*uglyj/rij |
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dwjpduy = -2.0d0*xj*uglyj/rij |
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dwjpduz = 0.0d0 |
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|
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! do the torques first since they are easy: |
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! remember that these are still in the body fixed axes |
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|
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txi = 0.5d0*SSD_v0*(s*dwidux + sp*dwipdux) |
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tyi = 0.5d0*SSD_v0*(s*dwiduy + sp*dwipduy) |
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tzi = 0.5d0*SSD_v0*(s*dwiduz + sp*dwipduz) |
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|
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txj = 0.5d0*SSD_v0*(s*dwjdux + sp*dwjpdux) |
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tyj = 0.5d0*SSD_v0*(s*dwjduy + sp*dwjpduy) |
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tzj = 0.5d0*SSD_v0*(s*dwjduz + sp*dwjpduz) |
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|
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! go back to lab frame using transpose of rotation matrix: |
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|
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tlx(atom1) = tlx(atom1) + a(1,i)*txi + a(4,i)*tyi + a(7,i)*tzi |
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tly(atom1) = tly(atom1) + a(2,i)*txi + a(5,i)*tyi + a(8,i)*tzi |
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tlz(atom1) = tlz(atom1) + a(3,i)*txi + a(6,i)*tyi + a(9,i)*tzi |
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|
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tlx(atom2) = tlx(atom2) + a(1,j)*txj + a(4,j)*tyj + a(7,j)*tzj |
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tly(atom2) = tly(atom2) + a(2,j)*txj + a(5,j)*tyj + a(8,j)*tzj |
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tlz(atom2) = tlz(atom2) + a(3,j)*txj + a(6,j)*tyj + a(9,j)*tzj |
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|
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! Now, on to the forces: |
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|
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! first rotate the i terms back into the lab frame: |
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|
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fxii = a(1,i)*(s*dwidx+sp*dwipdx) + & |
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a(4,i)*(s*dwidy+sp*dwipdy) + & |
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a(7,i)*(s*dwidz+sp*dwipdz) |
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fyii = a(2,i)*(s*dwidx+sp*dwipdx) + & |
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a(5,i)*(s*dwidy+sp*dwipdy) + & |
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a(8,i)*(s*dwidz+sp*dwipdz) |
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fzii = a(3,i)*(s*dwidx+sp*dwipdx) + & |
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a(6,i)*(s*dwidy+sp*dwipdy) + & |
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a(9,i)*(s*dwidz+sp*dwipdz) |
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|
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fxij = -fxii |
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fyij = -fyii |
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fzij = -fzii |
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|
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fxjj = a(1,j)*(s*dwjdx+sp*dwjpdx) + & |
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a(4,j)*(s*dwjdy+sp*dwjpdy) + & |
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a(7,j)*(s*dwjdz+sp*dwjpdz) |
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fyjj = a(2,j)*(s*dwjdx+sp*dwjpdx) + & |
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a(5,j)*(s*dwjdy+sp*dwjpdy) + & |
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a(8,j)*(s*dwjdz+sp*dwjpdz) |
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fzjj = a(3,j)*(s*dwjdx+sp*dwjpdx)+ & |
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a(6,j)*(s*dwjdy+sp*dwjpdy) + & |
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a(9,j)*(s*dwjdz+sp*dwjpdz) |
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|
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fxji = -fxjj |
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fyji = -fyjj |
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fzji = -fzjj |
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|
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! now assemble these with the radial-only terms: |
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|
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flx(atom1) = flx(atom1) + 0.5d0*SSD_v0*(dsdr*drdx*w + dspdr*drdx*wp + & |
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fxii + fxji) |
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fly(atom1) = fly(atom1) + 0.5d0*SSD_v0*(dsdr*drdy*w + dspdr*drdy*wp + & |
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fyii + fyji) |
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flz(atom1) = flz(atom1) + 0.5d0*SSD_v0*(dsdr*drdz*w + dspdr*drdz*wp + & |
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fzii + fzji) |
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|
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flx(atom2) = flx(atom2) + 0.5d0*SSD_v0*(-dsdr*drdx*w - dspdr*drdx*wp + & |
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fxjj + fxij) |
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fly(atom2) = fly(atom2) + 0.5d0*SSD_v0*(-dsdr*drdy*w - dspdr*drdy*wp + & |
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fyjj + fyij) |
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flz(atom2) = flz(atom2) + 0.5d0*SSD_v0*(-dsdr*drdz*w - dspdr*drdz*wp + & |
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fzjj + fzij) |
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|
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return |
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end subroutine ssd_forces |
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|
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subroutine calc_s(r, s, sp, dsdr, dspdr) |
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|
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! calculates the switching functions and their derivatives for a given |
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! value of r |
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|
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double precision r, s, sp, dsdr, dspdr |
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double precision rl, ru, rup |
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! distances are in angstroms |
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parameter(rl = 2.75d0, ru = 3.35d0, rup = 4.0d0) |
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|
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if (r.lt.rl) then |
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s = 1.0d0 |
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sp = 1.0d0 |
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dsdr = 0.0d0 |
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dspdr = 0.0d0 |
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elseif (r.gt.rup) then |
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s = 0.0d0 |
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sp = 0.0d0 |
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dsdr = 0.0d0 |
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dspdr = 0.0d0 |
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else |
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sp = ((rup + 2.0d0*r - 3.0d0*rl) * (rup-r)**2)/((rup - rl)**3) |
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dspdr = 6.0d0*(r-rup)*(r-rl)/((rup - rl)**3) |
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|
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if (r.gt.ru) then |
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s = 0.0d0 |
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dsdr = 0.0d0 |
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else |
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s = ((ru + 2.0d0*r - 3.0d0*rl) * (ru-r)**2)/((ru - rl)**3) |
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dsdr = 6.0d0*(r-ru)*(r-rl)/((ru - rl)**3) |
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endif |
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endif |
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|
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return |
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end subroutine calc_s |
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