2 * This file is part of the GROMACS molecular simulation package.
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.
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.
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.
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.
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.
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.
39 #include "gromacs/math/units.h"
40 #include "gromacs/math/utilities.h"
41 #include "gromacs/math/vec.h"
42 #include "gromacs/topology/idef.h"
44 /* This function computes factors needed for restricted angle potential.
45 * For explanations on formula used see file "restcbt.h" */
47 void compute_factors_restangles(int type, const t_iparams forceparams[],
48 rvec delta_ante, rvec delta_post,
49 real *prefactor, real *ratio_ante, real *ratio_post, real *v)
51 real theta_equil, k_bending;
52 real cosine_theta_equil;
53 real c_ante, c_cros, c_post;
55 real delta_cosine, cosine_theta;
57 real term_theta_theta_equil;
59 k_bending = forceparams[type].harmonic.krA;
60 theta_equil = forceparams[type].harmonic.rA*DEG2RAD;
61 theta_equil = M_PI - theta_equil;
62 cosine_theta_equil = cos(theta_equil);
64 c_ante = iprod(delta_ante, delta_ante);
65 c_cros = iprod(delta_ante, delta_post);
66 c_post = iprod(delta_post, delta_post);
68 norm = gmx_invsqrt(c_ante * c_post);
69 cosine_theta = c_cros * norm;
70 sine_theta_sq = 1 - cosine_theta * cosine_theta;
72 *ratio_ante = c_cros / c_ante;
73 *ratio_post = c_cros / c_post;
75 delta_cosine = cosine_theta - cosine_theta_equil;
76 term_theta_theta_equil = 1 - cosine_theta * cosine_theta_equil;
77 *prefactor = -(k_bending) * delta_cosine * norm * term_theta_theta_equil / (sine_theta_sq * sine_theta_sq);
79 *v = k_bending * 0.5 * delta_cosine * delta_cosine / sine_theta_sq;
84 /* Compute factors for restricted dihedral potential
85 * For explanations on formula used see file "restcbt.h" */
86 void compute_factors_restrdihs(int type, const t_iparams forceparams[],
87 rvec delta_ante, rvec delta_crnt, rvec delta_post,
88 real *factor_phi_ai_ante, real *factor_phi_ai_crnt, real *factor_phi_ai_post,
89 real *factor_phi_aj_ante, real *factor_phi_aj_crnt, real *factor_phi_aj_post,
90 real *factor_phi_ak_ante, real *factor_phi_ak_crnt, real *factor_phi_ak_post,
91 real *factor_phi_al_ante, real *factor_phi_al_crnt, real *factor_phi_al_post,
92 real *prefactor_phi, real *v)
95 real phi0, sine_phi0, cosine_phi0;
97 real c_self_ante, c_self_crnt, c_self_post;
98 real c_cros_ante, c_cros_acrs, c_cros_post;
99 real c_prod, d_post, d_ante;
100 real sine_phi_sq, cosine_phi;
101 real delta_cosine, term_phi_phi0;
102 real ratio_phi_ante, ratio_phi_post;
103 real cos_phi, norm_phi;
105 /* Read parameters phi0 and k_torsion */
106 phi0 = forceparams[type].pdihs.phiA * DEG2RAD;
107 cosine_phi0 = cos(phi0);
108 sine_phi0 = sin(phi0);
109 k_torsion = forceparams[type].pdihs.cpA;
111 /* Computation of the cosine of the dihedral angle. The scalar ("dot") product method
112 * is used. c_*_* cummulate the scalar products of the differences of particles
113 * positions while c_prod, d_ante and d_post are differences of products of scalar
114 * terms that are parts of the derivatives of forces */
115 c_self_ante = iprod(delta_ante, delta_ante);
116 c_self_crnt = iprod(delta_crnt, delta_crnt);
117 c_self_post = iprod(delta_post, delta_post);
118 c_cros_ante = iprod(delta_ante, delta_crnt);
119 c_cros_acrs = iprod(delta_ante, delta_post);
120 c_cros_post = iprod(delta_crnt, delta_post);
121 c_prod = c_cros_ante * c_cros_post - c_self_crnt * c_cros_acrs;
122 d_ante = c_self_ante * c_self_crnt - c_cros_ante * c_cros_ante;
123 d_post = c_self_post * c_self_crnt - c_cros_post * c_cros_post;
125 /* When three consecutive beads align, we obtain values close to zero.
126 * Here we avoid small values to prevent round-off errors. */
127 if (d_ante < GMX_REAL_EPS)
129 d_ante = GMX_REAL_EPS;
131 if (d_post < GMX_REAL_EPS)
133 d_post = GMX_REAL_EPS;
136 /* Computes the square of the sinus of phi in sine_phi_sq */
137 norm_phi = gmx_invsqrt(d_ante * d_post);
138 cosine_phi = c_prod * norm_phi;
139 sine_phi_sq = 1.0 - cosine_phi * cosine_phi;
141 /* It is possible that cosine_phi is slightly bigger than 1.0 due to round-off errors. */
142 if (sine_phi_sq < 0.0)
147 /* Computation of the differences of cosines (delta_cosine) and a term (term_phi_phi0)
148 * that is part of the common prefactor_phi */
150 delta_cosine = cosine_phi - cosine_phi0;
151 term_phi_phi0 = 1 - cosine_phi * cosine_phi0;
154 /* Computation of ratios */
155 ratio_phi_ante = c_prod / d_ante;
156 ratio_phi_post = c_prod / d_post;
158 /* Computation of the prefactor - common term for all forces */
159 *prefactor_phi = -(k_torsion) * delta_cosine * norm_phi * term_phi_phi0 / (sine_phi_sq * sine_phi_sq);
161 /* Computation of force factors. Factors factor_phi_* are coming from the
162 * derivatives of the torsion angle (phi) with respect to the beads ai, aj, al, ak,
163 * (four) coordinates and they are multiplied in the force computations with the
164 * differences of the particles positions stored in parameters delta_ante,
165 * delta_crnt, delta_post. For formulas see file "restcbt.h" */
167 *factor_phi_ai_ante = ratio_phi_ante * c_self_crnt;
168 *factor_phi_ai_crnt = -c_cros_post - ratio_phi_ante * c_cros_ante;
169 *factor_phi_ai_post = c_self_crnt;
170 *factor_phi_aj_ante = -c_cros_post - ratio_phi_ante * (c_self_crnt + c_cros_ante);
171 *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;
172 *factor_phi_aj_post = -(c_cros_ante + c_self_crnt) - ratio_phi_post * c_cros_post;
173 *factor_phi_ak_ante = c_cros_post + c_self_crnt + ratio_phi_ante * c_cros_ante;
174 *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);
175 *factor_phi_ak_post = c_cros_ante + ratio_phi_post * (c_self_crnt + c_cros_post);
176 *factor_phi_al_ante = -c_self_crnt;
177 *factor_phi_al_crnt = c_cros_ante + ratio_phi_post * c_cros_post;
178 *factor_phi_al_post = -ratio_phi_post * c_self_crnt;
180 /* Contribution to energy - see formula in file "restcbt.h"*/
181 *v = k_torsion * 0.5 * delta_cosine * delta_cosine / sine_phi_sq;
186 /* Compute factors for CBT potential
187 * For explanations on formula used see file "restcbt.h" */
189 void compute_factors_cbtdihs(int type, const t_iparams forceparams[],
190 rvec delta_ante, rvec delta_crnt, rvec delta_post,
191 rvec f_phi_ai, rvec f_phi_aj, rvec f_phi_ak, rvec f_phi_al,
192 rvec f_theta_ante_ai, rvec f_theta_ante_aj, rvec f_theta_ante_ak,
193 rvec f_theta_post_aj, rvec f_theta_post_ak, rvec f_theta_post_al,
197 real torsion_coef[NR_CBTDIHS];
198 real c_self_ante, c_self_crnt, c_self_post;
199 real c_cros_ante, c_cros_acrs, c_cros_post;
200 real c_prod, d_ante, d_post;
201 real norm_phi, norm_theta_ante, norm_theta_post;
202 real cosine_phi, cosine_theta_ante, cosine_theta_post;
203 real sine_theta_ante_sq, sine_theta_post_sq;
204 real sine_theta_ante, sine_theta_post;
206 real ratio_phi_ante, ratio_phi_post;
208 real factor_phi_ai_ante, factor_phi_ai_crnt, factor_phi_ai_post;
209 real factor_phi_aj_ante, factor_phi_aj_crnt, factor_phi_aj_post;
210 real factor_phi_ak_ante, factor_phi_ak_crnt, factor_phi_ak_post;
211 real factor_phi_al_ante, factor_phi_al_crnt, factor_phi_al_post;
212 real prefactor_theta_ante, ratio_theta_ante_ante, ratio_theta_ante_crnt;
213 real prefactor_theta_post, ratio_theta_post_crnt, ratio_theta_post_post;
215 /* The formula for combined bending-torsion potential (see file "restcbt.h") contains
216 * in its expression not only the dihedral angle \f[\phi\f] but also \f[\theta_{i-1}\f]
217 * (theta_ante bellow) and \f[\theta_{i}\f] (theta_post bellow)--- the adjacent bending
218 * angles. The forces for the particles ai, aj, ak, al have components coming from the
219 * derivatives of the potential with respect to all three angles.
220 * This function is organised in 4 parts
221 * PART 1 - Computes force factors common to all the derivatives for the four particles
222 * PART 2 - Computes the force components due to the derivatives of dihedral angle Phi
223 * PART 3 - Computes the force components due to the derivatives of bending angle Theta_Ante
224 * PART 4 - Computes the force components due to the derivatives of bending angle Theta_Post
225 * Bellow we will respct thuis structure */
228 /* PART 1 - COMPUTES FORCE FACTORS COMMON TO ALL DERIVATIVES FOR THE FOUR PARTICLES */
231 for (j = 0; (j < NR_CBTDIHS); j++)
233 torsion_coef[j] = forceparams[type].cbtdihs.cbtcA[j];
236 /* Computation of the cosine of the dihedral angle. The scalar ("dot") product method
237 * is used. c_*_* cummulate the scalar products of the differences of particles
238 * positions while c_prod, d_ante and d_post are differences of products of scalar
239 * terms that are parts of the derivatives of forces */
241 c_self_ante = iprod(delta_ante, delta_ante);
242 c_self_crnt = iprod(delta_crnt, delta_crnt);
243 c_self_post = iprod(delta_post, delta_post);
244 c_cros_ante = iprod(delta_ante, delta_crnt);
245 c_cros_acrs = iprod(delta_ante, delta_post);
246 c_cros_post = iprod(delta_crnt, delta_post);
247 c_prod = c_cros_ante * c_cros_post - c_self_crnt * c_cros_acrs;
248 d_ante = c_self_ante * c_self_crnt - c_cros_ante * c_cros_ante;
249 d_post = c_self_post * c_self_crnt - c_cros_post * c_cros_post;
251 /* When three consecutive beads align, we obtain values close to zero.
252 Here we avoid small values to prevent round-off errors. */
253 if (d_ante < GMX_REAL_EPS)
255 d_ante = GMX_REAL_EPS;
257 if (d_post < GMX_REAL_EPS)
259 d_post = GMX_REAL_EPS;
262 /* Computations of cosines */
263 norm_phi = gmx_invsqrt(d_ante * d_post);
264 norm_theta_ante = gmx_invsqrt(c_self_ante * c_self_crnt);
265 norm_theta_post = gmx_invsqrt(c_self_crnt * c_self_post);
266 cosine_phi = c_prod * norm_phi;
267 cosine_theta_ante = c_cros_ante * norm_theta_ante;
268 cosine_theta_post = c_cros_post * norm_theta_post;
269 sine_theta_ante_sq = 1 - cosine_theta_ante * cosine_theta_ante;
270 sine_theta_post_sq = 1 - cosine_theta_post * cosine_theta_post;
272 /* It is possible that cosine_theta is slightly bigger than 1.0 due to round-off errors. */
273 if (sine_theta_ante_sq < 0.0)
275 sine_theta_ante_sq = 0.0;
277 if (sine_theta_post_sq < 0.0)
279 sine_theta_post_sq = 0.0;
282 sine_theta_ante = sqrt(sine_theta_ante_sq);
283 sine_theta_post = sqrt(sine_theta_post_sq);
285 /* PART 2 - COMPUTES FORCE COMPONENTS DUE TO DERIVATIVES TO DIHEDRAL ANGLE PHI */
287 /* Computation of ratios */
288 ratio_phi_ante = c_prod / d_ante;
289 ratio_phi_post = c_prod / d_post;
291 /* Computation of the prefactor */
292 /* Computing 2nd power */
295 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) *
296 sine_theta_ante_sq * sine_theta_ante * sine_theta_post_sq * sine_theta_post;
298 /* Computation of factors (important for gaining speed). Factors factor_phi_* are coming from the
299 * derivatives of the torsion angle (phi) with respect to the beads ai, aj, al, ak,
300 * (four) coordinates and they are multiplied in the force computations with the
301 * differences of the particles positions stored in parameters delta_ante,
302 * delta_crnt, delta_post. For formulas see file "restcbt.h" */
304 factor_phi_ai_ante = ratio_phi_ante * c_self_crnt;
305 factor_phi_ai_crnt = -c_cros_post - ratio_phi_ante * c_cros_ante;
306 factor_phi_ai_post = c_self_crnt;
307 factor_phi_aj_ante = -c_cros_post - ratio_phi_ante * (c_self_crnt + c_cros_ante);
308 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;
309 factor_phi_aj_post = -(c_cros_ante + c_self_crnt) - ratio_phi_post * c_cros_post;
310 factor_phi_ak_ante = c_cros_post + c_self_crnt + ratio_phi_ante * c_cros_ante;
311 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);
312 factor_phi_ak_post = c_cros_ante + ratio_phi_post * (c_self_crnt + c_cros_post);
313 factor_phi_al_ante = -c_self_crnt;
314 factor_phi_al_crnt = c_cros_ante + ratio_phi_post * c_cros_post;
315 factor_phi_al_post = -ratio_phi_post * c_self_crnt;
317 /* Computation of forces due to the derivatives of dihedral angle phi*/
318 for (d = 0; d < DIM; d++)
320 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]);
321 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]);
322 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]);
323 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]);
326 /* PART 3 - COMPUTES THE FORCE COMPONENTS DUE TO THE DERIVATIVES OF BENDING ANGLE THETHA_ANTHE */
327 /* Computation of ratios */
328 ratio_theta_ante_ante = c_cros_ante / c_self_ante;
329 ratio_theta_ante_crnt = c_cros_ante / c_self_crnt;
331 /* Computation of the prefactor */
332 /* Computing 2nd power */
334 /* Computing 3rd power */
337 prefactor_theta_ante = -torsion_coef[0] * norm_theta_ante * ( torsion_coef[1] + torsion_coef[2] * cosine_phi + torsion_coef[3] * (r1 * r1) +
338 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;
341 /* Computation of forces due to the derivatives of bending angle theta_ante */
342 for (d = 0; d < DIM; d++)
344 f_theta_ante_ai[d] = prefactor_theta_ante * (ratio_theta_ante_ante * delta_ante[d] - delta_crnt[d]);
345 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]);
346 f_theta_ante_ak[d] = prefactor_theta_ante * (delta_ante[d] - ratio_theta_ante_crnt * delta_crnt[d]);
349 /* PART 4 - COMPUTES THE FORCE COMPONENTS DUE TO THE DERIVATIVES OF THE BENDING ANGLE THETA_POST */
351 /* Computation of ratios */
352 ratio_theta_post_crnt = c_cros_post / c_self_crnt;
353 ratio_theta_post_post = c_cros_post / c_self_post;
355 /* Computation of the prefactor */
356 /* Computing 2nd power */
358 /* Computing 3rd power */
361 prefactor_theta_post = -torsion_coef[0] * norm_theta_post * (torsion_coef[1] + torsion_coef[2] * cosine_phi + torsion_coef[3] * (r1 * r1) +
362 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;
365 /* Computation of forces due to the derivatives of bending angle Theta_Post */
366 for (d = 0; d < DIM; d++)
368 f_theta_post_aj[d] = prefactor_theta_post * (ratio_theta_post_crnt * delta_crnt[d] - delta_post[d]);
369 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]);
370 f_theta_post_al[d] = prefactor_theta_post * (delta_crnt[d] - ratio_theta_post_post * delta_post[d]);
375 /* Contribution to energy - for formula see file "restcbt.h" */
376 *v = torsion_coef[0] * (torsion_coef[1] + torsion_coef[2] * cosine_phi + torsion_coef[3] * (r1 * r1) +
377 torsion_coef[4] * (r2 * (r2 * r2)) + torsion_coef[5] * (r2 * (r2 * (r2 * r2)))) * sine_theta_ante_sq *
378 sine_theta_ante * sine_theta_post_sq * sine_theta_post;