| 1 |
module gb_pair |
| 2 |
use force_globals |
| 3 |
use definitions |
| 4 |
#ifdef IS_MPI |
| 5 |
use mpiSimulation |
| 6 |
#endif |
| 7 |
|
| 8 |
implicit none |
| 9 |
|
| 10 |
PRIVATE |
| 11 |
|
| 12 |
logical, save :: gb_pair_initialized = .false. |
| 13 |
real(kind=dp), save :: gb_sigma |
| 14 |
real(kind=dp), save :: gb_l2b_ratio |
| 15 |
real(kind=dp), save :: gb_eps |
| 16 |
real(kind=dp), save :: gb_eps_ratio |
| 17 |
real(kind=dp), save :: gb_mu |
| 18 |
real(kind=dp), save :: gb_nu |
| 19 |
|
| 20 |
public :: check_gb_pair_FF |
| 21 |
public :: set_gb_pair_params |
| 22 |
public :: do_gb_pair |
| 23 |
|
| 24 |
contains |
| 25 |
|
| 26 |
subroutine check_gb_pair_FF(status) |
| 27 |
integer :: status |
| 28 |
status = -1 |
| 29 |
if (gb_pair_initialized) status = 0 |
| 30 |
return |
| 31 |
end subroutine check_gb_pair_FF |
| 32 |
|
| 33 |
subroutine set_gb_pair_params(sigma, l2b_ratio, eps, eps_ratio, mu, nu) |
| 34 |
real( kind = dp ), intent(in) :: sigma, l2b_ratio, eps, eps_ratio |
| 35 |
real( kind = dp ), intent(in) :: mu, nu |
| 36 |
|
| 37 |
gb_sigma = sigma |
| 38 |
gb_l2b_ratio = l2b_ratio |
| 39 |
gb_eps = eps |
| 40 |
gb_eps_ratio = eps_ratio |
| 41 |
gb_mu = mu |
| 42 |
gb_nu = nu |
| 43 |
|
| 44 |
gb_pair_initialized = .true. |
| 45 |
return |
| 46 |
end subroutine set_gb_pair_params |
| 47 |
|
| 48 |
|
| 49 |
subroutine do_gb_pair(atom1, atom2, d, r, r2, u_l, pot, f, t, & |
| 50 |
do_pot, do_stress) |
| 51 |
|
| 52 |
integer, intent(in) :: atom1, atom2 |
| 53 |
real (kind=dp), intent(inout) :: r, r2 |
| 54 |
real (kind=dp), dimension(3), intent(in) :: d |
| 55 |
real (kind=dp) :: pot |
| 56 |
real (kind=dp), dimension(:,:) :: u_l |
| 57 |
real (kind=dp), dimension(:,:) :: f |
| 58 |
real (kind=dp), dimension(:,:) :: t |
| 59 |
logical, intent(in) :: do_pot, do_stress |
| 60 |
real (kind = dp), dimension(3) :: ul1 |
| 61 |
real (kind = dp), dimension(3) :: ul2 |
| 62 |
|
| 63 |
real(kind=dp) :: chi, chiprime, emu, s2 |
| 64 |
real(kind=dp) :: r4, rdotu1, rdotu2, u1dotu2, g, gp, gpi, gmu, gmum |
| 65 |
real(kind=dp) :: curlyE, enu, enum, eps, dotsum, dotdiff, ds2, dd2 |
| 66 |
real(kind=dp) :: opXdot, omXdot, opXpdot, omXpdot, pref, gfact |
| 67 |
real(kind=dp) :: BigR, Ri, Ri2, Ri6, Ri7, Ri12, Ri13, R126, R137 |
| 68 |
real(kind=dp) :: dru1dx, dru1dy, dru1dz |
| 69 |
real(kind=dp) :: dru2dx, dru2dy, dru2dz |
| 70 |
real(kind=dp) :: dBigRdx, dBigRdy, dBigRdz |
| 71 |
real(kind=dp) :: dBigRdu1x, dBigRdu1y, dBigRdu1z |
| 72 |
real(kind=dp) :: dBigRdu2x, dBigRdu2y, dBigRdu2z |
| 73 |
real(kind=dp) :: dUdx, dUdy, dUdz |
| 74 |
real(kind=dp) :: dUdu1x, dUdu1y, dUdu1z, dUdu2x, dUdu2y, dUdu2z |
| 75 |
real(kind=dp) :: dcE, dcEdu1x, dcEdu1y, dcEdu1z, dcEdu2x, dcEdu2y, dcEdu2z |
| 76 |
real(kind=dp) :: depsdu1x, depsdu1y, depsdu1z, depsdu2x, depsdu2y, depsdu2z |
| 77 |
real(kind=dp) :: drdx, drdy, drdz |
| 78 |
real(kind=dp) :: dgdx, dgdy, dgdz |
| 79 |
real(kind=dp) :: dgdu1x, dgdu1y, dgdu1z, dgdu2x, dgdu2y, dgdu2z |
| 80 |
real(kind=dp) :: dgpdx, dgpdy, dgpdz |
| 81 |
real(kind=dp) :: dgpdu1x, dgpdu1y, dgpdu1z, dgpdu2x, dgpdu2y, dgpdu2z |
| 82 |
real(kind=dp) :: line1a, line1bx, line1by, line1bz |
| 83 |
real(kind=dp) :: line2a, line2bx, line2by, line2bz |
| 84 |
real(kind=dp) :: line3a, line3b, line3, line3x, line3y, line3z |
| 85 |
real(kind=dp) :: term1x, term1y, term1z, term1u1x, term1u1y, term1u1z |
| 86 |
real(kind=dp) :: term1u2x, term1u2y, term1u2z |
| 87 |
real(kind=dp) :: term2a, term2b, term2u1x, term2u1y, term2u1z |
| 88 |
real(kind=dp) :: term2u2x, term2u2y, term2u2z |
| 89 |
real(kind=dp) :: yick1, yick2, mess1, mess2 |
| 90 |
|
| 91 |
s2 = (gb_l2b_ratio)**2 |
| 92 |
emu = (gb_eps_ratio)**(1.0d0/gb_mu) |
| 93 |
|
| 94 |
chi = (s2 - 1.0d0)/(s2 + 1.0d0) |
| 95 |
chiprime = (1.0d0 - emu)/(1.0d0 + emu) |
| 96 |
|
| 97 |
r4 = r2*r2 |
| 98 |
|
| 99 |
#ifdef IS_MPI |
| 100 |
ul1(1) = u_l_Row(1,atom1) |
| 101 |
ul1(2) = u_l_Row(2,atom1) |
| 102 |
ul1(3) = u_l_Row(3,atom1) |
| 103 |
|
| 104 |
ul2(1) = u_l_Col(1,atom2) |
| 105 |
ul2(2) = u_l_Col(2,atom2) |
| 106 |
ul2(3) = u_l_Col(3,atom2) |
| 107 |
#else |
| 108 |
ul1(1) = u_l(1,atom1) |
| 109 |
ul1(2) = u_l(2,atom1) |
| 110 |
ul1(3) = u_l(3,atom1) |
| 111 |
|
| 112 |
ul2(1) = u_l(1,atom2) |
| 113 |
ul2(2) = u_l(2,atom2) |
| 114 |
ul2(3) = u_l(3,atom2) |
| 115 |
#endif |
| 116 |
|
| 117 |
dru1dx = ul1(1) |
| 118 |
dru2dx = ul2(1) |
| 119 |
dru1dy = ul1(2) |
| 120 |
dru2dy = ul2(2) |
| 121 |
dru1dz = ul1(3) |
| 122 |
dru2dz = ul2(3) |
| 123 |
|
| 124 |
drdx = d(1) / r |
| 125 |
drdy = d(2) / r |
| 126 |
drdz = d(3) / r |
| 127 |
|
| 128 |
! do some dot products: |
| 129 |
! NB the r in these dot products is the actual intermolecular vector, |
| 130 |
! and is not the unit vector in that direction. |
| 131 |
|
| 132 |
rdotu1 = d(1)*ul1(1) + d(2)*ul1(2) + d(3)*ul1(3) |
| 133 |
rdotu2 = d(1)*ul2(1) + d(2)*ul2(2) + d(3)*ul2(3) |
| 134 |
u1dotu2 = ul1(1)*ul2(1) + ul1(2)*ul2(2) + ul1(3)*ul2(3) |
| 135 |
|
| 136 |
! This stuff is all for the calculation of g(Chi) and dgdx |
| 137 |
! Line numbers roughly follow the lines in equation A25 of Luckhurst |
| 138 |
! et al. Liquid Crystals 8, 451-464 (1990). |
| 139 |
! We note however, that there are some major typos in that Appendix |
| 140 |
! of the Luckhurst paper, particularly in equations A23, A29 and A31 |
| 141 |
! We have attempted to correct them below. |
| 142 |
|
| 143 |
dotsum = rdotu1+rdotu2 |
| 144 |
dotdiff = rdotu1-rdotu2 |
| 145 |
ds2 = dotsum*dotsum |
| 146 |
dd2 = dotdiff*dotdiff |
| 147 |
|
| 148 |
opXdot = 1.0d0 + Chi*u1dotu2 |
| 149 |
omXdot = 1.0d0 - Chi*u1dotu2 |
| 150 |
opXpdot = 1.0d0 + ChiPrime*u1dotu2 |
| 151 |
omXpdot = 1.0d0 - ChiPrime*u1dotu2 |
| 152 |
|
| 153 |
line1a = dotsum/opXdot |
| 154 |
line1bx = dru1dx + dru2dx |
| 155 |
line1by = dru1dy + dru2dy |
| 156 |
line1bz = dru1dz + dru2dz |
| 157 |
|
| 158 |
line2a = dotdiff/omXdot |
| 159 |
line2bx = dru1dx - dru2dx |
| 160 |
line2by = dru1dy - dru2dy |
| 161 |
line2bz = dru1dz - dru2dz |
| 162 |
|
| 163 |
term1x = -Chi*(line1a*line1bx + line2a*line2bx)/r2 |
| 164 |
term1y = -Chi*(line1a*line1by + line2a*line2by)/r2 |
| 165 |
term1z = -Chi*(line1a*line1bz + line2a*line2bz)/r2 |
| 166 |
|
| 167 |
line3a = ds2/opXdot |
| 168 |
line3b = dd2/omXdot |
| 169 |
line3 = Chi*(line3a + line3b)/r4 |
| 170 |
line3x = d(1)*line3 |
| 171 |
line3y = d(2)*line3 |
| 172 |
line3z = d(3)*line3 |
| 173 |
|
| 174 |
dgdx = term1x + line3x |
| 175 |
dgdy = term1y + line3y |
| 176 |
dgdz = term1z + line3z |
| 177 |
|
| 178 |
term1u1x = 2.0d0*(line1a+line2a)*d(1) |
| 179 |
term1u1y = 2.0d0*(line1a+line2a)*d(2) |
| 180 |
term1u1z = 2.0d0*(line1a+line2a)*d(3) |
| 181 |
term1u2x = 2.0d0*(line1a-line2a)*d(1) |
| 182 |
term1u2y = 2.0d0*(line1a-line2a)*d(2) |
| 183 |
term1u2z = 2.0d0*(line1a-line2a)*d(3) |
| 184 |
|
| 185 |
term2a = -line3a/opXdot |
| 186 |
term2b = line3b/omXdot |
| 187 |
|
| 188 |
term2u1x = Chi*ul2(1)*(term2a + term2b) |
| 189 |
term2u1y = Chi*ul2(2)*(term2a + term2b) |
| 190 |
term2u1z = Chi*ul2(3)*(term2a + term2b) |
| 191 |
term2u2x = Chi*ul1(1)*(term2a + term2b) |
| 192 |
term2u2y = Chi*ul1(2)*(term2a + term2b) |
| 193 |
term2u2z = Chi*ul1(3)*(term2a + term2b) |
| 194 |
|
| 195 |
pref = -Chi*0.5d0/r2 |
| 196 |
|
| 197 |
dgdu1x = pref*(term1u1x+term2u1x) |
| 198 |
dgdu1y = pref*(term1u1y+term2u1y) |
| 199 |
dgdu1z = pref*(term1u1z+term2u1z) |
| 200 |
dgdu2x = pref*(term1u2x+term2u2x) |
| 201 |
dgdu2y = pref*(term1u2y+term2u2y) |
| 202 |
dgdu2z = pref*(term1u2z+term2u2z) |
| 203 |
|
| 204 |
g = 1.0d0 - Chi*(line3a + line3b)/(2.0d0*r2) |
| 205 |
|
| 206 |
BigR = (r - gb_sigma*(g**(-0.5d0)) + gb_sigma)/gb_sigma |
| 207 |
Ri = 1.0d0/BigR |
| 208 |
Ri2 = Ri*Ri |
| 209 |
Ri6 = Ri2*Ri2*Ri2 |
| 210 |
Ri7 = Ri6*Ri |
| 211 |
Ri12 = Ri6*Ri6 |
| 212 |
Ri13 = Ri6*Ri7 |
| 213 |
|
| 214 |
gfact = (g**(-1.5d0))*0.5d0 |
| 215 |
|
| 216 |
dBigRdx = drdx/gb_sigma + dgdx*gfact |
| 217 |
dBigRdy = drdy/gb_sigma + dgdy*gfact |
| 218 |
dBigRdz = drdz/gb_sigma + dgdz*gfact |
| 219 |
dBigRdu1x = dgdu1x*gfact |
| 220 |
dBigRdu1y = dgdu1y*gfact |
| 221 |
dBigRdu1z = dgdu1z*gfact |
| 222 |
dBigRdu2x = dgdu2x*gfact |
| 223 |
dBigRdu2y = dgdu2y*gfact |
| 224 |
dBigRdu2z = dgdu2z*gfact |
| 225 |
|
| 226 |
! Now, we must do it again for g(ChiPrime) and dgpdx |
| 227 |
|
| 228 |
line1a = dotsum/opXpdot |
| 229 |
line2a = dotdiff/omXpdot |
| 230 |
term1x = -ChiPrime*(line1a*line1bx + line2a*line2bx)/r2 |
| 231 |
term1y = -ChiPrime*(line1a*line1by + line2a*line2by)/r2 |
| 232 |
term1z = -ChiPrime*(line1a*line1bz + line2a*line2bz)/r2 |
| 233 |
line3a = ds2/opXpdot |
| 234 |
line3b = dd2/omXpdot |
| 235 |
line3 = ChiPrime*(line3a + line3b)/r4 |
| 236 |
line3x = d(1)*line3 |
| 237 |
line3y = d(2)*line3 |
| 238 |
line3z = d(3)*line3 |
| 239 |
|
| 240 |
dgpdx = term1x + line3x |
| 241 |
dgpdy = term1y + line3y |
| 242 |
dgpdz = term1z + line3z |
| 243 |
|
| 244 |
term1u1x = 2.0d0*(line1a+line2a)*d(1) |
| 245 |
term1u1y = 2.0d0*(line1a+line2a)*d(2) |
| 246 |
term1u1z = 2.0d0*(line1a+line2a)*d(3) |
| 247 |
term1u2x = 2.0d0*(line1a-line2a)*d(1) |
| 248 |
term1u2y = 2.0d0*(line1a-line2a)*d(2) |
| 249 |
term1u2z = 2.0d0*(line1a-line2a)*d(3) |
| 250 |
|
| 251 |
term2a = -line3a/opXpdot |
| 252 |
term2b = line3b/omXpdot |
| 253 |
|
| 254 |
term2u1x = ChiPrime*ul2(1)*(term2a + term2b) |
| 255 |
term2u1y = ChiPrime*ul2(2)*(term2a + term2b) |
| 256 |
term2u1z = ChiPrime*ul2(3)*(term2a + term2b) |
| 257 |
term2u2x = ChiPrime*ul1(1)*(term2a + term2b) |
| 258 |
term2u2y = ChiPrime*ul1(2)*(term2a + term2b) |
| 259 |
term2u2z = ChiPrime*ul1(3)*(term2a + term2b) |
| 260 |
|
| 261 |
pref = -ChiPrime*0.5d0/r2 |
| 262 |
|
| 263 |
dgpdu1x = pref*(term1u1x+term2u1x) |
| 264 |
dgpdu1y = pref*(term1u1y+term2u1y) |
| 265 |
dgpdu1z = pref*(term1u1z+term2u1z) |
| 266 |
dgpdu2x = pref*(term1u2x+term2u2x) |
| 267 |
dgpdu2y = pref*(term1u2y+term2u2y) |
| 268 |
dgpdu2z = pref*(term1u2z+term2u2z) |
| 269 |
|
| 270 |
gp = 1.0d0 - ChiPrime*(line3a + line3b)/(2.0d0*r2) |
| 271 |
gmu = gp**gb_mu |
| 272 |
gpi = 1.0d0 / gp |
| 273 |
gmum = gmu*gpi |
| 274 |
|
| 275 |
! write(*,*) atom1, atom2, Chi, u1dotu2 |
| 276 |
curlyE = 1.0d0/dsqrt(1.0d0 - Chi*Chi*u1dotu2*u1dotu2) |
| 277 |
|
| 278 |
dcE = (curlyE**3)*Chi*Chi*u1dotu2 |
| 279 |
|
| 280 |
dcEdu1x = dcE*ul2(1) |
| 281 |
dcEdu1y = dcE*ul2(2) |
| 282 |
dcEdu1z = dcE*ul2(3) |
| 283 |
dcEdu2x = dcE*ul1(1) |
| 284 |
dcEdu2y = dcE*ul1(2) |
| 285 |
dcEdu2z = dcE*ul1(3) |
| 286 |
|
| 287 |
enu = curlyE**gb_nu |
| 288 |
enum = enu/curlyE |
| 289 |
|
| 290 |
eps = gb_eps*enu*gmu |
| 291 |
|
| 292 |
yick1 = gb_eps*enu*gb_mu*gmum |
| 293 |
yick2 = gb_eps*gmu*gb_nu*enum |
| 294 |
|
| 295 |
depsdu1x = yick1*dgpdu1x + yick2*dcEdu1x |
| 296 |
depsdu1y = yick1*dgpdu1y + yick2*dcEdu1y |
| 297 |
depsdu1z = yick1*dgpdu1z + yick2*dcEdu1z |
| 298 |
depsdu2x = yick1*dgpdu2x + yick2*dcEdu2x |
| 299 |
depsdu2y = yick1*dgpdu2y + yick2*dcEdu2y |
| 300 |
depsdu2z = yick1*dgpdu2z + yick2*dcEdu2z |
| 301 |
|
| 302 |
R126 = Ri12 - Ri6 |
| 303 |
R137 = 6.0d0*Ri7 - 12.0d0*Ri13 |
| 304 |
|
| 305 |
mess1 = gmu*R137 |
| 306 |
mess2 = R126*gb_mu*gmum |
| 307 |
|
| 308 |
dUdx = 4.0d0*gb_eps*enu*(mess1*dBigRdx + mess2*dgpdx) |
| 309 |
dUdy = 4.0d0*gb_eps*enu*(mess1*dBigRdy + mess2*dgpdy) |
| 310 |
dUdz = 4.0d0*gb_eps*enu*(mess1*dBigRdz + mess2*dgpdz) |
| 311 |
|
| 312 |
dUdu1x = 4.0d0*(R126*depsdu1x + eps*R137*dBigRdu1x) |
| 313 |
dUdu1y = 4.0d0*(R126*depsdu1y + eps*R137*dBigRdu1y) |
| 314 |
dUdu1z = 4.0d0*(R126*depsdu1z + eps*R137*dBigRdu1z) |
| 315 |
dUdu2x = 4.0d0*(R126*depsdu2x + eps*R137*dBigRdu2x) |
| 316 |
dUdu2y = 4.0d0*(R126*depsdu2y + eps*R137*dBigRdu2y) |
| 317 |
dUdu2z = 4.0d0*(R126*depsdu2z + eps*R137*dBigRdu2z) |
| 318 |
|
| 319 |
#ifdef IS_MPI |
| 320 |
f_Row(1,atom1) = f_Row(1,atom1) + dUdx |
| 321 |
f_Row(2,atom1) = f_Row(2,atom1) + dUdy |
| 322 |
f_Row(3,atom1) = f_Row(3,atom1) + dUdz |
| 323 |
|
| 324 |
f_Col(1,atom2) = f_Col(1,atom2) - dUdx |
| 325 |
f_Col(2,atom2) = f_Col(2,atom2) - dUdy |
| 326 |
f_Col(3,atom2) = f_Col(3,atom2) - dUdz |
| 327 |
|
| 328 |
t_Row(1,atom1) = t_Row(1,atom1) - ul1(2)*dUdu1z + ul1(3)*dUdu1y |
| 329 |
t_Row(2,atom1) = t_Row(2,atom1) - ul1(3)*dUdu1x + ul1(1)*dUdu1z |
| 330 |
t_Row(3,atom1) = t_Row(3,atom1) - ul1(1)*dUdu1y + ul1(2)*dUdu1x |
| 331 |
|
| 332 |
t_Col(1,atom2) = t_Col(1,atom2) - ul2(2)*dUdu2z + ul2(3)*dUdu2y |
| 333 |
t_Col(2,atom2) = t_Col(2,atom2) - ul2(3)*dUdu2x + ul2(1)*dUdu2z |
| 334 |
t_Col(3,atom2) = t_Col(3,atom2) - ul2(1)*dUdu2y + ul2(2)*dUdu2x |
| 335 |
#else |
| 336 |
f(1,atom1) = f(1,atom1) + dUdx |
| 337 |
f(2,atom1) = f(2,atom1) + dUdy |
| 338 |
f(3,atom1) = f(3,atom1) + dUdz |
| 339 |
|
| 340 |
f(1,atom2) = f(1,atom2) - dUdx |
| 341 |
f(2,atom2) = f(2,atom2) - dUdy |
| 342 |
f(3,atom2) = f(3,atom2) - dUdz |
| 343 |
|
| 344 |
t(1,atom1) = t(1,atom1) - ul1(2)*dUdu1z + ul1(3)*dUdu1y |
| 345 |
t(2,atom1) = t(2,atom1) - ul1(3)*dUdu1x + ul1(1)*dUdu1z |
| 346 |
t(3,atom1) = t(3,atom1) - ul1(1)*dUdu1y + ul1(2)*dUdu1x |
| 347 |
|
| 348 |
t(1,atom2) = t(1,atom2) - ul2(2)*dUdu2z + ul2(3)*dUdu2y |
| 349 |
t(2,atom2) = t(2,atom2) - ul2(3)*dUdu2x + ul2(1)*dUdu2z |
| 350 |
t(3,atom2) = t(3,atom2) - ul2(1)*dUdu2y + ul2(2)*dUdu2x |
| 351 |
#endif |
| 352 |
|
| 353 |
if (do_stress) then |
| 354 |
tau_Temp(1) = tau_Temp(1) + dUdx * d(1) |
| 355 |
tau_Temp(2) = tau_Temp(2) + dUdx * d(2) |
| 356 |
tau_Temp(3) = tau_Temp(3) + dUdx * d(3) |
| 357 |
tau_Temp(4) = tau_Temp(4) + dUdy * d(1) |
| 358 |
tau_Temp(5) = tau_Temp(5) + dUdy * d(2) |
| 359 |
tau_Temp(6) = tau_Temp(6) + dUdy * d(3) |
| 360 |
tau_Temp(7) = tau_Temp(7) + dUdz * d(1) |
| 361 |
tau_Temp(8) = tau_Temp(8) + dUdz * d(2) |
| 362 |
tau_Temp(9) = tau_Temp(9) + dUdz * d(3) |
| 363 |
virial_Temp = virial_Temp + (tau_Temp(1) + tau_Temp(5) + tau_Temp(9)) |
| 364 |
endif |
| 365 |
|
| 366 |
if (do_pot) then |
| 367 |
#ifdef IS_MPI |
| 368 |
pot_row(atom1) = pot_row(atom1) + 2.0d0*eps*R126 |
| 369 |
pot_col(atom2) = pot_col(atom2) + 2.0d0*eps*R126 |
| 370 |
#else |
| 371 |
pot = pot + 4.0*eps*R126 |
| 372 |
#endif |
| 373 |
endif |
| 374 |
|
| 375 |
return |
| 376 |
end subroutine do_gb_pair |
| 377 |
|
| 378 |
end module gb_pair |
| 379 |
|
| 380 |
|
