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41 #include "gromacs/math/units.h"
42 #include "gromacs/math/utilities.h"
43 #include "gromacs/math/vec.h"
44 #include "gromacs/topology/idef.h"
46 /* This function computes factors needed for restricted angle potential.
47 * For explanations on formula used see file "restcbt.h" */
49 void compute_factors_restangles(int type, const t_iparams forceparams[],
50 rvec delta_ante, rvec delta_post,
51 real *prefactor, real *ratio_ante, real *ratio_post, real *v)
53 real theta_equil, k_bending;
54 real cosine_theta_equil;
55 real c_ante, c_cros, c_post;
57 real delta_cosine, cosine_theta;
59 real term_theta_theta_equil;
61 k_bending = forceparams[type].harmonic.krA;
62 theta_equil = forceparams[type].harmonic.rA*DEG2RAD;
63 theta_equil = M_PI - theta_equil;
64 cosine_theta_equil = cos(theta_equil);
66 c_ante = iprod(delta_ante, delta_ante);
67 c_cros = iprod(delta_ante, delta_post);
68 c_post = iprod(delta_post, delta_post);
70 norm = gmx_invsqrt(c_ante * c_post);
71 cosine_theta = c_cros * norm;
72 sine_theta_sq = 1 - cosine_theta * cosine_theta;
74 *ratio_ante = c_cros / c_ante;
75 *ratio_post = c_cros / c_post;
77 delta_cosine = cosine_theta - cosine_theta_equil;
78 term_theta_theta_equil = 1 - cosine_theta * cosine_theta_equil;
79 *prefactor = -(k_bending) * delta_cosine * norm * term_theta_theta_equil / (sine_theta_sq * sine_theta_sq);
81 *v = k_bending * 0.5 * delta_cosine * delta_cosine / sine_theta_sq;
86 /* Compute factors for restricted dihedral potential
87 * For explanations on formula used see file "restcbt.h" */
88 void compute_factors_restrdihs(int type, const t_iparams forceparams[],
89 rvec delta_ante, rvec delta_crnt, rvec delta_post,
90 real *factor_phi_ai_ante, real *factor_phi_ai_crnt, real *factor_phi_ai_post,
91 real *factor_phi_aj_ante, real *factor_phi_aj_crnt, real *factor_phi_aj_post,
92 real *factor_phi_ak_ante, real *factor_phi_ak_crnt, real *factor_phi_ak_post,
93 real *factor_phi_al_ante, real *factor_phi_al_crnt, real *factor_phi_al_post,
94 real *prefactor_phi, real *v)
97 real phi0, cosine_phi0;
99 real c_self_ante, c_self_crnt, c_self_post;
100 real c_cros_ante, c_cros_acrs, c_cros_post;
101 real c_prod, d_post, d_ante;
102 real sine_phi_sq, cosine_phi;
103 real delta_cosine, term_phi_phi0;
104 real ratio_phi_ante, ratio_phi_post;
107 /* Read parameters phi0 and k_torsion */
108 phi0 = forceparams[type].pdihs.phiA * DEG2RAD;
109 cosine_phi0 = cos(phi0);
110 k_torsion = forceparams[type].pdihs.cpA;
112 /* Computation of the cosine of the dihedral angle. The scalar ("dot") product method
113 * is used. c_*_* cummulate the scalar products of the differences of particles
114 * positions while c_prod, d_ante and d_post are differences of products of scalar
115 * terms that are parts of the derivatives of forces */
116 c_self_ante = iprod(delta_ante, delta_ante);
117 c_self_crnt = iprod(delta_crnt, delta_crnt);
118 c_self_post = iprod(delta_post, delta_post);
119 c_cros_ante = iprod(delta_ante, delta_crnt);
120 c_cros_acrs = iprod(delta_ante, delta_post);
121 c_cros_post = iprod(delta_crnt, delta_post);
122 c_prod = c_cros_ante * c_cros_post - c_self_crnt * c_cros_acrs;
123 d_ante = c_self_ante * c_self_crnt - c_cros_ante * c_cros_ante;
124 d_post = c_self_post * c_self_crnt - c_cros_post * c_cros_post;
126 /* When three consecutive beads align, we obtain values close to zero.
127 * Here we avoid small values to prevent round-off errors. */
128 if (d_ante < GMX_REAL_EPS)
130 d_ante = GMX_REAL_EPS;
132 if (d_post < GMX_REAL_EPS)
134 d_post = GMX_REAL_EPS;
137 /* Computes the square of the sinus of phi in sine_phi_sq */
138 norm_phi = gmx_invsqrt(d_ante * d_post);
139 cosine_phi = c_prod * norm_phi;
140 sine_phi_sq = 1.0 - cosine_phi * cosine_phi;
142 /* It is possible that cosine_phi is slightly bigger than 1.0 due to round-off errors. */
143 if (sine_phi_sq < 0.0)
148 /* Computation of the differences of cosines (delta_cosine) and a term (term_phi_phi0)
149 * that is part of the common prefactor_phi */
151 delta_cosine = cosine_phi - cosine_phi0;
152 term_phi_phi0 = 1 - cosine_phi * cosine_phi0;
155 /* Computation of ratios */
156 ratio_phi_ante = c_prod / d_ante;
157 ratio_phi_post = c_prod / d_post;
159 /* Computation of the prefactor - common term for all forces */
160 *prefactor_phi = -(k_torsion) * delta_cosine * norm_phi * term_phi_phi0 / (sine_phi_sq * sine_phi_sq);
162 /* Computation of force factors. Factors factor_phi_* are coming from the
163 * derivatives of the torsion angle (phi) with respect to the beads ai, aj, al, ak,
164 * (four) coordinates and they are multiplied in the force computations with the
165 * differences of the particles positions stored in parameters delta_ante,
166 * delta_crnt, delta_post. For formulas see file "restcbt.h" */
168 *factor_phi_ai_ante = ratio_phi_ante * c_self_crnt;
169 *factor_phi_ai_crnt = -c_cros_post - ratio_phi_ante * c_cros_ante;
170 *factor_phi_ai_post = c_self_crnt;
171 *factor_phi_aj_ante = -c_cros_post - ratio_phi_ante * (c_self_crnt + c_cros_ante);
172 *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;
173 *factor_phi_aj_post = -(c_cros_ante + c_self_crnt) - ratio_phi_post * c_cros_post;
174 *factor_phi_ak_ante = c_cros_post + c_self_crnt + ratio_phi_ante * c_cros_ante;
175 *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);
176 *factor_phi_ak_post = c_cros_ante + ratio_phi_post * (c_self_crnt + c_cros_post);
177 *factor_phi_al_ante = -c_self_crnt;
178 *factor_phi_al_crnt = c_cros_ante + ratio_phi_post * c_cros_post;
179 *factor_phi_al_post = -ratio_phi_post * c_self_crnt;
181 /* Contribution to energy - see formula in file "restcbt.h"*/
182 *v = k_torsion * 0.5 * delta_cosine * delta_cosine / sine_phi_sq;
187 /* Compute factors for CBT potential
188 * For explanations on formula used see file "restcbt.h" */
190 void compute_factors_cbtdihs(int type, const t_iparams forceparams[],
191 rvec delta_ante, rvec delta_crnt, rvec delta_post,
192 rvec f_phi_ai, rvec f_phi_aj, rvec f_phi_ak, rvec f_phi_al,
193 rvec f_theta_ante_ai, rvec f_theta_ante_aj, rvec f_theta_ante_ak,
194 rvec f_theta_post_aj, rvec f_theta_post_ak, rvec f_theta_post_al,
198 real torsion_coef[NR_CBTDIHS];
199 real c_self_ante, c_self_crnt, c_self_post;
200 real c_cros_ante, c_cros_acrs, c_cros_post;
201 real c_prod, d_ante, d_post;
202 real norm_phi, norm_theta_ante, norm_theta_post;
203 real cosine_phi, cosine_theta_ante, cosine_theta_post;
204 real sine_theta_ante_sq, sine_theta_post_sq;
205 real sine_theta_ante, sine_theta_post;
207 real ratio_phi_ante, ratio_phi_post;
209 real factor_phi_ai_ante, factor_phi_ai_crnt, factor_phi_ai_post;
210 real factor_phi_aj_ante, factor_phi_aj_crnt, factor_phi_aj_post;
211 real factor_phi_ak_ante, factor_phi_ak_crnt, factor_phi_ak_post;
212 real factor_phi_al_ante, factor_phi_al_crnt, factor_phi_al_post;
213 real prefactor_theta_ante, ratio_theta_ante_ante, ratio_theta_ante_crnt;
214 real prefactor_theta_post, ratio_theta_post_crnt, ratio_theta_post_post;
216 /* The formula for combined bending-torsion potential (see file "restcbt.h") contains
217 * in its expression not only the dihedral angle \f[\phi\f] but also \f[\theta_{i-1}\f]
218 * (theta_ante bellow) and \f[\theta_{i}\f] (theta_post bellow)--- the adjacent bending
219 * angles. The forces for the particles ai, aj, ak, al have components coming from the
220 * derivatives of the potential with respect to all three angles.
221 * This function is organised in 4 parts
222 * PART 1 - Computes force factors common to all the derivatives for the four particles
223 * PART 2 - Computes the force components due to the derivatives of dihedral angle Phi
224 * PART 3 - Computes the force components due to the derivatives of bending angle Theta_Ante
225 * PART 4 - Computes the force components due to the derivatives of bending angle Theta_Post
226 * Bellow we will respct thuis structure */
229 /* PART 1 - COMPUTES FORCE FACTORS COMMON TO ALL DERIVATIVES FOR THE FOUR PARTICLES */
232 for (j = 0; (j < NR_CBTDIHS); j++)
234 torsion_coef[j] = forceparams[type].cbtdihs.cbtcA[j];
237 /* Computation of the cosine of the dihedral angle. The scalar ("dot") product method
238 * is used. c_*_* cummulate the scalar products of the differences of particles
239 * positions while c_prod, d_ante and d_post are differences of products of scalar
240 * terms that are parts of the derivatives of forces */
242 c_self_ante = iprod(delta_ante, delta_ante);
243 c_self_crnt = iprod(delta_crnt, delta_crnt);
244 c_self_post = iprod(delta_post, delta_post);
245 c_cros_ante = iprod(delta_ante, delta_crnt);
246 c_cros_acrs = iprod(delta_ante, delta_post);
247 c_cros_post = iprod(delta_crnt, delta_post);
248 c_prod = c_cros_ante * c_cros_post - c_self_crnt * c_cros_acrs;
249 d_ante = c_self_ante * c_self_crnt - c_cros_ante * c_cros_ante;
250 d_post = c_self_post * c_self_crnt - c_cros_post * c_cros_post;
252 /* When three consecutive beads align, we obtain values close to zero.
253 Here we avoid small values to prevent round-off errors. */
254 if (d_ante < GMX_REAL_EPS)
256 d_ante = GMX_REAL_EPS;
258 if (d_post < GMX_REAL_EPS)
260 d_post = GMX_REAL_EPS;
263 /* Computations of cosines */
264 norm_phi = gmx_invsqrt(d_ante * d_post);
265 norm_theta_ante = gmx_invsqrt(c_self_ante * c_self_crnt);
266 norm_theta_post = gmx_invsqrt(c_self_crnt * c_self_post);
267 cosine_phi = c_prod * norm_phi;
268 cosine_theta_ante = c_cros_ante * norm_theta_ante;
269 cosine_theta_post = c_cros_post * norm_theta_post;
270 sine_theta_ante_sq = 1 - cosine_theta_ante * cosine_theta_ante;
271 sine_theta_post_sq = 1 - cosine_theta_post * cosine_theta_post;
273 /* It is possible that cosine_theta is slightly bigger than 1.0 due to round-off errors. */
274 if (sine_theta_ante_sq < 0.0)
276 sine_theta_ante_sq = 0.0;
278 if (sine_theta_post_sq < 0.0)
280 sine_theta_post_sq = 0.0;
283 sine_theta_ante = sqrt(sine_theta_ante_sq);
284 sine_theta_post = sqrt(sine_theta_post_sq);
286 /* PART 2 - COMPUTES FORCE COMPONENTS DUE TO DERIVATIVES TO DIHEDRAL ANGLE PHI */
288 /* Computation of ratios */
289 ratio_phi_ante = c_prod / d_ante;
290 ratio_phi_post = c_prod / d_post;
292 /* Computation of the prefactor */
293 /* Computing 2nd power */
296 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) *
297 sine_theta_ante_sq * sine_theta_ante * sine_theta_post_sq * sine_theta_post;
299 /* Computation of factors (important for gaining speed). Factors factor_phi_* are coming from the
300 * derivatives of the torsion angle (phi) with respect to the beads ai, aj, al, ak,
301 * (four) coordinates and they are multiplied in the force computations with the
302 * differences of the particles positions stored in parameters delta_ante,
303 * delta_crnt, delta_post. For formulas see file "restcbt.h" */
305 factor_phi_ai_ante = ratio_phi_ante * c_self_crnt;
306 factor_phi_ai_crnt = -c_cros_post - ratio_phi_ante * c_cros_ante;
307 factor_phi_ai_post = c_self_crnt;
308 factor_phi_aj_ante = -c_cros_post - ratio_phi_ante * (c_self_crnt + c_cros_ante);
309 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;
310 factor_phi_aj_post = -(c_cros_ante + c_self_crnt) - ratio_phi_post * c_cros_post;
311 factor_phi_ak_ante = c_cros_post + c_self_crnt + ratio_phi_ante * c_cros_ante;
312 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);
313 factor_phi_ak_post = c_cros_ante + ratio_phi_post * (c_self_crnt + c_cros_post);
314 factor_phi_al_ante = -c_self_crnt;
315 factor_phi_al_crnt = c_cros_ante + ratio_phi_post * c_cros_post;
316 factor_phi_al_post = -ratio_phi_post * c_self_crnt;
318 /* Computation of forces due to the derivatives of dihedral angle phi*/
319 for (d = 0; d < DIM; d++)
321 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]);
322 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]);
323 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]);
324 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]);
327 /* PART 3 - COMPUTES THE FORCE COMPONENTS DUE TO THE DERIVATIVES OF BENDING ANGLE THETHA_ANTHE */
328 /* Computation of ratios */
329 ratio_theta_ante_ante = c_cros_ante / c_self_ante;
330 ratio_theta_ante_crnt = c_cros_ante / c_self_crnt;
332 /* Computation of the prefactor */
333 /* Computing 2nd power */
335 /* Computing 3rd power */
338 prefactor_theta_ante = -torsion_coef[0] * norm_theta_ante * ( torsion_coef[1] + torsion_coef[2] * cosine_phi + torsion_coef[3] * (r1 * r1) +
339 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;
342 /* Computation of forces due to the derivatives of bending angle theta_ante */
343 for (d = 0; d < DIM; d++)
345 f_theta_ante_ai[d] = prefactor_theta_ante * (ratio_theta_ante_ante * delta_ante[d] - delta_crnt[d]);
346 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]);
347 f_theta_ante_ak[d] = prefactor_theta_ante * (delta_ante[d] - ratio_theta_ante_crnt * delta_crnt[d]);
350 /* PART 4 - COMPUTES THE FORCE COMPONENTS DUE TO THE DERIVATIVES OF THE BENDING ANGLE THETA_POST */
352 /* Computation of ratios */
353 ratio_theta_post_crnt = c_cros_post / c_self_crnt;
354 ratio_theta_post_post = c_cros_post / c_self_post;
356 /* Computation of the prefactor */
357 /* Computing 2nd power */
359 /* Computing 3rd power */
362 prefactor_theta_post = -torsion_coef[0] * norm_theta_post * (torsion_coef[1] + torsion_coef[2] * cosine_phi + torsion_coef[3] * (r1 * r1) +
363 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;
366 /* Computation of forces due to the derivatives of bending angle Theta_Post */
367 for (d = 0; d < DIM; d++)
369 f_theta_post_aj[d] = prefactor_theta_post * (ratio_theta_post_crnt * delta_crnt[d] - delta_post[d]);
370 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]);
371 f_theta_post_al[d] = prefactor_theta_post * (delta_crnt[d] - ratio_theta_post_post * delta_post[d]);
376 /* Contribution to energy - for formula see file "restcbt.h" */
377 *v = torsion_coef[0] * (torsion_coef[1] + torsion_coef[2] * cosine_phi + torsion_coef[3] * (r1 * r1) +
378 torsion_coef[4] * (r2 * (r2 * r2)) + torsion_coef[5] * (r2 * (r2 * (r2 * r2)))) * sine_theta_ante_sq *
379 sine_theta_ante * sine_theta_post_sq * sine_theta_post;