src/gromacs/gmxlib/restcbt.c

   1 /*
   2  * This file is part of the GROMACS molecular simulation package.
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   4  * Copyright (c) 2014, by the GROMACS development team, led by
   5  * Mark Abraham, David van der Spoel, Berk Hess, and Erik Lindahl,
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  35
  36 #include <math.h>
  37 #include <assert.h>
  38 #include "physics.h"
  39 #include "vec.h"
  40 #include "gromacs/math/utilities.h"
  41 #include "txtdump.h"
  42 #include "bondf.h"
  43 #include "gromacs/utility/smalloc.h"
  44 #include "pbc.h"
  45 #include "ns.h"
  46 #include "macros.h"
  47 #include "names.h"
  48 #include "mshift.h"
  49 #include "main.h"
  50 #include "disre.h"
  51 #include "orires.h"
  52 #include "force.h"
  53 #include "nonbonded.h"
  54
  55 /* This function computes factors needed for restricted angle potential.
  56  * For explanations on formula used see file "restcbt.h" */
  57
  58 void compute_factors_restangles(int type, const t_iparams forceparams[],
  59                                 rvec delta_ante,  rvec delta_post,
  60                                 real *prefactor, real *ratio_ante, real *ratio_post, real *v)
  61 {
  62     real theta_equil, k_bending;
  63     real cosine_theta_equil;
  64     real c_ante, c_cros, c_post;
  65     real norm;
  66     real delta_cosine, cosine_theta;
  67     real sine_theta_sq;
  68     real term_theta_theta_equil;
  69
  70     k_bending          = forceparams[type].harmonic.krA;
  71     theta_equil        =  forceparams[type].harmonic.rA*DEG2RAD;
  72     theta_equil        = M_PI - theta_equil;
  73     cosine_theta_equil = cos(theta_equil);
  74
  75     c_ante = iprod(delta_ante, delta_ante);
  76     c_cros = iprod(delta_ante, delta_post);
  77     c_post = iprod(delta_post, delta_post);
  78
  79     norm          = gmx_invsqrt(c_ante * c_post);
  80     cosine_theta  = c_cros * norm;
  81     sine_theta_sq = 1 - cosine_theta * cosine_theta;
  82
  83     *ratio_ante = c_cros / c_ante;
  84     *ratio_post = c_cros / c_post;
  85
  86     delta_cosine           = cosine_theta - cosine_theta_equil;
  87     term_theta_theta_equil = 1 - cosine_theta * cosine_theta_equil;
  88     *prefactor             = -(k_bending) * delta_cosine * norm * term_theta_theta_equil / (sine_theta_sq * sine_theta_sq);
  89
  90     *v = k_bending * 0.5 * delta_cosine * delta_cosine / sine_theta_sq;
  91
  92 }
  93
  94
  95 /* Compute factors for restricted dihedral potential
  96  * For explanations on formula used see file "restcbt.h" */
  97 void compute_factors_restrdihs(int type,  const t_iparams forceparams[],
  98                                rvec delta_ante, rvec delta_crnt, rvec delta_post,
  99                                real *factor_phi_ai_ante, real *factor_phi_ai_crnt, real *factor_phi_ai_post,
 100                                real *factor_phi_aj_ante, real *factor_phi_aj_crnt, real *factor_phi_aj_post,
 101                                real *factor_phi_ak_ante, real *factor_phi_ak_crnt, real *factor_phi_ak_post,
 102                                real *factor_phi_al_ante, real *factor_phi_al_crnt, real *factor_phi_al_post,
 103                                real *prefactor_phi, real *v)
 104 {
 105
 106     real phi0, sine_phi0, cosine_phi0;
 107     real k_torsion;
 108     real c_self_ante, c_self_crnt, c_self_post;
 109     real c_cros_ante, c_cros_acrs, c_cros_post;
 110     real c_prod, d_post, d_ante;
 111     real sine_phi_sq, cosine_phi;
 112     real delta_cosine, term_phi_phi0;
 113     real ratio_phi_ante, ratio_phi_post;
 114     real cos_phi, norm_phi;
 115
 116     /* Read parameters phi0 and k_torsion */
 117     phi0        = forceparams[type].pdihs.phiA * DEG2RAD;
 118     cosine_phi0 = cos(phi0);
 119     sine_phi0   = sin(phi0);
 120     k_torsion   = forceparams[type].pdihs.cpA;
 121
 122     /* Computation of the cosine of the dihedral angle. The scalar ("dot") product  method
 123      * is used. c_*_* cummulate the scalar products of the differences of particles
 124      * positions while c_prod, d_ante and d_post are differences of products of scalar
 125      * terms that are parts of the derivatives of forces */
 126     c_self_ante = iprod(delta_ante, delta_ante);
 127     c_self_crnt = iprod(delta_crnt, delta_crnt);
 128     c_self_post = iprod(delta_post, delta_post);
 129     c_cros_ante = iprod(delta_ante, delta_crnt);
 130     c_cros_acrs = iprod(delta_ante, delta_post);
 131     c_cros_post = iprod(delta_crnt, delta_post);
 132     c_prod      = c_cros_ante * c_cros_post - c_self_crnt * c_cros_acrs;
 133     d_ante      = c_self_ante * c_self_crnt - c_cros_ante * c_cros_ante;
 134     d_post      = c_self_post * c_self_crnt - c_cros_post * c_cros_post;
 135
 136     /*  When three consecutive beads align, we obtain values close to zero.
 137      *  Here we avoid small values to prevent round-off errors. */
 138     if (d_ante < GMX_REAL_EPS)
 139     {
 140         d_ante = GMX_REAL_EPS;
 141     }
 142     if (d_post < GMX_REAL_EPS)
 143     {
 144         d_post = GMX_REAL_EPS;
 145     }
 146
 147     /* Computes the square of the sinus of phi  in sine_phi_sq */
 148     norm_phi    = gmx_invsqrt(d_ante * d_post);
 149     cosine_phi  = c_prod * norm_phi;
 150     sine_phi_sq = 1.0 - cosine_phi * cosine_phi;
 151
 152     /*  It is possible that cosine_phi is slightly bigger than 1.0 due to round-off errors. */
 153     if (sine_phi_sq < 0.0)
 154     {
 155         sine_phi_sq = 0.0;
 156     }
 157
 158     /* Computation of the differences of cosines (delta_cosine) and a term (term_phi_phi0)
 159      * that is part of the common prefactor_phi */
 160
 161     delta_cosine  = cosine_phi - cosine_phi0;
 162     term_phi_phi0 = 1 - cosine_phi * cosine_phi0;
 163
 164
 165     /*      Computation of ratios */
 166     ratio_phi_ante = c_prod / d_ante;
 167     ratio_phi_post = c_prod / d_post;
 168
 169     /*      Computation of the prefactor - common term for all forces */
 170     *prefactor_phi = -(k_torsion) * delta_cosine * norm_phi * term_phi_phi0 / (sine_phi_sq * sine_phi_sq);
 171
 172     /* Computation of force factors.  Factors factor_phi_*  are coming from the
 173      * derivatives of the torsion angle (phi) with respect to the beads ai, aj, al, ak,
 174      * (four) coordinates and they are multiplied in the force computations with the
 175      * differences of the particles positions stored in parameters delta_ante,
 176      * delta_crnt, delta_post. For formulas see file "restcbt.h" */
 177
 178     *factor_phi_ai_ante = ratio_phi_ante * c_self_crnt;
 179     *factor_phi_ai_crnt = -c_cros_post - ratio_phi_ante * c_cros_ante;
 180     *factor_phi_ai_post = c_self_crnt;
 181     *factor_phi_aj_ante = -c_cros_post - ratio_phi_ante * (c_self_crnt + c_cros_ante);
 182     *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;
 183     *factor_phi_aj_post = -(c_cros_ante + c_self_crnt) - ratio_phi_post * c_cros_post;
 184     *factor_phi_ak_ante = c_cros_post + c_self_crnt + ratio_phi_ante * c_cros_ante;
 185     *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);
 186     *factor_phi_ak_post = c_cros_ante + ratio_phi_post * (c_self_crnt + c_cros_post);
 187     *factor_phi_al_ante = -c_self_crnt;
 188     *factor_phi_al_crnt = c_cros_ante + ratio_phi_post * c_cros_post;
 189     *factor_phi_al_post = -ratio_phi_post * c_self_crnt;
 190
 191     /* Contribution to energy  - see formula in file "restcbt.h"*/
 192     *v = k_torsion * 0.5 * delta_cosine * delta_cosine / sine_phi_sq;
 193 }
 194
 195
 196
 197 /* Compute factors for CBT potential
 198  * For explanations on formula used see file "restcbt.h" */
 199
 200 void compute_factors_cbtdihs(int type,  const t_iparams forceparams[],
 201                              rvec delta_ante, rvec delta_crnt, rvec delta_post,
 202                              rvec f_phi_ai, rvec f_phi_aj, rvec f_phi_ak, rvec f_phi_al,
 203                              rvec f_theta_ante_ai, rvec f_theta_ante_aj, rvec f_theta_ante_ak,
 204                              rvec f_theta_post_aj, rvec f_theta_post_ak, rvec f_theta_post_al,
 205                              real * v)
 206 {
 207     int  j, d;
 208     real torsion_coef[NR_CBTDIHS];
 209     real c_self_ante, c_self_crnt, c_self_post;
 210     real c_cros_ante, c_cros_acrs, c_cros_post;
 211     real c_prod, d_ante,  d_post;
 212     real norm_phi, norm_theta_ante, norm_theta_post;
 213     real cosine_phi, cosine_theta_ante, cosine_theta_post;
 214     real sine_theta_ante_sq, sine_theta_post_sq;
 215     real sine_theta_ante, sine_theta_post;
 216     real prefactor_phi;
 217     real ratio_phi_ante, ratio_phi_post;
 218     real r1, r2;
 219     real factor_phi_ai_ante, factor_phi_ai_crnt, factor_phi_ai_post;
 220     real factor_phi_aj_ante, factor_phi_aj_crnt, factor_phi_aj_post;
 221     real factor_phi_ak_ante, factor_phi_ak_crnt, factor_phi_ak_post;
 222     real factor_phi_al_ante, factor_phi_al_crnt, factor_phi_al_post;
 223     real prefactor_theta_ante, ratio_theta_ante_ante, ratio_theta_ante_crnt;
 224     real prefactor_theta_post, ratio_theta_post_crnt, ratio_theta_post_post;
 225
 226     /* The formula for combined bending-torsion potential (see file "restcbt.h") contains
 227      * in its expression not only the dihedral angle \f[\phi\f] but also \f[\theta_{i-1}\f]
 228      * (theta_ante bellow) and \f[\theta_{i}\f] (theta_post bellow)--- the adjacent bending
 229      * angles. The forces for the particles ai, aj, ak, al have components coming from the
 230      * derivatives of the potential with respect to all three angles.
 231      * This function is organised in 4 parts
 232      * PART 1 - Computes force factors common to all the derivatives for the four particles
 233      * PART 2 - Computes the force components due to the derivatives of dihedral angle Phi
 234      * PART 3 - Computes the force components due to the derivatives of bending angle Theta_Ante
 235      * PART 4 - Computes the force components due to the derivatives of bending angle Theta_Post
 236      * Bellow we will respct thuis structure */
 237
 238
 239     /* PART 1 - COMPUTES FORCE FACTORS COMMON TO ALL DERIVATIVES FOR THE FOUR PARTICLES */
 240
 241
 242     for (j = 0; (j < NR_CBTDIHS); j++)
 243     {
 244         torsion_coef[j]  = forceparams[type].cbtdihs.cbtcA[j];
 245     }
 246
 247     /* Computation of the cosine of the dihedral angle. The scalar ("dot") product  method
 248      * is used. c_*_* cummulate the scalar products of the differences of particles
 249      * positions while c_prod, d_ante and d_post are differences of products of scalar
 250      * terms that are parts of the derivatives of forces */
 251
 252     c_self_ante = iprod(delta_ante, delta_ante);
 253     c_self_crnt = iprod(delta_crnt, delta_crnt);
 254     c_self_post = iprod(delta_post, delta_post);
 255     c_cros_ante = iprod(delta_ante, delta_crnt);
 256     c_cros_acrs = iprod(delta_ante, delta_post);
 257     c_cros_post = iprod(delta_crnt, delta_post);
 258     c_prod      = c_cros_ante * c_cros_post - c_self_crnt * c_cros_acrs;
 259     d_ante      = c_self_ante * c_self_crnt - c_cros_ante * c_cros_ante;
 260     d_post      = c_self_post * c_self_crnt - c_cros_post * c_cros_post;
 261
 262     /*  When three consecutive beads align, we obtain values close to zero.
 263        Here we avoid small values to prevent round-off errors. */
 264     if (d_ante < GMX_REAL_EPS)
 265     {
 266         d_ante = GMX_REAL_EPS;
 267     }
 268     if (d_post < GMX_REAL_EPS)
 269     {
 270         d_post = GMX_REAL_EPS;
 271     }
 272
 273     /* Computations of cosines */
 274     norm_phi           = gmx_invsqrt(d_ante * d_post);
 275     norm_theta_ante    = gmx_invsqrt(c_self_ante * c_self_crnt);
 276     norm_theta_post    = gmx_invsqrt(c_self_crnt * c_self_post);
 277     cosine_phi         = c_prod * norm_phi;
 278     cosine_theta_ante  = c_cros_ante * norm_theta_ante;
 279     cosine_theta_post  = c_cros_post * norm_theta_post;
 280     sine_theta_ante_sq = 1 - cosine_theta_ante * cosine_theta_ante;
 281     sine_theta_post_sq = 1 - cosine_theta_post * cosine_theta_post;
 282
 283     /*  It is possible that cosine_theta is slightly bigger than 1.0 due to round-off errors. */
 284     if (sine_theta_ante_sq < 0.0)
 285     {
 286         sine_theta_ante_sq = 0.0;
 287     }
 288     if (sine_theta_post_sq < 0.0)
 289     {
 290         sine_theta_post_sq = 0.0;
 291     }
 292
 293     sine_theta_ante = sqrt(sine_theta_ante_sq);
 294     sine_theta_post = sqrt(sine_theta_post_sq);
 295
 296     /* PART 2 - COMPUTES FORCE COMPONENTS DUE TO DERIVATIVES TO DIHEDRAL ANGLE PHI */
 297
 298     /*      Computation of ratios */
 299     ratio_phi_ante = c_prod / d_ante;
 300     ratio_phi_post = c_prod / d_post;
 301
 302     /*       Computation of the prefactor */
 303     /*      Computing 2nd power */
 304     r1 = cosine_phi;
 305
 306     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) *
 307         sine_theta_ante_sq * sine_theta_ante * sine_theta_post_sq * sine_theta_post;
 308
 309     /* Computation of factors (important for gaining speed). Factors factor_phi_*  are coming from the
 310      * derivatives of the torsion angle (phi) with respect to the beads ai, aj, al, ak,
 311      * (four) coordinates and they are multiplied in the force computations with the
 312      * differences of the particles positions stored in parameters delta_ante,
 313      * delta_crnt, delta_post. For formulas see file "restcbt.h" */
 314
 315     factor_phi_ai_ante = ratio_phi_ante * c_self_crnt;
 316     factor_phi_ai_crnt = -c_cros_post - ratio_phi_ante * c_cros_ante;
 317     factor_phi_ai_post = c_self_crnt;
 318     factor_phi_aj_ante = -c_cros_post - ratio_phi_ante * (c_self_crnt + c_cros_ante);
 319     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;
 320     factor_phi_aj_post = -(c_cros_ante + c_self_crnt) - ratio_phi_post * c_cros_post;
 321     factor_phi_ak_ante = c_cros_post + c_self_crnt + ratio_phi_ante * c_cros_ante;
 322     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);
 323     factor_phi_ak_post = c_cros_ante + ratio_phi_post * (c_self_crnt + c_cros_post);
 324     factor_phi_al_ante = -c_self_crnt;
 325     factor_phi_al_crnt = c_cros_ante + ratio_phi_post * c_cros_post;
 326     factor_phi_al_post = -ratio_phi_post * c_self_crnt;
 327
 328     /* Computation of forces due to the derivatives of dihedral angle phi*/
 329     for (d = 0; d < DIM; d++)
 330     {
 331         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]);
 332         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]);
 333         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]);
 334         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]);
 335     }
 336
 337     /* PART 3 - COMPUTES THE FORCE COMPONENTS DUE TO THE DERIVATIVES OF BENDING ANGLE THETHA_ANTHE */
 338     /*      Computation of ratios */
 339     ratio_theta_ante_ante = c_cros_ante / c_self_ante;
 340     ratio_theta_ante_crnt = c_cros_ante / c_self_crnt;
 341
 342     /*      Computation of the prefactor */
 343     /*      Computing 2nd power */
 344     r1 = cosine_phi;
 345     /*      Computing 3rd power */
 346     r2 = cosine_phi;
 347
 348     prefactor_theta_ante = -torsion_coef[0] * norm_theta_ante * ( torsion_coef[1] + torsion_coef[2] * cosine_phi + torsion_coef[3] * (r1 * r1) +
 349                                                                   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;
 350
 351
 352     /*      Computation of forces due to the derivatives of bending angle theta_ante */
 353     for (d = 0; d < DIM; d++)
 354     {
 355         f_theta_ante_ai[d] = prefactor_theta_ante * (ratio_theta_ante_ante * delta_ante[d] - delta_crnt[d]);
 356         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]);
 357         f_theta_ante_ak[d] = prefactor_theta_ante * (delta_ante[d] - ratio_theta_ante_crnt * delta_crnt[d]);
 358     }
 359
 360     /* PART 4 - COMPUTES THE FORCE COMPONENTS DUE TO THE DERIVATIVES OF THE BENDING ANGLE THETA_POST */
 361
 362     /*      Computation of ratios */
 363     ratio_theta_post_crnt = c_cros_post / c_self_crnt;
 364     ratio_theta_post_post = c_cros_post / c_self_post;
 365
 366     /*     Computation of the prefactor */
 367     /*      Computing 2nd power */
 368     r1 = cosine_phi;
 369     /*      Computing 3rd power */
 370     r2 = cosine_phi;
 371
 372     prefactor_theta_post = -torsion_coef[0] * norm_theta_post * (torsion_coef[1] + torsion_coef[2] * cosine_phi + torsion_coef[3] * (r1 * r1) +
 373                                                                  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;
 374
 375
 376     /*      Computation of forces due to the derivatives of bending angle Theta_Post */
 377     for (d = 0; d < DIM; d++)
 378     {
 379         f_theta_post_aj[d] = prefactor_theta_post * (ratio_theta_post_crnt * delta_crnt[d] - delta_post[d]);
 380         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]);
 381         f_theta_post_al[d] = prefactor_theta_post * (delta_crnt[d] - ratio_theta_post_post * delta_post[d]);
 382     }
 383     r1 = cosine_phi;
 384     r2 = cosine_phi;
 385
 386     /* Contribution to energy - for formula see file "restcbt.h" */
 387     *v = torsion_coef[0] * (torsion_coef[1] + torsion_coef[2] * cosine_phi + torsion_coef[3] * (r1 * r1) +
 388                             torsion_coef[4] * (r2 * (r2 * r2)) + torsion_coef[5] * (r2 * (r2 * (r2 * r2)))) * sine_theta_ante_sq *
 389         sine_theta_ante * sine_theta_post_sq * sine_theta_post;
 390
 391
 392 }