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41 #include <sys/types.h>
45 #include "gromacs/utility/smalloc.h"
46 #include "gmx_fatal.h"
50 #include "calc_verletbuf.h"
51 #include "../mdlib/nbnxn_consts.h"
52 #include "../mdlib/nbnxn_simd.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 gmx_unused bSIMD,
123 verletbuf_list_setup_t *list_setup)
127 list_setup->cluster_size_i = NBNXN_GPU_CLUSTER_SIZE;
128 list_setup->cluster_size_j = NBNXN_GPU_CLUSTER_SIZE;
132 list_setup->cluster_size_i = NBNXN_CPU_CLUSTER_I_SIZE;
133 list_setup->cluster_size_j = NBNXN_CPU_CLUSTER_I_SIZE;
134 #ifdef GMX_NBNXN_SIMD
137 list_setup->cluster_size_j = GMX_SIMD_REAL_WIDTH;
138 #ifdef GMX_NBNXN_SIMD_2XNN
139 /* We assume the smallest cluster size to be on the safe side */
140 list_setup->cluster_size_j /= 2;
148 atom_nonbonded_kinetic_prop_equal(const atom_nonbonded_kinetic_prop_t *prop1,
149 const atom_nonbonded_kinetic_prop_t *prop2)
151 return (prop1->mass == prop2->mass &&
152 prop1->type == prop2->type &&
153 prop1->q == prop2->q &&
154 prop1->bConstr == prop2->bConstr &&
155 prop1->con_mass == prop2->con_mass &&
156 prop1->con_len == prop2->con_len);
159 static void add_at(verletbuf_atomtype_t **att_p, int *natt_p,
160 const atom_nonbonded_kinetic_prop_t *prop,
163 verletbuf_atomtype_t *att;
168 /* Ignore massless particles */
176 while (i < natt && !atom_nonbonded_kinetic_prop_equal(prop, &att[i].prop))
188 srenew(*att_p, *natt_p);
189 (*att_p)[i].prop = *prop;
190 (*att_p)[i].n = nmol;
194 static void get_vsite_masses(const gmx_moltype_t *moltype,
195 const gmx_ffparams_t *ffparams,
204 /* Check for virtual sites, determine mass from constructing atoms */
205 for (ft = 0; ft < F_NRE; ft++)
209 il = &moltype->ilist[ft];
211 for (i = 0; i < il->nr; i += 1+NRAL(ft))
214 real cam[5], inv_mass, coeff, m_aj;
217 ip = &ffparams->iparams[il->iatoms[i]];
219 a1 = il->iatoms[i+1];
223 for (j = 1; j < NRAL(ft); j++)
225 cam[j] = moltype->atoms.atom[il->iatoms[i+1+j]].m;
228 cam[j] = vsite_m[il->iatoms[i+1+j]];
232 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.",
234 interaction_function[ft].longname,
235 il->iatoms[i+1+j]+1);
244 vsite_m[a1] = (cam[1]*cam[2])/(cam[2]*sqr(1-ip->vsite.a) + cam[1]*sqr(ip->vsite.a));
248 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));
253 for (j = 0; j < 3*ffparams->iparams[il->iatoms[i]].vsiten.n; j += 3)
255 aj = il->iatoms[i+j+2];
256 coeff = ffparams->iparams[il->iatoms[i+j]].vsiten.a;
257 if (moltype->atoms.atom[aj].ptype == eptVSite)
263 m_aj = moltype->atoms.atom[aj].m;
267 gmx_incons("The mass of a vsiten constructing atom is <= 0");
269 inv_mass += coeff*coeff/m_aj;
271 vsite_m[a1] = 1/inv_mass;
272 /* Correct for loop increment of i */
273 i += j - 1 - NRAL(ft);
276 /* Use the mass of the lightest constructing atom.
277 * This is an approximation.
278 * If the distance of the virtual site to the
279 * constructing atom is less than all distances
280 * between constructing atoms, this is a safe
281 * over-estimate of the displacement of the vsite.
282 * This condition holds for all H mass replacement
283 * vsite constructions, except for SP2/3 groups.
284 * In SP3 groups one H will have a F_VSITE3
285 * construction, so even there the total drift
286 * estimate shouldn't be far off.
289 vsite_m[a1] = cam[1];
290 for (j = 2; j < NRAL(ft); j++)
292 vsite_m[a1] = min(vsite_m[a1], cam[j]);
299 fprintf(debug, "atom %4d %-20s mass %6.3f\n",
300 a1, interaction_function[ft].longname, vsite_m[a1]);
307 static void get_verlet_buffer_atomtypes(const gmx_mtop_t *mtop,
308 verletbuf_atomtype_t **att_p,
312 verletbuf_atomtype_t *att;
314 int mb, nmol, ft, i, a1, a2, a3, a;
315 const t_atoms *atoms;
318 atom_nonbonded_kinetic_prop_t *prop;
320 int n_nonlin_vsite_mol;
325 if (n_nonlin_vsite != NULL)
330 for (mb = 0; mb < mtop->nmolblock; mb++)
332 nmol = mtop->molblock[mb].nmol;
334 atoms = &mtop->moltype[mtop->molblock[mb].type].atoms;
336 /* Check for constraints, as they affect the kinetic energy.
337 * For virtual sites we need the masses and geometry of
338 * the constructing atoms to determine their velocity distribution.
340 snew(prop, atoms->nr);
341 snew(vsite_m, atoms->nr);
343 for (ft = F_CONSTR; ft <= F_CONSTRNC; ft++)
345 il = &mtop->moltype[mtop->molblock[mb].type].ilist[ft];
347 for (i = 0; i < il->nr; i += 1+NRAL(ft))
349 ip = &mtop->ffparams.iparams[il->iatoms[i]];
350 a1 = il->iatoms[i+1];
351 a2 = il->iatoms[i+2];
352 if (atoms->atom[a2].m > prop[a1].con_mass)
354 prop[a1].con_mass = atoms->atom[a2].m;
355 prop[a1].con_len = ip->constr.dA;
357 if (atoms->atom[a1].m > prop[a2].con_mass)
359 prop[a2].con_mass = atoms->atom[a1].m;
360 prop[a2].con_len = ip->constr.dA;
365 il = &mtop->moltype[mtop->molblock[mb].type].ilist[F_SETTLE];
367 for (i = 0; i < il->nr; i += 1+NRAL(F_SETTLE))
369 ip = &mtop->ffparams.iparams[il->iatoms[i]];
370 a1 = il->iatoms[i+1];
371 a2 = il->iatoms[i+2];
372 a3 = il->iatoms[i+3];
373 /* Usually the mass of a1 (usually oxygen) is larger than a2/a3.
374 * If this is not the case, we overestimate the displacement,
375 * which leads to a larger buffer (ok since this is an exotic case).
377 prop[a1].con_mass = atoms->atom[a2].m;
378 prop[a1].con_len = ip->settle.doh;
380 prop[a2].con_mass = atoms->atom[a1].m;
381 prop[a2].con_len = ip->settle.doh;
383 prop[a3].con_mass = atoms->atom[a1].m;
384 prop[a3].con_len = ip->settle.doh;
387 get_vsite_masses(&mtop->moltype[mtop->molblock[mb].type],
390 &n_nonlin_vsite_mol);
391 if (n_nonlin_vsite != NULL)
393 *n_nonlin_vsite += nmol*n_nonlin_vsite_mol;
396 for (a = 0; a < atoms->nr; a++)
398 if (atoms->atom[a].ptype == eptVSite)
400 prop[a].mass = vsite_m[a];
404 prop[a].mass = atoms->atom[a].m;
406 prop[a].type = atoms->atom[a].type;
407 prop[a].q = atoms->atom[a].q;
408 /* We consider an atom constrained, #DOF=2, when it is
409 * connected with constraints to (at least one) atom with
410 * a mass of more than 0.4x its own mass. This is not a critical
411 * parameter, since with roughly equal masses the unconstrained
412 * and constrained displacement will not differ much (and both
413 * overestimate the displacement).
415 prop[a].bConstr = (prop[a].con_mass > 0.4*prop[a].mass);
417 add_at(&att, &natt, &prop[a], nmol);
426 for (a = 0; a < natt; a++)
428 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",
429 a, att[a].prop.mass, att[a].prop.type, att[a].prop.q,
430 att[a].prop.bConstr, att[a].prop.con_mass, att[a].prop.con_len,
439 /* This function computes two components of the estimate of the variance
440 * in the displacement of one atom in a system of two constrained atoms.
441 * Returns in sigma2_2d the variance due to rotation of the constrained
442 * atom around the atom to which it constrained.
443 * Returns in sigma2_3d the variance due to displacement of the COM
444 * of the whole system of the two constrained atoms.
446 * Note that we only take a single constraint (the one to the heaviest atom)
447 * into account. If an atom has multiple constraints, this will result in
448 * an overestimate of the displacement, which gives a larger drift and buffer.
450 static void constrained_atom_sigma2(real kT_fac,
451 const atom_nonbonded_kinetic_prop_t *prop,
460 /* Here we decompose the motion of a constrained atom into two
461 * components: rotation around the COM and translation of the COM.
464 /* Determine the variance for the displacement of the rotational mode */
465 sigma2_rot = kT_fac/(prop->mass*(prop->mass + prop->con_mass)/prop->con_mass);
467 /* The distance from the atom to the COM, i.e. the rotational arm */
468 com_dist = prop->con_len*prop->con_mass/(prop->mass + prop->con_mass);
470 /* The variance relative to the arm */
471 sigma2_rel = sigma2_rot/(com_dist*com_dist);
472 /* At 6 the scaling formula has slope 0,
473 * so we keep sigma2_2d constant after that.
477 /* A constrained atom rotates around the atom it is constrained to.
478 * This results in a smaller linear displacement than for a free atom.
479 * For a perfectly circular displacement, this lowers the displacement
480 * by: 1/arcsin(arc_length)
481 * and arcsin(x) = 1 + x^2/6 + ...
482 * For sigma2_rel<<1 the displacement distribution is erfc
483 * (exact formula is provided below). For larger sigma, it is clear
484 * that the displacement can't be larger than 2*com_dist.
485 * It turns out that the distribution becomes nearly uniform.
486 * For intermediate sigma2_rel, scaling down sigma with the third
487 * order expansion of arcsin with argument sigma_rel turns out
488 * to give a very good approximation of the distribution and variance.
489 * Even for larger values, the variance is only slightly overestimated.
490 * Note that the most relevant displacements are in the long tail.
491 * This rotation approximation always overestimates the tail (which
492 * runs to infinity, whereas it should be <= 2*com_dist).
493 * Thus we always overestimate the drift and the buffer size.
495 scale = 1/(1 + sigma2_rel/6);
496 *sigma2_2d = sigma2_rot*scale*scale;
500 /* sigma_2d is set to the maximum given by the scaling above.
501 * For large sigma2 the real displacement distribution is close
502 * to uniform over -2*con_len to 2*com_dist.
503 * Our erfc with sigma_2d=sqrt(1.5)*com_dist (which means the sigma
504 * of the erfc output distribution is con_dist) overestimates
505 * the variance and additionally has a long tail. This means
506 * we have a (safe) overestimation of the drift.
508 *sigma2_2d = 1.5*com_dist*com_dist;
511 /* The constrained atom also moves (in 3D) with the COM of both atoms */
512 *sigma2_3d = kT_fac/(prop->mass + prop->con_mass);
515 static void get_atom_sigma2(real kT_fac,
516 const atom_nonbonded_kinetic_prop_t *prop,
522 /* Complicated constraint calculation in a separate function */
523 constrained_atom_sigma2(kT_fac, prop, sigma2_2d, sigma2_3d);
527 /* Unconstrained atom: trivial */
529 *sigma2_3d = kT_fac/prop->mass;
533 static void approx_2dof(real s2, real x, real *shift, real *scale)
535 /* A particle with 1 DOF constrained has 2 DOFs instead of 3.
536 * This code is also used for particles with multiple constraints,
537 * in which case we overestimate the displacement.
538 * The 2DOF distribution is sqrt(pi/2)*erfc(r/(sqrt(2)*s))/(2*s).
539 * We approximate this with scale*Gaussian(s,r+shift),
540 * by matching the distribution value and derivative at x.
541 * This is a tight overestimate for all r>=0 at any s and x.
545 ex = exp(-x*x/(2*s2));
546 er = gmx_erfc(x/sqrt(2*s2));
548 *shift = -x + sqrt(2*s2/M_PI)*ex/er;
549 *scale = 0.5*M_PI*exp(ex*ex/(M_PI*er*er))*er;
552 static real ener_drift(const verletbuf_atomtype_t *att, int natt,
553 const gmx_ffparams_t *ffp,
555 real md1_ljd, real d2_ljd, real md3_ljd,
556 real md1_ljr, real d2_ljr, real md3_ljr,
557 real md1_el, real d2_el,
559 real rlist, real boxvol)
561 /* Erfc(8)=1e-29, use this limit so we have some space for arithmetic
562 * on the result when using float precision.
564 const real erfc_arg_max = 8.0;
566 double drift_tot, pot1, pot2, pot3, pot;
568 real s2i_2d, s2i_3d, s2j_2d, s2j_3d, s2, s;
571 real sc_fac, rsh, rsh2;
572 double c_exp, c_erfc;
576 /* Loop over the different atom type pairs */
577 for (i = 0; i < natt; i++)
579 get_atom_sigma2(kT_fac, &att[i].prop, &s2i_2d, &s2i_3d);
580 ti = att[i].prop.type;
582 for (j = i; j < natt; j++)
584 get_atom_sigma2(kT_fac, &att[j].prop, &s2j_2d, &s2j_3d);
585 tj = att[j].prop.type;
587 /* Add up the up to four independent variances */
588 s2 = s2i_2d + s2i_3d + s2j_2d + s2j_3d;
590 /* Note that attractive and repulsive potentials for individual
591 * pairs will partially cancel.
593 /* -dV/dr at the cut-off for LJ + Coulomb */
595 md1_ljd*ffp->iparams[ti*ffp->atnr+tj].lj.c6 +
596 md1_ljr*ffp->iparams[ti*ffp->atnr+tj].lj.c12 +
597 md1_el*att[i].prop.q*att[j].prop.q;
599 /* d2V/dr2 at the cut-off for LJ + Coulomb */
601 d2_ljd*ffp->iparams[ti*ffp->atnr+tj].lj.c6 +
602 d2_ljr*ffp->iparams[ti*ffp->atnr+tj].lj.c12 +
603 d2_el*att[i].prop.q*att[j].prop.q;
605 /* -d3V/dr3 at the cut-off for LJ, we neglect Coulomb */
607 md3_ljd*ffp->iparams[ti*ffp->atnr+tj].lj.c6 +
608 md3_ljr*ffp->iparams[ti*ffp->atnr+tj].lj.c12;
613 if (rsh*rsh > 2*s2*erfc_arg_max*erfc_arg_max)
615 /* Erfc might run out of float and become 0, somewhat before
616 * c_exp becomes 0. To avoid this and to avoid NaN in
617 * approx_2dof, we set both c_expc and c_erfc to zero.
618 * In any relevant case this has no effect on the results,
619 * since c_exp < 6e-29, so the displacement is completely
620 * negligible for such atom pairs (and an overestimate).
621 * In nearly all use cases, there will be other atom
622 * pairs that contribute much more to the total, so zeroing
623 * this particular contribution has no effect at all.
630 /* For constraints: adapt r and scaling for the Gaussian */
631 if (att[i].prop.bConstr)
635 approx_2dof(s2i_2d, r_buffer*s2i_2d/s2, &sh, &sc);
639 if (att[j].prop.bConstr)
643 approx_2dof(s2j_2d, r_buffer*s2j_2d/s2, &sh, &sc);
648 /* Exact contribution of an atom pair with Gaussian displacement
649 * with sigma s to the energy drift for a potential with
650 * derivative -md and second derivative dd at the cut-off.
651 * The only catch is that for potentials that change sign
652 * near the cut-off there could be an unlucky compensation
653 * of positive and negative energy drift.
654 * Such potentials are extremely rare though.
656 * Note that pot has unit energy*length, as the linear
657 * atom density still needs to be put in.
659 c_exp = exp(-rsh*rsh/(2*s2))/sqrt(2*M_PI);
660 c_erfc = 0.5*gmx_erfc(rsh/(sqrt(2*s2)));
666 md1/2*((rsh2 + s2)*c_erfc - rsh*s*c_exp);
668 d2/6*(s*(rsh2 + 2*s2)*c_exp - rsh*(rsh2 + 3*s2)*c_erfc);
670 md3/24*((rsh2*rsh2 + 6*rsh2*s2 + 3*s2*s2)*c_erfc - rsh*s*(rsh2 + 5*s2)*c_exp);
671 pot = pot1 + pot2 + pot3;
675 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",
677 sqrt(s2i_2d), sqrt(s2i_3d),
678 sqrt(s2j_2d), sqrt(s2j_3d),
679 att[i].prop.bConstr+att[j].prop.bConstr,
681 pot1, pot2, pot3, pot);
684 /* Multiply by the number of atom pairs */
687 pot *= (double)att[i].n*(att[i].n - 1)/2;
691 pot *= (double)att[i].n*att[j].n;
693 /* We need the line density to get the energy drift of the system.
694 * The effective average r^2 is close to (rlist+sigma)^2.
696 pot *= 4*M_PI*sqr(rlist + s)/boxvol;
698 /* Add the unsigned drift to avoid cancellation of errors */
699 drift_tot += fabs(pot);
706 static real surface_frac(int cluster_size, real particle_distance, real rlist)
710 if (rlist < 0.5*particle_distance)
712 /* We have non overlapping spheres */
716 /* Half the inter-particle distance relative to rlist */
717 d = 0.5*particle_distance/rlist;
719 /* Determine the area of the surface at distance rlist to the closest
720 * particle, relative to surface of a sphere of radius rlist.
721 * The formulas below assume close to cubic cells for the pair search grid,
722 * which the pair search code tries to achieve.
723 * Note that in practice particle distances will not be delta distributed,
724 * but have some spread, often involving shorter distances,
725 * as e.g. O-H bonds in a water molecule. Thus the estimates below will
726 * usually be slightly too high and thus conservative.
728 switch (cluster_size)
731 /* One particle: trivial */
735 /* Two particles: two spheres at fractional distance 2*a */
739 /* We assume a perfect, symmetric tetrahedron geometry.
740 * The surface around a tetrahedron is too complex for a full
741 * analytical solution, so we use a Taylor expansion.
743 area_rel = (1.0 + 1/M_PI*(6*acos(1/sqrt(3))*d +
747 83.0/756.0*d*d*d*d*d*d)));
750 gmx_incons("surface_frac called with unsupported cluster_size");
754 return area_rel/cluster_size;
757 /* Returns the negative of the third derivative of a potential r^-p
758 * with a force-switch function, evaluated at the cut-off rc.
760 static real md3_force_switch(real p, real rswitch, real rc)
762 /* The switched force function is:
763 * p*r^-(p+1) + a*(r - rswitch)^2 + b*(r - rswitch)^3
766 real md3_pot, md3_sw;
768 a = -((p + 4)*rc - (p + 1)*rswitch)/(pow(rc, p+2)*pow(rc-rswitch, 2));
769 b = ((p + 3)*rc - (p + 1)*rswitch)/(pow(rc, p+2)*pow(rc-rswitch, 3));
771 md3_pot = (p + 2)*(p + 1)*p*pow(rc, p+3);
772 md3_sw = 2*a + 6*b*(rc - rswitch);
774 return md3_pot + md3_sw;
777 void calc_verlet_buffer_size(const gmx_mtop_t *mtop, real boxvol,
778 const t_inputrec *ir,
779 real reference_temperature,
780 const verletbuf_list_setup_t *list_setup,
787 real particle_distance;
788 real nb_clust_frac_pairs_not_in_list_at_cutoff;
790 verletbuf_atomtype_t *att = NULL;
793 real md1_ljd, d2_ljd, md3_ljd;
794 real md1_ljr, d2_ljr, md3_ljr;
797 real kT_fac, mass_min;
802 if (reference_temperature < 0)
804 if (EI_MD(ir->eI) && ir->etc == etcNO)
806 /* This case should be handled outside calc_verlet_buffer_size */
807 gmx_incons("calc_verlet_buffer_size called with an NVE ensemble and reference_temperature < 0");
810 /* We use the maximum temperature with multiple T-coupl groups.
811 * We could use a per particle temperature, but since particles
812 * interact, this might underestimate the buffer size.
814 reference_temperature = 0;
815 for (i = 0; i < ir->opts.ngtc; i++)
817 if (ir->opts.tau_t[i] >= 0)
819 reference_temperature = max(reference_temperature,
825 /* Resolution of the buffer size */
828 env = getenv("GMX_VERLET_BUFFER_RES");
831 sscanf(env, "%lf", &resolution);
834 /* In an atom wise pair-list there would be no pairs in the list
835 * beyond the pair-list cut-off.
836 * However, we use a pair-list of groups vs groups of atoms.
837 * For groups of 4 atoms, the parallelism of SSE instructions, only
838 * 10% of the atoms pairs are not in the list just beyond the cut-off.
839 * As this percentage increases slowly compared to the decrease of the
840 * Gaussian displacement distribution over this range, we can simply
841 * reduce the drift by this fraction.
842 * For larger groups, e.g. of 8 atoms, this fraction will be lower,
843 * so then buffer size will be on the conservative (large) side.
845 * Note that the formulas used here do not take into account
846 * cancellation of errors which could occur by missing both
847 * attractive and repulsive interactions.
849 * The only major assumption is homogeneous particle distribution.
850 * For an inhomogeneous system, such as a liquid-vapor system,
851 * the buffer will be underestimated. The actual energy drift
852 * will be higher by the factor: local/homogeneous particle density.
854 * The results of this estimate have been checked againt simulations.
855 * In most cases the real drift differs by less than a factor 2.
858 /* Worst case assumption: HCP packing of particles gives largest distance */
859 particle_distance = pow(boxvol*sqrt(2)/mtop->natoms, 1.0/3.0);
861 get_verlet_buffer_atomtypes(mtop, &att, &natt, n_nonlin_vsite);
862 assert(att != NULL && natt >= 0);
866 fprintf(debug, "particle distance assuming HCP packing: %f nm\n",
868 fprintf(debug, "energy drift atom types: %d\n", natt);
871 reppow = mtop->ffparams.reppow;
878 if (ir->vdwtype == evdwCUT)
880 real sw_range, md3_pswf;
882 switch (ir->vdw_modifier)
885 case eintmodPOTSHIFT:
886 /* -dV/dr of -r^-6 and r^-reppow */
887 md1_ljd = -6*pow(ir->rvdw, -7.0);
888 md1_ljr = reppow*pow(ir->rvdw, -(reppow+1));
889 /* The contribution of the higher derivatives is negligible */
891 case eintmodFORCESWITCH:
892 /* At the cut-off: V=V'=V''=0, so we use only V''' */
893 md3_ljd = -md3_force_switch(6.0, ir->rvdw_switch, ir->rvdw);
894 md3_ljr = md3_force_switch(reppow, ir->rvdw_switch, ir->rvdw);
896 case eintmodPOTSWITCH:
897 /* At the cut-off: V=V'=V''=0.
898 * V''' is given by the original potential times
899 * the third derivative of the switch function.
901 sw_range = ir->rvdw - ir->rvdw_switch;
902 md3_pswf = 60.0*pow(sw_range, -3.0);
904 md3_ljd = -pow(ir->rvdw, -6.0 )*md3_pswf;
905 md3_ljr = pow(ir->rvdw, -reppow)*md3_pswf;
908 gmx_incons("Unimplemented VdW modifier");
911 else if (EVDW_PME(ir->vdwtype))
913 real b, r, br, br2, br4, br6;
914 b = calc_ewaldcoeff_lj(ir->rvdw, ir->ewald_rtol_lj);
920 /* -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 */
921 md1_ljd = -exp(-br2)*(br6 + 3.0*br4 + 6.0*br2 + 6.0)*pow(r, -7.0);
922 md1_ljr = reppow*pow(r, -(reppow+1));
923 /* The contribution of the higher derivatives is negligible */
927 gmx_fatal(FARGS, "Energy drift calculation is only implemented for plain cut-off Lennard-Jones interactions");
930 elfac = ONE_4PI_EPS0/ir->epsilon_r;
932 /* Determine md=-dV/dr and dd=d^2V/dr^2 */
935 if (ir->coulombtype == eelCUT || EEL_RF(ir->coulombtype))
939 if (ir->coulombtype == eelCUT)
946 eps_rf = ir->epsilon_rf/ir->epsilon_r;
949 k_rf = pow(ir->rcoulomb, -3.0)*(eps_rf - ir->epsilon_r)/(2*eps_rf + ir->epsilon_r);
953 /* epsilon_rf = infinity */
954 k_rf = 0.5*pow(ir->rcoulomb, -3.0);
960 md1_el = elfac*(pow(ir->rcoulomb, -2.0) - 2*k_rf*ir->rcoulomb);
962 d2_el = elfac*(2*pow(ir->rcoulomb, -3.0) + 2*k_rf);
964 else if (EEL_PME(ir->coulombtype) || ir->coulombtype == eelEWALD)
968 b = calc_ewaldcoeff_q(ir->rcoulomb, ir->ewald_rtol);
971 md1_el = elfac*(b*exp(-br*br)*M_2_SQRTPI/rc + gmx_erfc(br)/(rc*rc));
972 d2_el = elfac/(rc*rc)*(2*b*(1 + br*br)*exp(-br*br)*M_2_SQRTPI + 2*gmx_erfc(br)/rc);
976 gmx_fatal(FARGS, "Energy drift calculation is only implemented for Reaction-Field and Ewald electrostatics");
979 /* Determine the variance of the atomic displacement
980 * over nstlist-1 steps: kT_fac
981 * For inertial dynamics (not Brownian dynamics) the mass factor
982 * is not included in kT_fac, it is added later.
986 /* Get the displacement distribution from the random component only.
987 * With accurate integration the systematic (force) displacement
988 * should be negligible (unless nstlist is extremely large, which
989 * you wouldn't do anyhow).
991 kT_fac = 2*BOLTZ*reference_temperature*(ir->nstlist-1)*ir->delta_t;
994 /* This is directly sigma^2 of the displacement */
995 kT_fac /= ir->bd_fric;
997 /* Set the masses to 1 as kT_fac is the full sigma^2,
998 * but we divide by m in ener_drift().
1000 for (i = 0; i < natt; i++)
1002 att[i].prop.mass = 1;
1009 /* Per group tau_t is not implemented yet, use the maximum */
1010 tau_t = ir->opts.tau_t[0];
1011 for (i = 1; i < ir->opts.ngtc; i++)
1013 tau_t = max(tau_t, ir->opts.tau_t[i]);
1017 /* This kT_fac needs to be divided by the mass to get sigma^2 */
1022 kT_fac = BOLTZ*reference_temperature*sqr((ir->nstlist-1)*ir->delta_t);
1025 mass_min = att[0].prop.mass;
1026 for (i = 1; i < natt; i++)
1028 mass_min = min(mass_min, att[i].prop.mass);
1033 fprintf(debug, "md1_ljd %9.2e d2_ljd %9.2e md3_ljd %9.2e\n", md1_ljd, d2_ljd, md3_ljd);
1034 fprintf(debug, "md1_ljr %9.2e d2_ljr %9.2e md3_ljr %9.2e\n", md1_ljr, d2_ljr, md3_ljr);
1035 fprintf(debug, "md1_el %9.2e d2_el %9.2e\n", md1_el, d2_el);
1036 fprintf(debug, "sqrt(kT_fac) %f\n", sqrt(kT_fac));
1037 fprintf(debug, "mass_min %f\n", mass_min);
1040 /* Search using bisection */
1042 /* The drift will be neglible at 5 times the max sigma */
1043 ib1 = (int)(5*2*sqrt(kT_fac/mass_min)/resolution) + 1;
1044 while (ib1 - ib0 > 1)
1048 rl = max(ir->rvdw, ir->rcoulomb) + rb;
1050 /* Calculate the average energy drift at the last step
1051 * of the nstlist steps at which the pair-list is used.
1053 drift = ener_drift(att, natt, &mtop->ffparams,
1055 md1_ljd, d2_ljd, md3_ljd,
1056 md1_ljr, d2_ljr, md3_ljr,
1061 /* Correct for the fact that we are using a Ni x Nj particle pair list
1062 * and not a 1 x 1 particle pair list. This reduces the drift.
1064 /* We don't have a formula for 8 (yet), use 4 which is conservative */
1065 nb_clust_frac_pairs_not_in_list_at_cutoff =
1066 surface_frac(min(list_setup->cluster_size_i, 4),
1067 particle_distance, rl)*
1068 surface_frac(min(list_setup->cluster_size_j, 4),
1069 particle_distance, rl);
1070 drift *= nb_clust_frac_pairs_not_in_list_at_cutoff;
1072 /* Convert the drift to drift per unit time per atom */
1073 drift /= ir->nstlist*ir->delta_t*mtop->natoms;
1077 fprintf(debug, "ib %3d %3d %3d rb %.3f %dx%d fac %.3f drift %.1e\n",
1079 list_setup->cluster_size_i, list_setup->cluster_size_j,
1080 nb_clust_frac_pairs_not_in_list_at_cutoff,
1084 if (fabs(drift) > ir->verletbuf_tol)
1096 *rlist = max(ir->rvdw, ir->rcoulomb) + ib1*resolution;