static real ener_drift(const verletbuf_atomtype_t *att, int natt,
const gmx_ffparams_t *ffp,
real kT_fac,
real md1_ljd, real d2_ljd, real md3_ljd,
real md1_ljr, real d2_ljr, real md3_ljr,
real md1_el, real d2_el,
real r_buffer,
real rlist, real boxvol)
{
/* Erfc(8)=1e-29, use this limit so we have some space for arithmetic
* on the result when using float precision.
*/
const real erfc_arg_max = 8.0;
double drift_tot, pot1, pot2, pot3, pot;
int i, j;
real s2i_2d, s2i_3d, s2j_2d, s2j_3d, s2, s;
int ti, tj;
real md1, d2, md3;
real sc_fac, rsh, rsh2;
double c_exp, c_erfc;
drift_tot = 0;
/* Loop over the different atom type pairs */
for (i = 0; i < natt; i++)
{
get_atom_sigma2(kT_fac, &att[i].prop, &s2i_2d, &s2i_3d);
ti = att[i].prop.type;
for (j = i; j < natt; j++)
{
get_atom_sigma2(kT_fac, &att[j].prop, &s2j_2d, &s2j_3d);
tj = att[j].prop.type;
/* Add up the up to four independent variances */
s2 = s2i_2d + s2i_3d + s2j_2d + s2j_3d;
/* Note that attractive and repulsive potentials for individual
* pairs will partially cancel.
*/
/* -dV/dr at the cut-off for LJ + Coulomb */
md1 =
md1_ljd*ffp->iparams[ti*ffp->atnr+tj].lj.c6 +
md1_ljr*ffp->iparams[ti*ffp->atnr+tj].lj.c12 +
md1_el*att[i].prop.q*att[j].prop.q;
/* d2V/dr2 at the cut-off for LJ + Coulomb */
d2 =
d2_ljd*ffp->iparams[ti*ffp->atnr+tj].lj.c6 +
d2_ljr*ffp->iparams[ti*ffp->atnr+tj].lj.c12 +
d2_el*att[i].prop.q*att[j].prop.q;
/* -d3V/dr3 at the cut-off for LJ, we neglect Coulomb */
md3 =
md3_ljd*ffp->iparams[ti*ffp->atnr+tj].lj.c6 +
md3_ljr*ffp->iparams[ti*ffp->atnr+tj].lj.c12;
rsh = r_buffer;
sc_fac = 1.0;
if (rsh*rsh > 2*s2*erfc_arg_max*erfc_arg_max)
{
/* Erfc might run out of float and become 0, somewhat before
* c_exp becomes 0. To avoid this and to avoid NaN in
* approx_2dof, we set both c_expc and c_erfc to zero.
* In any relevant case this has no effect on the results,
* since c_exp < 6e-29, so the displacement is completely
* negligible for such atom pairs (and an overestimate).
* In nearly all use cases, there will be other atom
* pairs that contribute much more to the total, so zeroing
* this particular contribution has no effect at all.
*/
c_exp = 0;
c_erfc = 0;
}
else
{
/* For constraints: adapt r and scaling for the Gaussian */
if (att[i].prop.bConstr)
{
real sh, sc;
approx_2dof(s2i_2d, r_buffer*s2i_2d/s2, &sh, &sc);
rsh += sh;
sc_fac *= sc;
}
if (att[j].prop.bConstr)
{
real sh, sc;
approx_2dof(s2j_2d, r_buffer*s2j_2d/s2, &sh, &sc);
rsh += sh;
sc_fac *= sc;
}
/* Exact contribution of an atom pair with Gaussian displacement
* with sigma s to the energy drift for a potential with
* derivative -md and second derivative dd at the cut-off.
* The only catch is that for potentials that change sign
* near the cut-off there could be an unlucky compensation
* of positive and negative energy drift.
* Such potentials are extremely rare though.
*
* Note that pot has unit energy*length, as the linear
* atom density still needs to be put in.
*/
c_exp = exp(-rsh*rsh/(2*s2))/sqrt(2*M_PI);
c_erfc = 0.5*gmx_erfc(rsh/(sqrt(2*s2)));
}
s = sqrt(s2);
rsh2 = rsh*rsh;
pot1 = sc_fac*
md1/2*((rsh2 + s2)*c_erfc - rsh*s*c_exp);
pot2 = sc_fac*
d2/6*(s*(rsh2 + 2*s2)*c_exp - rsh*(rsh2 + 3*s2)*c_erfc);
pot3 = sc_fac*
md3/24*((rsh2*rsh2 + 6*rsh2*s2 + 3*s2*s2)*c_erfc - rsh*s*(rsh2 + 5*s2)*c_exp);
pot = pot1 + pot2 + pot3;
if (gmx_debug_at)
{
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",
att[i].n, att[j].n,
sqrt(s2i_2d), sqrt(s2i_3d),
sqrt(s2j_2d), sqrt(s2j_3d),
att[i].prop.bConstr+att[j].prop.bConstr,
md1, d2, md3,
pot1, pot2, pot3, pot);
}
/* Multiply by the number of atom pairs */
if (j == i)
{
pot *= (double)att[i].n*(att[i].n - 1)/2;
}
else
{
pot *= (double)att[i].n*att[j].n;
}
/* We need the line density to get the energy drift of the system.
* The effective average r^2 is close to (rlist+sigma)^2.
*/
pot *= 4*M_PI*sqr(rlist + s)/boxvol;
/* Add the unsigned drift to avoid cancellation of errors */
drift_tot += fabs(pot);
}
}
return drift_tot;
}
static real ener_drift(const verletbuf_atomtype_t *att, int natt,
const gmx_ffparams_t *ffp,
real kT_fac,
real md_ljd, real md_ljr, real md_el, real dd_el,
real r_buffer,
real rlist, real boxvol)
{
double drift_tot, pot1, pot2, pot;
int i, j;
real s2i_2d, s2i_3d, s2j_2d, s2j_3d, s2, s;
int ti, tj;
real md, dd;
real sc_fac, rsh;
double c_exp, c_erfc;
drift_tot = 0;
/* Loop over the different atom type pairs */
for (i = 0; i < natt; i++)
{
get_atom_sigma2(kT_fac, &att[i].prop, &s2i_2d, &s2i_3d);
ti = att[i].prop.type;
for (j = i; j < natt; j++)
{
get_atom_sigma2(kT_fac, &att[j].prop, &s2j_2d, &s2j_3d);
tj = att[j].prop.type;
/* Add up the up to four independent variances */
s2 = s2i_2d + s2i_3d + s2j_2d + s2j_3d;
/* Note that attractive and repulsive potentials for individual
* pairs will partially cancel.
*/
/* -dV/dr at the cut-off for LJ + Coulomb */
md =
md_ljd*ffp->iparams[ti*ffp->atnr+tj].lj.c6 +
md_ljr*ffp->iparams[ti*ffp->atnr+tj].lj.c12 +
md_el*att[i].prop.q*att[j].prop.q;
/* d2V/dr2 at the cut-off for Coulomb, we neglect LJ */
dd = dd_el*att[i].prop.q*att[j].prop.q;
rsh = r_buffer;
sc_fac = 1.0;
/* For constraints: adapt r and scaling for the Gaussian */
if (att[i].prop.bConstr)
{
real sh, sc;
approx_2dof(s2i_2d, r_buffer*s2i_2d/s2, &sh, &sc);
rsh += sh;
sc_fac *= sc;
}
if (att[j].prop.bConstr)
{
real sh, sc;
approx_2dof(s2j_2d, r_buffer*s2j_2d/s2, &sh, &sc);
rsh += sh;
sc_fac *= sc;
}
/* Exact contribution of an atom pair with Gaussian displacement
* with sigma s to the energy drift for a potential with
* derivative -md and second derivative dd at the cut-off.
* The only catch is that for potentials that change sign
* near the cut-off there could be an unlucky compensation
* of positive and negative energy drift.
* Such potentials are extremely rare though.
*
* Note that pot has unit energy*length, as the linear
* atom density still needs to be put in.
*/
c_exp = exp(-rsh*rsh/(2*s2))/sqrt(2*M_PI);
c_erfc = 0.5*gmx_erfc(rsh/(sqrt(2*s2)));
s = sqrt(s2);
pot1 = sc_fac*
md/2*((rsh*rsh + s2)*c_erfc - rsh*s*c_exp);
pot2 = sc_fac*
dd/6*(s*(rsh*rsh + 2*s2)*c_exp - rsh*(rsh*rsh + 3*s2)*c_erfc);
pot = pot1 + pot2;
if (gmx_debug_at)
{
fprintf(debug, "n %d %d d s %.3f %.3f %.3f %.3f con %d md %8.1e dd %8.1e pot1 %8.1e pot2 %8.1e pot %8.1e\n",
att[i].n, att[j].n,
sqrt(s2i_2d), sqrt(s2i_3d),
sqrt(s2j_2d), sqrt(s2j_3d),
att[i].prop.bConstr+att[j].prop.bConstr,
md, dd, pot1, pot2, pot);
}
/* Multiply by the number of atom pairs */
if (j == i)
{
pot *= (double)att[i].n*(att[i].n - 1)/2;
}
else
{
pot *= (double)att[i].n*att[j].n;
}
/* We need the line density to get the energy drift of the system.
* The effective average r^2 is close to (rlist+sigma)^2.
*/
pot *= 4*M_PI*sqr(rlist + s)/boxvol;
/* Add the unsigned drift to avoid cancellation of errors */
drift_tot += fabs(pot);
}
}
return drift_tot;
}
