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gay_berne.hpp
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gay_berne.hpp
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/*
Copyright (C) 2010-2018 The ESPResSo project
Copyright (C) 2002,2003,2004,2005,2006,2007,2008,2009,2010
Max-Planck-Institute for Polymer Research, Theory Group
This file is part of ESPResSo.
ESPResSo is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
ESPResSo is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef _GB_HPP
#define _GB_HPP
/** \file
* Routines to calculate the Gay-Berne potential between particle pairs.
*
* Implementation in \ref gay_berne.cpp.
*/
#include "nonbonded_interaction_data.hpp"
#include "particle_data.hpp"
#include <utils/math/int_pow.hpp>
#include <utils/math/sqr.hpp>
#ifdef GAY_BERNE
int gay_berne_set_params(int part_type_a, int part_type_b, double eps,
double sig, double cut, double k1, double k2,
double mu, double nu);
inline void add_gb_pair_force(Particle const *const p1,
Particle const *const p2,
IA_parameters const *const ia_params,
Utils::Vector3d const &d, double dist,
Utils::Vector3d &force,
Utils::Vector3d *const torque1,
Utils::Vector3d *const torque2) {
using Utils::int_pow;
using Utils::sqr;
if (dist >= ia_params->gay_berne.cut) {
return;
}
auto const u1 = p1->r.calc_director();
auto const u2 = p2->r.calc_director();
auto const a = d * u1;
auto const b = d * u2;
auto const c = u1 * u2;
auto const E1 = 1 / sqrt(1 - ia_params->gay_berne.chi1 *
ia_params->gay_berne.chi1 * c * c);
auto const Plus1 = (a + b) / (1 + ia_params->gay_berne.chi1 * c);
auto const Plus2 = (a + b) / (1 + ia_params->gay_berne.chi2 * c);
auto const Minus1 = (a - b) / (1 - ia_params->gay_berne.chi1 * c);
auto const Minus2 = (a - b) / (1 - ia_params->gay_berne.chi2 * c);
auto const Brhi2 = (ia_params->gay_berne.chi2 / dist / dist) *
(Plus2 * (a + b) + Minus2 * (a - b));
auto const E2 = 1 - 0.5 * Brhi2;
auto const E = 4 * ia_params->gay_berne.eps *
pow(E1, ia_params->gay_berne.nu) *
pow(E2, ia_params->gay_berne.mu);
auto const Brhi1 = (ia_params->gay_berne.chi1 / dist / dist) *
(Plus1 * (a + b) + Minus1 * (a - b));
auto const Sigma = ia_params->gay_berne.sig / sqrt(1 - 0.5 * Brhi1);
auto Koef1 = ia_params->gay_berne.mu / E2;
auto Koef2 = int_pow<3>(Sigma) * 0.5 / int_pow<3>(ia_params->gay_berne.sig);
auto const X =
ia_params->gay_berne.sig / (dist - Sigma + ia_params->gay_berne.sig);
auto const Xcut =
ia_params->gay_berne.sig /
(ia_params->gay_berne.cut - Sigma + ia_params->gay_berne.sig);
auto const X6 = int_pow<6>(X);
auto const Xcut6 = int_pow<6>(Xcut);
auto const Bra12 = 6 * X6 * X * (2 * X6 - 1);
auto const Bra12Cut = 6 * Xcut6 * Xcut * (2 * Xcut6 - 1);
auto const Brack = X6 * (X6 - 1);
auto const BrackCut = Xcut6 * (Xcut6 - 1);
/*-------- Here we calculate derivatives -----------------------------*/
auto const dU_dr =
E *
(Koef1 * Brhi2 * (Brack - BrackCut) - Koef2 * Brhi1 * (Bra12 - Bra12Cut) -
Bra12 * dist / ia_params->gay_berne.sig) /
sqr(dist);
Koef1 *= ia_params->gay_berne.chi2 / sqr(dist);
Koef2 *= ia_params->gay_berne.chi1 / sqr(dist);
auto const dU_da = E * (Koef1 * (Minus2 + Plus2) * (BrackCut - Brack) +
Koef2 * (Plus1 + Minus1) * (Bra12 - Bra12Cut));
auto const dU_db = E * (Koef1 * (Minus2 - Plus2) * (Brack - BrackCut) +
Koef2 * (Plus1 - Minus1) * (Bra12 - Bra12Cut));
auto const dU_dc =
E * ((Brack - BrackCut) * (ia_params->gay_berne.nu *
sqr(E1 * ia_params->gay_berne.chi1) * c +
0.5 * Koef1 * ia_params->gay_berne.chi2 *
(sqr(Plus2) - sqr(Minus2))) -
(Bra12 - Bra12Cut) * 0.5 * Koef2 * ia_params->gay_berne.chi1 *
(sqr(Plus1) - sqr(Minus1)));
/*--------------------------------------------------------------------*/
force -= dU_dr * d + dU_da * u1 + dU_db * u2;
if (torque1 != nullptr) {
/* calculate torque: torque = u_1 x G */
auto const G2 = -dU_da * d - dU_dc * u2;
*torque1 += vector_product(u1, G2);
if (torque2 != nullptr) {
/* calculate torque: torque = u_2 x G */
auto const G1 = -dU_db * d - dU_dc * u1;
*torque2 += vector_product(u2, G1);
}
}
}
inline double gb_pair_energy(Particle const *const p1, Particle const *const p2,
IA_parameters const *const ia_params,
Utils::Vector3d const &d, double dist) {
using Utils::int_pow;
using Utils::sqr;
if (dist >= ia_params->gay_berne.cut) {
return 0.0;
}
auto const e0 = ia_params->gay_berne.eps;
auto const s0 = ia_params->gay_berne.sig;
auto const chi1 = ia_params->gay_berne.chi1;
auto const chi2 = ia_params->gay_berne.chi2;
auto const mu = ia_params->gay_berne.mu;
auto const nu = ia_params->gay_berne.nu;
auto const r = Utils::Vector3d({d[0], d[1], d[2]}).normalize();
auto const ui = p1->r.calc_director();
auto const uj = p2->r.calc_director();
auto const uij = ui * uj;
auto const rui = r * ui;
auto const ruj = r * uj;
auto const e1 = std::pow(1. - sqr(chi1 * uij), -0.5 * nu);
auto const t1 = sqr(rui + ruj) / (1 + chi2 * uij);
auto const t2 = sqr(rui - ruj) / (1 - chi2 * uij);
auto const e2 = std::pow(1. - 0.5 * chi2 * (t1 + t2), mu);
auto const e = e0 * e1 * e2;
auto const s = s0 / std::sqrt(1. - 0.5 * chi1 *
(sqr(rui + ruj) / (1 + chi1 * uij) +
sqr(rui - ruj) / (1 - chi1 * uij)));
auto r_eff = [=](double r) { return (r - s + s0) / s0; };
auto E = [=](double r) {
return 4. * e * (int_pow<12>(1. / r) - int_pow<6>(1. / r));
};
return E(r_eff(dist)) - E(r_eff(ia_params->gay_berne.cut));
}
#endif
#endif