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41 #include <sys/types.h>
44 #include "gromacs/math/units.h"
46 #include "gromacs/math/vec.h"
48 #include "calc_verletbuf.h"
49 #include "../mdlib/nbnxn_consts.h"
51 #include "gromacs/utility/fatalerror.h"
52 #include "gromacs/utility/smalloc.h"
55 /* The include below sets the SIMD instruction type (precision+width)
56 * for all nbnxn SIMD search and non-bonded kernel code.
58 #ifdef GMX_NBNXN_HALF_WIDTH_SIMD
59 #define GMX_USE_HALF_WIDTH_SIMD_HERE
61 #include "gromacs/simd/simd.h"
65 /* The code in this file estimates a pairlist buffer length
66 * given a target energy drift per atom per picosecond.
67 * This is done by estimating the drift given a buffer length.
68 * Ideally we would like to have a tight overestimate of the drift,
69 * but that can be difficult to achieve.
71 * Significant approximations used:
73 * Uniform particle density. UNDERESTIMATES the drift by rho_global/rho_local.
75 * Interactions don't affect particle motion. OVERESTIMATES the drift on longer
76 * time scales. This approximation probably introduces the largest errors.
78 * Only take one constraint per particle into account: OVERESTIMATES the drift.
80 * For rotating constraints assume the same functional shape for time scales
81 * where the constraints rotate significantly as the exact expression for
82 * short time scales. OVERESTIMATES the drift on long time scales.
84 * For non-linear virtual sites use the mass of the lightest constructing atom
85 * to determine the displacement. OVER/UNDERESTIMATES the drift, depending on
86 * the geometry and masses of constructing atoms.
88 * Note that the formulas for normal atoms and linear virtual sites are exact,
89 * apart from the first two approximations.
91 * Note that apart from the effect of the above approximations, the actual
92 * drift of the total energy of a system can be order of magnitude smaller
93 * due to cancellation of positive and negative drift for different pairs.
97 /* Struct for unique atom type for calculating the energy drift.
98 * The atom displacement depends on mass and constraints.
99 * The energy jump for given distance depend on LJ type and q.
103 real mass; /* mass */
104 int type; /* type (used for LJ parameters) */
106 gmx_bool bConstr; /* constrained, if TRUE, use #DOF=2 iso 3 */
107 real con_mass; /* mass of heaviest atom connected by constraints */
108 real con_len; /* constraint length to the heaviest atom */
109 } atom_nonbonded_kinetic_prop_t;
111 /* Struct for unique atom type for calculating the energy drift.
112 * The atom displacement depends on mass and constraints.
113 * The energy jump for given distance depend on LJ type and q.
117 atom_nonbonded_kinetic_prop_t prop; /* non-bonded and kinetic atom prop. */
118 int n; /* #atoms of this type in the system */
119 } verletbuf_atomtype_t;
121 void verletbuf_get_list_setup(gmx_bool bGPU,
122 verletbuf_list_setup_t *list_setup)
124 list_setup->cluster_size_i = NBNXN_CPU_CLUSTER_I_SIZE;
128 list_setup->cluster_size_j = NBNXN_GPU_CLUSTER_SIZE;
132 #ifndef GMX_NBNXN_SIMD
133 list_setup->cluster_size_j = NBNXN_CPU_CLUSTER_I_SIZE;
135 list_setup->cluster_size_j = GMX_SIMD_REAL_WIDTH;
136 #ifdef GMX_NBNXN_SIMD_2XNN
137 /* We assume the smallest cluster size to be on the safe side */
138 list_setup->cluster_size_j /= 2;
145 atom_nonbonded_kinetic_prop_equal(const atom_nonbonded_kinetic_prop_t *prop1,
146 const atom_nonbonded_kinetic_prop_t *prop2)
148 return (prop1->mass == prop2->mass &&
149 prop1->type == prop2->type &&
150 prop1->q == prop2->q &&
151 prop1->bConstr == prop2->bConstr &&
152 prop1->con_mass == prop2->con_mass &&
153 prop1->con_len == prop2->con_len);
156 static void add_at(verletbuf_atomtype_t **att_p, int *natt_p,
157 const atom_nonbonded_kinetic_prop_t *prop,
160 verletbuf_atomtype_t *att;
165 /* Ignore massless particles */
173 while (i < natt && !atom_nonbonded_kinetic_prop_equal(prop, &att[i].prop))
185 srenew(*att_p, *natt_p);
186 (*att_p)[i].prop = *prop;
187 (*att_p)[i].n = nmol;
191 static void get_vsite_masses(const gmx_moltype_t *moltype,
192 const gmx_ffparams_t *ffparams,
201 /* Check for virtual sites, determine mass from constructing atoms */
202 for (ft = 0; ft < F_NRE; ft++)
206 il = &moltype->ilist[ft];
208 for (i = 0; i < il->nr; i += 1+NRAL(ft))
211 real cam[5] = {0}, inv_mass, m_aj;
212 int a1, j, aj, coeff;
214 ip = &ffparams->iparams[il->iatoms[i]];
216 a1 = il->iatoms[i+1];
220 for (j = 1; j < NRAL(ft); j++)
222 cam[j] = moltype->atoms.atom[il->iatoms[i+1+j]].m;
225 cam[j] = vsite_m[il->iatoms[i+1+j]];
229 gmx_fatal(FARGS, "In molecule type '%s' %s construction involves atom %d, which is a virtual site of equal or high complexity. This is not supported.",
231 interaction_function[ft].longname,
232 il->iatoms[i+1+j]+1);
241 vsite_m[a1] = (cam[1]*cam[2])/(cam[2]*sqr(1-ip->vsite.a) + cam[1]*sqr(ip->vsite.a));
245 vsite_m[a1] = (cam[1]*cam[2]*cam[3])/(cam[2]*cam[3]*sqr(1-ip->vsite.a-ip->vsite.b) + cam[1]*cam[3]*sqr(ip->vsite.a) + cam[1]*cam[2]*sqr(ip->vsite.b));
250 for (j = 0; j < 3*ip->vsiten.n; j += 3)
252 aj = il->iatoms[i+j+2];
253 coeff = ip[il->iatoms[i+j]].vsiten.a;
254 if (moltype->atoms.atom[aj].ptype == eptVSite)
260 m_aj = moltype->atoms.atom[aj].m;
264 gmx_incons("The mass of a vsiten constructing atom is <= 0");
266 inv_mass += coeff*coeff/m_aj;
268 vsite_m[a1] = 1/inv_mass;
271 /* Use the mass of the lightest constructing atom.
272 * This is an approximation.
273 * If the distance of the virtual site to the
274 * constructing atom is less than all distances
275 * between constructing atoms, this is a safe
276 * over-estimate of the displacement of the vsite.
277 * This condition holds for all H mass replacement
278 * vsite constructions, except for SP2/3 groups.
279 * In SP3 groups one H will have a F_VSITE3
280 * construction, so even there the total drift
281 * estimate shouldn't be far off.
284 vsite_m[a1] = cam[1];
285 for (j = 2; j < NRAL(ft); j++)
287 vsite_m[a1] = min(vsite_m[a1], cam[j]);
294 fprintf(debug, "atom %4d %-20s mass %6.3f\n",
295 a1, interaction_function[ft].longname, vsite_m[a1]);
302 static void get_verlet_buffer_atomtypes(const gmx_mtop_t *mtop,
303 verletbuf_atomtype_t **att_p,
307 verletbuf_atomtype_t *att;
309 int mb, nmol, ft, i, a1, a2, a3, a;
310 const t_atoms *atoms;
313 atom_nonbonded_kinetic_prop_t *prop;
315 int n_nonlin_vsite_mol;
320 if (n_nonlin_vsite != NULL)
325 for (mb = 0; mb < mtop->nmolblock; mb++)
327 nmol = mtop->molblock[mb].nmol;
329 atoms = &mtop->moltype[mtop->molblock[mb].type].atoms;
331 /* Check for constraints, as they affect the kinetic energy.
332 * For virtual sites we need the masses and geometry of
333 * the constructing atoms to determine their velocity distribution.
335 snew(prop, atoms->nr);
336 snew(vsite_m, atoms->nr);
338 for (ft = F_CONSTR; ft <= F_CONSTRNC; ft++)
340 il = &mtop->moltype[mtop->molblock[mb].type].ilist[ft];
342 for (i = 0; i < il->nr; i += 1+NRAL(ft))
344 ip = &mtop->ffparams.iparams[il->iatoms[i]];
345 a1 = il->iatoms[i+1];
346 a2 = il->iatoms[i+2];
347 if (atoms->atom[a2].m > prop[a1].con_mass)
349 prop[a1].con_mass = atoms->atom[a2].m;
350 prop[a1].con_len = ip->constr.dA;
352 if (atoms->atom[a1].m > prop[a2].con_mass)
354 prop[a2].con_mass = atoms->atom[a1].m;
355 prop[a2].con_len = ip->constr.dA;
360 il = &mtop->moltype[mtop->molblock[mb].type].ilist[F_SETTLE];
362 for (i = 0; i < il->nr; i += 1+NRAL(F_SETTLE))
364 ip = &mtop->ffparams.iparams[il->iatoms[i]];
365 a1 = il->iatoms[i+1];
366 a2 = il->iatoms[i+2];
367 a3 = il->iatoms[i+3];
368 /* Usually the mass of a1 (usually oxygen) is larger than a2/a3.
369 * If this is not the case, we overestimate the displacement,
370 * which leads to a larger buffer (ok since this is an exotic case).
372 prop[a1].con_mass = atoms->atom[a2].m;
373 prop[a1].con_len = ip->settle.doh;
375 prop[a2].con_mass = atoms->atom[a1].m;
376 prop[a2].con_len = ip->settle.doh;
378 prop[a3].con_mass = atoms->atom[a1].m;
379 prop[a3].con_len = ip->settle.doh;
382 get_vsite_masses(&mtop->moltype[mtop->molblock[mb].type],
385 &n_nonlin_vsite_mol);
386 if (n_nonlin_vsite != NULL)
388 *n_nonlin_vsite += nmol*n_nonlin_vsite_mol;
391 for (a = 0; a < atoms->nr; a++)
393 if (atoms->atom[a].ptype == eptVSite)
395 prop[a].mass = vsite_m[a];
399 prop[a].mass = atoms->atom[a].m;
401 prop[a].type = atoms->atom[a].type;
402 prop[a].q = atoms->atom[a].q;
403 /* We consider an atom constrained, #DOF=2, when it is
404 * connected with constraints to (at least one) atom with
405 * a mass of more than 0.4x its own mass. This is not a critical
406 * parameter, since with roughly equal masses the unconstrained
407 * and constrained displacement will not differ much (and both
408 * overestimate the displacement).
410 prop[a].bConstr = (prop[a].con_mass > 0.4*prop[a].mass);
412 add_at(&att, &natt, &prop[a], nmol);
415 /* cppcheck-suppress uninitvar Fixed in cppcheck 1.65 */
422 for (a = 0; a < natt; a++)
424 fprintf(debug, "type %d: m %5.2f t %d q %6.3f con %d con_m %5.3f con_l %5.3f n %d\n",
425 a, att[a].prop.mass, att[a].prop.type, att[a].prop.q,
426 att[a].prop.bConstr, att[a].prop.con_mass, att[a].prop.con_len,
435 /* This function computes two components of the estimate of the variance
436 * in the displacement of one atom in a system of two constrained atoms.
437 * Returns in sigma2_2d the variance due to rotation of the constrained
438 * atom around the atom to which it constrained.
439 * Returns in sigma2_3d the variance due to displacement of the COM
440 * of the whole system of the two constrained atoms.
442 * Note that we only take a single constraint (the one to the heaviest atom)
443 * into account. If an atom has multiple constraints, this will result in
444 * an overestimate of the displacement, which gives a larger drift and buffer.
446 static void constrained_atom_sigma2(real kT_fac,
447 const atom_nonbonded_kinetic_prop_t *prop,
456 /* Here we decompose the motion of a constrained atom into two
457 * components: rotation around the COM and translation of the COM.
460 /* Determine the variance for the displacement of the rotational mode */
461 sigma2_rot = kT_fac/(prop->mass*(prop->mass + prop->con_mass)/prop->con_mass);
463 /* The distance from the atom to the COM, i.e. the rotational arm */
464 com_dist = prop->con_len*prop->con_mass/(prop->mass + prop->con_mass);
466 /* The variance relative to the arm */
467 sigma2_rel = sigma2_rot/(com_dist*com_dist);
468 /* At 6 the scaling formula has slope 0,
469 * so we keep sigma2_2d constant after that.
473 /* A constrained atom rotates around the atom it is constrained to.
474 * This results in a smaller linear displacement than for a free atom.
475 * For a perfectly circular displacement, this lowers the displacement
476 * by: 1/arcsin(arc_length)
477 * and arcsin(x) = 1 + x^2/6 + ...
478 * For sigma2_rel<<1 the displacement distribution is erfc
479 * (exact formula is provided below). For larger sigma, it is clear
480 * that the displacement can't be larger than 2*com_dist.
481 * It turns out that the distribution becomes nearly uniform.
482 * For intermediate sigma2_rel, scaling down sigma with the third
483 * order expansion of arcsin with argument sigma_rel turns out
484 * to give a very good approximation of the distribution and variance.
485 * Even for larger values, the variance is only slightly overestimated.
486 * Note that the most relevant displacements are in the long tail.
487 * This rotation approximation always overestimates the tail (which
488 * runs to infinity, whereas it should be <= 2*com_dist).
489 * Thus we always overestimate the drift and the buffer size.
491 scale = 1/(1 + sigma2_rel/6);
492 *sigma2_2d = sigma2_rot*scale*scale;
496 /* sigma_2d is set to the maximum given by the scaling above.
497 * For large sigma2 the real displacement distribution is close
498 * to uniform over -2*con_len to 2*com_dist.
499 * Our erfc with sigma_2d=sqrt(1.5)*com_dist (which means the sigma
500 * of the erfc output distribution is con_dist) overestimates
501 * the variance and additionally has a long tail. This means
502 * we have a (safe) overestimation of the drift.
504 *sigma2_2d = 1.5*com_dist*com_dist;
507 /* The constrained atom also moves (in 3D) with the COM of both atoms */
508 *sigma2_3d = kT_fac/(prop->mass + prop->con_mass);
511 static void get_atom_sigma2(real kT_fac,
512 const atom_nonbonded_kinetic_prop_t *prop,
518 /* Complicated constraint calculation in a separate function */
519 constrained_atom_sigma2(kT_fac, prop, sigma2_2d, sigma2_3d);
523 /* Unconstrained atom: trivial */
525 *sigma2_3d = kT_fac/prop->mass;
529 static void approx_2dof(real s2, real x, real *shift, real *scale)
531 /* A particle with 1 DOF constrained has 2 DOFs instead of 3.
532 * This code is also used for particles with multiple constraints,
533 * in which case we overestimate the displacement.
534 * The 2DOF distribution is sqrt(pi/2)*erfc(r/(sqrt(2)*s))/(2*s).
535 * We approximate this with scale*Gaussian(s,r+shift),
536 * by matching the distribution value and derivative at x.
537 * This is a tight overestimate for all r>=0 at any s and x.
541 ex = exp(-x*x/(2*s2));
542 er = gmx_erfc(x/sqrt(2*s2));
544 *shift = -x + sqrt(2*s2/M_PI)*ex/er;
545 *scale = 0.5*M_PI*exp(ex*ex/(M_PI*er*er))*er;
548 static real ener_drift(const verletbuf_atomtype_t *att, int natt,
549 const gmx_ffparams_t *ffp,
551 real md1_ljd, real d2_ljd, real md3_ljd,
552 real md1_ljr, real d2_ljr, real md3_ljr,
553 real md1_el, real d2_el,
555 real rlist, real boxvol)
557 double drift_tot, pot1, pot2, pot3, pot;
559 real s2i_2d, s2i_3d, s2j_2d, s2j_3d, s2, s;
562 real sc_fac, rsh, rsh2;
563 double c_exp, c_erfc;
567 /* Loop over the different atom type pairs */
568 for (i = 0; i < natt; i++)
570 get_atom_sigma2(kT_fac, &att[i].prop, &s2i_2d, &s2i_3d);
571 ti = att[i].prop.type;
573 for (j = i; j < natt; j++)
575 get_atom_sigma2(kT_fac, &att[j].prop, &s2j_2d, &s2j_3d);
576 tj = att[j].prop.type;
578 /* Add up the up to four independent variances */
579 s2 = s2i_2d + s2i_3d + s2j_2d + s2j_3d;
581 /* Note that attractive and repulsive potentials for individual
582 * pairs will partially cancel.
584 /* -dV/dr at the cut-off for LJ + Coulomb */
586 md1_ljd*ffp->iparams[ti*ffp->atnr+tj].lj.c6 +
587 md1_ljr*ffp->iparams[ti*ffp->atnr+tj].lj.c12 +
588 md1_el*att[i].prop.q*att[j].prop.q;
590 /* d2V/dr2 at the cut-off for LJ + Coulomb */
592 d2_ljd*ffp->iparams[ti*ffp->atnr+tj].lj.c6 +
593 d2_ljr*ffp->iparams[ti*ffp->atnr+tj].lj.c12 +
594 d2_el*att[i].prop.q*att[j].prop.q;
596 /* -d3V/dr3 at the cut-off for LJ, we neglect Coulomb */
598 md3_ljd*ffp->iparams[ti*ffp->atnr+tj].lj.c6 +
599 md3_ljr*ffp->iparams[ti*ffp->atnr+tj].lj.c12;
603 /* For constraints: adapt r and scaling for the Gaussian */
604 if (att[i].prop.bConstr)
608 approx_2dof(s2i_2d, r_buffer*s2i_2d/s2, &sh, &sc);
612 if (att[j].prop.bConstr)
616 approx_2dof(s2j_2d, r_buffer*s2j_2d/s2, &sh, &sc);
621 /* Exact contribution of an atom pair with Gaussian displacement
622 * with sigma s to the energy drift for a potential with
623 * derivative -md and second derivative dd at the cut-off.
624 * The only catch is that for potentials that change sign
625 * near the cut-off there could be an unlucky compensation
626 * of positive and negative energy drift.
627 * Such potentials are extremely rare though.
629 * Note that pot has unit energy*length, as the linear
630 * atom density still needs to be put in.
632 c_exp = exp(-rsh*rsh/(2*s2))/sqrt(2*M_PI);
633 c_erfc = 0.5*gmx_erfc(rsh/(sqrt(2*s2)));
638 md1/2*((rsh2 + s2)*c_erfc - rsh*s*c_exp);
640 d2/6*(s*(rsh2 + 2*s2)*c_exp - rsh*(rsh2 + 3*s2)*c_erfc);
642 md3/24*((rsh2*rsh2 + 6*rsh2*s2 + 3*s2*s2)*c_erfc - rsh*s*(rsh2 + 5*s2)*c_exp);
643 pot = pot1 + pot2 + pot3;
647 fprintf(debug, "n %d %d d s %.3f %.3f %.3f %.3f con %d -d1 %8.1e d2 %8.1e -d3 %8.1e pot1 %8.1e pot2 %8.1e pot3 %8.1e pot %8.1e\n",
649 sqrt(s2i_2d), sqrt(s2i_3d),
650 sqrt(s2j_2d), sqrt(s2j_3d),
651 att[i].prop.bConstr+att[j].prop.bConstr,
653 pot1, pot2, pot3, pot);
656 /* Multiply by the number of atom pairs */
659 pot *= (double)att[i].n*(att[i].n - 1)/2;
663 pot *= (double)att[i].n*att[j].n;
665 /* We need the line density to get the energy drift of the system.
666 * The effective average r^2 is close to (rlist+sigma)^2.
668 pot *= 4*M_PI*sqr(rlist + s)/boxvol;
670 /* Add the unsigned drift to avoid cancellation of errors */
671 drift_tot += fabs(pot);
678 static real surface_frac(int cluster_size, real particle_distance, real rlist)
682 if (rlist < 0.5*particle_distance)
684 /* We have non overlapping spheres */
688 /* Half the inter-particle distance relative to rlist */
689 d = 0.5*particle_distance/rlist;
691 /* Determine the area of the surface at distance rlist to the closest
692 * particle, relative to surface of a sphere of radius rlist.
693 * The formulas below assume close to cubic cells for the pair search grid,
694 * which the pair search code tries to achieve.
695 * Note that in practice particle distances will not be delta distributed,
696 * but have some spread, often involving shorter distances,
697 * as e.g. O-H bonds in a water molecule. Thus the estimates below will
698 * usually be slightly too high and thus conservative.
700 switch (cluster_size)
703 /* One particle: trivial */
707 /* Two particles: two spheres at fractional distance 2*a */
711 /* We assume a perfect, symmetric tetrahedron geometry.
712 * The surface around a tetrahedron is too complex for a full
713 * analytical solution, so we use a Taylor expansion.
715 area_rel = (1.0 + 1/M_PI*(6*acos(1/sqrt(3))*d +
719 83.0/756.0*d*d*d*d*d*d)));
722 gmx_incons("surface_frac called with unsupported cluster_size");
726 return area_rel/cluster_size;
729 /* Returns the negative of the third derivative of a potential r^-p
730 * with a force-switch function, evaluated at the cut-off rc.
732 static real md3_force_switch(real p, real rswitch, real rc)
734 /* The switched force function is:
735 * p*r^-(p+1) + a*(r - rswitch)^2 + b*(r - rswitch)^3
738 real md3_pot, md3_sw;
740 a = -((p + 4)*rc - (p + 1)*rswitch)/(pow(rc, p+2)*pow(rc-rswitch, 2));
741 b = ((p + 3)*rc - (p + 1)*rswitch)/(pow(rc, p+2)*pow(rc-rswitch, 3));
743 md3_pot = (p + 2)*(p + 1)*p*pow(rc, p+3);
744 md3_sw = 2*a + 6*b*(rc - rswitch);
746 return md3_pot + md3_sw;
749 void calc_verlet_buffer_size(const gmx_mtop_t *mtop, real boxvol,
750 const t_inputrec *ir,
751 real reference_temperature,
752 const verletbuf_list_setup_t *list_setup,
759 real particle_distance;
760 real nb_clust_frac_pairs_not_in_list_at_cutoff;
762 verletbuf_atomtype_t *att = NULL;
765 real md1_ljd, d2_ljd, md3_ljd;
766 real md1_ljr, d2_ljr, md3_ljr;
769 real kT_fac, mass_min;
774 if (reference_temperature < 0)
776 if (EI_MD(ir->eI) && ir->etc == etcNO)
778 /* This case should be handled outside calc_verlet_buffer_size */
779 gmx_incons("calc_verlet_buffer_size called with an NVE ensemble and reference_temperature < 0");
782 /* We use the maximum temperature with multiple T-coupl groups.
783 * We could use a per particle temperature, but since particles
784 * interact, this might underestimate the buffer size.
786 reference_temperature = 0;
787 for (i = 0; i < ir->opts.ngtc; i++)
789 if (ir->opts.tau_t[i] >= 0)
791 reference_temperature = max(reference_temperature,
797 /* Resolution of the buffer size */
800 env = getenv("GMX_VERLET_BUFFER_RES");
803 sscanf(env, "%lf", &resolution);
806 /* In an atom wise pair-list there would be no pairs in the list
807 * beyond the pair-list cut-off.
808 * However, we use a pair-list of groups vs groups of atoms.
809 * For groups of 4 atoms, the parallelism of SSE instructions, only
810 * 10% of the atoms pairs are not in the list just beyond the cut-off.
811 * As this percentage increases slowly compared to the decrease of the
812 * Gaussian displacement distribution over this range, we can simply
813 * reduce the drift by this fraction.
814 * For larger groups, e.g. of 8 atoms, this fraction will be lower,
815 * so then buffer size will be on the conservative (large) side.
817 * Note that the formulas used here do not take into account
818 * cancellation of errors which could occur by missing both
819 * attractive and repulsive interactions.
821 * The only major assumption is homogeneous particle distribution.
822 * For an inhomogeneous system, such as a liquid-vapor system,
823 * the buffer will be underestimated. The actual energy drift
824 * will be higher by the factor: local/homogeneous particle density.
826 * The results of this estimate have been checked againt simulations.
827 * In most cases the real drift differs by less than a factor 2.
830 /* Worst case assumption: HCP packing of particles gives largest distance */
831 particle_distance = pow(boxvol*sqrt(2)/mtop->natoms, 1.0/3.0);
833 get_verlet_buffer_atomtypes(mtop, &att, &natt, n_nonlin_vsite);
834 assert(att != NULL && natt >= 0);
838 fprintf(debug, "particle distance assuming HCP packing: %f nm\n",
840 fprintf(debug, "energy drift atom types: %d\n", natt);
843 reppow = mtop->ffparams.reppow;
850 if (ir->vdwtype == evdwCUT)
852 real sw_range, md3_pswf;
854 switch (ir->vdw_modifier)
857 case eintmodPOTSHIFT:
858 /* -dV/dr of -r^-6 and r^-reppow */
859 md1_ljd = -6*pow(ir->rvdw, -7.0);
860 md1_ljr = reppow*pow(ir->rvdw, -(reppow+1));
861 /* The contribution of the higher derivatives is negligible */
863 case eintmodFORCESWITCH:
864 /* At the cut-off: V=V'=V''=0, so we use only V''' */
865 md3_ljd = -md3_force_switch(6.0, ir->rvdw_switch, ir->rvdw);
866 md3_ljr = md3_force_switch(reppow, ir->rvdw_switch, ir->rvdw);
868 case eintmodPOTSWITCH:
869 /* At the cut-off: V=V'=V''=0.
870 * V''' is given by the original potential times
871 * the third derivative of the switch function.
873 sw_range = ir->rvdw - ir->rvdw_switch;
874 md3_pswf = 60.0*pow(sw_range, -3.0);
876 md3_ljd = -pow(ir->rvdw, -6.0 )*md3_pswf;
877 md3_ljr = pow(ir->rvdw, -reppow)*md3_pswf;
880 gmx_incons("Unimplemented VdW modifier");
883 else if (EVDW_PME(ir->vdwtype))
885 real b, r, br, br2, br4, br6;
886 b = calc_ewaldcoeff_lj(ir->rvdw, ir->ewald_rtol_lj);
892 /* -dV/dr of g(br)*r^-6 [where g(x) = exp(-x^2)(1+x^2+x^4/2), see LJ-PME equations in manual] and r^-reppow */
893 md1_ljd = -exp(-br2)*(br6 + 3.0*br4 + 6.0*br2 + 6.0)*pow(r, -7.0);
894 md1_ljr = reppow*pow(r, -(reppow+1));
895 /* The contribution of the higher derivatives is negligible */
899 gmx_fatal(FARGS, "Energy drift calculation is only implemented for plain cut-off Lennard-Jones interactions");
902 elfac = ONE_4PI_EPS0/ir->epsilon_r;
904 /* Determine md=-dV/dr and dd=d^2V/dr^2 */
907 if (ir->coulombtype == eelCUT || EEL_RF(ir->coulombtype))
911 if (ir->coulombtype == eelCUT)
918 eps_rf = ir->epsilon_rf/ir->epsilon_r;
921 k_rf = pow(ir->rcoulomb, -3.0)*(eps_rf - ir->epsilon_r)/(2*eps_rf + ir->epsilon_r);
925 /* epsilon_rf = infinity */
926 k_rf = 0.5*pow(ir->rcoulomb, -3.0);
932 md1_el = elfac*(pow(ir->rcoulomb, -2.0) - 2*k_rf*ir->rcoulomb);
934 d2_el = elfac*(2*pow(ir->rcoulomb, -3.0) + 2*k_rf);
936 else if (EEL_PME(ir->coulombtype) || ir->coulombtype == eelEWALD)
940 b = calc_ewaldcoeff_q(ir->rcoulomb, ir->ewald_rtol);
943 md1_el = elfac*(b*exp(-br*br)*M_2_SQRTPI/rc + gmx_erfc(br)/(rc*rc));
944 d2_el = elfac/(rc*rc)*(2*b*(1 + br*br)*exp(-br*br)*M_2_SQRTPI + 2*gmx_erfc(br)/rc);
948 gmx_fatal(FARGS, "Energy drift calculation is only implemented for Reaction-Field and Ewald electrostatics");
951 /* Determine the variance of the atomic displacement
952 * over nstlist-1 steps: kT_fac
953 * For inertial dynamics (not Brownian dynamics) the mass factor
954 * is not included in kT_fac, it is added later.
958 /* Get the displacement distribution from the random component only.
959 * With accurate integration the systematic (force) displacement
960 * should be negligible (unless nstlist is extremely large, which
961 * you wouldn't do anyhow).
963 kT_fac = 2*BOLTZ*reference_temperature*(ir->nstlist-1)*ir->delta_t;
966 /* This is directly sigma^2 of the displacement */
967 kT_fac /= ir->bd_fric;
969 /* Set the masses to 1 as kT_fac is the full sigma^2,
970 * but we divide by m in ener_drift().
972 for (i = 0; i < natt; i++)
974 att[i].prop.mass = 1;
981 /* Per group tau_t is not implemented yet, use the maximum */
982 tau_t = ir->opts.tau_t[0];
983 for (i = 1; i < ir->opts.ngtc; i++)
985 tau_t = max(tau_t, ir->opts.tau_t[i]);
989 /* This kT_fac needs to be divided by the mass to get sigma^2 */
994 kT_fac = BOLTZ*reference_temperature*sqr((ir->nstlist-1)*ir->delta_t);
997 mass_min = att[0].prop.mass;
998 for (i = 1; i < natt; i++)
1000 mass_min = min(mass_min, att[i].prop.mass);
1005 fprintf(debug, "md1_ljd %9.2e d2_ljd %9.2e md3_ljd %9.2e\n", md1_ljd, d2_ljd, md3_ljd);
1006 fprintf(debug, "md1_ljr %9.2e d2_ljr %9.2e md3_ljr %9.2e\n", md1_ljr, d2_ljr, md3_ljr);
1007 fprintf(debug, "md1_el %9.2e d2_el %9.2e\n", md1_el, d2_el);
1008 fprintf(debug, "sqrt(kT_fac) %f\n", sqrt(kT_fac));
1009 fprintf(debug, "mass_min %f\n", mass_min);
1012 /* Search using bisection */
1014 /* The drift will be neglible at 5 times the max sigma */
1015 ib1 = (int)(5*2*sqrt(kT_fac/mass_min)/resolution) + 1;
1016 while (ib1 - ib0 > 1)
1020 rl = max(ir->rvdw, ir->rcoulomb) + rb;
1022 /* Calculate the average energy drift at the last step
1023 * of the nstlist steps at which the pair-list is used.
1025 drift = ener_drift(att, natt, &mtop->ffparams,
1027 md1_ljd, d2_ljd, md3_ljd,
1028 md1_ljr, d2_ljr, md3_ljr,
1033 /* Correct for the fact that we are using a Ni x Nj particle pair list
1034 * and not a 1 x 1 particle pair list. This reduces the drift.
1036 /* We don't have a formula for 8 (yet), use 4 which is conservative */
1037 nb_clust_frac_pairs_not_in_list_at_cutoff =
1038 surface_frac(min(list_setup->cluster_size_i, 4),
1039 particle_distance, rl)*
1040 surface_frac(min(list_setup->cluster_size_j, 4),
1041 particle_distance, rl);
1042 drift *= nb_clust_frac_pairs_not_in_list_at_cutoff;
1044 /* Convert the drift to drift per unit time per atom */
1045 drift /= ir->nstlist*ir->delta_t*mtop->natoms;
1049 fprintf(debug, "ib %3d %3d %3d rb %.3f %dx%d fac %.3f drift %f\n",
1051 list_setup->cluster_size_i, list_setup->cluster_size_j,
1052 nb_clust_frac_pairs_not_in_list_at_cutoff,
1056 if (fabs(drift) > ir->verletbuf_tol)
1068 *rlist = max(ir->rvdw, ir->rcoulomb) + ib1*resolution;