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37 #include "calc_verletbuf.h"
45 #include "gromacs/ewald/ewald-utils.h"
46 #include "gromacs/math/functions.h"
47 #include "gromacs/math/units.h"
48 #include "gromacs/math/vec.h"
49 #include "gromacs/mdlib/nb_verlet.h"
50 #include "gromacs/mdlib/nbnxn_simd.h"
51 #include "gromacs/mdlib/nbnxn_util.h"
52 #include "gromacs/mdtypes/inputrec.h"
53 #include "gromacs/mdtypes/md_enums.h"
54 #include "gromacs/topology/ifunc.h"
55 #include "gromacs/topology/topology.h"
56 #include "gromacs/utility/fatalerror.h"
57 #include "gromacs/utility/smalloc.h"
58 #include "gromacs/utility/strconvert.h"
60 /* The code in this file estimates a pairlist buffer length
61 * given a target energy drift per atom per picosecond.
62 * This is done by estimating the drift given a buffer length.
63 * Ideally we would like to have a tight overestimate of the drift,
64 * but that can be difficult to achieve.
66 * Significant approximations used:
68 * Uniform particle density. UNDERESTIMATES the drift by rho_global/rho_local.
70 * Interactions don't affect particle motion. OVERESTIMATES the drift on longer
71 * time scales. This approximation probably introduces the largest errors.
73 * Only take one constraint per particle into account: OVERESTIMATES the drift.
75 * For rotating constraints assume the same functional shape for time scales
76 * where the constraints rotate significantly as the exact expression for
77 * short time scales. OVERESTIMATES the drift on long time scales.
79 * For non-linear virtual sites use the mass of the lightest constructing atom
80 * to determine the displacement. OVER/UNDERESTIMATES the drift, depending on
81 * the geometry and masses of constructing atoms.
83 * Note that the formulas for normal atoms and linear virtual sites are exact,
84 * apart from the first two approximations.
86 * Note that apart from the effect of the above approximations, the actual
87 * drift of the total energy of a system can be orders of magnitude smaller
88 * due to cancellation of positive and negative drift for different pairs.
92 /* Struct for unique atom type for calculating the energy drift.
93 * The atom displacement depends on mass and constraints.
94 * The energy jump for given distance depend on LJ type and q.
98 atom_nonbonded_kinetic_prop_t prop; /* non-bonded and kinetic atom prop. */
99 int n; /* #atoms of this type in the system */
100 } verletbuf_atomtype_t;
102 // Struct for derivatives of a non-bonded interaction potential
105 real md1; // -V' at the cutoff
106 real d2; // V'' at the cutoff
107 real md3; // -V''' at the cutoff
110 VerletbufListSetup verletbufGetListSetup(int nbnxnKernelType)
112 /* Note that the current buffer estimation code only handles clusters
113 * of size 1, 2 or 4, so for 4x8 or 8x8 we use the estimate for 4x4.
115 VerletbufListSetup listSetup;
117 listSetup.cluster_size_i = nbnxn_kernel_to_cluster_i_size(nbnxnKernelType);
118 listSetup.cluster_size_j = nbnxn_kernel_to_cluster_j_size(nbnxnKernelType);
120 if (nbnxnKernelType == nbnxnk8x8x8_GPU ||
121 nbnxnKernelType == nbnxnk8x8x8_PlainC)
123 /* The GPU kernels (except for OpenCL) split the j-clusters in two halves */
124 listSetup.cluster_size_j /= 2;
130 VerletbufListSetup verletbufGetSafeListSetup(ListSetupType listType)
132 /* When calling this function we often don't know which kernel type we
133 * are going to use. We choose the kernel type with the smallest possible
134 * i- and j-cluster sizes, so we potentially overestimate, but never
135 * underestimate, the buffer drift.
139 if (listType == ListSetupType::Gpu)
141 nbnxnKernelType = nbnxnk8x8x8_GPU;
143 else if (GMX_SIMD && listType == ListSetupType::CpuSimdWhenSupported)
145 #ifdef GMX_NBNXN_SIMD_2XNN
146 /* We use the smallest cluster size to be on the safe side */
147 nbnxnKernelType = nbnxnk4xN_SIMD_2xNN;
149 nbnxnKernelType = nbnxnk4xN_SIMD_4xN;
154 nbnxnKernelType = nbnxnk4x4_PlainC;
157 return verletbufGetListSetup(nbnxnKernelType);
161 atom_nonbonded_kinetic_prop_equal(const atom_nonbonded_kinetic_prop_t *prop1,
162 const atom_nonbonded_kinetic_prop_t *prop2)
164 return (prop1->mass == prop2->mass &&
165 prop1->type == prop2->type &&
166 prop1->q == prop2->q &&
167 prop1->bConstr == prop2->bConstr &&
168 prop1->con_mass == prop2->con_mass &&
169 prop1->con_len == prop2->con_len);
172 static void add_at(verletbuf_atomtype_t **att_p, int *natt_p,
173 const atom_nonbonded_kinetic_prop_t *prop,
176 verletbuf_atomtype_t *att;
181 /* Ignore massless particles */
189 while (i < natt && !atom_nonbonded_kinetic_prop_equal(prop, &att[i].prop))
201 srenew(*att_p, *natt_p);
202 (*att_p)[i].prop = *prop;
203 (*att_p)[i].n = nmol;
207 /* Returns the mass of atom atomIndex or 1 when setMassesToOne=true */
208 static real getMass(const t_atoms &atoms,
214 return atoms.atom[atomIndex].m;
222 static void get_vsite_masses(const gmx_moltype_t *moltype,
223 const gmx_ffparams_t *ffparams,
233 /* Check for virtual sites, determine mass from constructing atoms */
234 for (ft = 0; ft < F_NRE; ft++)
238 il = &moltype->ilist[ft];
240 for (i = 0; i < il->nr; i += 1+NRAL(ft))
243 real inv_mass, coeff, m_aj;
246 ip = &ffparams->iparams[il->iatoms[i]];
248 a1 = il->iatoms[i+1];
252 /* Only vsiten can have more than four
253 constructing atoms, so NRAL(ft) <= 5 */
256 const int maxj = NRAL(ft);
260 for (j = 1; j < maxj; j++)
262 int aj = il->iatoms[i + 1 + j];
263 cam[j] = getMass(moltype->atoms, aj, setMassesToOne);
266 cam[j] = vsite_m[aj];
270 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.",
272 interaction_function[ft].longname,
281 vsite_m[a1] = (cam[1]*cam[2])/(cam[2]*gmx::square(1-ip->vsite.a) + cam[1]*gmx::square(ip->vsite.a));
285 vsite_m[a1] = (cam[1]*cam[2]*cam[3])/(cam[2]*cam[3]*gmx::square(1-ip->vsite.a-ip->vsite.b) + cam[1]*cam[3]*gmx::square(ip->vsite.a) + cam[1]*cam[2]*gmx::square(ip->vsite.b));
288 gmx_incons("Invalid vsite type");
290 /* Use the mass of the lightest constructing atom.
291 * This is an approximation.
292 * If the distance of the virtual site to the
293 * constructing atom is less than all distances
294 * between constructing atoms, this is a safe
295 * over-estimate of the displacement of the vsite.
296 * This condition holds for all H mass replacement
297 * vsite constructions, except for SP2/3 groups.
298 * In SP3 groups one H will have a F_VSITE3
299 * construction, so even there the total drift
300 * estimate shouldn't be far off.
302 vsite_m[a1] = cam[1];
303 for (j = 2; j < maxj; j++)
305 vsite_m[a1] = std::min(vsite_m[a1], cam[j]);
318 for (j = 0; j < 3*ffparams->iparams[il->iatoms[i]].vsiten.n; j += 3)
320 int aj = il->iatoms[i + j + 2];
321 coeff = ffparams->iparams[il->iatoms[i+j]].vsiten.a;
322 if (moltype->atoms.atom[aj].ptype == eptVSite)
328 m_aj = moltype->atoms.atom[aj].m;
332 gmx_incons("The mass of a vsiten constructing atom is <= 0");
334 inv_mass += coeff*coeff/m_aj;
336 vsite_m[a1] = 1/inv_mass;
337 /* Correct for loop increment of i */
338 i += j - 1 - NRAL(ft);
342 fprintf(debug, "atom %4d %-20s mass %6.3f\n",
343 a1, interaction_function[ft].longname, vsite_m[a1]);
350 static void get_verlet_buffer_atomtypes(const gmx_mtop_t *mtop,
352 verletbuf_atomtype_t **att_p,
356 verletbuf_atomtype_t *att;
358 int ft, i, a1, a2, a3, a;
361 atom_nonbonded_kinetic_prop_t *prop;
363 int n_nonlin_vsite_mol;
368 if (n_nonlin_vsite != nullptr)
373 for (const gmx_molblock_t &molblock : mtop->molblock)
375 int nmol = molblock.nmol;
376 const gmx_moltype_t &moltype = mtop->moltype[molblock.type];
377 const t_atoms *atoms = &moltype.atoms;
379 /* Check for constraints, as they affect the kinetic energy.
380 * For virtual sites we need the masses and geometry of
381 * the constructing atoms to determine their velocity distribution.
383 snew(prop, atoms->nr);
384 snew(vsite_m, atoms->nr);
386 for (ft = F_CONSTR; ft <= F_CONSTRNC; ft++)
388 il = &moltype.ilist[ft];
390 for (i = 0; i < il->nr; i += 1+NRAL(ft))
392 ip = &mtop->ffparams.iparams[il->iatoms[i]];
393 a1 = il->iatoms[i+1];
394 a2 = il->iatoms[i+2];
395 real mass1 = getMass(*atoms, a1, setMassesToOne);
396 real mass2 = getMass(*atoms, a2, setMassesToOne);
397 if (mass2 > prop[a1].con_mass)
399 prop[a1].con_mass = mass2;
400 prop[a1].con_len = ip->constr.dA;
402 if (mass1 > prop[a2].con_mass)
404 prop[a2].con_mass = mass1;
405 prop[a2].con_len = ip->constr.dA;
410 il = &moltype.ilist[F_SETTLE];
412 for (i = 0; i < il->nr; i += 1+NRAL(F_SETTLE))
414 ip = &mtop->ffparams.iparams[il->iatoms[i]];
415 a1 = il->iatoms[i+1];
416 a2 = il->iatoms[i+2];
417 a3 = il->iatoms[i+3];
418 /* Usually the mass of a1 (usually oxygen) is larger than a2/a3.
419 * If this is not the case, we overestimate the displacement,
420 * which leads to a larger buffer (ok since this is an exotic case).
422 prop[a1].con_mass = getMass(*atoms, a2, setMassesToOne);
423 prop[a1].con_len = ip->settle.doh;
425 prop[a2].con_mass = getMass(*atoms, a1, setMassesToOne);
426 prop[a2].con_len = ip->settle.doh;
428 prop[a3].con_mass = getMass(*atoms, a1, setMassesToOne);
429 prop[a3].con_len = ip->settle.doh;
432 get_vsite_masses(&moltype,
436 &n_nonlin_vsite_mol);
437 if (n_nonlin_vsite != nullptr)
439 *n_nonlin_vsite += nmol*n_nonlin_vsite_mol;
442 for (a = 0; a < atoms->nr; a++)
444 if (atoms->atom[a].ptype == eptVSite)
446 prop[a].mass = vsite_m[a];
450 prop[a].mass = getMass(*atoms, a, setMassesToOne);
452 prop[a].type = atoms->atom[a].type;
453 prop[a].q = atoms->atom[a].q;
454 /* We consider an atom constrained, #DOF=2, when it is
455 * connected with constraints to (at least one) atom with
456 * a mass of more than 0.4x its own mass. This is not a critical
457 * parameter, since with roughly equal masses the unconstrained
458 * and constrained displacement will not differ much (and both
459 * overestimate the displacement).
461 prop[a].bConstr = (prop[a].con_mass > 0.4*prop[a].mass);
463 add_at(&att, &natt, &prop[a], nmol);
472 for (a = 0; a < natt; a++)
474 fprintf(debug, "type %d: m %5.2f t %d q %6.3f con %s con_m %5.3f con_l %5.3f n %d\n",
475 a, att[a].prop.mass, att[a].prop.type, att[a].prop.q,
476 gmx::boolToString(att[a].prop.bConstr), att[a].prop.con_mass, att[a].prop.con_len,
485 /* This function computes two components of the estimate of the variance
486 * in the displacement of one atom in a system of two constrained atoms.
487 * Returns in sigma2_2d the variance due to rotation of the constrained
488 * atom around the atom to which it constrained.
489 * Returns in sigma2_3d the variance due to displacement of the COM
490 * of the whole system of the two constrained atoms.
492 * Note that we only take a single constraint (the one to the heaviest atom)
493 * into account. If an atom has multiple constraints, this will result in
494 * an overestimate of the displacement, which gives a larger drift and buffer.
496 void constrained_atom_sigma2(real kT_fac,
497 const atom_nonbonded_kinetic_prop_t *prop,
501 /* Here we decompose the motion of a constrained atom into two
502 * components: rotation around the COM and translation of the COM.
505 /* Determine the variance of the arc length for the two rotational DOFs */
506 real massFraction = prop->con_mass/(prop->mass + prop->con_mass);
507 real sigma2_rot = kT_fac*massFraction/prop->mass;
509 /* The distance from the atom to the COM, i.e. the rotational arm */
510 real comDistance = prop->con_len*massFraction;
512 /* The variance relative to the arm */
513 real sigma2_rel = sigma2_rot/gmx::square(comDistance);
515 /* For sigma2_rel << 1 we don't notice the rotational effect and
516 * we have a normal, Gaussian displacement distribution.
517 * For larger sigma2_rel the displacement is much less, in fact it can
518 * not exceed 2*comDistance. We can calculate MSD/arm^2 as:
519 * integral_x=0-inf distance2(x) x/sigma2_rel exp(-x^2/(2 sigma2_rel)) dx
520 * where x is angular displacement and distance2(x) is the distance^2
521 * between points at angle 0 and x:
522 * distance2(x) = (sin(x) - sin(0))^2 + (cos(x) - cos(0))^2
523 * The limiting value of this MSD is 2, which is also the value for
524 * a uniform rotation distribution that would be reached at long time.
525 * The maximum is 2.5695 at sigma2_rel = 4.5119.
526 * We approximate this integral with a rational polynomial with
527 * coefficients from a Taylor expansion. This approximation is an
528 * overestimate for all values of sigma2_rel. Its maximum value
529 * of 2.6491 is reached at sigma2_rel = sqrt(45/2) = 4.7434.
530 * We keep the approximation constant after that.
531 * We use this approximate MSD as the variance for a Gaussian distribution.
533 * NOTE: For any sensible buffer tolerance this will result in a (large)
534 * overestimate of the buffer size, since the Gaussian has a long tail,
535 * whereas the actual distribution can not reach values larger than 2.
537 /* Coeffients obtained from a Taylor expansion */
538 const real a = 1.0/3.0;
539 const real b = 2.0/45.0;
541 /* Our approximation is constant after sigma2_rel = 1/sqrt(b) */
542 sigma2_rel = std::min(sigma2_rel, 1/std::sqrt(b));
544 /* Compute the approximate sigma^2 for 2D motion due to the rotation */
545 *sigma2_2d = gmx::square(comDistance)*
546 sigma2_rel/(1 + a*sigma2_rel + b*gmx::square(sigma2_rel));
548 /* The constrained atom also moves (in 3D) with the COM of both atoms */
549 *sigma2_3d = kT_fac/(prop->mass + prop->con_mass);
552 static void get_atom_sigma2(real kT_fac,
553 const atom_nonbonded_kinetic_prop_t *prop,
559 /* Complicated constraint calculation in a separate function */
560 constrained_atom_sigma2(kT_fac, prop, sigma2_2d, sigma2_3d);
564 /* Unconstrained atom: trivial */
566 *sigma2_3d = kT_fac/prop->mass;
570 static void approx_2dof(real s2, real x, real *shift, real *scale)
572 /* A particle with 1 DOF constrained has 2 DOFs instead of 3.
573 * This code is also used for particles with multiple constraints,
574 * in which case we overestimate the displacement.
575 * The 2DOF distribution is sqrt(pi/2)*erfc(r/(sqrt(2)*s))/(2*s).
576 * We approximate this with scale*Gaussian(s,r+shift),
577 * by matching the distribution value and derivative at x.
578 * This is a tight overestimate for all r>=0 at any s and x.
582 ex = std::exp(-x*x/(2*s2));
583 er = std::erfc(x/std::sqrt(2*s2));
585 *shift = -x + std::sqrt(2*s2/M_PI)*ex/er;
586 *scale = 0.5*M_PI*std::exp(ex*ex/(M_PI*er*er))*er;
589 // Returns an (over)estimate of the energy drift for a single atom pair,
590 // given the kinetic properties, displacement variances and list buffer.
591 static real energyDriftAtomPair(bool isConstrained_i,
592 bool isConstrained_j,
593 real s2, real s2i_2d, real s2j_2d,
595 const pot_derivatives_t *der)
597 // For relatively small arguments erfc() is so small that if will be 0.0
598 // when stored in a float. We set an argument limit of 8 (Erfc(8)=1e-29),
599 // such that we can divide by erfc and have some space left for arithmetic.
600 const real erfc_arg_max = 8.0;
607 if (rsh*rsh > 2*s2*erfc_arg_max*erfc_arg_max)
609 // Below we calculate c_erfc = 0.5*erfc(rsh/sqrt(2*s2))
610 // When rsh/sqrt(2*s2) increases, this erfc will be the first
611 // result that underflows and becomes 0.0. To avoid this,
612 // we set c_exp=0 and c_erfc=0 for large arguments.
613 // This also avoids NaN in approx_2dof().
614 // In any relevant case this has no effect on the results,
615 // since c_exp < 6e-29, so the displacement is completely
616 // negligible for such atom pairs (and an overestimate).
617 // In nearly all use cases, there will be other atom pairs
618 // that contribute much more to the total, so zeroing
619 // this particular contribution has no effect at all.
625 /* For constraints: adapt r and scaling for the Gaussian */
630 approx_2dof(s2i_2d, r_buffer*s2i_2d/s2, &sh, &sc);
638 approx_2dof(s2j_2d, r_buffer*s2j_2d/s2, &sh, &sc);
643 /* Exact contribution of an atom pair with Gaussian displacement
644 * with sigma s to the energy drift for a potential with
645 * derivative -md and second derivative dd at the cut-off.
646 * The only catch is that for potentials that change sign
647 * near the cut-off there could be an unlucky compensation
648 * of positive and negative energy drift.
649 * Such potentials are extremely rare though.
651 * Note that pot has unit energy*length, as the linear
652 * atom density still needs to be put in.
654 c_exp = std::exp(-rsh*rsh/(2*s2))/std::sqrt(2*M_PI);
655 c_erfc = 0.5*std::erfc(rsh/(std::sqrt(2*s2)));
657 real s = std::sqrt(s2);
661 der->md1/2*((rsh2 + s2)*c_erfc - rsh*s*c_exp);
663 der->d2/6*(s*(rsh2 + 2*s2)*c_exp - rsh*(rsh2 + 3*s2)*c_erfc);
665 der->md3/24*((rsh2*rsh2 + 6*rsh2*s2 + 3*s2*s2)*c_erfc - rsh*s*(rsh2 + 5*s2)*c_exp);
667 return pot1 + pot2 + pot3;
670 static real energyDrift(const verletbuf_atomtype_t *att, int natt,
671 const gmx_ffparams_t *ffp,
673 const pot_derivatives_t *ljDisp,
674 const pot_derivatives_t *ljRep,
675 const pot_derivatives_t *elec,
676 real rlj, real rcoulomb,
677 real rlist, real boxvol)
679 double drift_tot = 0;
683 /* No atom displacements: no drift, avoid division by 0 */
687 // Here add up the contribution of all atom pairs in the system to
688 // (estimated) energy drift by looping over all atom type pairs.
689 for (int i = 0; i < natt; i++)
691 // Get the thermal displacement variance for the i-atom type
692 const atom_nonbonded_kinetic_prop_t *prop_i = &att[i].prop;
694 get_atom_sigma2(kT_fac, prop_i, &s2i_2d, &s2i_3d);
696 for (int j = i; j < natt; j++)
698 // Get the thermal displacement variance for the j-atom type
699 const atom_nonbonded_kinetic_prop_t *prop_j = &att[j].prop;
701 get_atom_sigma2(kT_fac, prop_j, &s2j_2d, &s2j_3d);
703 /* Add up the up to four independent variances */
704 real s2 = s2i_2d + s2i_3d + s2j_2d + s2j_3d;
706 // Set -V', V'' and -V''' at the cut-off for LJ */
707 real c6 = ffp->iparams[prop_i->type*ffp->atnr + prop_j->type].lj.c6;
708 real c12 = ffp->iparams[prop_i->type*ffp->atnr + prop_j->type].lj.c12;
709 pot_derivatives_t lj;
710 lj.md1 = c6*ljDisp->md1 + c12*ljRep->md1;
711 lj.d2 = c6*ljDisp->d2 + c12*ljRep->d2;
712 lj.md3 = c6*ljDisp->md3 + c12*ljRep->md3;
714 real pot_lj = energyDriftAtomPair(prop_i->bConstr, prop_j->bConstr,
719 // Set -V' and V'' at the cut-off for Coulomb
720 pot_derivatives_t elec_qq;
721 elec_qq.md1 = elec->md1*prop_i->q*prop_j->q;
722 elec_qq.d2 = elec->d2 *prop_i->q*prop_j->q;
725 real pot_q = energyDriftAtomPair(prop_i->bConstr, prop_j->bConstr,
730 // Note that attractive and repulsive potentials for individual
731 // pairs can partially cancel.
732 real pot = pot_lj + pot_q;
734 /* Multiply by the number of atom pairs */
737 pot *= static_cast<double>(att[i].n)*(att[i].n - 1)/2;
741 pot *= static_cast<double>(att[i].n)*att[j].n;
743 /* We need the line density to get the energy drift of the system.
744 * The effective average r^2 is close to (rlist+sigma)^2.
746 pot *= 4*M_PI*gmx::square(rlist + std::sqrt(s2))/boxvol;
748 /* Add the unsigned drift to avoid cancellation of errors */
749 drift_tot += std::abs(pot);
756 static real surface_frac(int cluster_size, real particle_distance, real rlist)
760 if (rlist < 0.5*particle_distance)
762 /* We have non overlapping spheres */
766 /* Half the inter-particle distance relative to rlist */
767 d = 0.5*particle_distance/rlist;
769 /* Determine the area of the surface at distance rlist to the closest
770 * particle, relative to surface of a sphere of radius rlist.
771 * The formulas below assume close to cubic cells for the pair search grid,
772 * which the pair search code tries to achieve.
773 * Note that in practice particle distances will not be delta distributed,
774 * but have some spread, often involving shorter distances,
775 * as e.g. O-H bonds in a water molecule. Thus the estimates below will
776 * usually be slightly too high and thus conservative.
778 switch (cluster_size)
781 /* One particle: trivial */
785 /* Two particles: two spheres at fractional distance 2*a */
789 /* We assume a perfect, symmetric tetrahedron geometry.
790 * The surface around a tetrahedron is too complex for a full
791 * analytical solution, so we use a Taylor expansion.
793 area_rel = (1.0 + 1/M_PI*(6*std::acos(1/std::sqrt(3))*d +
794 std::sqrt(3)*d*d*(1.0 +
797 83.0/756.0*d*d*d*d*d*d)));
800 gmx_incons("surface_frac called with unsupported cluster_size");
803 return area_rel/cluster_size;
806 /* Returns the negative of the third derivative of a potential r^-p
807 * with a force-switch function, evaluated at the cut-off rc.
809 static real md3_force_switch(real p, real rswitch, real rc)
811 /* The switched force function is:
812 * p*r^-(p+1) + a*(r - rswitch)^2 + b*(r - rswitch)^3
815 real md3_pot, md3_sw;
817 a = -((p + 4)*rc - (p + 1)*rswitch)/(pow(rc, p+2)*gmx::square(rc-rswitch));
818 b = ((p + 3)*rc - (p + 1)*rswitch)/(pow(rc, p+2)*gmx::power3(rc-rswitch));
820 md3_pot = (p + 2)*(p + 1)*p*pow(rc, p+3);
821 md3_sw = 2*a + 6*b*(rc - rswitch);
823 return md3_pot + md3_sw;
826 /* Returns the maximum reference temperature over all coupled groups */
827 static real maxReferenceTemperature(const t_inputrec &ir)
829 if (EI_MD(ir.eI) && ir.etc == etcNO)
831 /* This case should be handled outside calc_verlet_buffer_size */
832 gmx_incons("calc_verlet_buffer_size called with an NVE ensemble and reference_temperature < 0");
835 real maxTemperature = 0;
836 for (int i = 0; i < ir.opts.ngtc; i++)
838 if (ir.opts.tau_t[i] >= 0)
840 maxTemperature = std::max(maxTemperature, ir.opts.ref_t[i]);
844 return maxTemperature;
847 /* Returns the variance of the atomic displacement over timePeriod.
849 * Note: When not using BD with a non-mass dependendent friction coefficient,
850 * the return value still needs to be divided by the particle mass.
852 static real displacementVariance(const t_inputrec &ir,
860 /* Get the displacement distribution from the random component only.
861 * With accurate integration the systematic (force) displacement
862 * should be negligible (unless nstlist is extremely large, which
863 * you wouldn't do anyhow).
865 kT_fac = 2*BOLTZ*temperature*timePeriod;
868 /* This is directly sigma^2 of the displacement */
869 kT_fac /= ir.bd_fric;
873 /* Per group tau_t is not implemented yet, use the maximum */
874 real tau_t = ir.opts.tau_t[0];
875 for (int i = 1; i < ir.opts.ngtc; i++)
877 tau_t = std::max(tau_t, ir.opts.tau_t[i]);
881 /* This kT_fac needs to be divided by the mass to get sigma^2 */
886 kT_fac = BOLTZ*temperature*gmx::square(timePeriod);
892 /* Returns the largest sigma of the Gaussian displacement over all particle
893 * types. This ignores constraints, so is an overestimate.
895 static real maxSigma(real kT_fac,
897 const verletbuf_atomtype_t *att)
900 real smallestMass = att[0].prop.mass;
901 for (int i = 1; i < natt; i++)
903 smallestMass = std::min(smallestMass, att[i].prop.mass);
906 return 2*std::sqrt(kT_fac/smallestMass);
909 void calc_verlet_buffer_size(const gmx_mtop_t *mtop, real boxvol,
910 const t_inputrec *ir,
913 real reference_temperature,
914 const VerletbufListSetup *list_setup,
921 real particle_distance;
922 real nb_clust_frac_pairs_not_in_list_at_cutoff;
924 verletbuf_atomtype_t *att = nullptr;
931 if (!EI_DYNAMICS(ir->eI))
933 gmx_incons("Can only determine the Verlet buffer size for integrators that perform dynamics");
935 if (ir->verletbuf_tol <= 0)
937 gmx_incons("The Verlet buffer tolerance needs to be larger than zero");
940 if (reference_temperature < 0)
942 /* We use the maximum temperature with multiple T-coupl groups.
943 * We could use a per particle temperature, but since particles
944 * interact, this might underestimate the buffer size.
946 reference_temperature = maxReferenceTemperature(*ir);
949 /* Resolution of the buffer size */
952 env = getenv("GMX_VERLET_BUFFER_RES");
955 sscanf(env, "%lf", &resolution);
958 /* In an atom wise pair-list there would be no pairs in the list
959 * beyond the pair-list cut-off.
960 * However, we use a pair-list of groups vs groups of atoms.
961 * For groups of 4 atoms, the parallelism of SSE instructions, only
962 * 10% of the atoms pairs are not in the list just beyond the cut-off.
963 * As this percentage increases slowly compared to the decrease of the
964 * Gaussian displacement distribution over this range, we can simply
965 * reduce the drift by this fraction.
966 * For larger groups, e.g. of 8 atoms, this fraction will be lower,
967 * so then buffer size will be on the conservative (large) side.
969 * Note that the formulas used here do not take into account
970 * cancellation of errors which could occur by missing both
971 * attractive and repulsive interactions.
973 * The only major assumption is homogeneous particle distribution.
974 * For an inhomogeneous system, such as a liquid-vapor system,
975 * the buffer will be underestimated. The actual energy drift
976 * will be higher by the factor: local/homogeneous particle density.
978 * The results of this estimate have been checked againt simulations.
979 * In most cases the real drift differs by less than a factor 2.
982 /* Worst case assumption: HCP packing of particles gives largest distance */
983 particle_distance = std::cbrt(boxvol*std::sqrt(2)/mtop->natoms);
985 /* TODO: Obtain masses through (future) integrator functionality
986 * to avoid scattering the code with (or forgetting) checks.
988 const bool setMassesToOne = (ir->eI == eiBD && ir->bd_fric > 0);
989 get_verlet_buffer_atomtypes(mtop, setMassesToOne, &att, &natt, n_nonlin_vsite);
990 assert(att != nullptr && natt >= 0);
994 fprintf(debug, "particle distance assuming HCP packing: %f nm\n",
996 fprintf(debug, "energy drift atom types: %d\n", natt);
999 pot_derivatives_t ljDisp = { 0, 0, 0 };
1000 pot_derivatives_t ljRep = { 0, 0, 0 };
1001 real repPow = mtop->ffparams.reppow;
1003 if (ir->vdwtype == evdwCUT)
1005 real sw_range, md3_pswf;
1007 switch (ir->vdw_modifier)
1010 case eintmodPOTSHIFT:
1011 /* -dV/dr of -r^-6 and r^-reppow */
1012 ljDisp.md1 = -6*std::pow(ir->rvdw, -7.0);
1013 ljRep.md1 = repPow*std::pow(ir->rvdw, -(repPow + 1));
1014 /* The contribution of the higher derivatives is negligible */
1016 case eintmodFORCESWITCH:
1017 /* At the cut-off: V=V'=V''=0, so we use only V''' */
1018 ljDisp.md3 = -md3_force_switch(6.0, ir->rvdw_switch, ir->rvdw);
1019 ljRep.md3 = md3_force_switch(repPow, ir->rvdw_switch, ir->rvdw);
1021 case eintmodPOTSWITCH:
1022 /* At the cut-off: V=V'=V''=0.
1023 * V''' is given by the original potential times
1024 * the third derivative of the switch function.
1026 sw_range = ir->rvdw - ir->rvdw_switch;
1027 md3_pswf = 60.0/gmx::power3(sw_range);
1029 ljDisp.md3 = -std::pow(ir->rvdw, -6.0 )*md3_pswf;
1030 ljRep.md3 = std::pow(ir->rvdw, -repPow)*md3_pswf;
1033 gmx_incons("Unimplemented VdW modifier");
1036 else if (EVDW_PME(ir->vdwtype))
1038 real b = calc_ewaldcoeff_lj(ir->rvdw, ir->ewald_rtol_lj);
1044 // -dV/dr of g(br)*r^-6 [where g(x) = exp(-x^2)(1+x^2+x^4/2),
1045 // see LJ-PME equations in manual] and r^-reppow
1046 ljDisp.md1 = -std::exp(-br2)*(br6 + 3.0*br4 + 6.0*br2 + 6.0)*std::pow(r, -7.0);
1047 ljRep.md1 = repPow*pow(r, -(repPow + 1));
1048 // The contribution of the higher derivatives is negligible
1052 gmx_fatal(FARGS, "Energy drift calculation is only implemented for plain cut-off Lennard-Jones interactions");
1055 elfac = ONE_4PI_EPS0/ir->epsilon_r;
1057 // Determine the 1st and 2nd derivative for the electostatics
1058 pot_derivatives_t elec = { 0, 0, 0 };
1060 if (ir->coulombtype == eelCUT || EEL_RF(ir->coulombtype))
1064 if (ir->coulombtype == eelCUT)
1071 eps_rf = ir->epsilon_rf/ir->epsilon_r;
1074 k_rf = (eps_rf - ir->epsilon_r)/( gmx::power3(ir->rcoulomb) * (2*eps_rf + ir->epsilon_r) );
1078 /* epsilon_rf = infinity */
1079 k_rf = 0.5/gmx::power3(ir->rcoulomb);
1085 elec.md1 = elfac*(1.0/gmx::square(ir->rcoulomb) - 2*k_rf*ir->rcoulomb);
1087 elec.d2 = elfac*(2.0/gmx::power3(ir->rcoulomb) + 2*k_rf);
1089 else if (EEL_PME(ir->coulombtype) || ir->coulombtype == eelEWALD)
1093 b = calc_ewaldcoeff_q(ir->rcoulomb, ir->ewald_rtol);
1096 elec.md1 = elfac*(b*std::exp(-br*br)*M_2_SQRTPI/rc + std::erfc(br)/(rc*rc));
1097 elec.d2 = elfac/(rc*rc)*(2*b*(1 + br*br)*std::exp(-br*br)*M_2_SQRTPI + 2*std::erfc(br)/rc);
1101 gmx_fatal(FARGS, "Energy drift calculation is only implemented for Reaction-Field and Ewald electrostatics");
1104 /* Determine the variance of the atomic displacement
1105 * over list_lifetime steps: kT_fac
1106 * For inertial dynamics (not Brownian dynamics) the mass factor
1107 * is not included in kT_fac, it is added later.
1109 const real kT_fac = displacementVariance(*ir, reference_temperature,
1110 list_lifetime*ir->delta_t);
1114 fprintf(debug, "Derivatives of non-bonded potentials at the cut-off:\n");
1115 fprintf(debug, "LJ disp. -V' %9.2e V'' %9.2e -V''' %9.2e\n", ljDisp.md1, ljDisp.d2, ljDisp.md3);
1116 fprintf(debug, "LJ rep. -V' %9.2e V'' %9.2e -V''' %9.2e\n", ljRep.md1, ljRep.d2, ljRep.md3);
1117 fprintf(debug, "Electro. -V' %9.2e V'' %9.2e\n", elec.md1, elec.d2);
1118 fprintf(debug, "sqrt(kT_fac) %f\n", std::sqrt(kT_fac));
1121 /* Search using bisection */
1123 /* The drift will be neglible at 5 times the max sigma */
1124 ib1 = static_cast<int>(5*maxSigma(kT_fac, natt, att)/resolution) + 1;
1125 while (ib1 - ib0 > 1)
1129 rl = std::max(ir->rvdw, ir->rcoulomb) + rb;
1131 /* Calculate the average energy drift at the last step
1132 * of the nstlist steps at which the pair-list is used.
1134 drift = energyDrift(att, natt, &mtop->ffparams,
1136 &ljDisp, &ljRep, &elec,
1137 ir->rvdw, ir->rcoulomb,
1140 /* Correct for the fact that we are using a Ni x Nj particle pair list
1141 * and not a 1 x 1 particle pair list. This reduces the drift.
1143 /* We don't have a formula for 8 (yet), use 4 which is conservative */
1144 nb_clust_frac_pairs_not_in_list_at_cutoff =
1145 surface_frac(std::min(list_setup->cluster_size_i, 4),
1146 particle_distance, rl)*
1147 surface_frac(std::min(list_setup->cluster_size_j, 4),
1148 particle_distance, rl);
1149 drift *= nb_clust_frac_pairs_not_in_list_at_cutoff;
1151 /* Convert the drift to drift per unit time per atom */
1152 drift /= nstlist*ir->delta_t*mtop->natoms;
1156 fprintf(debug, "ib %3d %3d %3d rb %.3f %dx%d fac %.3f drift %.1e\n",
1158 list_setup->cluster_size_i, list_setup->cluster_size_j,
1159 nb_clust_frac_pairs_not_in_list_at_cutoff,
1163 if (std::abs(drift) > ir->verletbuf_tol)
1175 *rlist = std::max(ir->rvdw, ir->rcoulomb) + ib1*resolution;
1178 /* Returns the pairlist buffer size for use as a minimum buffer size
1180 * Note that this is a rather crude estimate. It is ok for a buffer
1181 * set for good energy conservation or RF electrostatics. But it is
1182 * too small with PME and the buffer set with the default tolerance.
1184 static real minCellSizeFromPairlistBuffer(const t_inputrec &ir)
1186 return ir.rlist - std::max(ir.rvdw, ir.rcoulomb);
1189 real minCellSizeForAtomDisplacement(const gmx_mtop_t &mtop,
1190 const t_inputrec &ir,
1191 real chanceRequested)
1193 if (!EI_DYNAMICS(ir.eI) || (EI_MD(ir.eI) && ir.etc == etcNO))
1195 return minCellSizeFromPairlistBuffer(ir);
1198 /* We use the maximum temperature with multiple T-coupl groups.
1199 * We could use a per particle temperature, but since particles
1200 * interact, this might underestimate the displacements.
1202 const real temperature = maxReferenceTemperature(ir);
1204 const bool setMassesToOne = (ir.eI == eiBD && ir.bd_fric > 0);
1206 verletbuf_atomtype_t *att = nullptr;
1208 get_verlet_buffer_atomtypes(&mtop, setMassesToOne, &att, &natt, nullptr);
1210 const real kT_fac = displacementVariance(ir, temperature,
1211 ir.nstlist*ir.delta_t);
1213 /* Resolution of the cell size */
1214 real resolution = 0.001;
1216 /* Search using bisection, avoid 0 and start at 1 */
1218 /* The chance will be neglible at 10 times the max sigma */
1219 int ib1 = int(10*maxSigma(kT_fac, natt, att)/resolution) + 1;
1221 while (ib1 - ib0 > 1)
1223 int ib = (ib0 + ib1)/2;
1224 cellSize = ib*resolution;
1226 /* We assumes atom are distributed uniformly over the cell width.
1227 * Once an atom has moved by more than the cellSize (as passed
1228 * as the buffer argument to energyDriftAtomPair() below),
1229 * the chance of crossing the boundary of the neighbor cell
1230 * thus increases as 1/cellSize with the additional displacement
1231 * on to of cellSize. We thus create a linear interaction with
1232 * derivative = -1/cellSize. Using this in the energyDriftAtomPair
1233 * function will return the chance of crossing the next boundary.
1235 const pot_derivatives_t boundaryInteraction = { 1/cellSize, 0, 0 };
1238 for (int i = 0; i < natt; i++)
1240 const atom_nonbonded_kinetic_prop_t &propAtom = att[i].prop;
1243 get_atom_sigma2(kT_fac, &propAtom, &s2_2d, &s2_3d);
1245 real chancePerAtom = energyDriftAtomPair(propAtom.bConstr, false,
1246 s2_2d + s2_3d, s2_2d, 0,
1248 &boundaryInteraction);
1250 if (propAtom.bConstr)
1252 /* energyDriftAtomPair() uses an unlimited Gaussian displacement
1253 * distribution for constrained atoms, whereas they can
1254 * actually not move more than the COM of the two constrained
1255 * atoms plus twice the distance from the COM.
1256 * Use this maximum, limited displacement when this results in
1257 * a smaller chance (note that this is still an overestimate).
1259 real massFraction = propAtom.con_mass/(propAtom.mass + propAtom.con_mass);
1260 real comDistance = propAtom.con_len*massFraction;
1262 real chanceWithMaxDistance =
1263 energyDriftAtomPair(false, false,
1265 cellSize - 2*comDistance,
1266 &boundaryInteraction);
1267 chancePerAtom = std::min(chancePerAtom, chanceWithMaxDistance);
1270 /* Take into account the line density of the boundary */
1271 chancePerAtom /= cellSize;
1273 chance += att[i].n*chancePerAtom;
1276 /* Note: chance is for every nstlist steps */
1277 if (chance > chanceRequested*ir.nstlist)