src/gromacs/listed-forces/restcbt.cpp

   1 /*
   2  * This file is part of the GROMACS molecular simulation package.
   3  *
   4  * Copyright (c) 2014, by the GROMACS development team, led by
   5  * Mark Abraham, David van der Spoel, Berk Hess, and Erik Lindahl,
   6  * and including many others, as listed in the AUTHORS file in the
   7  * top-level source directory and at http://www.gromacs.org.
   8  *
   9  * GROMACS is free software; you can redistribute it and/or
  10  * modify it under the terms of the GNU Lesser General Public License
  11  * as published by the Free Software Foundation; either version 2.1
  12  * of the License, or (at your option) any later version.
  13  *
  14  * GROMACS is distributed in the hope that it will be useful,
  15  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  16  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  17  * Lesser General Public License for more details.
  18  *
  19  * You should have received a copy of the GNU Lesser General Public
  20  * License along with GROMACS; if not, see
  21  * http://www.gnu.org/licenses, or write to the Free Software Foundation,
  22  * Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA.
  23  *
  24  * If you want to redistribute modifications to GROMACS, please
  25  * consider that scientific software is very special. Version
  26  * control is crucial - bugs must be traceable. We will be happy to
  27  * consider code for inclusion in the official distribution, but
  28  * derived work must not be called official GROMACS. Details are found
  29  * in the README & COPYING files - if they are missing, get the
  30  * official version at http://www.gromacs.org.
  31  *
  32  * To help us fund GROMACS development, we humbly ask that you cite
  33  * the research papers on the package. Check out http://www.gromacs.org.
  34  */
  35 /*! \internal \file
  36  *
  37  * \brief
  38  * This file contains function definitions necessary
  39  * for computations of forces due to restricted angle, restricted dihedral and
  40  * combined bending-torsion potentials.
  41  *
  42  * \author Nicolae Goga
  43  *
  44  * \ingroup module_listed-forces
  45  */
  46 #include "gmxpre.h"
  47
  48 #include "restcbt.h"
  49
  50 #include <math.h>
  51
  52 #include "gromacs/math/units.h"
  53 #include "gromacs/math/utilities.h"
  54 #include "gromacs/math/vec.h"
  55 #include "gromacs/topology/idef.h"
  56
  57 /* This function computes factors needed for restricted angle potential.
  58  * For explanations on formula used see file "restcbt.h" */
  59
  60 void compute_factors_restangles(int type, const t_iparams forceparams[],
  61                                 rvec delta_ante,  rvec delta_post,
  62                                 real *prefactor, real *ratio_ante, real *ratio_post, real *v)
  63 {
  64     real theta_equil, k_bending;
  65     real cosine_theta_equil;
  66     real c_ante, c_cros, c_post;
  67     real norm;
  68     real delta_cosine, cosine_theta;
  69     real sine_theta_sq;
  70     real term_theta_theta_equil;
  71
  72     k_bending          = forceparams[type].harmonic.krA;
  73     theta_equil        =  forceparams[type].harmonic.rA*DEG2RAD;
  74     theta_equil        = M_PI - theta_equil;
  75     cosine_theta_equil = cos(theta_equil);
  76
  77     c_ante = iprod(delta_ante, delta_ante);
  78     c_cros = iprod(delta_ante, delta_post);
  79     c_post = iprod(delta_post, delta_post);
  80
  81     norm          = gmx_invsqrt(c_ante * c_post);
  82     cosine_theta  = c_cros * norm;
  83     sine_theta_sq = 1 - cosine_theta * cosine_theta;
  84
  85     *ratio_ante = c_cros / c_ante;
  86     *ratio_post = c_cros / c_post;
  87
  88     delta_cosine           = cosine_theta - cosine_theta_equil;
  89     term_theta_theta_equil = 1 - cosine_theta * cosine_theta_equil;
  90     *prefactor             = -(k_bending) * delta_cosine * norm * term_theta_theta_equil / (sine_theta_sq * sine_theta_sq);
  91
  92     *v = k_bending * 0.5 * delta_cosine * delta_cosine / sine_theta_sq;
  93
  94 }
  95
  96
  97 /* Compute factors for restricted dihedral potential
  98  * For explanations on formula used see file "restcbt.h" */
  99 void compute_factors_restrdihs(int type,  const t_iparams forceparams[],
 100                                rvec delta_ante, rvec delta_crnt, rvec delta_post,
 101                                real *factor_phi_ai_ante, real *factor_phi_ai_crnt, real *factor_phi_ai_post,
 102                                real *factor_phi_aj_ante, real *factor_phi_aj_crnt, real *factor_phi_aj_post,
 103                                real *factor_phi_ak_ante, real *factor_phi_ak_crnt, real *factor_phi_ak_post,
 104                                real *factor_phi_al_ante, real *factor_phi_al_crnt, real *factor_phi_al_post,
 105                                real *prefactor_phi, real *v)
 106 {
 107
 108     real phi0, cosine_phi0;
 109     real k_torsion;
 110     real c_self_ante, c_self_crnt, c_self_post;
 111     real c_cros_ante, c_cros_acrs, c_cros_post;
 112     real c_prod, d_post, d_ante;
 113     real sine_phi_sq, cosine_phi;
 114     real delta_cosine, term_phi_phi0;
 115     real ratio_phi_ante, ratio_phi_post;
 116     real norm_phi;
 117
 118     /* Read parameters phi0 and k_torsion */
 119     phi0        = forceparams[type].pdihs.phiA * DEG2RAD;
 120     cosine_phi0 = cos(phi0);
 121     k_torsion   = forceparams[type].pdihs.cpA;
 122
 123     /* Computation of the cosine of the dihedral angle. The scalar ("dot") product  method
 124      * is used. c_*_* cummulate the scalar products of the differences of particles
 125      * positions while c_prod, d_ante and d_post are differences of products of scalar
 126      * terms that are parts of the derivatives of forces */
 127     c_self_ante = iprod(delta_ante, delta_ante);
 128     c_self_crnt = iprod(delta_crnt, delta_crnt);
 129     c_self_post = iprod(delta_post, delta_post);
 130     c_cros_ante = iprod(delta_ante, delta_crnt);
 131     c_cros_acrs = iprod(delta_ante, delta_post);
 132     c_cros_post = iprod(delta_crnt, delta_post);
 133     c_prod      = c_cros_ante * c_cros_post - c_self_crnt * c_cros_acrs;
 134     d_ante      = c_self_ante * c_self_crnt - c_cros_ante * c_cros_ante;
 135     d_post      = c_self_post * c_self_crnt - c_cros_post * c_cros_post;
 136
 137     /*  When three consecutive beads align, we obtain values close to zero.
 138      *  Here we avoid small values to prevent round-off errors. */
 139     if (d_ante < GMX_REAL_EPS)
 140     {
 141         d_ante = GMX_REAL_EPS;
 142     }
 143     if (d_post < GMX_REAL_EPS)
 144     {
 145         d_post = GMX_REAL_EPS;
 146     }
 147
 148     /* Computes the square of the sinus of phi  in sine_phi_sq */
 149     norm_phi    = gmx_invsqrt(d_ante * d_post);
 150     cosine_phi  = c_prod * norm_phi;
 151     sine_phi_sq = 1.0 - cosine_phi * cosine_phi;
 152
 153     /*  It is possible that cosine_phi is slightly bigger than 1.0 due to round-off errors. */
 154     if (sine_phi_sq < 0.0)
 155     {
 156         sine_phi_sq = 0.0;
 157     }
 158
 159     /* Computation of the differences of cosines (delta_cosine) and a term (term_phi_phi0)
 160      * that is part of the common prefactor_phi */
 161
 162     delta_cosine  = cosine_phi - cosine_phi0;
 163     term_phi_phi0 = 1 - cosine_phi * cosine_phi0;
 164
 165
 166     /*      Computation of ratios */
 167     ratio_phi_ante = c_prod / d_ante;
 168     ratio_phi_post = c_prod / d_post;
 169
 170     /*      Computation of the prefactor - common term for all forces */
 171     *prefactor_phi = -(k_torsion) * delta_cosine * norm_phi * term_phi_phi0 / (sine_phi_sq * sine_phi_sq);
 172
 173     /* Computation of force factors.  Factors factor_phi_*  are coming from the
 174      * derivatives of the torsion angle (phi) with respect to the beads ai, aj, al, ak,
 175      * (four) coordinates and they are multiplied in the force computations with the
 176      * differences of the particles positions stored in parameters delta_ante,
 177      * delta_crnt, delta_post. For formulas see file "restcbt.h" */
 178
 179     *factor_phi_ai_ante = ratio_phi_ante * c_self_crnt;
 180     *factor_phi_ai_crnt = -c_cros_post - ratio_phi_ante * c_cros_ante;
 181     *factor_phi_ai_post = c_self_crnt;
 182     *factor_phi_aj_ante = -c_cros_post - ratio_phi_ante * (c_self_crnt + c_cros_ante);
 183     *factor_phi_aj_crnt = c_cros_post + c_cros_acrs * 2.0 + ratio_phi_ante * (c_self_ante + c_cros_ante) + ratio_phi_post * c_self_post;
 184     *factor_phi_aj_post = -(c_cros_ante + c_self_crnt) - ratio_phi_post * c_cros_post;
 185     *factor_phi_ak_ante = c_cros_post + c_self_crnt + ratio_phi_ante * c_cros_ante;
 186     *factor_phi_ak_crnt = -(c_cros_ante + c_cros_acrs * 2.0)- ratio_phi_ante * c_self_ante - ratio_phi_post * (c_self_post + c_cros_post);
 187     *factor_phi_ak_post = c_cros_ante + ratio_phi_post * (c_self_crnt + c_cros_post);
 188     *factor_phi_al_ante = -c_self_crnt;
 189     *factor_phi_al_crnt = c_cros_ante + ratio_phi_post * c_cros_post;
 190     *factor_phi_al_post = -ratio_phi_post * c_self_crnt;
 191
 192     /* Contribution to energy  - see formula in file "restcbt.h"*/
 193     *v = k_torsion * 0.5 * delta_cosine * delta_cosine / sine_phi_sq;
 194 }
 195
 196
 197
 198 /* Compute factors for CBT potential
 199  * For explanations on formula used see file "restcbt.h" */
 200
 201 void compute_factors_cbtdihs(int type,  const t_iparams forceparams[],
 202                              rvec delta_ante, rvec delta_crnt, rvec delta_post,
 203                              rvec f_phi_ai, rvec f_phi_aj, rvec f_phi_ak, rvec f_phi_al,
 204                              rvec f_theta_ante_ai, rvec f_theta_ante_aj, rvec f_theta_ante_ak,
 205                              rvec f_theta_post_aj, rvec f_theta_post_ak, rvec f_theta_post_al,
 206                              real * v)
 207 {
 208     int  j, d;
 209     real torsion_coef[NR_CBTDIHS];
 210     real c_self_ante, c_self_crnt, c_self_post;
 211     real c_cros_ante, c_cros_acrs, c_cros_post;
 212     real c_prod, d_ante,  d_post;
 213     real norm_phi, norm_theta_ante, norm_theta_post;
 214     real cosine_phi, cosine_theta_ante, cosine_theta_post;
 215     real sine_theta_ante_sq, sine_theta_post_sq;
 216     real sine_theta_ante, sine_theta_post;
 217     real prefactor_phi;
 218     real ratio_phi_ante, ratio_phi_post;
 219     real r1, r2;
 220     real factor_phi_ai_ante, factor_phi_ai_crnt, factor_phi_ai_post;
 221     real factor_phi_aj_ante, factor_phi_aj_crnt, factor_phi_aj_post;
 222     real factor_phi_ak_ante, factor_phi_ak_crnt, factor_phi_ak_post;
 223     real factor_phi_al_ante, factor_phi_al_crnt, factor_phi_al_post;
 224     real prefactor_theta_ante, ratio_theta_ante_ante, ratio_theta_ante_crnt;
 225     real prefactor_theta_post, ratio_theta_post_crnt, ratio_theta_post_post;
 226
 227     /* The formula for combined bending-torsion potential (see file "restcbt.h") contains
 228      * in its expression not only the dihedral angle \f[\phi\f] but also \f[\theta_{i-1}\f]
 229      * (theta_ante bellow) and \f[\theta_{i}\f] (theta_post bellow)--- the adjacent bending
 230      * angles. The forces for the particles ai, aj, ak, al have components coming from the
 231      * derivatives of the potential with respect to all three angles.
 232      * This function is organised in 4 parts
 233      * PART 1 - Computes force factors common to all the derivatives for the four particles
 234      * PART 2 - Computes the force components due to the derivatives of dihedral angle Phi
 235      * PART 3 - Computes the force components due to the derivatives of bending angle Theta_Ante
 236      * PART 4 - Computes the force components due to the derivatives of bending angle Theta_Post
 237      * Bellow we will respct thuis structure */
 238
 239
 240     /* PART 1 - COMPUTES FORCE FACTORS COMMON TO ALL DERIVATIVES FOR THE FOUR PARTICLES */
 241
 242
 243     for (j = 0; (j < NR_CBTDIHS); j++)
 244     {
 245         torsion_coef[j]  = forceparams[type].cbtdihs.cbtcA[j];
 246     }
 247
 248     /* Computation of the cosine of the dihedral angle. The scalar ("dot") product  method
 249      * is used. c_*_* cummulate the scalar products of the differences of particles
 250      * positions while c_prod, d_ante and d_post are differences of products of scalar
 251      * terms that are parts of the derivatives of forces */
 252
 253     c_self_ante = iprod(delta_ante, delta_ante);
 254     c_self_crnt = iprod(delta_crnt, delta_crnt);
 255     c_self_post = iprod(delta_post, delta_post);
 256     c_cros_ante = iprod(delta_ante, delta_crnt);
 257     c_cros_acrs = iprod(delta_ante, delta_post);
 258     c_cros_post = iprod(delta_crnt, delta_post);
 259     c_prod      = c_cros_ante * c_cros_post - c_self_crnt * c_cros_acrs;
 260     d_ante      = c_self_ante * c_self_crnt - c_cros_ante * c_cros_ante;
 261     d_post      = c_self_post * c_self_crnt - c_cros_post * c_cros_post;
 262
 263     /*  When three consecutive beads align, we obtain values close to zero.
 264        Here we avoid small values to prevent round-off errors. */
 265     if (d_ante < GMX_REAL_EPS)
 266     {
 267         d_ante = GMX_REAL_EPS;
 268     }
 269     if (d_post < GMX_REAL_EPS)
 270     {
 271         d_post = GMX_REAL_EPS;
 272     }
 273
 274     /* Computations of cosines */
 275     norm_phi           = gmx_invsqrt(d_ante * d_post);
 276     norm_theta_ante    = gmx_invsqrt(c_self_ante * c_self_crnt);
 277     norm_theta_post    = gmx_invsqrt(c_self_crnt * c_self_post);
 278     cosine_phi         = c_prod * norm_phi;
 279     cosine_theta_ante  = c_cros_ante * norm_theta_ante;
 280     cosine_theta_post  = c_cros_post * norm_theta_post;
 281     sine_theta_ante_sq = 1 - cosine_theta_ante * cosine_theta_ante;
 282     sine_theta_post_sq = 1 - cosine_theta_post * cosine_theta_post;
 283
 284     /*  It is possible that cosine_theta is slightly bigger than 1.0 due to round-off errors. */
 285     if (sine_theta_ante_sq < 0.0)
 286     {
 287         sine_theta_ante_sq = 0.0;
 288     }
 289     if (sine_theta_post_sq < 0.0)
 290     {
 291         sine_theta_post_sq = 0.0;
 292     }
 293
 294     sine_theta_ante = sqrt(sine_theta_ante_sq);
 295     sine_theta_post = sqrt(sine_theta_post_sq);
 296
 297     /* PART 2 - COMPUTES FORCE COMPONENTS DUE TO DERIVATIVES TO DIHEDRAL ANGLE PHI */
 298
 299     /*      Computation of ratios */
 300     ratio_phi_ante = c_prod / d_ante;
 301     ratio_phi_post = c_prod / d_post;
 302
 303     /*       Computation of the prefactor */
 304     /*      Computing 2nd power */
 305     r1 = cosine_phi;
 306
 307     prefactor_phi = -torsion_coef[0] * norm_phi * (torsion_coef[2] + torsion_coef[3] * 2.0 * cosine_phi + torsion_coef[4] * 3.0 * (r1 * r1) + 4*torsion_coef[5]*r1*r1*r1) *
 308         sine_theta_ante_sq * sine_theta_ante * sine_theta_post_sq * sine_theta_post;
 309
 310     /* Computation of factors (important for gaining speed). Factors factor_phi_*  are coming from the
 311      * derivatives of the torsion angle (phi) with respect to the beads ai, aj, al, ak,
 312      * (four) coordinates and they are multiplied in the force computations with the
 313      * differences of the particles positions stored in parameters delta_ante,
 314      * delta_crnt, delta_post. For formulas see file "restcbt.h" */
 315
 316     factor_phi_ai_ante = ratio_phi_ante * c_self_crnt;
 317     factor_phi_ai_crnt = -c_cros_post - ratio_phi_ante * c_cros_ante;
 318     factor_phi_ai_post = c_self_crnt;
 319     factor_phi_aj_ante = -c_cros_post - ratio_phi_ante * (c_self_crnt + c_cros_ante);
 320     factor_phi_aj_crnt = c_cros_post + c_cros_acrs * 2.0 + ratio_phi_ante * (c_self_ante + c_cros_ante) +  ratio_phi_post * c_self_post;
 321     factor_phi_aj_post = -(c_cros_ante + c_self_crnt) - ratio_phi_post * c_cros_post;
 322     factor_phi_ak_ante = c_cros_post + c_self_crnt + ratio_phi_ante * c_cros_ante;
 323     factor_phi_ak_crnt = -(c_cros_ante + c_cros_acrs * 2.0) - ratio_phi_ante * c_self_ante - ratio_phi_post * (c_self_post + c_cros_post);
 324     factor_phi_ak_post = c_cros_ante + ratio_phi_post * (c_self_crnt + c_cros_post);
 325     factor_phi_al_ante = -c_self_crnt;
 326     factor_phi_al_crnt = c_cros_ante + ratio_phi_post * c_cros_post;
 327     factor_phi_al_post = -ratio_phi_post * c_self_crnt;
 328
 329     /* Computation of forces due to the derivatives of dihedral angle phi*/
 330     for (d = 0; d < DIM; d++)
 331     {
 332         f_phi_ai[d] = prefactor_phi * (factor_phi_ai_ante * delta_ante[d] + factor_phi_ai_crnt * delta_crnt[d] + factor_phi_ai_post * delta_post[d]);
 333         f_phi_aj[d] = prefactor_phi * (factor_phi_aj_ante * delta_ante[d] + factor_phi_aj_crnt * delta_crnt[d] + factor_phi_aj_post * delta_post[d]);
 334         f_phi_ak[d] = prefactor_phi * (factor_phi_ak_ante * delta_ante[d] + factor_phi_ak_crnt * delta_crnt[d] + factor_phi_ak_post * delta_post[d]);
 335         f_phi_al[d] = prefactor_phi * (factor_phi_al_ante * delta_ante[d] + factor_phi_al_crnt * delta_crnt[d] + factor_phi_al_post * delta_post[d]);
 336     }
 337
 338     /* PART 3 - COMPUTES THE FORCE COMPONENTS DUE TO THE DERIVATIVES OF BENDING ANGLE THETHA_ANTHE */
 339     /*      Computation of ratios */
 340     ratio_theta_ante_ante = c_cros_ante / c_self_ante;
 341     ratio_theta_ante_crnt = c_cros_ante / c_self_crnt;
 342
 343     /*      Computation of the prefactor */
 344     /*      Computing 2nd power */
 345     r1 = cosine_phi;
 346     /*      Computing 3rd power */
 347     r2 = cosine_phi;
 348
 349     prefactor_theta_ante = -torsion_coef[0] * norm_theta_ante * ( torsion_coef[1] + torsion_coef[2] * cosine_phi + torsion_coef[3] * (r1 * r1) +
 350                                                                   torsion_coef[4] * (r2 * (r2 * r2))+ torsion_coef[5] * (r2 * (r2 * (r2 * r2)))) * (-3.0) * cosine_theta_ante * sine_theta_ante * sine_theta_post_sq * sine_theta_post;
 351
 352
 353     /*      Computation of forces due to the derivatives of bending angle theta_ante */
 354     for (d = 0; d < DIM; d++)
 355     {
 356         f_theta_ante_ai[d] = prefactor_theta_ante * (ratio_theta_ante_ante * delta_ante[d] - delta_crnt[d]);
 357         f_theta_ante_aj[d] = prefactor_theta_ante * ((ratio_theta_ante_crnt + 1.0) * delta_crnt[d] - (ratio_theta_ante_ante + 1.0) * delta_ante[d]);
 358         f_theta_ante_ak[d] = prefactor_theta_ante * (delta_ante[d] - ratio_theta_ante_crnt * delta_crnt[d]);
 359     }
 360
 361     /* PART 4 - COMPUTES THE FORCE COMPONENTS DUE TO THE DERIVATIVES OF THE BENDING ANGLE THETA_POST */
 362
 363     /*      Computation of ratios */
 364     ratio_theta_post_crnt = c_cros_post / c_self_crnt;
 365     ratio_theta_post_post = c_cros_post / c_self_post;
 366
 367     /*     Computation of the prefactor */
 368     /*      Computing 2nd power */
 369     r1 = cosine_phi;
 370     /*      Computing 3rd power */
 371     r2 = cosine_phi;
 372
 373     prefactor_theta_post = -torsion_coef[0] * norm_theta_post * (torsion_coef[1] + torsion_coef[2] * cosine_phi + torsion_coef[3] * (r1 * r1) +
 374                                                                  torsion_coef[4] * (r2 * (r2 * r2)) + torsion_coef[5] * (r2 * (r2 * (r2 * r2)))) * sine_theta_ante_sq * sine_theta_ante * (-3.0) * cosine_theta_post * sine_theta_post;
 375
 376
 377     /*      Computation of forces due to the derivatives of bending angle Theta_Post */
 378     for (d = 0; d < DIM; d++)
 379     {
 380         f_theta_post_aj[d] = prefactor_theta_post * (ratio_theta_post_crnt * delta_crnt[d] - delta_post[d]);
 381         f_theta_post_ak[d] = prefactor_theta_post * ((ratio_theta_post_post + 1.0) * delta_post[d] - (ratio_theta_post_crnt + 1.0) * delta_crnt[d]);
 382         f_theta_post_al[d] = prefactor_theta_post * (delta_crnt[d] - ratio_theta_post_post * delta_post[d]);
 383     }
 384     r1 = cosine_phi;
 385     r2 = cosine_phi;
 386
 387     /* Contribution to energy - for formula see file "restcbt.h" */
 388     *v = torsion_coef[0] * (torsion_coef[1] + torsion_coef[2] * cosine_phi + torsion_coef[3] * (r1 * r1) +
 389                             torsion_coef[4] * (r2 * (r2 * r2)) + torsion_coef[5] * (r2 * (r2 * (r2 * r2)))) * sine_theta_ante_sq *
 390         sine_theta_ante * sine_theta_post_sq * sine_theta_post;
 391
 392
 393 }