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256 lines
8.7 KiB
C++
256 lines
8.7 KiB
C++
// $Id$
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//
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// Copyright (C) 2004-2013 Rational Discovery LLC
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//
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// @@ All Rights Reserved @@
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// This file is part of the RDKit.
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// The contents are covered by the terms of the BSD license
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// which is included in the file license.txt, found at the root
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// of the RDKit source tree.
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//
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#include "AngleBend.h"
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#include "BondStretch.h"
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#include "Params.h"
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#include <cmath>
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#include <ForceField/ForceField.h>
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#include <RDGeneral/Invariant.h>
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#include <RDGeneral/utils.h>
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namespace ForceFields {
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namespace UFF {
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namespace Utils {
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double calcAngleForceConstant(double theta0, double bondOrder12,
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double bondOrder23, const AtomicParams *at1Params,
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const AtomicParams *at2Params,
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const AtomicParams *at3Params) {
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double cosTheta0 = cos(theta0);
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double r12 = calcBondRestLength(bondOrder12, at1Params, at2Params);
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double r23 = calcBondRestLength(bondOrder23, at2Params, at3Params);
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double r13 = sqrt(r12 * r12 + r23 * r23 - 2. * r12 * r23 * cosTheta0);
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double beta = 2. * Params::G / (r12 * r23);
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double preFactor = beta * at1Params->Z1 * at3Params->Z1 / int_pow<5>(r13);
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double rTerm = r12 * r23;
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double innerBit =
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3. * rTerm * (1. - cosTheta0 * cosTheta0) - r13 * r13 * cosTheta0;
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double res = preFactor * rTerm * innerBit;
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return res;
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}
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void calcAngleBendGrad(RDGeom::Point3D *r, double *dist, double **g,
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double &dE_dTheta, double &cosTheta, double &sinTheta) {
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// -------
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// dTheta/dx is trickier:
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double dCos_dS[6] = {1.0 / dist[0] * (r[1].x - cosTheta * r[0].x),
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1.0 / dist[0] * (r[1].y - cosTheta * r[0].y),
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1.0 / dist[0] * (r[1].z - cosTheta * r[0].z),
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1.0 / dist[1] * (r[0].x - cosTheta * r[1].x),
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1.0 / dist[1] * (r[0].y - cosTheta * r[1].y),
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1.0 / dist[1] * (r[0].z - cosTheta * r[1].z)};
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g[0][0] += dE_dTheta * dCos_dS[0] / (-sinTheta);
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g[0][1] += dE_dTheta * dCos_dS[1] / (-sinTheta);
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g[0][2] += dE_dTheta * dCos_dS[2] / (-sinTheta);
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g[1][0] += dE_dTheta * (-dCos_dS[0] - dCos_dS[3]) / (-sinTheta);
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g[1][1] += dE_dTheta * (-dCos_dS[1] - dCos_dS[4]) / (-sinTheta);
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g[1][2] += dE_dTheta * (-dCos_dS[2] - dCos_dS[5]) / (-sinTheta);
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g[2][0] += dE_dTheta * dCos_dS[3] / (-sinTheta);
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g[2][1] += dE_dTheta * dCos_dS[4] / (-sinTheta);
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g[2][2] += dE_dTheta * dCos_dS[5] / (-sinTheta);
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}
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} // end of namespace Utils
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AngleBendContrib::AngleBendContrib(ForceField *owner, unsigned int idx1,
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unsigned int idx2, unsigned int idx3,
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double bondOrder12, double bondOrder23,
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const AtomicParams *at1Params,
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const AtomicParams *at2Params,
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const AtomicParams *at3Params,
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unsigned int order) {
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PRECONDITION(owner, "bad owner");
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PRECONDITION(at1Params, "bad params pointer");
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PRECONDITION(at2Params, "bad params pointer");
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PRECONDITION(at3Params, "bad params pointer");
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PRECONDITION((idx1 != idx2 && idx2 != idx3 && idx1 != idx3),
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"degenerate points");
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URANGE_CHECK(idx1, owner->positions().size());
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URANGE_CHECK(idx2, owner->positions().size());
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URANGE_CHECK(idx3, owner->positions().size());
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// the following is a hack to get decent geometries
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// with 3- and 4-membered rings incorporating sp2 atoms
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double theta0 = at2Params->theta0;
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if (order >= 30) {
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switch (order) {
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case 30:
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theta0 = 150.0 / 180.0 * M_PI;
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break;
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case 35:
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theta0 = 60.0 / 180.0 * M_PI;
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break;
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case 40:
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theta0 = 135.0 / 180.0 * M_PI;
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break;
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case 45:
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theta0 = 90.0 / 180.0 * M_PI;
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break;
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}
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order = 0;
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}
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// end of the hack
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dp_forceField = owner;
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d_at1Idx = idx1;
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d_at2Idx = idx2;
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d_at3Idx = idx3;
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d_order = order;
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d_forceConstant = Utils::calcAngleForceConstant(
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theta0, bondOrder12, bondOrder23, at1Params, at2Params, at3Params);
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if (order == 0) {
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double sinTheta0 = sin(theta0);
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double cosTheta0 = cos(theta0);
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d_C2 = 1. / (4. * std::max(sinTheta0 * sinTheta0, 1e-8));
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d_C1 = -4. * d_C2 * cosTheta0;
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d_C0 = d_C2 * (2. * cosTheta0 * cosTheta0 + 1.);
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}
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}
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double AngleBendContrib::getEnergy(double *pos) const {
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PRECONDITION(dp_forceField, "no owner");
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PRECONDITION(pos, "bad vector");
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double dist1 = dp_forceField->distance(d_at1Idx, d_at2Idx, pos);
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double dist2 = dp_forceField->distance(d_at2Idx, d_at3Idx, pos);
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RDGeom::Point3D p1(pos[3 * d_at1Idx], pos[3 * d_at1Idx + 1],
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pos[3 * d_at1Idx + 2]);
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RDGeom::Point3D p2(pos[3 * d_at2Idx], pos[3 * d_at2Idx + 1],
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pos[3 * d_at2Idx + 2]);
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RDGeom::Point3D p3(pos[3 * d_at3Idx], pos[3 * d_at3Idx + 1],
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pos[3 * d_at3Idx + 2]);
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RDGeom::Point3D p12 = p1 - p2;
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RDGeom::Point3D p32 = p3 - p2;
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double cosTheta = p12.dotProduct(p32) / (dist1 * dist2);
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clipToOne(cosTheta);
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// we need sin^2(theta) to get cos(2*theta), so compute that:
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double sinThetaSq = 1. - cosTheta * cosTheta;
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double angleTerm = getEnergyTerm(cosTheta, sinThetaSq);
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double res = d_forceConstant * angleTerm;
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return res;
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}
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void AngleBendContrib::getGrad(double *pos, double *grad) const {
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PRECONDITION(dp_forceField, "no owner");
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PRECONDITION(pos, "bad vector");
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PRECONDITION(grad, "bad vector");
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double dist[2] = {dp_forceField->distance(d_at1Idx, d_at2Idx, pos),
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dp_forceField->distance(d_at2Idx, d_at3Idx, pos)};
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RDGeom::Point3D p1(pos[3 * d_at1Idx], pos[3 * d_at1Idx + 1],
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pos[3 * d_at1Idx + 2]);
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RDGeom::Point3D p2(pos[3 * d_at2Idx], pos[3 * d_at2Idx + 1],
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pos[3 * d_at2Idx + 2]);
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RDGeom::Point3D p3(pos[3 * d_at3Idx], pos[3 * d_at3Idx + 1],
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pos[3 * d_at3Idx + 2]);
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double *g[3] = {&(grad[3 * d_at1Idx]), &(grad[3 * d_at2Idx]),
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&(grad[3 * d_at3Idx])};
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RDGeom::Point3D r[2] = {(p1 - p2) / dist[0], (p3 - p2) / dist[1]};
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double cosTheta = r[0].dotProduct(r[1]);
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clipToOne(cosTheta);
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double sinThetaSq = 1.0 - cosTheta * cosTheta;
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double sinTheta =
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std::max(((sinThetaSq > 0.0) ? sqrt(sinThetaSq) : 0.0), 1.0e-8);
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// std::cerr << "GRAD: " << cosTheta << " (" << acos(cosTheta)<< "), ";
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// std::cerr << sinTheta << " (" << asin(sinTheta)<< ")" << std::endl;
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// use the chain rule:
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// dE/dx = dE/dTheta * dTheta/dx
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// dE/dTheta is independent of cartesians:
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double dE_dTheta = getThetaDeriv(cosTheta, sinTheta);
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Utils::calcAngleBendGrad(r, dist, g, dE_dTheta, cosTheta, sinTheta);
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}
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double AngleBendContrib::getEnergyTerm(double cosTheta,
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double sinThetaSq) const {
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PRECONDITION(d_order == 0 || d_order == 1 || d_order == 2 || d_order == 3 ||
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d_order == 4,
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"bad order");
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// cos(2x) = cos^2(x) - sin^2(x);
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double cos2Theta = cosTheta * cosTheta - sinThetaSq;
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double res = 0.0;
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if (d_order == 0) {
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res = d_C0 + d_C1 * cosTheta + d_C2 * cos2Theta;
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} else {
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switch (d_order) {
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case 1:
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res = -cosTheta;
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break;
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case 2:
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res = cos2Theta;
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break;
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case 3:
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// cos(3x) = cos^3(x) - 3*cos(x)*sin^2(x)
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res = cosTheta * (cosTheta * cosTheta - 3. * sinThetaSq);
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break;
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case 4:
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// cos(4x) = cos^4(x) - 6*cos^2(x)*sin^2(x)+sin^4(x)
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res = int_pow<4>(cosTheta) - 6. * cosTheta * cosTheta * sinThetaSq +
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sinThetaSq * sinThetaSq;
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break;
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}
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res = 1. - res;
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res /= (double)(d_order * d_order);
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}
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return res;
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}
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double AngleBendContrib::getThetaDeriv(double cosTheta, double sinTheta) const {
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PRECONDITION(d_order == 0 || d_order == 1 || d_order == 2 || d_order == 3 ||
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d_order == 4,
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"bad order");
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double dE_dTheta = 0.0;
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double sin2Theta = 2. * sinTheta * cosTheta;
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if (d_order == 0) {
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dE_dTheta =
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-1. * d_forceConstant * (d_C1 * sinTheta + 2. * d_C2 * sin2Theta);
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} else {
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// E = k/n^2 [1-cos(n theta)]
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// dE = - k/n^2 * d cos(n theta)
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// these all use:
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// d cos(ax) = -a sin(ax)
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switch (d_order) {
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case 1:
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dE_dTheta = -sinTheta;
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break;
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case 2:
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// sin(2*x) = 2*cos(x)*sin(x)
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dE_dTheta = sin2Theta;
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break;
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case 3:
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// sin(3*x) = 3*sin(x) - 4*sin^3(x)
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dE_dTheta = sinTheta * (3. - 4. * sinTheta * sinTheta);
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break;
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case 4:
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// sin(4*x) = cos(x)*(4*sin(x) - 8*sin^3(x))
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dE_dTheta = cosTheta * sinTheta * (4. - 8. * sinTheta * sinTheta);
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break;
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}
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dE_dTheta *= d_forceConstant / (double)(d_order);
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}
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return dE_dTheta;
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}
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}
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}
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